From 683c0fd9c8d0d47cec7bf6493f60189e145e6ce1 Mon Sep 17 00:00:00 2001 From: Mike Croucher Date: Thu, 13 Aug 2020 12:11:02 +0100 Subject: [PATCH 001/182] Update README.md --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index a94f7f0..cb4d799 100644 --- a/README.md +++ b/README.md @@ -41,7 +41,7 @@ Install using the following command python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces ``` -**Obtaining a license** +## Obtaining a license Before you can use the NAG Library for Python, you'll need a license. Free trial licenses are available! @@ -56,7 +56,7 @@ python -m naginterfaces.kusari * More detailed installation instructions are [available in the official documentation](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). * More detailed license management instructions are available at [https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) -**Official documentation links** +## List of Chapters in the NAG Library for Python The following links take you to the relevant section in the official documentation From 21270832dd98baecc0d3ab42a692f22e692b10a9 Mon Sep 17 00:00:00 2001 From: Mike Croucher Date: Fri, 14 Aug 2020 15:05:51 +0100 Subject: [PATCH 002/182] FOAS updates from Andrew --- local_optimization/FOAS/README.md | 59 ++- .../images/KF_DG_unconst_tokyo_notriv-NF.png | Bin 0 -> 45317 bytes .../images/KF_DG_unconst_tokyo_notriv-NG.png | Bin 0 -> 46913 bytes .../images/KF_DG_unconst_tokyo_notriv-NT.png | Bin 0 -> 45750 bytes .../FOAS/images/Rosenbrock2dw.png | Bin 0 -> 638792 bytes local_optimization/FOAS/images/animated.gif | Bin 0 -> 841650 bytes .../images/handle_solve_bounds_foas_ex.png | Bin 0 -> 87305 bytes local_optimization/FOAS/rosenbrock2d.ipynb | 452 ++++++++++++++++++ 8 files changed, 510 insertions(+), 1 deletion(-) create mode 100644 local_optimization/FOAS/images/KF_DG_unconst_tokyo_notriv-NF.png create mode 100644 local_optimization/FOAS/images/KF_DG_unconst_tokyo_notriv-NG.png create mode 100644 local_optimization/FOAS/images/KF_DG_unconst_tokyo_notriv-NT.png create mode 100644 local_optimization/FOAS/images/Rosenbrock2dw.png create mode 100644 local_optimization/FOAS/images/animated.gif create mode 100644 local_optimization/FOAS/images/handle_solve_bounds_foas_ex.png create mode 100644 local_optimization/FOAS/rosenbrock2d.ipynb diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index ed229aa..c715a2b 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -1 +1,58 @@ -# First-order active-set method +[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) + +# First-order active-set method (FOAS, e04kf) + +Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. + +FOAS is a [first-order nonlinear conjugate method](https://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method) for large-scale bound-constrained nonlinear optimization. The solver is ideal for very large problems (tens of thousands or more variables) where the first-order derivatives are available or are relatively _cheap_ to estimate. + +e04kf is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. + +The following example illustrates the simple usage of FOAS to solve the bound-constrained 2D version of the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is a classical test function to measure and profile performance of solvers. Source of this example is avaible in [rosenbrock2d.ipynb](rosenbrock2d.ipynb). + + + + +
2D Rosenbrock example2D Rosenbrock with bounds
+ +**Figure 1.** 2D Rosenbrock function, (left) the minimum is shown as a yellow dot at x=(1,1). On the right a bound constrained version showing with a purple dotted line a path towards the constrained solution point on the border. + +# More info [TODO fix links] + 1. [FOAS information leaflet]() + 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) + 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example)] + +# A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) +One of the main design objectives for e04kf was to provide a modern and attractive replacement for the CG solver e04dg introduced in Mark 12. While this solver was targeted for unconstrained NLPs, e04kf has been extended with an active-set method in order to solve bound-constrained NLPs. + +More recent and modern methods have been incorporated into e04kf making it much faster than e04dg. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers e04kf and e04dg. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. + + + + + +
Perf profile e04kf/e04dg time (s)Perf profile e04kf/e04dg function evaluationsPerf profile e04kf/e04dg gradient evaluations
+ +**Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. + +# Beale's function +This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. + +Both solvers are used to find a minimum to the function and are started at the same initial point (2, 2). The following figure shows an animation of the steps taken by each solver to find a minimum to the function. +It illustrates the agressive steps taken by the [Conjugate Gradient method](https://en.wikipedia.org/wiki/Conjugate_gradient_method) compared to the more conservative steps of BFGS. + +Beale function solved using e04kf and L-BFGS-B + +**Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star in the. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. + +# References + + * Hager W W and Zhang H (2005) _A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search_. SIAM J. Optim. 16(1) 170–192 + * Hager W W and Zhang H (2006a) _Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent_. ACM Trans. Math. Software 32(1) 113–137 + * Hager W W and Zhang H (2006b) _A New Active Set Algorithm for Box Constrained Optimization_. SIAM J. Optim. 17(2) 525–557 + * Hager W W and Zhang H (2013) _The Limited Memory Conjugate Gradient Method_. SIAM J. Optim. 23(4) 2150–2168 + * Nocedal J and Wright S J (2006) _Numerical Optimization_. 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from matplotlib import cm\n", + "fig = plt.figure()\n", + "ax = Axes3D(fig)\n", + "ax = fig.gca(projection='3d')\n", + "ax.grid(False)\n", + "ax.plot(box[0], box[1], z_box, 'k-', linewidth=1.5)\n", + "ax.plot([bl[0], bu[0], bu[0], bl[0], bl[0]], [bl[1], bl[1], bu[1], bu[1], bl[1]], -1.2*np.ones(5), 'k-')\n", + "ax.contour(X, Y, z_m, 15, offset=-1.2, cmap=cm.jet)\n", + "ax.plot_surface(X, Y, z_m, cmap=cm.jet, alpha=0.5)\n", + "ax.set_title('Rosenbrock Function')\n", + "ax.set_xlabel(r'$\\mathit{x}$')\n", + "ax.set_ylabel(r'$\\mathit{y}$')\n", + "ax.plot(steps[0], steps[1], steps[2], 'o-', color='red', markersize=3, linewidth=2)\n", + "ax.azim = 160\n", + "ax.elev = 35\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From c7b6b2aa6ebeb9d04948c8ab28f7379de2c126e7 Mon Sep 17 00:00:00 2001 From: "michael.p.croucher@googlemail.com" Date: Fri, 14 Aug 2020 16:37:14 +0100 Subject: [PATCH 003/182] Update for 27.0.2 --- local_optimization/FOAS/rosenbrock2d.ipynb | 84 +++++++++++----------- 1 file changed, 40 insertions(+), 44 deletions(-) diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index 8550b23..5a741c3 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -33,7 +33,7 @@ "metadata": {}, "outputs": [], "source": [ - "objfun = lambda x, inform: ((1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2, inform)\n", + "objfun = lambda x, _inform: (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", "\n", "def objgrd(x, fdx, inform):\n", " \"\"\"The objective's gradient.\"\"\"\n", @@ -161,11 +161,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "\n", - " ----------------------------------------------------------\n", + " -------------------------------------------------------------------------------\n", " E04KF, First order method for bound-constrained problems\n", - " ----------------------------------------------------------\n", - "\n", + " -------------------------------------------------------------------------------\n", " Begin of Options\n", " Print File = 9 * d\n", " Print Level = 2 * U\n", @@ -194,12 +192,14 @@ " Foas Tolerance Norm = Infinity * d\n", " End of Options\n", "\n", - " Problem Statistics\n", - " No of variables 2\n", - " free (unconstrained) 0\n", - " bounded 2\n", - " Objective function Nonlinear\n", - "\n", + " Problem statistics\n", + " Number of variables 2\n", + " Number of free variables 0\n", + " Number of fixed variables 0\n", + " Number of variables with only lower bound 0\n", + " Number of variables with only upper bound 0\n", + " Number of variables with bounds 2\n", + " Objective type Nonlinear\n", "\n", " -------------------------------------------------------------------------------\n", " iters | objective | optim | dir\n", @@ -222,51 +222,47 @@ " 15 1.12429E+00 2.33E+00 2.01E+00\n", " 16 1.01998E+00 5.04E+00 2.02E+00\n", " 17 8.94996E-01 8.97E+00 2.02E+00\n", - " 18 7.06184E-01 1.32E+00 1.10E+00\n", - " 19 5.06340E-01 5.11E+00 1.91E+00\n", + " 18 7.06235E-01 1.32E+00 1.11E+00\n", + " 19 5.06072E-01 5.09E+00 1.91E+00\n", " -------------------------------------------------------------------------------\n", " iters | objective | optim | dir\n", " -------------------------------------------------------------------------------\n", - " 20 3.21115E-01 1.03E+00 3.67E-01\n", - " 21 2.99551E-01 9.31E-01 9.31E-01\n", - " 22 2.51003E-01 2.68E+00 1.75E+00\n", - " 23 2.14196E-01 4.82E+00 1.66E+00\n", - " 24 1.15236E-01 1.17E+00 3.70E-01\n", - " 25 8.06733E-02 1.98E+00 1.73E+00\n", - " 26 6.60815E-02 4.33E+00 1.79E+00\n", - " 27 5.37636E-02 3.33E+00 1.80E+00\n", - " 28 4.02960E-02 3.44E-01 3.44E-01\n", - " 29 4.02960E-02 3.44E-01 3.44E-01\n", - " 30 4.00937E-02 1.94E-01 1.94E-01\n", - " 31 4.00937E-02 1.94E-01 1.94E-01\n", - " 32 4.00000E-02 0.00E+00 0.00E+00\n", + " 20 3.18869E-01 9.51E-01 3.65E-01\n", + " 21 2.98131E-01 1.03E+00 1.03E+00\n", + " 22 2.48807E-01 2.90E+00 1.74E+00\n", + " 23 2.10033E-01 5.38E+00 1.65E+00\n", + " 24 1.19320E-01 1.40E+00 5.40E-01\n", + " 25 8.38051E-02 4.97E+00 1.77E+00\n", + " 26 6.45222E-02 8.65E-01 8.65E-01\n", + " 27 5.31881E-02 6.17E-01 6.17E-01\n", + " 28 4.20831E-02 7.71E-01 7.71E-01\n", + " 29 4.04842E-02 4.40E-01 4.40E-01\n", + " 30 4.04842E-02 4.40E-01 4.40E-01\n", + " 31 4.01532E-02 2.48E-01 2.48E-01\n", + " 32 4.01532E-02 2.48E-01 2.48E-01\n", + " 33 4.00000E-02 0.00E+00 0.00E+00\n", " -------------------------------------------------------------------------------\n", " Status: converged, an optimal solution was found\n", " -------------------------------------------------------------------------------\n", " Value of the objective 4.00000E-02\n", " Norm of inactive gradient 0.00000E+00\n", " Norm of projected direction 0.00000E+00\n", - " Iterations 32\n", - " Function evaluations 75\n", + " Iterations 33\n", + " Function evaluations 80\n", " FD func. evaluations 0\n", - " Gradient evaluations 36\n", + " Gradient evaluations 40\n", " NPG function calls 18\n", " NPG gradient calls 3\n", " CG function calls 9\n", " CG gradient calls 5\n", - " LCG function calls 48\n", - " LCG gradient calls 28\n", + " LCG function calls 53\n", + " LCG gradient calls 32\n", " -------------------------------------------------------------------------------\n", "\n", - " Primal variables:\n", - " idx Lower bound Value Upper bound\n", - " 1 -1.00000E+00 8.00000E-01 8.00000E-01\n", - " 2 -2.00000E+00 6.40000E-01 2.00000E+00\n", - "\n", - " Box bounds dual variables:\n", - " idx Lower bound Value Upper bound Value\n", - " 1 -1.00000E+00 0.00000E+00 8.00000E-01 4.00000E-01\n", - " 2 -2.00000E+00 0.00000E+00 2.00000E+00 0.00000E+00\n" + " Variables:\n", + " idx lower bound value upper bound gradient\n", + " 1 -1.00000E+00 8.00000E-01 8.00000E-01 -4.00000E-01\n", + " 2 -2.00000E+00 6.40000E-01 2.00000E+00 0.00000E+00\n" ] } ], @@ -339,7 +335,7 @@ "j = y_m[0]\n", "for i in range(0, 101):\n", " for j in range(0, 101):\n", - " z_m[i, j], _inform = objfun([x_m[i], y_m[j]], 1)\n", + " z_m[i, j] = objfun([x_m[i], y_m[j]], 0)\n", "nb = 25\n", "x_box = np.linspace(bl[0], bu[0], nb)\n", "y_box = np.linspace(bl[1], bu[1], nb)\n", @@ -347,7 +343,7 @@ " np.concatenate([bl[1]*np.ones(nb), y_box, bu[1]*np.ones(nb), y_box[::-1]])])\n", "z_box = np.empty(box[0].shape)\n", "for i in range(0, (box[0].size)):\n", - " z_box[i], _inform = objfun([box[0][i], box[1][i]], 1)\n", + " z_box[i] = objfun([box[0][i], box[1][i]], 0)\n", "\n", "X, Y = np.meshgrid(x_m, y_m, indexing='ij')" ] @@ -377,7 +373,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -426,7 +422,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.7.0" }, "latex_envs": { "LaTeX_envs_menu_present": true, From d3957ba2036185d858ffe5ae8dd4d2c3c6662e28 Mon Sep 17 00:00:00 2001 From: "michael.p.croucher@googlemail.com" Date: Fri, 14 Aug 2020 16:44:52 +0100 Subject: [PATCH 004/182] Install information --- local_optimization/FOAS/rosenbrock2d.ipynb | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index 5a741c3..2547cf9 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -404,6 +404,17 @@ "ax.elev = 35\n", "plt.show()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Obtaining the NAG Library for Python\n", + "\n", + "The [NAG Library for Python](https://www.nag.com/content/nag-library-python) is commercially licensed software but this notebook is licensed under the [BSD 3-Clause License](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/LICENSE)\n", + "* [Click here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples#nag-library-for-python-installation) for NAG Library for Python installation details\n", + "* [Click here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples#obtaining-a-license) for details on how to obtain a license for the NAG Library for Python" + ] } ], "metadata": { From 706471677b275262c103ac336970c76038f6a755 Mon Sep 17 00:00:00 2001 From: Mike Croucher Date: Fri, 14 Aug 2020 16:54:49 +0100 Subject: [PATCH 005/182] Update README.md --- local_optimization/FOAS/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index c715a2b..dbd4406 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -17,8 +17,8 @@ The following example illustrates the simple usage of FOAS to solve the bound-co **Figure 1.** 2D Rosenbrock function, (left) the minimum is shown as a yellow dot at x=(1,1). On the right a bound constrained version showing with a purple dotted line a path towards the constrained solution point on the border. -# More info [TODO fix links] - 1. [FOAS information leaflet]() +# More information + 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example)] From 7c2afa28230d5fde340d9e667022eb3ef0de0fd8 Mon Sep 17 00:00:00 2001 From: A Date: Mon, 17 Aug 2020 14:49:07 +0100 Subject: [PATCH 006/182] Add files via upload --- local_optimization/BXNL/Readme.md | 98 +++++++++++++++++++++++++++++++ 1 file changed, 98 insertions(+) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index 8b13789..d6f8710 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -1 +1,99 @@ +[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) +# Nonlinear Least-Squares Trust-Region Method (BXNL) + +Data fitting and calibrating parameters of complex numerical models is one of the most common +problems found in numerous industries such as physics, space exploration, simulations, engineering, amongs many others. +[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems ([`e04gg`]((https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)), [`handle_solve_bxnl`]((https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html))). It offers a significant variety of algorithms and regularisation techniques. + +The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small- to mid-scale (100s to 1000s of parameters) bound-constrained nonlinear least-squares problems +and is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. + +Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook](./python/orbit_ex.ipynb)). The task is to find the optimal orbit path given a variety of measurements for which the orbit has to approximatly pass-by. + + + + + +
Optimal orbit from data orbit measurements. + Weighted optimal orbit from data orbit measurements.
+ +**Figure 1.** Example of a NLLS orbital data fitting. + Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 232.9 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 247.6 units wich is withing the suggested tolerance. Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help). + + +# More Info [TODO fix links] + 1. [BXNL information leaflet]() + 2. [BXNL in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) + 3. [BXNL documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] + + # Unfolding Nuclear Track Data + + [[Python Jupyter notebook for this example](./python/simple_BXNL.ipynb)] + +This example illustrates the usage of `e04gg` to fit PADC +etched nuclear track data of alpha particles to a convoluted distribution. A target +sheet is scanned and track diameters are recorded (red wedges, +left in Figure 2) into a histogram (Blue bars right plot of Figure 2) +and a mixed Normal and log-Normal model is to be fitted +to the obtained experimental histogram. + +The [Jupyter notebook](./simple_BXNL.ipynb) uses `e04gg` to fit the +six parameter model φ(t, x = (a,b,Al,μ,σ,Ag)) = Al log-Normal(a, b) + Ag Normal(μ, σ) with 0 ≤ x, +using as data the histogram heights. The NLLS solution provides the unfolded +parameters for the two distributions (red and blue curves in right plot in Figure 2). +Adding these together produces the green curve which is the one used to perform the fitting with. + + + + + + +
PADC etch track diameter histogram unfoldingExperimental histogram of track diameter
+ +**Figure 2.** Left: example of a PADC target with alpha +particle etched tracks, wedges in red show the track diameter. +Right: experimental data histogram of track diameters (blue bars), +aggregated model used in the fitting (green curve) and unfolded models (blue and red curves). +Optimal parameter values are reported in the legend. + + +# Modern Replacement Alternative +Solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is a modern and attractive replacement for the unconstrained nonlinear least-squares solver [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) introduced at Mark 7. + +More recent and modern methods have been incorporated into [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) making it much faster than [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html). Our benchmarks comparing [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) to [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) using 68 unconstrained nonlinear least-squares CUTEst problems is reported in Figure 3 using performance profiles. + +Contrasting the three plots, it can be seen that the new solver is more efficient in time: solves 60% +of the problems faster (left plot). In general terms it is more robust (solves 25% more problems) and less expensive in terms of user call-backs: 55% of problems +require less function calls (center plot) and 65% of the problems require less gradient evaluations (right plot). + + +[`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) +should present significant improvement for unconstrained or bound-constrained nonlinear +least-squares solvers in the NAG Library and current users of [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) ([`nagf_opt_lsq_uncon_quasi_deriv_comp`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04gbc.html) ) +are highly encourage to try out the new solver. + + + + +
Performance Profile (time:seconds) + Performance Profile (number of function calls) + Performance Profile (number of gradient calls) +
+ +**Figure 3.** Performance profiles comparing solvers e04gg and e04gb over 68 CUTEst unconstrained nonlinear least-squares problems. +Performance measure are: time in seconds (left), number of function calls (center) and number of gradient calls +(right). For the time plot (left), higher line indicates faster solver. For the center and right plots, higher line +represent less functions and gradients calls. + + + +# References + + * Gould N I M, Rees T, and Scott J A (2017) _A higher order method for solving nonlinear least-squares problems_. Technical report, RAL-P-1027-010 RAL Library. STFC Rutherford Appleton Laboratory http://www.numerical.rl.ac.uk/people/rees/pdf/RAL-P-2017-010.pdf + * Kanzow C, Yamashita N, and Fukushima M (2004) _Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints_. Journal of Computational and Applied Mathematics 174 375–397 + * Nocedal J and Wright S J (2006) _Numerical Optimization_. (2nd Edition) Springer Series in Operations Research, Springer, New York + * Adachi S, Iwata S, Nakatsukasa Y, and Takeda A (2015) _Solving the trust region subproblem by a generalized eigenvalue problem_. Technical report, METR 2015-14. Mathematical Engineering, The University of Tokyo https://www.keisu.t.u-tokyo.ac.jp/data/2015/METR15-14.pdf + * Conn A R, Gould N I M and Toint Ph L (2000) _Trust Region Methods_. 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images --- local_optimization/BXNL/images | 1 + 1 file changed, 1 insertion(+) create mode 100644 local_optimization/BXNL/images diff --git a/local_optimization/BXNL/images b/local_optimization/BXNL/images new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/local_optimization/BXNL/images @@ -0,0 +1 @@ + From 16e4381161a6778df7b4fec4077a6ef4efda14ca Mon Sep 17 00:00:00 2001 From: A Date: Mon, 17 Aug 2020 14:53:40 +0100 Subject: [PATCH 009/182] Delete images --- local_optimization/BXNL/images | 1 - 1 file changed, 1 deletion(-) delete mode 100644 local_optimization/BXNL/images diff --git a/local_optimization/BXNL/images b/local_optimization/BXNL/images deleted file mode 100644 index 8b13789..0000000 --- a/local_optimization/BXNL/images +++ /dev/null @@ -1 +0,0 @@ - From 619dbe8fa89fdf892151e814e334f2116b3c0a26 Mon Sep 17 00:00:00 2001 From: A Date: Mon, 17 Aug 2020 14:54:06 +0100 Subject: [PATCH 010/182] Delete fig-unfolding.png --- local_optimization/BXNL/fig-unfolding.png | 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b/local_optimization/BXNL/notebooks/orbit_ex.ipynb new file mode 100644 index 0000000..e290bbd --- /dev/null +++ b/local_optimization/BXNL/notebooks/orbit_ex.ipynb @@ -0,0 +1,388 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Orbital Data Fitting\n", + "\n", + "Example of a nonlinear least-square orbital data fitting. Given a set of orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.patches as pch\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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sMk+zc43+pM49VccLbVJmiru9G3g4uO0hQcchbfigqARKmoGtcPHF93j5lasHj+OoTLZ8lEg8D0jXdcaTCe3RNsWkxR4DsrksdnOC6zgEoU8Y7O9PXP7oMqqqooQRqqLiBR6KorJn7qCg4Houl9+/zLWr+1N5UmaK7mhAIpnk7R/+Cbfv32FpaZFXnn+JheISNzY/omhW8KYu5cQ8g0EbP5pQzdSYr6xCFOKnu/Q2uyj6BC8zx0bLZmT7/JcfVHn7T14nl8vwL//Fbx2ZyZaPEonnAWmqzqg/QdE0QiUglTPYvLWL67jouk5CNQg+icd1XRRFQdd03MAliiI0TSMIAjRVxfM9Qk1D13QGkzGRouB4Ln7oMxgFECrsrG8TjgK+8a2vc2H1RQa9Lnm9yF5/i0iJUJWQyI5otbrMV+ZZKJ/GOBFgdobsDHyu3W0zsl1QIqxklun00Zqec5RIPA8oCsEdeGgFk7HfIzejsGTm2Lzaw516BKFCGIYoQDadIZlM4jgOo/EIgCAIiKKIiTMlCEOCKCQCoihi6jooqooaKvhBQKPVwPd9Fo4tgKqAF9LZu489spkvrpFOWqw3brHe3uFYzcQdTrl94wa1+SxGuUZ79x7V8iwoHXRXIwgiojDBD36nBHQOcxgfSRLPA/I8F11XmXou5VKNcdBkrlAhX1BgaLBxd0whX+Hj27eIgPF4jOs5VEvl/UCcKWtLa9zdvEcYRiSTJr1hH03TUVQFQ9cwjARje4Lre5h6gn6rw91rtzhxfIntu9e4ufUxy8vnKZ+8yPHSGRQ2mI4mDPwtahkP1VVZ39lmb7fDqbXT5EtFypUs167dpdvp8zs/kHjikHge0NSZEvhQZxPPzZLTDWrZKjo+ej4in9f5yrOv82//7f9Fr99DV1UMXadUKtHtdrnwzLOkzBSDyZD+oM9sbQZNVXE9l6SZAmBi20CErmtEWsRwNOS//vFbhC+dZ69Vx3MCOq0W26l7OJMOvd4uE9+HXI5KJkE2XeT+1lUMTcdKWRRrGZIpjexGmp3tOo7zaJ/X4LBIPA9oOrWZTFzUgsrUH5EKEuxuXsV3JqTTOUwr5Nrty0RhSDGfp1Iuk0lnUD85qfutj2+Rz+ZpNBskDINGs04xX6TZbWNPbQzDwDQMEoaOnjTwfZ/BZMTYGXPjbmr/lTcvoFvfY9TvYCYUNDUknbDoNDYppE6hqjqO42DbKteuX+X5/EX6vR7NVhvd0B75k4IcFonnAbmeS3fYIZHTCKcD7MhD8VR0RaNQWKNjdmmtD6iUK0SBz+zMLJVKhdFwyHg8RtdUNnc2iKKIhGkQ+D6bu1sYCZNsOoOuaZw5eQrLMFFNg+FoSLfeZK6Q5fTSST683WES9tE0m8BRcUiRNBOMhnUSqsdOax1X1XCdIe2uS7MNrd9vEYYRmUwey0riutPDHsZHksTzgIIgoNFdZ7aUJa1opJJZMqbFaLhLa3qPqZdH8SySqRSmrjMZj2krCvfu3SWbzVGr1ji+tIxlWQzHIwq5PEEUcO36DfK5HL/4i19ndW2VYX+EPZnQb3dobu3RH0/o99po0ZCkGeAHHqGvELo+CS1NFEX7LzI02nhTG1OH/rCPooDrOyiqTiKZwrddPDkcOxaJ5wvQ6zUo+hZpR0FRXFQzj6qaOJMhYzfN9sYmnU6bbCZDsVhAmU4plspYlkW9XqfZbqOqCqqmsrO3x0ytRtpK0x8N2Gvt0Zv0abfa2BObxdocupng+sY9qqUWCWOKoQdEQEJXcYIAIp+UEWHoaVx/ShgEqEoWoiZrJ+cpFOawbR/Xddlc3yQI5HS8cRyZeI7SmSA/r2arz6qr4ygqjjpl0N/GD33K6RX6Y49GYw9N10kkErSaLYbjIZVyhdFkjD21SZgJfN8nmHqkUinqzSa6oRMBV65cQVFVxqMRuWwOTVFRDI20pZMvqEymCumUTioCDQU/UMhm8kRKxHTqkUq6jGyHO+sDVpeLPHX2Ka7f2GRi2yhaRKO5c9jD98g6MgfD/fh5uR41o9GY6cCBKIPtaYQBBCjoaoa8VSUMI8IwpNfv0+52caZTMtks9XqdXq/LoN/HmToEQcBwNGQ4HNJutZlOp7TbbZzplFKxRLlcwXVdbt75mIQBVirDfK1MrZCimDHJZhIUsiZmIqJSXcIw02y1J7z7QY+JbbO8YHH91se4gUPKSuC5Nr2uHMsT15GJ51EWhiGbm9so/hQ/MHBCnQiVyaDP3t5dslYGQ9UZDod4vofne6zfv890OmXqOHiex3g8wvM9NE1D13UMXSdpmmQzGdJpi9W1VU6fOYWRMAijkI3dHt0+BGECXU+QtZJYZop82kILHYat+zTaPW7fcXAcKOVMAkVnNHGBiDDyadR3cR+xE4AcJYe62XZUzwQZx+5unePLc1QqZRKmySTosdfus73do9keo6kK2WyWWrVGfzhg0O+RtiymUxvP81EUBddxCYOA+dkFLMtCN3QMQyeXy2EYBjdv3qTT7eAFPiPb4f7uhFIxi64Z6KpCytAY2y4TJ2IwGTGdeEShhqZGrB4r0u4qGJpBFEZ4vsve7vZhD9sj7VDjOapngozDcRzWN3ZJJS2SqSTp7Dwf3rpHt70/uzqKFAI/oN6oUy6XKRaK7NV38QOfMAgxEgkK+f0jUI8tHsP3Pfb29lhcWGBudo5Ov0en22UynqAqKqqq0h/Z+EGRXCqH5zn4gcdw4uD4MA2StPoB+WyOTr9Hsx8ycSckk0miMKTV3GUwGBz2sD3SjswLBo+D7e09qpUKVibP3NwsF89n+Yv3LjMaj9F1DT/wUUKFbreL4ziYpkm5VAXAtid0Oh1Mc396zlNPPUWlWsWburRbbTb3dpjYNqPRCMd1MQyDie3RGYKeMEnqMJ46aIk0ugKRX2CuCkFYpzscsl0fkc1mCDwfVQ25v35PDr1+QEcmnqN0Jsi4XNfl3v0NUhkTJ7JZXjjBKy9/jY+u3mAy2T8K1PN9bGdKFIaM7TFRFJFKWRxbWsKe2Extm93dXQzdYHl5GSNhsrWxwfbmFuPJBNue7E80VWCn2WfsWoz9PCOvRRDlMQtFlhdOkjCrtJttbv7Wm1gpC9udEkURppng9u1rDGWt88COzAsGj9o+zk/TarXZ2qrT6XW4cu0KXuDy1ecvkM2l0TQN2J8xnc3lyOcLpNNpFGBza4swCvnK8xd55unzTJ0pW1tbbG1u4roeCT2BM50SBOEnLyoY2G7Axs4WW5tb9G0D36hxd7NFpOVQdBU/9JgrVdE0lWw6TSmfp9XaY3Nz43AH6TFxZOJ5XERRxMb6Fv3mmOnI5coHH9Futzl79gS5fIYwCgHwfZ8oCkkkEqTTaarVKigKV69dwzANzp8/i+d7JJImVibN/OI8CwsLzM/Pkk6nSaaSJFNJRp5Dvd+nb4d0Bj6KXiLwQzbWN+m2uwREOJ5LwjTo9tvcunVdPp/nC3JkNtseJ57rcu/OfZaWl7GsDDs7O9RqVc6cXqVSLlBvNBlPHDwvRNc1DMPAspIsLizS7/e4ceMm5UqZZ545S9JMEkbQbrZZnJul1Wpw5/46tjMll81gTxTCAFrdDebmZykVcozHY7q9HuP+AHSNTDrFYNBje3Od0Wh02MPz2JB4HpLJZMLW5iYLi4tk0hbD0ZAgCKjVqqTTKfbqLcYTG01VSSYTZDMWxUKGQj7NdDrl/r37bNzf5OLFCzz11FlmZys0my32mrsoqoKm7ken6xoT20ZV9g918H2PdrdNu9tmPBziBROIPOq7W3Jywy+YxPMQjUYjNjc3CIKAMAwYJ1NMp1OKxQLVShGjrxMG7E/WdB0azQa6ZpC2LKxUmkzaotXq0Ov1MAydZDLBsWMLjMYjWq3uJ3PSIqJo/6VuTVXwPI/t7W2GwyGDwYBGo8G9e/fodORgty+axPOQTcYTNjc28FyXSrVCEPioqsJ0OgUUkikT295/lc1Pp8hk0qTTKWZnq5hmAl3X0DSVfr+P7/v4voeqgK6ruK5HFIXomkYum0bXVYbDIY7j0O12aTQabG5uyqbaQyLxfAkcx2FrawvbtqlUq0ynUxKJBIqq4jgOgR8w9gM832cwHBEGIaqqkM6kURSFKIoIw4jJeEK318dxHBRFgShC0ww0VcX3Xba2thiPxwyHQ1qtFo1GA9eVww0eFonnSxIEAc1mk9FoRKlUIpfLkUym0I0EqqqRTJpEUbQ//83zcV0Po9NFVRU81yMCFCD65L5SSRPXcwl8j0hVqNd72J+8idrpdBgOh/Im6EMm8XyJoihiMpkwnU7p9/vkcjnSmQypZAqiAM/T0VQVXdewUon9k4AokDB0omg/Gj/w0TQD19s/2864P8L3PSbjCf1Bn9FwhO/L8TlfBonnEIRhyPCTw7CTSZN0OoNlWSSTSQzDwDAMNE1D0zQUVUXXNCL2z9TjuR6u6+J5Ho7rYE9sxuMx0+n04Pxw4ssh8RyiMAyZTGwmExtVVTEMg0QiQSKRQDd0NFXb37eBT/Z7QnzfP4jHdV0J5hBJPEdEGIY4joPj/M3xNZ+G8ynZhzlaJJ4jTGI52mRumxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEIz63N9447CU4GiQe8bl95zuHvQRHg8QjREwSzwN6UjZh3ngDLl3av8DffP+kPP6/UxRFP+sSRVEUXbp0KVJVNQLk8rculy4d/jLIY/7iLqqqRm+//Xb0Y35qH7LmESIm+TTsGN544yd3mj/dlPne9+D73z+MJfpyfe97h70ER4RstskmjFz+5iKbbUJ8CSSeBySbME8uiecBPQn7OOLvJvEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxPERLS0ucPHkSRVEAMAwDwzD+h9uVSiU0Tfs770NVVarVKoZhUCqVDv5/pVJBVff/+crl8k/8fLlc5uTJk2SzWU6fPk06nebs2bOk02lOnz6NZVlf5MN8YsmnYT8kpmny+uuvs7m5SRRFHDt2DNM00XWd9957j3K5TLVapd/v89JLL/HOO+9QKBRoNpt0Oh0cx6HX63Hu3Dlefvllrl+/zszMDG+++SYAr776Krdu3aLT6fDKK68cfL+3t8fa2hrLy8tkMhmazSYnTpzA8zxeeukl6vU6S0tLvPXWW4c8Qo8+WfM8JGEYcvXqVWq1GmfOnOHpp59meXmZZDLJysoKr7zyCjMzM5w7d452u83Jkyd58cUXefbZZ3n99dcP7ufWrVs0m03ef/99xuMxAPl8HlVVee655zh9+jSFQoHz58/z8ssvEwQBm5ubqKrKZDLh3r179Pt9CoUCjUaD+/fvk0wmD2tYHisSz0OiKAqzs7N4noeu64zHY+r1Op7ncfr0aYbDIXfu3KHb7ZLL5TBNk16vx82bN9F1nZWVFRRFIQgC2u02vu/T7XYBeOGFF0gkErRaLVZXV6nX66yvr9Pv9wmCgF/5lV/BMAx2dnZ49tlnKZfLzM/Ps7e3x7PPPsu9e/cOeXQeEz/rc+Y//SD6S5cuRaqqPpTPvX+cL4qiRKqq/sTXH//+77rNmTNnotXV1ahcLv/E/fztr3/7vl588cWoWCxGQKSqaqRp2k9c/+P/fdjjcpQvqqpGb7/9dvRjfmofn2mfZ21tjd/4jd8gDMPPcnMhHlmKonDixInPdtsoin7W9T/zSiGeAMpPu0L2eYSISeIRIiaJR4iYJB4hYpIZBuLIiKKI3Uaft965hpVK8MuvnCOXTR1MbzpqJB5xJERRxIc3t/nH//q73N9uo6DwD/7+8/yb//0foarg+QEKCooKqqIQhNH/EFUURkREqIpCGEX7t1cgjCJ0XQ/Q+0YAAAUJSURBVCMMwv03nj95y0VTVTQt/sZX7HiiKGI6nWIYBr7v47oupmmiKAphGOL7Pp7nkUwmCYLg4N1y0zSJoghVVQmCgDAMD24TRdHBz6XTaYIgwHEcFEXBsiw8zzv4nUEQkMlkAA7uR9M0bNtG13VSqRSTyQRVVdH1/YfpeR6GYRBFEUEQ4LruwfKmUimiKDr4fZqmoWkaQRAc3Menb475vk8YhqiqiqZpJBIJxuMxmqbhui6ZTObgd34enucB4Ps+QRBgGMbBMiuKgq7rB5NBH0e/+eafcW+rDYCqKTTbI65c32Rxrsi//D9+i5e+cgLPC3j+wnH+yx/+iGNzJTxv/3mTSZtcvrrJqZUaa8s1fvv3/oqXLq5xf6tNKmnwz//BL/Kbv/0Oq8eq3N1scme9yb/6Z3+Prz27Gnt5H2jN87u/+7uUSiXu3r3L+fPn2draOnjyFItFms0m+XwewzC4e/cuiUSCbDZLo9FgYWHh4El54cIF3n33XQaDAb7vH8wGvnz5MsViEVVVMU2Tra0tVFUlm83S6/X4hV/4BWzbZmNjg729PRYXFw/mcV28eJEPPviAVCpFOp3Gtm3++q//mpWVFUzTZGNjg9nZWQzDYHd3l9dee43bt2/jui7b29skk0lKpRK6rnP16lVOnz5NsVhkOBwymUzodDqkUinG4zHnzp3D933a7TZhGPLNb36TbDb7ucfz2rVrbG5u0mg0sCzr4LEbhkGr1eLrX/861Wr1Qf7JjrT+YALsr1lOLFf55ktn0HUNzwv4eL3Br/3yc1y+ukF/aHNnvYkC3Flv4gchtXKWuxstzp6Y49uvnucP//Qq//Dvv8C//j9/m3QqwW69x/vXNtne6/G//qNX+fe/85e8cGHlgZb3gf6M1Wo1dnZ2KJVK+L6PaZrUajV6vR6VSoXl5WUSiQRhGFIsFimXy+i6ztraGru7uyiKwmAwwDRNbNsmnU5Tq9VQFIX19XWy2SyZTIa5uTlM08QwjIMn0+zsLKqqUq/XCYKAubk5dnd3gf13iVVVJYoiXNdlc3OTyWRCrVaj3W7TbDYpl8sYhsHc3NzBWtCyLE6dOsXc3NzBkz8MQ+bm5qjX66TTaTKZDOPxmGq1yvnz56lUKmxsbBysLRRF4ee88fxTWZZFp9OhXC6Ty+UYDAZEUUS9Xj9YCz3OXv+lCxTzFv/bd77J//0b/4xvvXKOlcUKALl0Ck1TURSF967cQ1EU7m+1ma3lWZwr0uyMSCYNysU0g6GNpqlEEfzSS2fYrvf4d//xh2TSJvX2gK3dLpqmPPC+VOwZBp9u+ny6+fLjmxdBEKBp2sFmThAE6Lp+cN2nT+woigjDENM08X3/4Innui66rqPr+sH9w/7m2acTLT/djAIONr1gf5NHVVUSiQSO4xws26ebPJ/+jK7rB8synU5JJBKoqnoQEuyHE4bhwXJomkYYhj/xeD59TL7vo2nawabqTzs+52cJguAnNnF/fLNR07SDPwqPK98P+P0/+YjL1zZImQb/y+vPs7xQxnV9Pry1jaaqzFRyrG+3qZay+EFAOmWiKDAYTXE9H9cLOLUyQ7s7Yraa5/rt/T/SxbxFIZdiMJpiGBqO47NyrPJZFuunFibTc8SREkXRJzv7HPxxOmQSjxAxydw2Ib5oEo8QMUk8QsT0897nOfS9NSGOKlnzCBGTxCNETBKPEDFJPELEJPEIEZPEI0RM/z8IQzNejW+6LgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "im = plt.imread(\"earth.png\")\n", + "implot = plt.imshow(im)\n", + "tx = np.array([441.23, 484.31, 265.15, 98.25, 180.66, 439.13, 596.54])\n", + "ty = np.array([333.92, 563.46, 577.40, 379.23, 148.62, 100.28, 285.99])\n", + "cc = np.array([355.00, 347.00])\n", + "tr = (tx-cc[0])**2 + (ty-cc[1])**2\n", + "plt.plot(tx,ty,'y+')\n", + "plt.axis('off')\n", + "plt.savefig('dat_orbit.png', bbox_inches='tight', dpi=150)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help).\n", + "\n", + "\n", + "The previous image shows the orbit measurements to which an optimal orbit, `r`, must be estimated. \n", + "The simple univariate problem to solve is:\n", + "\n", + "![LaTeX equation: min f(x) = sum i=1 to nres of (tr[i]^2 - r^2)^2](ltx_optprb.png)\n", + "\n", + "Here `tr[i]` contains the squared norm for the measurement point `i`, given by the coordinate pair `(tx[i], ty[i])`. Note that the coordinates for the center of the planet are provided by the vector `cc`." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# problem data\n", + "# number of observations\n", + "nres = len(tx)\n", + "# observations\n", + "# Define the data structure to be passed to the callback functions\n", + "data = {'tr': tr}\n", + "# number of parameter to fit\n", + "nvar = 1" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Define the least-square function and add first derivatives.\n", + "def lsqfun(x, nres, inform, data):\n", + " \"\"\"\n", + " Objective function call back passed to the least squares solver.\n", + " Return the difference between the current estimated radius squared, r^2=x^2 and \n", + " the squared norm of the data point stored in tr[i] for i = 1 to nres:\n", + " rx[i] = r^2 - tr[i], i = 1, ..., nres.\n", + " \"\"\"\n", + " rx = x**2 - data['tr']\n", + " return rx, inform\n", + "\n", + "def lsqgrd(x, nres, rdx, inform, data):\n", + " \"\"\"\n", + " Computes the Jacobian of the least square residuals.\n", + " Simply return rdx[i] = 2r, i = 1, ..., nres.\n", + " \"\"\"\n", + " rdx = 2.0*np.ones(nres)*x\n", + " return rdx, inform" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize the model handle\n", + "handle = opt.handle_init(nvar)\n", + "\n", + "# Define a dense nonlinear least-squares objective function\n", + "opt.handle_set_nlnls(handle, nres)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Restrict parameter space (0 <= x)\n", + "opt.handle_set_simplebounds(handle, np.zeros(nvar), 1000.0*np.ones(nvar))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Set some optional parameters to control the output of the solver\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print Solution = X',\n", + " 'Bxnl Iteration Limit = 100'\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# Define initial guess (starting point) Away from zero which is problematic.\n", + "x = np.ones(nvar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the solver" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GG, Nonlinear least squares method for bound-constrained problems\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 1.45373E+09\n", + " Norm of projected gradient 2.23690E-01\n", + " Norm of scaled projected gradient 4.14848E-06\n", + " Norm of step 3.75533E-06\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 2.38765E+02 1.00000E+03\n" + ] + } + ], + "source": [ + "# Call the solver\n", + "slv = opt.handle_solve_bxnl(handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal Orbit Height: 238.76\n" + ] + } + ], + "source": [ + "# Optimal parameter values\n", + "rstar = slv.x\n", + "print('Optimal Orbit Height: %3.2f' % rstar)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "figure, axes = plt.figure(), plt.gca()\n", + "implot = plt.imshow(im)\n", + "orbit = plt.Circle(cc, radius=rstar, color='w', fill=False)\n", + "axes.add_patch(orbit)\n", + "plt.plot(tx, ty, 'y+')\n", + "plt.axis('off')\n", + "plt.savefig('est_orbit.png', bbox_inches='tight', dpi=150)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose expert knowledge provides insight on the reliability of each measurement and that for this satellite configuration, operational orbit height should be around 250 +/-6 units. The previous image shows a fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to Earth surface) is unreliable. Unreliability should be taken into account while doing the fitting. For this end, weights for each residuals are introduced (weights should be set to be proportional to the inverse of their variability). For this example, suppose we are provided with the accuracy for each of the data measurements. \n", + "\n", + "With this new information, the problem is solved again using weighted nonlinear least-squares. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GG, Nonlinear least squares method for bound-constrained problems\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 1.25035E+06\n", + " Norm of projected gradient 6.26959E-03\n", + " Norm of scaled projected gradient 3.96468E-06\n", + " Norm of step 8.72328E-03\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 2.54896E+02 1.00000E+03\n", + "Optimal Orbit Height: 254.90\n" + ] + } + ], + "source": [ + "# Add weights for each residual\n", + "weights = np.array([0.10, 0.98, 1.01, 1.00, 0.92, 0.97, 1.02])\n", + "weights /= weights.sum()\n", + "\n", + "# Define the reliability of the measurements (weights)\n", + "opt.handle_set_get_real(handle, 'rw', rarr=weights)\n", + "\n", + "# Indicate to the solver that weights are to be used\n", + "for option in [\n", + " 'Bxnl Use weights = Yes',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Solve again\n", + "slv = opt.handle_solve_bxnl(handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom) # monit=monit,\n", + "\n", + "# Objective and solution\n", + "rstar = slv.x\n", + "print('Optimal Orbit Height: %3.2f' % rstar)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal Orbit Height: 254.90 (should be between 244 and 256)\n" + ] + } + ], + "source": [ + "figure, axes = plt.figure(), plt.gca()\n", + "implot = plt.imshow(im)\n", + "orbit = plt.Circle(cc, radius=rstar, color='w', fill=False)\n", + "axes.add_patch(orbit)\n", + "plt.plot(tx, ty,'y+')\n", + "plt.axis('off')\n", + "plt.savefig('estw_orbit.png', bbox_inches='tight', dpi=150)\n", + "plt.show()\n", + "print('Optimal Orbit Height: %3.2f (should be between 244 and 256)' % rstar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this weighted model the orbital solution provided concurs with expert advice." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb new file mode 100644 index 0000000..5c49cde --- /dev/null +++ b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb @@ -0,0 +1,552 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simple Nonlinear Least-Squares Fitting Example\n", + "\n", + "This example demontrates how to fit data to a model using weighted nonlinear least-squares. \n", + "\n", + "**handle_solve_bxnl** (`e04gg`) is a bound-constrained nonlinear least squares trust region solver (BXNL) from the NAG optimization modelling suite aimed for small to medium-scale problems. It solves the problem:\n", + "\n", + "$$\n", + "\\begin{array}{ll}\n", + "{\\underset{x \\in \\mathbb{R}^{n_{\\text{var}}}}{minimize}\\ } & \n", + "\\frac{1}{2} \\sum_{i=1}^{n_{\\text{res}}} w_i r_i(x)^2 + \\frac{\\sigma}{p}\\|x\\|^p_2\\\\\n", + "\\text{subject to} & l_{x} \\leq x \\leq u_{x}\n", + "\\end{array}\n", + "$$\n", + "\n", + "\n", + "where $r_i(x),i=1,\\dots,n_{\\text{res}}$, are smooth nonlinear functions called residuals, $w_i ,i=1,\\dots,n_{\\text{res}}$ are weights (by default they are all defined to 1, and the rightmost element represents the regularization term with parameter $\\sigma\\geq0$ and power $p>0$. The constraint elements $l_x$ and $u_x$ are $n_{\\text{var}}$-dimensional vectors defining the bounds on the variables.\n", + "\n", + "Typically in a calibration or data fitting context, the residuals will be defined as the difference between the observed values $y_i$ at $t_i$ and the values provided by a nonlinear model $\\phi(t;x)$, i.e., $$r_i(x)≔y_i-\\phi(t_i;x).$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example illustrates the usage of `e04gg` to fit PADC target with $\\alpha$ particle\n", + "etched nuclear track data to a convoluted distribution. A target\n", + "sheet is scanned and track diameters (red wedges in\n", + "the following Figure 1) are recorded into a histogram and a mixed Normal and log-Normal model is to be fitted to the experimental histogram (see Figure 2).\n", + "![PADC](tracks.png)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Figure 1**: PADC with etched $\\alpha$ particle tracks." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`e04gg` is used to fit the six parameter model\n", + "$$\n", + "\\begin{array}{ll}\n", + "\\phi\\big(t, x = (a, b, A_{\\ell}, \\mu, \\sigma, A_g)\\big) = \\text{log-Normal}(a, b, A_l) + \\text{Normal}(\\mu, \\sigma^2, A_g)\\\\\n", + "\\text{subject to } 0 \\leq x,\n", + "\\end{array}$$\n", + "using the histogram heights reported in Figure 2." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt\n", + "\n", + "# problem data\n", + "# number of observations\n", + "nres = 64\n", + "# observations\n", + "diameter = range(1, nres+1)\n", + "density = [\n", + " 0.0722713864, 0.0575221239, 0.0604719764, 0.0405604720, 0.0317109145, \n", + " 0.0309734513, 0.0258112094, 0.0228613569, 0.0213864307, 0.0213864307,\n", + " 0.0147492625, 0.0213864307, 0.0243362832, 0.0169616519, 0.0095870206,\n", + " 0.0147492625, 0.0140117994, 0.0132743363, 0.0147492625, 0.0140117994,\n", + " 0.0140117994, 0.0132743363, 0.0117994100, 0.0132743363, 0.0110619469,\n", + " 0.0103244838, 0.0117994100, 0.0117994100, 0.0147492625, 0.0110619469,\n", + " 0.0132743363, 0.0206489676, 0.0169616519, 0.0169616519, 0.0280235988,\n", + " 0.0221238938, 0.0235988201, 0.0221238938, 0.0206489676, 0.0228613569,\n", + " 0.0184365782, 0.0176991150, 0.0132743363, 0.0132743363, 0.0088495575,\n", + " 0.0095870206, 0.0073746313, 0.0110619469, 0.0036873156, 0.0051622419,\n", + " 0.0058997050, 0.0014749263, 0.0022123894, 0.0029498525, 0.0014749263,\n", + " 0.0007374631, 0.0014749263, 0.0014749263, 0.0007374631, 0.0000000000,\n", + " 0.0000000000, 0.0000000000, 0.0000000000, 0.0000000000\n", + " ]\n", + "\n", + "# Define the data structure to be passed to the callback functions\n", + "data = {'d': diameter, 'y': density}" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot histogram of PADC etch track diameter count (densities)\n", + "dh = np.arange(1, 10*nres+9)/10.0\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "ax.set_title('PADC etch track diameter histogram', fontsize=16)\n", + "ax.set_xlabel('Diameter (nm)')\n", + "ax.set_ylabel('Density')\n", + "ax.set_xlim(xmin=1, xmax=65)\n", + "ax.bar(diameter, data['y'], color='lightsteelblue')\n", + "ax.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Figure 2**: Histogram of etched track diameter of $\\alpha$ particles. Bar heights are the data that will be fitted unsing the aggregated model $\\phi(x, t)$. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Define Normal and log-Normal distributions\n", + "def lognormal(d, a, b, Al):\n", + " return Al/(d*b*np.sqrt(2*math.pi))*np.exp(-((np.log(d)-a)**2)/(2*b**2))\n", + "\n", + "def gaussian(d, mu, sigma, Ag):\n", + " return Ag*np.exp(-0.5*((d-mu)/sigma)**2)/(sigma*np.sqrt(2*math.pi))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In terms of solving this problem, the function to minimize is the sum of residuals using the model $\\phi(x;t)$\n", + "and the data pair (`diameter`, `density`). The parameter vector is $x = (a, b, A_l, \\mu, \\sigma, A_g)$. The next step is to define a function to return the residual vector \n", + "$\\text{lsqfun}(x) := \\big[r_1(x), r_2(x), \\dots, r_{n_{\\text{res}}}(x)\\big]$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Define the least-square function as a mixture of Normal and log-Normal \n", + "# functions. Also add its first derivatives\n", + "def lsqfun(x, nres, inform, data):\n", + " \"\"\"\n", + " Objective function callback passed to the least squares solver.\n", + " x = (a, b, Al, mu, sigma, Ag)\n", + " \"\"\"\n", + " rx = np.zeros(nres)\n", + " d = data['d']\n", + " y = data['y']\n", + " a = x[0]\n", + " b = x[1]\n", + " Al = x[2]\n", + " mu = x[3]\n", + " sigma = x[4]\n", + " Ag = x[5]\n", + " for i in range(nres):\n", + " rx[i] = lognormal(d[i], a, b, Al) + gaussian(d[i], mu, sigma, Ag) - y[i]\n", + " return rx, inform\n", + "\n", + "def lsqgrd(x, nres, rdx, inform, data):\n", + " \"\"\"\n", + " Computes the Jacobian of the least square residuals.\n", + " x = (a, b, Al, mu, sigma, Ag)\n", + " \"\"\"\n", + " n = len(x)\n", + " d = data['d']\n", + " a = x[0]\n", + " b = x[1]\n", + " Al = x[2]\n", + " mu = x[3]\n", + " sigma = x[4]\n", + " Ag = x[5]\n", + " for i in range(nres):\n", + " # log-Normal derivatives\n", + " l = lognormal(d[i], a, b, Al)\n", + " # dl/da\n", + " rdx[i*n+0] = (np.log(d[i])-a)/(b**2) * l\n", + " # dl/db\n", + " rdx[i*n+1] = ((np.log(d[i])-a)**2 - b**2)/b**3 * l\n", + " # dl/dAl\n", + " rdx[i*n+2] = lognormal(d[i], a, b, 1.0)\n", + " # Gaussian derivatives\n", + " g = gaussian(d[i], mu, sigma, Ag)\n", + " # dg/dmu\n", + " rdx[i*n+3] = (d[i] - mu) / sigma**2 * g\n", + " # dg/dsigma\n", + " rdx[i*n+4] = ((d[i] - mu)**2 - sigma**2)/sigma**3 * g\n", + " # dg/dAg\n", + " rdx[i*n+5] = gaussian(d[i], mu, sigma, 1.0)\n", + " return rdx, inform" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# parameter vector: x = (a, b, Al, mu, sigma, Ag)\n", + "nvar = 6" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize the model handle\n", + "handle = opt.handle_init(nvar)\n", + "\n", + "# Define a dense nonlinear least-squares objective function\n", + "opt.handle_set_nlnls(handle, nres)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "HandleSetGetRealReturnData(lrarr=64, rarr=None)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Add weights for each residual\n", + "weights = np.ones(nres)\n", + "weights[55:63] = 5.0\n", + "weights /= weights.sum()\n", + "\n", + "# Define the reliability of the measurements (weights)\n", + "opt.handle_set_get_real(handle, 'rw', rarr=weights)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# Restrict parameter space (0 <= x)\n", + "opt.handle_set_simplebounds(handle, np.zeros(nvar), 100.0*np.ones(nvar))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# Set some optional parameters to control the output of the solver\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print Solution = X',\n", + " 'Bxnl Iteration Limit = 100',\n", + " 'Bxnl Use weights = YES',\n", + " # Add cubic regularization term (avoid overfitting)\n", + " 'Bxnl Reg Order = 3',\n", + " 'Bxnl Glob Method = REG',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# Define initial guess (starting point)\n", + "x = np.array([1.63, 0.88, 1.0, 30, 1.52, 0.24], dtype=float)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Call the solver" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GG, Nonlinear least squares method for bound-constrained problems\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 4.44211E-08\n", + " Norm of projected gradient 1.18757E-09\n", + " Norm of scaled projected gradient 3.98428E-06\n", + " Norm of step 1.66812E-01\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 2.02043E+00 1.00000E+02\n", + " 2 0.00000E+00 1.39726E+00 1.00000E+02\n", + " 3 0.00000E+00 6.93255E-01 1.00000E+02\n", + " 4 0.00000E+00 3.65929E+01 1.00000E+02\n", + " 5 0.00000E+00 7.01808E+00 1.00000E+02\n", + " 6 0.00000E+00 3.36877E-01 1.00000E+02\n" + ] + } + ], + "source": [ + "# Call the solver\n", + "slv = opt.handle_solve_bxnl(handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal solution $x$ provides the unfolded parameters for the two distributions, Normal and log-Normal (blue and red curves in Figure 4). Adding these together produces the aggragated curve (shown in color green of Figure 3 and 4) this last one is the one used to perform the fitting with. The optimal solution is" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Optimal parameter values\n", + "# Al * log-Normal(a, b):\n", + "aopt = slv.x[0]\n", + "bopt = slv.x[1]\n", + "Alopt = slv.x[2]\n", + "\n", + "# Ag * gaussian(mu, sigma):\n", + "muopt = slv.x[3]\n", + "sigmaopt = slv.x[4]\n", + "Agopt = slv.x[5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and the objective function value is " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.4421102582032486e-08\n" + ] + } + ], + "source": [ + "print(slv.rinfo[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next plot in Figure 3 illustrates the mixed-distribution fit over the histogram:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lopt = lognormal(dh, aopt, bopt, Alopt)\n", + "gopt = gaussian(dh, muopt, sigmaopt, Agopt)\n", + "w = lopt + gopt\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "ax.set_title('PADC etch track diameter histogram and fit', fontsize=16)\n", + "ax.set_xlabel('Diameter (nm)')\n", + "ax.set_ylabel('Density')\n", + "ax.set_xlim(xmin=1, xmax=65)\n", + "ax.bar(diameter, data['y'], color='lightsteelblue')\n", + "ax.plot(dh, w, '-', linewidth=3, color='tab:green')\n", + "ax.grid()\n", + "ax.legend(['Aggregated', 'Measured track diameter density'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Figure 3**: Histogram with aggregated fit.\n", + "\n", + "The plot below in Figure 4 shows the unfolded fit, in red the log-Normal distribution and blue the Normal one:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot(111)\n", + "ax.set_title('PADC etch track diameter histogram unfolding', fontsize=16)\n", + "ax.set_xlabel('Diameter (nm)')\n", + "ax.set_ylabel('Density')\n", + "ax.set_xlim(xmin=1, xmax=65)\n", + "ax.bar(diameter, data['y'], color='lightsteelblue')\n", + "ax.plot(dh, lopt, '-', linewidth=4, color='tab:red')\n", + "ax.plot(dh, gopt, '-', linewidth=4, color='tab:blue')\n", + "ax.plot(dh, w, '-', linewidth=3, color='tab:green')\n", + "ax.grid()\n", + "glab = 'Unfolded Normal($\\\\mu=%1.2f$, $\\\\sigma=%1.2f, A=%1.2f$)' % (muopt, sigmaopt, Agopt)\n", + "llab = 'Unfolded log-Normal($a=%1.2f$, $b=%1.2f, A=%1.2f$)' % (aopt, bopt, Alopt)\n", + "ax.legend([llab, glab, 'Aggregated', 'Measured track diameter density'])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Figure 4**: Aggregated model used for the fitting (green curve) and unfolded models (blue and red curves).\n", + "Optimal parameter values are ported in the legend." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, clean up and destroy the handle" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# Destroy the handle:\n", + "opt.handle_free(handle)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From d56cb1de16e2b40780e6ea4f01ba15eb6c24b0de Mon Sep 17 00:00:00 2001 From: A Date: Mon, 17 Aug 2020 14:58:01 +0100 Subject: [PATCH 016/182] Delete Readme.md --- local_optimization/BXNL/notebooks/Readme.md | 1 - 1 file changed, 1 deletion(-) delete mode 100644 local_optimization/BXNL/notebooks/Readme.md diff --git a/local_optimization/BXNL/notebooks/Readme.md b/local_optimization/BXNL/notebooks/Readme.md deleted file mode 100644 index 8b13789..0000000 --- a/local_optimization/BXNL/notebooks/Readme.md +++ /dev/null @@ -1 +0,0 @@ - From 69f4368a8936ec7620a2b6eea25352396192077b Mon Sep 17 00:00:00 2001 From: A Date: Mon, 17 Aug 2020 15:04:16 +0100 Subject: [PATCH 017/182] Update Readme.md --- local_optimization/BXNL/Readme.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index d6f8710..0414e59 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -4,12 +4,12 @@ Data fitting and calibrating parameters of complex numerical models is one of the most common problems found in numerous industries such as physics, space exploration, simulations, engineering, amongs many others. -[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems ([`e04gg`]((https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)), [`handle_solve_bxnl`]((https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html))). It offers a significant variety of algorithms and regularisation techniques. +[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html), [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html)). It offers a significant variety of algorithms and regularisation techniques. The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small- to mid-scale (100s to 1000s of parameters) bound-constrained nonlinear least-squares problems and is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. -Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook](./python/orbit_ex.ipynb)). The task is to find the optimal orbit path given a variety of measurements for which the orbit has to approximatly pass-by. +Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook](./notebooks/orbit_ex.ipynb)). The task is to find the optimal orbit path given a variety of measurements for which the orbit has to approximatly pass-by. @@ -19,17 +19,17 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook
**Figure 1.** Example of a NLLS orbital data fitting. - Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 232.9 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 247.6 units wich is withing the suggested tolerance. Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help). + Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 254.90 units wich is withing the suggested tolerance. Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help). -# More Info [TODO fix links] +# More Info 1. [BXNL information leaflet]() 2. [BXNL in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) 3. [BXNL documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] # Unfolding Nuclear Track Data - [[Python Jupyter notebook for this example](./python/simple_BXNL.ipynb)] + [[Python Jupyter notebook for this example](./notebooks/simple_BXNL.ipynb)] This example illustrates the usage of `e04gg` to fit PADC etched nuclear track data of alpha particles to a convoluted distribution. A target @@ -38,7 +38,7 @@ left in Figure 2) into a histogram (Blue bars right plot of Figure 2) and a mixed Normal and log-Normal model is to be fitted to the obtained experimental histogram. -The [Jupyter notebook](./simple_BXNL.ipynb) uses `e04gg` to fit the +The [Jupyter notebook](./notebooks/simple_BXNL.ipynb) uses `e04gg` to fit the six parameter model φ(t, x = (a,b,Al,μ,σ,Ag)) = Al log-Normal(a, b) + Ag Normal(μ, σ) with 0 ≤ x, using as data the histogram heights. The NLLS solution provides the unfolded parameters for the two distributions (red and blue curves in right plot in Figure 2). From 1a0f9aaa3a8faf8bf2bf72765633e262061379cd Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 14:57:43 +0100 Subject: [PATCH 018/182] Create Migrating.md --- local_optimization/FOAS/Migrating.md | 66 ++++++++++++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 local_optimization/FOAS/Migrating.md diff --git a/local_optimization/FOAS/Migrating.md b/local_optimization/FOAS/Migrating.md new file mode 100644 index 0000000..9f693c7 --- /dev/null +++ b/local_optimization/FOAS/Migrating.md @@ -0,0 +1,66 @@ +[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) + +# First-order active-set method (FOAS, e04kf) + +Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. + +FOAS is a [first-order nonlinear conjugate method](https://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method) for large-scale bound-constrained nonlinear optimization. The solver is ideal for very large problems (tens of thousands or more variables) where the first-order derivatives are available or are relatively _cheap_ to estimate. + +e04kf is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. + +The following example illustrates the simple usage of FOAS to solve the bound-constrained 2D version of the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is a classical test function to measure and profile performance of solvers. Source of this example is avaible in [rosenbrock2d.ipynb](rosenbrock2d.ipynb). + + + + +
2D Rosenbrock example2D Rosenbrock with bounds
+ +**Figure 1.** 2D Rosenbrock function, (left) the minimum is shown as a yellow dot at x=(1,1). On the right a bound constrained version showing with a purple dotted line a path towards the constrained solution point on the border. + +# More information + 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) + 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) + 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example)] + +# A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) +One of the main design objectives for e04kf was to provide a modern and attractive replacement for the CG solver e04dg introduced in Mark 12. While this solver was targeted for unconstrained NLPs, e04kf has been extended with an active-set method in order to solve bound-constrained NLPs. + +More recent and modern methods have been incorporated into e04kf making it much faster than e04dg. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers e04kf and e04dg. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. + + + + + +
Perf profile e04kf/e04dg time (s)Perf profile e04kf/e04dg function evaluationsPerf profile e04kf/e04dg gradient evaluations
+ +**Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. + +# Beale's function +This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. + +Both solvers are used to find a minimum to the function and are started at the same initial point (2, 2). The following figure shows an animation of the steps taken by each solver to find a minimum to the function. +It illustrates the agressive steps taken by the [Conjugate Gradient method](https://en.wikipedia.org/wiki/Conjugate_gradient_method) compared to the more conservative steps of BFGS. + +Beale function solved using e04kf and L-BFGS-B + +**Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star in the. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. + +# Migrating from E04DG (Mark 26.x) to E04KF (Mark +27.x) + +Notes, source code and comments on migrating your code to support the new FOAS solver: + + * [Python](migration/python.md) + * [Fortran 90](migration/fotran.md) + * [C](migration/c.md) + +# References + + * Hager W W and Zhang H (2005) _A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search_. SIAM J. Optim. 16(1) 170–192 + * Hager W W and Zhang H (2006a) _Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent_. ACM Trans. Math. Software 32(1) 113–137 + * Hager W W and Zhang H (2006b) _A New Active Set Algorithm for Box Constrained Optimization_. SIAM J. Optim. 17(2) 525–557 + * Hager W W and Zhang H (2013) _The Limited Memory Conjugate Gradient Method_. SIAM J. Optim. 23(4) 2150–2168 + * Nocedal J and Wright S J (2006) _Numerical Optimization_. (2nd Edition) Springer Series in Operations Research, Springer, New York + + + + From a3d375078e37f8da561f17e45ad915970c43be8d Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 14:58:14 +0100 Subject: [PATCH 019/182] Create python.md --- local_optimization/FOAS/migration/python.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 local_optimization/FOAS/migration/python.md diff --git a/local_optimization/FOAS/migration/python.md b/local_optimization/FOAS/migration/python.md new file mode 100644 index 0000000..0c11020 --- /dev/null +++ b/local_optimization/FOAS/migration/python.md @@ -0,0 +1 @@ +# Migrating from From 389b524933685e70e3a71fca0ac0bfd0a407c3e9 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 14:58:32 +0100 Subject: [PATCH 020/182] Create fortran.md --- local_optimization/FOAS/migration/fortran.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 local_optimization/FOAS/migration/fortran.md diff --git a/local_optimization/FOAS/migration/fortran.md b/local_optimization/FOAS/migration/fortran.md new file mode 100644 index 0000000..1e0ca6a --- /dev/null +++ b/local_optimization/FOAS/migration/fortran.md @@ -0,0 +1 @@ +# From 3538754f1ec4279c540b975409f06855d111f50b Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 14:58:48 +0100 Subject: [PATCH 021/182] Create c.md --- local_optimization/FOAS/migration/c.md | 1 + 1 file changed, 1 insertion(+) create mode 100644 local_optimization/FOAS/migration/c.md diff --git a/local_optimization/FOAS/migration/c.md b/local_optimization/FOAS/migration/c.md new file mode 100644 index 0000000..792d600 --- /dev/null +++ b/local_optimization/FOAS/migration/c.md @@ -0,0 +1 @@ +# From 3d359ac90f4b008a6c2446b16d7f701d506e0b76 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 16:55:35 +0100 Subject: [PATCH 022/182] Update python.md --- local_optimization/FOAS/migration/python.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/local_optimization/FOAS/migration/python.md b/local_optimization/FOAS/migration/python.md index 0c11020..3313a8d 100644 --- a/local_optimization/FOAS/migration/python.md +++ b/local_optimization/FOAS/migration/python.md @@ -1 +1,7 @@ # Migrating from + + +```{python} +import in from nag +``` +# second From ac09d2c239b14a19148dd08dd1d28e4ad207de8e Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 16:55:48 +0100 Subject: [PATCH 023/182] Delete c.md --- local_optimization/FOAS/migration/c.md | 1 - 1 file changed, 1 deletion(-) delete mode 100644 local_optimization/FOAS/migration/c.md diff --git a/local_optimization/FOAS/migration/c.md b/local_optimization/FOAS/migration/c.md deleted file mode 100644 index 792d600..0000000 --- a/local_optimization/FOAS/migration/c.md +++ /dev/null @@ -1 +0,0 @@ -# From ce699d1e071f5d6106466078867d3c1e36da1940 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 20 Aug 2020 16:56:12 +0100 Subject: [PATCH 024/182] Update Migrating.md --- local_optimization/FOAS/Migrating.md | 1 - 1 file changed, 1 deletion(-) diff --git a/local_optimization/FOAS/Migrating.md b/local_optimization/FOAS/Migrating.md index 9f693c7..685d5c5 100644 --- a/local_optimization/FOAS/Migrating.md +++ b/local_optimization/FOAS/Migrating.md @@ -51,7 +51,6 @@ Notes, source code and comments on migrating your code to support the new FOAS s * [Python](migration/python.md) * [Fortran 90](migration/fotran.md) - * [C](migration/c.md) # References From 1e54a26cfd50b885ca849bdd75acfd94d400eae4 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 21 Aug 2020 18:27:57 +0100 Subject: [PATCH 025/182] Add files via upload --- .../migration/migration_e04dg_e04kf.ipynb | 218 ++++++++++++++++++ 1 file changed, 218 insertions(+) create mode 100644 local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb diff --git a/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb b/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb new file mode 100644 index 0000000..5bc5c7b --- /dev/null +++ b/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb @@ -0,0 +1,218 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Migrating from `uncon_conjgrd_comp` to `handle_solve_bounds_foas`\n", + "\n", + "This notebook illustrates the steps required to upgrade from the solver `uncon_conjgrd_comp` (`E04DG`) to `handle_solve_bounds_foas` (`E04KF`) introduced at Mark 27 of the NAG Library.\n", + "\n", + "From the usage perspective, the main difference between the solvers is the user call-backs,\n", + "`uncon_conjgrd_comp` has a single user call-back that can return *objective \n", + "function* and *gradient* evaluations, while `handle_solve_bounds_foas` has two separate user call-backs, \n", + "one for the *objective funtion* and one for the *objective gradient*.\n", + "\n", + "In this notebook the 2d Rosenbrock problem is solved with both solvers and illustrates the changes necessary for the migration to `handle_solve_bounds_foas`. The solution to the problem is (1, 1)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# NAG Copyright 2020.\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Define E04DG user call-back\n", + "def objfun_e04dg(mode, x, _nstate, _data=None):\n", + " objf = (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", + " if mode == 2:\n", + " fdx = [\n", + " 2.*x[0] - 400.*x[0]*(x[1]-x[0]**2) - 2.,\n", + " 200.*(x[1]-x[0]**2),\n", + " ]\n", + " return objf, fdx\n", + " return objf, np.zeros(len(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Define user call-backs for E04KF\n", + "def objfun_e04kf(x, _inform, _data=None): \n", + " \"\"\"Return the objective function value\"\"\"\n", + " objf = (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", + " return objf\n", + "\n", + "def objgrd_e04kf(x, fdx, inform, _data=None):\n", + " \"\"\"The objective's gradient. Note that fdx has to be updated IN-PLACE\"\"\"\n", + " fdx[:] = [\n", + " 2.*x[0] - 400.*x[0]*(x[1]-x[0]**2) - 2.,\n", + " 200.*(x[1]-x[0]**2),\n", + " ]\n", + " return inform" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# The initial guess\n", + "x = [-1.5, 1.9]\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output\n", + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the problem with `uncon_conjgrd_comp`" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution: \n", + " [1.00000676 1.00001354]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/andrews/ni3dev/lib/python3.5/site-packages/ipykernel_launcher.py:2: NagDeprecatedWarning: (NAG Python function naginterfaces.library.opt.uncon_conjgrd_comp)\n", + "This function is deprecated.\n", + "The following advice is given for making a replacement:\n", + "Please use handle_solve_bounds_foas instead.\n", + "See also https://www.nag.com/numeric/py/nagdoc_latest/replace.html\n", + " \n" + ] + } + ], + "source": [ + "comm = opt.nlp1_init('uncon_conjgrd_comp')\n", + "slv = opt.uncon_conjgrd_comp(objfun_e04dg, x, comm, io_manager=iom)\n", + "print('Solution: \\n', slv.x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Now solve with the new solver `handle_solve_bounds_foas`" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " -------------------------------------------------------------------------------\n", + " E04KF, First order method for bound-constrained problems\n", + " -------------------------------------------------------------------------------\n", + "\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 2.12807E-15\n", + " Norm of gradient 3.67342E-08\n", + "\n", + " Variables:\n", + " idx lower bound value upper bound gradient\n", + " 1 -inf 1.00000E+00 inf -1.87204E-08\n", + " 2 -inf 1.00000E+00 inf -3.67342E-08\n" + ] + } + ], + "source": [ + "# Create an empty handle for the problem\n", + "nvar = len(x)\n", + "handle = opt.handle_init(nvar)\n", + "\n", + "# Define the nonlinear objective in the handle\n", + "# Setup a gradient vector of length nvar\n", + "opt.handle_set_nlnobj(handle, idxfd=list(range(1, nvar+1)))\n", + "\n", + "# Set some algorithmic options\n", + "for option in [\n", + " 'Print Options = No', # print Options?\n", + " 'Print Solution = Yes', # print on the screen the solution point X\n", + " 'Print Level = 1', # print details of each iteration (screen)\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Solve the problem and print the solution\n", + "opt.handle_solve_bounds_foas(handle, x, objfun=objfun_e04kf, objgrd=objgrd_e04kf, \n", + " io_manager=iom)\n", + "\n", + "# Destroy the handle and free allocated memory\n", + "opt.handle_free(handle)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} From debd7868f6330ae97bed1dec11a8da7fa9e91035 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 21 Aug 2020 18:28:16 +0100 Subject: [PATCH 026/182] Delete python.md --- local_optimization/FOAS/migration/python.md | 7 ------- 1 file changed, 7 deletions(-) delete mode 100644 local_optimization/FOAS/migration/python.md diff --git a/local_optimization/FOAS/migration/python.md b/local_optimization/FOAS/migration/python.md deleted file mode 100644 index 3313a8d..0000000 --- a/local_optimization/FOAS/migration/python.md +++ /dev/null @@ -1,7 +0,0 @@ -# Migrating from - - -```{python} -import in from nag -``` -# second From 6f3f3a1a75e224027b18dcbbf28245d1ff778c3b Mon Sep 17 00:00:00 2001 From: A Date: Fri, 21 Aug 2020 18:28:27 +0100 Subject: [PATCH 027/182] Delete fortran.md --- local_optimization/FOAS/migration/fortran.md | 1 - 1 file changed, 1 deletion(-) delete mode 100644 local_optimization/FOAS/migration/fortran.md diff --git a/local_optimization/FOAS/migration/fortran.md b/local_optimization/FOAS/migration/fortran.md deleted file mode 100644 index 1e0ca6a..0000000 --- a/local_optimization/FOAS/migration/fortran.md +++ /dev/null @@ -1 +0,0 @@ -# From a8144835d430a7af92aeb354e35f556377378ac0 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 21 Aug 2020 18:29:20 +0100 Subject: [PATCH 028/182] Update Migrating.md --- local_optimization/FOAS/Migrating.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/FOAS/Migrating.md b/local_optimization/FOAS/Migrating.md index 685d5c5..ea544d5 100644 --- a/local_optimization/FOAS/Migrating.md +++ b/local_optimization/FOAS/Migrating.md @@ -49,8 +49,8 @@ It illustrates the agressive steps taken by the [Conjugate Gradient method](http Notes, source code and comments on migrating your code to support the new FOAS solver: - * [Python](migration/python.md) - * [Fortran 90](migration/fotran.md) + * [Python](migration/migration_e04dg_e04kf.ipynb) + * [Fortran 90](migration/migration_e04dg_e04kf.f90) # References From c4574ef0972240e5249a3427c52c8086c2d751c8 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 11:56:04 +0100 Subject: [PATCH 029/182] Update Migrating.md --- local_optimization/FOAS/Migrating.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/local_optimization/FOAS/Migrating.md b/local_optimization/FOAS/Migrating.md index ea544d5..1125c68 100644 --- a/local_optimization/FOAS/Migrating.md +++ b/local_optimization/FOAS/Migrating.md @@ -47,10 +47,11 @@ It illustrates the agressive steps taken by the [Conjugate Gradient method](http # Migrating from E04DG (Mark 26.x) to E04KF (Mark +27.x) -Notes, source code and comments on migrating your code to support the new FOAS solver: +Notes and comments on migrating your code to the new FOAS solver: * [Python](migration/migration_e04dg_e04kf.ipynb) - * [Fortran 90](migration/migration_e04dg_e04kf.f90) + * [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf) + * [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc) # References From b6c50f6ddb124a128fe9817d9a8e58026614bc4e Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 11:57:47 +0100 Subject: [PATCH 030/182] Add links and info on migrating to new solver --- local_optimization/FOAS/README.md | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index dbd4406..269e24e 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -35,6 +35,16 @@ More recent and modern methods have been incorporated into e04kf making it much **Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. + +# Migrating from E04DG (Mark 26.x) to E04KF (Mark +27.x) + +Notes and comments on migrating your code to the new FOAS solver: + + * [Python](migration/migration_e04dg_e04kf.ipynb) + * [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf) + * [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc) + + # Beale's function This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. From 99bf2c9ed94f13ee7acd1fc97f1331023d206137 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 11:58:07 +0100 Subject: [PATCH 031/182] Delete Migrating.md --- local_optimization/FOAS/Migrating.md | 66 ---------------------------- 1 file changed, 66 deletions(-) delete mode 100644 local_optimization/FOAS/Migrating.md diff --git a/local_optimization/FOAS/Migrating.md b/local_optimization/FOAS/Migrating.md deleted file mode 100644 index 1125c68..0000000 --- a/local_optimization/FOAS/Migrating.md +++ /dev/null @@ -1,66 +0,0 @@ -[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) - -# First-order active-set method (FOAS, e04kf) - -Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. - -FOAS is a [first-order nonlinear conjugate method](https://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method) for large-scale bound-constrained nonlinear optimization. The solver is ideal for very large problems (tens of thousands or more variables) where the first-order derivatives are available or are relatively _cheap_ to estimate. - -e04kf is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. - -The following example illustrates the simple usage of FOAS to solve the bound-constrained 2D version of the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is a classical test function to measure and profile performance of solvers. Source of this example is avaible in [rosenbrock2d.ipynb](rosenbrock2d.ipynb). - - - - -
2D Rosenbrock example2D Rosenbrock with bounds
- -**Figure 1.** 2D Rosenbrock function, (left) the minimum is shown as a yellow dot at x=(1,1). On the right a bound constrained version showing with a purple dotted line a path towards the constrained solution point on the border. - -# More information - 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) - 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) - 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example)] - -# A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) -One of the main design objectives for e04kf was to provide a modern and attractive replacement for the CG solver e04dg introduced in Mark 12. While this solver was targeted for unconstrained NLPs, e04kf has been extended with an active-set method in order to solve bound-constrained NLPs. - -More recent and modern methods have been incorporated into e04kf making it much faster than e04dg. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers e04kf and e04dg. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. - - - - - -
Perf profile e04kf/e04dg time (s)Perf profile e04kf/e04dg function evaluationsPerf profile e04kf/e04dg gradient evaluations
- -**Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. - -# Beale's function -This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. - -Both solvers are used to find a minimum to the function and are started at the same initial point (2, 2). The following figure shows an animation of the steps taken by each solver to find a minimum to the function. -It illustrates the agressive steps taken by the [Conjugate Gradient method](https://en.wikipedia.org/wiki/Conjugate_gradient_method) compared to the more conservative steps of BFGS. - -Beale function solved using e04kf and L-BFGS-B - -**Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star in the. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. - -# Migrating from E04DG (Mark 26.x) to E04KF (Mark +27.x) - -Notes and comments on migrating your code to the new FOAS solver: - - * [Python](migration/migration_e04dg_e04kf.ipynb) - * [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf) - * [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc) - -# References - - * Hager W W and Zhang H (2005) _A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search_. SIAM J. Optim. 16(1) 170–192 - * Hager W W and Zhang H (2006a) _Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent_. ACM Trans. Math. Software 32(1) 113–137 - * Hager W W and Zhang H (2006b) _A New Active Set Algorithm for Box Constrained Optimization_. SIAM J. Optim. 17(2) 525–557 - * Hager W W and Zhang H (2013) _The Limited Memory Conjugate Gradient Method_. SIAM J. Optim. 23(4) 2150–2168 - * Nocedal J and Wright S J (2006) _Numerical Optimization_. (2nd Edition) Springer Series in Operations Research, Springer, New York - - - - From 0b64b1ce357d2dbc98173f3c0b49b534d8929771 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 12:06:19 +0100 Subject: [PATCH 032/182] Update README.md --- local_optimization/FOAS/README.md | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index 269e24e..4314cbb 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -1,6 +1,6 @@ [![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) -# First-order active-set method (FOAS, e04kf) +# First-order active-set method (FOAS, [e04kf](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html)) Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. @@ -20,7 +20,8 @@ The following example illustrates the simple usage of FOAS to solve the bound-co # More information 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) - 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example)] + 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) [ [Fortran 90](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) | [C](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) ] + 4. Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] # A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) One of the main design objectives for e04kf was to provide a modern and attractive replacement for the CG solver e04dg introduced in Mark 12. While this solver was targeted for unconstrained NLPs, e04kf has been extended with an active-set method in order to solve bound-constrained NLPs. @@ -35,8 +36,7 @@ More recent and modern methods have been incorporated into e04kf making it much **Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. - -# Migrating from E04DG (Mark 26.x) to E04KF (Mark +27.x) +# Migrating from [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [e04kf](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) Notes and comments on migrating your code to the new FOAS solver: @@ -44,7 +44,6 @@ Notes and comments on migrating your code to the new FOAS solver: * [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf) * [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc) - # Beale's function This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. From 8c883d2867705802e362d15a71fe033281755cd2 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 12:08:19 +0100 Subject: [PATCH 033/182] Fix documentation order Python -> C -> Fortran --- local_optimization/FOAS/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index 4314cbb..4ed0aea 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -20,7 +20,7 @@ The following example illustrates the simple usage of FOAS to solve the bound-co # More information 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) - 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) [ [Fortran 90](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) | [C](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) ] + 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) [ [C](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) | [Fortran](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) ] 4. Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] # A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) From 47f77c358172fb929e35793cffc7c0e6c2be5246 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 25 Aug 2020 12:09:38 +0100 Subject: [PATCH 034/182] Delete Rosenbrock2dw.png --- local_optimization/FOAS/Rosenbrock2dw.png | Bin 638792 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 local_optimization/FOAS/Rosenbrock2dw.png diff --git a/local_optimization/FOAS/Rosenbrock2dw.png b/local_optimization/FOAS/Rosenbrock2dw.png deleted file mode 100644 index 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zJ)|NbARxHtdQ0E+nYrt8Sqtaq;17ZuqSs}viGu%b=vA%1G__?!-4cw97e=WepP1jJ*L_x;gssbp_;OXk;vd$@?2>=F|d*1*6 From eeeaa03cf4c6334e85db38f99ee0615a2c33a963 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 11 Sep 2020 10:00:46 +0100 Subject: [PATCH 035/182] Add python long_names --- local_optimization/FOAS/README.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index 4ed0aea..994fa0b 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -1,6 +1,6 @@ [![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) -# First-order active-set method (FOAS, [e04kf](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html)) +# First-order active-set method (FOAS) [`handle_solve_bounds_foas` (`e04kf`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. @@ -23,10 +23,10 @@ The following example illustrates the simple usage of FOAS to solve the bound-co 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) [ [C](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) | [Fortran](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) ] 4. Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] -# A modern replacement for NAG solver [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) -One of the main design objectives for e04kf was to provide a modern and attractive replacement for the CG solver e04dg introduced in Mark 12. While this solver was targeted for unconstrained NLPs, e04kf has been extended with an active-set method in order to solve bound-constrained NLPs. +# A modern replacement for NAG solver [`uncon_conjgrd_comp` (`e04dg`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) +One of the main design objectives for `handle_solve_bounds_foas` (`e04kf`) was to provide a modern and attractive replacement for the CG solver `e04dg` introduced in Mark 12. While this solver was targeted for unconstrained NLPs, `e04kf` has been extended with an active-set method in order to solve bound-constrained NLPs. -More recent and modern methods have been incorporated into e04kf making it much faster than e04dg. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers e04kf and e04dg. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. +More recent and modern methods have been incorporated into `e04kf` making it much faster than `e04dg`. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers `e04kf` and `e04dg`. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. @@ -34,9 +34,9 @@ More recent and modern methods have been incorporated into e04kf making it much
Perf profile e04kf/e04dg time (s)Perf profile e04kf/e04dg gradient evaluations
-**Figure 2.** Performance profiles comparing solvers e04kf and e04dg. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that e04kf is 40% faster in time and requires less function and gradient calls. +**Figure 2.** Performance profiles comparing solvers `e04kf` and `e04dg`. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that `e04kf` is 40% faster in time and requires less function and gradient calls. -# Migrating from [e04dg](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [e04kf](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) +# Migrating from [`uncon_conjgrd_comp`, `e04dg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [`handle_solve_bounds_foas`, `e04kf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) Notes and comments on migrating your code to the new FOAS solver: From b1f1dd83cd7bb7b27154ee5b8f1613e0eb542511 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 11 Sep 2020 10:04:25 +0100 Subject: [PATCH 036/182] Update README.md fix to long/short names --- local_optimization/FOAS/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index 994fa0b..59dbe55 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -1,6 +1,6 @@ -[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) +[![NAG](https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) -# First-order active-set method (FOAS) [`handle_solve_bounds_foas` (`e04kf`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) +# First-order active-set method (FOAS) [`handle_solve_bounds_foas (e04kf)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. @@ -36,7 +36,7 @@ More recent and modern methods have been incorporated into `e04kf` making it muc **Figure 2.** Performance profiles comparing solvers `e04kf` and `e04dg`. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that `e04kf` is 40% faster in time and requires less function and gradient calls. -# Migrating from [`uncon_conjgrd_comp`, `e04dg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [`handle_solve_bounds_foas`, `e04kf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) +# Migrating from [`uncon_conjgrd_comp (e04dg)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [`handle_solve_bounds_foas (e04kf)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) Notes and comments on migrating your code to the new FOAS solver: From b2106fa109d63f56f961934ee29da64e30852bc0 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 11 Sep 2020 10:09:02 +0100 Subject: [PATCH 037/182] Update Readme.md Update long name --- local_optimization/BXNL/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index 0414e59..a4a63b1 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -1,4 +1,4 @@ -[![NAG](https://raw.githubusercontent.com/talassio/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) +[![NAG](https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) # Nonlinear Least-Squares Trust-Region Method (BXNL) @@ -70,7 +70,7 @@ require less function calls (center plot) and 65% of the problems require less g [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) should present significant improvement for unconstrained or bound-constrained nonlinear -least-squares solvers in the NAG Library and current users of [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) ([`nagf_opt_lsq_uncon_quasi_deriv_comp`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04gbc.html) ) +least-squares solvers in the NAG Library and current users of [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) ([`lsq_uncon_quasi_deriv_comp`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04gbc.html) ) are highly encourage to try out the new solver. From 6c8f8ca8d6111cee1fc4ee4603566d0f3fa31e5e Mon Sep 17 00:00:00 2001 From: A Date: Fri, 11 Sep 2020 10:17:48 +0100 Subject: [PATCH 038/182] Add long name --- local_optimization/BXNL/Readme.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index a4a63b1..d68313e 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -4,7 +4,7 @@ Data fitting and calibrating parameters of complex numerical models is one of the most common problems found in numerous industries such as physics, space exploration, simulations, engineering, amongs many others. -[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html), [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html)). It offers a significant variety of algorithms and regularisation techniques. +[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems, [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)). It offers a significant variety of algorithms and regularisation techniques. The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small- to mid-scale (100s to 1000s of parameters) bound-constrained nonlinear least-squares problems and is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. @@ -31,7 +31,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook [[Python Jupyter notebook for this example](./notebooks/simple_BXNL.ipynb)] -This example illustrates the usage of `e04gg` to fit PADC +This example illustrates the usage of [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)) to fit PADC etched nuclear track data of alpha particles to a convoluted distribution. A target sheet is scanned and track diameters are recorded (red wedges, left in Figure 2) into a histogram (Blue bars right plot of Figure 2) @@ -59,7 +59,7 @@ Optimal parameter values are reported in the legend. # Modern Replacement Alternative -Solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is a modern and attractive replacement for the unconstrained nonlinear least-squares solver [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) introduced at Mark 7. +Solver [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)) is a modern and attractive replacement for the unconstrained nonlinear least-squares solver [`lsq_uncon_quasi_deriv_comp`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04gbc.html) ([`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html)). More recent and modern methods have been incorporated into [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) making it much faster than [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html). Our benchmarks comparing [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) to [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) using 68 unconstrained nonlinear least-squares CUTEst problems is reported in Figure 3 using performance profiles. @@ -70,7 +70,7 @@ require less function calls (center plot) and 65% of the problems require less g [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) should present significant improvement for unconstrained or bound-constrained nonlinear -least-squares solvers in the NAG Library and current users of [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) ([`lsq_uncon_quasi_deriv_comp`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04gbc.html) ) +least-squares solvers in the NAG Library and current users of [`e04gb`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04gbf.html) are highly encourage to try out the new solver.
From bc4a2e5ef14d5a3342d89b884f7799e5ac7e5501 Mon Sep 17 00:00:00 2001 From: Mike Croucher Date: Tue, 22 Sep 2020 14:11:50 +0100 Subject: [PATCH 039/182] Update Readme.md --- local_optimization/SOCP/Readme.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/local_optimization/SOCP/Readme.md b/local_optimization/SOCP/Readme.md index f35f790..a3f331b 100644 --- a/local_optimization/SOCP/Readme.md +++ b/local_optimization/SOCP/Readme.md @@ -52,3 +52,7 @@ A mean-variance model with probability constraint using randomly generated data. # Poster A 2019 poster discussing NAG's SOCP functionality is [available on the NAG website](https://www.nag.com/market/posters/socp.pdf) + +# Obtaining the NAG Library for Python + +Instructions for how to download, install and license the NAG Library for Python can be found at https://github.com/numericalalgorithmsgroup/NAGPythonExamples#nag-library-for-python-installation From db1f46ae2fd6ffd5226c5322913203bc81ce6cb9 Mon Sep 17 00:00:00 2001 From: Mat Cross Date: Thu, 24 Sep 2020 16:09:58 +0100 Subject: [PATCH 040/182] Minor updates for pylint compliance. --- .../quantile_linreg_easy.ipynb | 2 +- .../dim2_spline_ts_sctr.ipynb | 4 +- .../web_site_classification_using_nnmf.ipynb | 8 ++-- global_optimization/PSO_demo.ipynb | 4 +- global_optimization/SQP_multistart.ipynb | 2 +- global_optimization/bnd_mcs_solve.ipynb | 2 +- linear_algebra/real_toeplitz_solve.ipynb | 4 +- .../triangular_matrix_multiply.ipynb | 6 ++- local_optimization/DFO_noisy.ipynb | 6 +-- local_optimization/FOAS/rosenbrock2d.ipynb | 5 +-- .../SDP/theta_optimization.ipynb | 9 ++-- .../portfolio_optimization_using_socp.ipynb | 1 - local_optimization/SOCP/robust_lp.ipynb | 1 - local_optimization/SOCP/simple_SOCP.ipynb | 8 ++-- .../bounds_quasi_func_easy.ipynb | 2 +- local_optimization/christmas_demo.ipynb | 18 ++++---- multivariate_methods/k-means.ipynb | 4 +- nearest_correlation_matrices/ncm_nag.ipynb | 10 ++--- random_number_generation/rand_corr_mat.ipynb | 8 ++-- roots/Anderson_Acceleration_Poisson.ipynb | 42 +++++++++---------- special_functions/mathieu_functions.ipynb | 1 - time_series_analysis/cp_pelt.ipynb | 2 +- time_series_analysis/inhom_iema.ipynb | 2 +- 23 files changed, 72 insertions(+), 79 deletions(-) diff --git a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb index 04dfe8d..22f2e52 100644 --- a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb +++ b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb @@ -992,7 +992,7 @@ " 'Quantile Regression\\n'\n", " 'Engels\\' 1857 Study of Household Expenditure on Food'\n", ")\n", - "plt.show();" + "plt.show()" ] } ], diff --git a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb index 2f38f43..813613a 100644 --- a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb +++ b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb @@ -914,7 +914,7 @@ "ax.azim = -20\n", "ax.elev = 20\n", "res = ax.scatter(x, y, f, marker='x')\n", - "plt.show();" + "plt.show()" ] }, { @@ -1876,7 +1876,7 @@ "ax.azim = -20\n", "ax.elev = 20\n", "res = ax.scatter(x, y, f, marker='x')\n", - "plt.show();" + "plt.show()" ] } ], diff --git a/dimension_reduction/web_site_classification_using_nnmf.ipynb b/dimension_reduction/web_site_classification_using_nnmf.ipynb index 2eef4ec..039eb77 100644 --- a/dimension_reduction/web_site_classification_using_nnmf.ipynb +++ b/dimension_reduction/web_site_classification_using_nnmf.ipynb @@ -98,10 +98,8 @@ "from naginterfaces.library.matop import real_nmf\n", "from collections import Counter\n", "import string\n", - "from string import punctuation\n", "import urllib.request\n", "import re\n", - "import scipy as sp\n", "from scipy.linalg import norm\n", "import numpy as np\n", "\n", @@ -464,8 +462,8 @@ "\n", "print(st, file=f2)\n", "\n", - "for i in range(len(words)):\n", - " st = words[i].ljust(14,' ')\n", + "for i, v in enumerate(words):\n", + " st = v.ljust(14,' ')\n", " for j in range(n_links):\n", " st += str(int(a[i,j])).center(8, ' ')\n", " print(st, file=f2)\n", @@ -620,7 +618,7 @@ ], "source": [ "for i in range(k):\n", - " tmp = sorted(words, key=lambda x: w[words.index(x),i], reverse=True)\n", + " tmp = sorted(words, key=lambda x, ind=i: w[words.index(x),ind], reverse=True)\n", " st = \"\\nThe most important words in column \" + str(i+1) + \" of w are:\"\n", " print(st)\n", " print(tmp[:10])" diff --git a/global_optimization/PSO_demo.ipynb b/global_optimization/PSO_demo.ipynb index 4067e5c..a610786 100644 --- a/global_optimization/PSO_demo.ipynb +++ b/global_optimization/PSO_demo.ipynb @@ -118,7 +118,7 @@ "source": [ "# Objective function in the form that the PSO solver wants\n", "# We don't need to use all of the input arguments, they just need to be included in the function definition\n", - "def objfun(mode, x, objf, vecout, nstate):\n", + "def objfun(_mode, x, objf, vecout, _nstate):\n", " # Evaluate the objective function using the ackley function defined earlier\n", " objf = ackley(x[0], x[1])\n", " return objf, vecout" @@ -323,7 +323,7 @@ "metadata": {}, "outputs": [], "source": [ - "def ackley_ndim(mode, x, objf, vecout, nstate):\n", + "def ackley_ndim(_mode, x, objf, vecout, _nstate):\n", " n = len(x)\n", " sum1 = np.sum(x**2)\n", " sum2 = np.sum(np.cos(2.0*np.pi*x))\n", diff --git a/global_optimization/SQP_multistart.ipynb b/global_optimization/SQP_multistart.ipynb index cec8b40..ac4937f 100644 --- a/global_optimization/SQP_multistart.ipynb +++ b/global_optimization/SQP_multistart.ipynb @@ -93,7 +93,7 @@ " self.npts = 0\n", " self.pts = []\n", " \n", - "def objfun(mode, x, objgrd, nstate, data=None):\n", + "def objfun(mode, x, objgrd, _nstate, data=None):\n", " # Himmelblau's function\n", " objf = (x[0]**2 + x[1] - 11)**2 + (x[0] + x[1]**2 - 7)**2\n", " if mode > 0:\n", diff --git a/global_optimization/bnd_mcs_solve.ipynb b/global_optimization/bnd_mcs_solve.ipynb index 1623059..ea3a070 100644 --- a/global_optimization/bnd_mcs_solve.ipynb +++ b/global_optimization/bnd_mcs_solve.ipynb @@ -112,7 +112,7 @@ "metadata": {}, "outputs": [], "source": [ - "glopt.bnd_mcs_solve(objfun, ibound, bl, bu, comm, monit=monit);" + "_ = glopt.bnd_mcs_solve(objfun, ibound, bl, bu, comm, monit=monit)" ] }, { diff --git a/linear_algebra/real_toeplitz_solve.ipynb b/linear_algebra/real_toeplitz_solve.ipynb index 948fa4b..cc71868 100644 --- a/linear_algebra/real_toeplitz_solve.ipynb +++ b/linear_algebra/real_toeplitz_solve.ipynb @@ -49,8 +49,8 @@ "\n", "# Construct a real, symmetric, positive definite toeplitz matrix \n", "matrix_size = 5000\n", - "t = np.arange(0, matrix_size);\n", - "a = np.exp(-np.abs(t)/10);\n", + "t = np.arange(0, matrix_size)\n", + "a = np.exp(-np.abs(t)/10)\n", "# The toeplitz matrix is defined by its diagonals. We can construct the full matrix from the diagonals using scipy\n", "A = scipy.linalg.toeplitz(a, a)\n", "# Construct and a random Righ hand side\n", diff --git a/linear_algebra/triangular_matrix_multiply.ipynb b/linear_algebra/triangular_matrix_multiply.ipynb index b4c4952..6299d16 100644 --- a/linear_algebra/triangular_matrix_multiply.ipynb +++ b/linear_algebra/triangular_matrix_multiply.ipynb @@ -150,7 +150,8 @@ " [0.0,0.0,0.0,7.4]]\n", ")\n", "\n", - "alpha*(np.transpose(A) @ B)" + "product = alpha*(np.transpose(A) @ B)\n", + "product" ] }, { @@ -234,7 +235,8 @@ "metadata": {}, "outputs": [], "source": [ - "from naginterfaces.library.blas import dtrmm" + "# The dtrmm import below is used in a timeit block:\n", + "from naginterfaces.library.blas import dtrmm # pylint: disable=unused-import " ] }, { diff --git a/local_optimization/DFO_noisy.ipynb b/local_optimization/DFO_noisy.ipynb index b3df82f..d82e08b 100644 --- a/local_optimization/DFO_noisy.ipynb +++ b/local_optimization/DFO_noisy.ipynb @@ -285,7 +285,7 @@ " data.noiselev = noiselevel\n", " print(data.fun)\n", " try:\n", - " sln = opt.bounds_quasi_func_easy(ibound, objfun_bob, xl, xu, xstart, data=data)\n", + " _ = opt.bounds_quasi_func_easy(ibound, objfun_bob, xl, xu, xstart, data=data)\n", " except utils.NagValueError as e:\n", " if e.errno == 2 and not data.ok:\n", " print('Maximum number of evaluations exceeded:', 400*n)\n", @@ -334,8 +334,8 @@ " opt.handle_opt_set(handle, optstr)\n", " # Call the solver\n", " try:\n", - " x, rinfo, stats = opt.handle_solve_dfno(handle, objfun, xstart, data=data, io_manager=iom)\n", - " except utils.NagCallbackTerminateWarning as e:\n", + " _ = opt.handle_solve_dfno(handle, objfun, xstart, data=data, io_manager=iom)\n", + " except utils.NagCallbackTerminateWarning as _e:\n", " pass\n", " # print results\n", " print(pname)\n", diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index 2547cf9..b801136 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -35,13 +35,12 @@ "source": [ "objfun = lambda x, _inform: (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", "\n", - "def objgrd(x, fdx, inform):\n", + "def objgrd(x, fdx, _inform):\n", " \"\"\"The objective's gradient.\"\"\"\n", " fdx[:] = [\n", " 2.*x[0] - 400.*x[0]*(x[1]-x[0]**2) - 2.,\n", " 200.*(x[1]-x[0]**2),\n", " ]\n", - " return inform\n", "\n", "\n", "steps = []\n", @@ -433,7 +432,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.0" + "version": "3.8.0" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SDP/theta_optimization.ipynb b/local_optimization/SDP/theta_optimization.ipynb index b35d79d..3b3a07c 100644 --- a/local_optimization/SDP/theta_optimization.ipynb +++ b/local_optimization/SDP/theta_optimization.ipynb @@ -10,7 +10,6 @@ "from naginterfaces.base import utils\n", "import numpy as np\n", "import networkx as nx \n", - "import matplotlib.pyplot as plt\n", "import warnings" ] }, @@ -148,10 +147,10 @@ "# A_2, A_3, ..., A_{ne+1} match the E_ij matrices\n", "nnza[2:ne+2] = 1\n", "for i in range(ne):\n", - " irowa[idx] = ed[i][0]\n", - " icola[idx] = ed[i][1]\n", - " a[idx] = 1.0\n", - " idx += 1\n", + " irowa[idx] = ed[i][0]\n", + " icola[idx] = ed[i][1]\n", + " a[idx] = 1.0\n", + " idx += 1\n", "\n", "idblk = opt.handle_set_linmatineq(handle, dima, nnza, irowa, icola, a, \n", " blksizea=None, idblk=0)" diff --git a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb index 7441bc6..968792e 100644 --- a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb @@ -225,7 +225,6 @@ "from naginterfaces.library import opt\n", "from naginterfaces.library import lapackeig\n", "# Import necessary math libraries\n", - "from scipy.sparse import coo_matrix\n", "import math as mt\n", "import warnings as wn" ] diff --git a/local_optimization/SOCP/robust_lp.ipynb b/local_optimization/SOCP/robust_lp.ipynb index eda3c8c..cd0673b 100644 --- a/local_optimization/SOCP/robust_lp.ipynb +++ b/local_optimization/SOCP/robust_lp.ipynb @@ -144,7 +144,6 @@ "# Import utility libraries and the NAG Library\n", "import numpy as np\n", "import math as mt\n", - "from scipy.sparse import coo_matrix\n", "from scipy.stats import norm\n", "from naginterfaces.library import opt\n", "from naginterfaces.library import lapackeig" diff --git a/local_optimization/SOCP/simple_SOCP.ipynb b/local_optimization/SOCP/simple_SOCP.ipynb index fdd1354..09eb643 100644 --- a/local_optimization/SOCP/simple_SOCP.ipynb +++ b/local_optimization/SOCP/simple_SOCP.ipynb @@ -120,14 +120,14 @@ "outputs": [], "source": [ "# Set linear constraints\n", - "opt.handle_set_linconstr(\n", + "_ = opt.handle_set_linconstr(\n", " handle,\n", " bl=[-1.e20, 1.0],\n", " bu=[1.5, 1.e20],\n", " irowb=[1, 1, 1, 2, 2, 2],\n", " icolb=[1, 2, 3, 1, 2, 3],\n", " b=[-0.1, -0.1, 1.0, -0.06, 1.0, 1.0]\n", - " );" + " )" ] }, { @@ -146,12 +146,12 @@ "outputs": [], "source": [ "# Set cone constraint\n", - "opt.handle_set_group(\n", + "_ = opt.handle_set_group(\n", " handle,\n", " gtype='Q',\n", " group=[ 3,1, 2],\n", " idgroup=0\n", - ");" + ")" ] }, { diff --git a/local_optimization/bounds_quasi_func_easy.ipynb b/local_optimization/bounds_quasi_func_easy.ipynb index 4431991..51020b5 100644 --- a/local_optimization/bounds_quasi_func_easy.ipynb +++ b/local_optimization/bounds_quasi_func_easy.ipynb @@ -1135,7 +1135,7 @@ "ax.set_zlim3d(-1.0, 10000.0)\n", "ax.azim = -20\n", "ax.elev = 20\n", - "plt.show();" + "plt.show()" ] }, { diff --git a/local_optimization/christmas_demo.ipynb b/local_optimization/christmas_demo.ipynb index 7ca80a6..644fe39 100644 --- a/local_optimization/christmas_demo.ipynb +++ b/local_optimization/christmas_demo.ipynb @@ -79,7 +79,7 @@ "metadata": {}, "outputs": [], "source": [ - "def plot_domain(orig,lb,ub,cm, axis, ax):\n", + "def plot_domain(orig,lb,ub,_cm, axis, ax):\n", " xmax = orig - lb\n", " X, Y = np.meshgrid(np.arange(-xmax,xmax,0.01), np.arange(lb,orig,0.01))\n", " Z = objf_plot(X,Y)\n", @@ -218,12 +218,12 @@ "outputs": [], "source": [ "# main callback function for the SQP solver\n", - "def objfun_e04wd(mode, x, grad, ntsate, data):\n", - " if mode == 0 or mode == 2:\n", + "def objfun_e04wd(mode, x, grad, _nstate, data):\n", + " if mode in (0, 2):\n", " objf = x[0]**2 + x[0] + np.cos(2*np.pi*x[1])**2 + 0.5*x[1]\n", " data.npts += 1\n", " data.pts.append((x[0], x[1]))\n", - " if mode == 1 or mode == 2:\n", + " if mode in (1, 2):\n", " grad[0] = 2*x[0] + 1\n", " grad[1] = -4*np.pi*np.sin(2*np.pi*x[1])*np.cos(2*np.pi*x[1]) + 0.5\n", " return mode, objf, grad" @@ -242,7 +242,7 @@ "ncnln = 0\n", "a = [[1.,1.],[-1.,1.]]\n", "bl = [-bigbnd,5,-bigbnd,-bigbnd]\n", - "bu = [bigbnd,bigbnd,6,6];\n", + "bu = [bigbnd,bigbnd,6,6]\n", "\n", "# Initialize the rest of the solver variables: we don't need warm starting information or 2nd derivative information\n", "istate = [0,0,0,0]\n", @@ -367,9 +367,9 @@ "outputs": [], "source": [ "# Main callback function for the MINLP solver\n", - "def objfun_h02da(mode, varcon, x, objgrd, nstate, data):\n", - " objmip = x[0]**2 + x[0] + np.cos(2*np.pi*x[1])**2 + 0.5*x[1];\n", - " data.npts = data.npts + 1;\n", + "def objfun_h02da(mode, varcon, x, objgrd, _nstate, data):\n", + " objmip = x[0]**2 + x[0] + np.cos(2*np.pi*x[1])**2 + 0.5*x[1]\n", + " data.npts = data.npts + 1\n", " data.pts.append((x[0], x[1]))\n", " if x[1] <= 1.8 and data.present:\n", " objmip = (x[0]+0.625)**2 + (x[1]-1.55)**2\n", @@ -405,7 +405,7 @@ "varcon = [0,0,1,1,4,4,4,4,4,4,4]\n", "\n", "# Choose a starting point and initialize the solver and user data\n", - "xstart = [0.5,4.5,0.,0.];\n", + "xstart = [0.5,4.5,0.,0.]\n", "x = xstart\n", "comm = {}\n", "data = usr_data()\n", diff --git a/multivariate_methods/k-means.ipynb b/multivariate_methods/k-means.ipynb index 68b92e1..3b342b1 100644 --- a/multivariate_methods/k-means.ipynb +++ b/multivariate_methods/k-means.ipynb @@ -58,7 +58,7 @@ "X = np.concatenate((X1, X2))\n", "\n", "# Plot the combined dataset\n", - "plt.plot(X[:,0], X[:,1], 'x');" + "_ = plt.plot(X[:,0], X[:,1], 'x')" ] }, { @@ -94,7 +94,7 @@ "source": [ "colours = ['orange', 'blue']\n", "plt.scatter(X[:,0], X[:,1], marker='x', c=kmeans.inc, cmap=matplotlib.colors.ListedColormap(colours))\n", - "plt.scatter(kmeans.cmeans[:,0], kmeans.cmeans[:,1], color='red', s=200);" + "_ = plt.scatter(kmeans.cmeans[:,0], kmeans.cmeans[:,1], color='red', s=200)" ] } ], diff --git a/nearest_correlation_matrices/ncm_nag.ipynb b/nearest_correlation_matrices/ncm_nag.ipynb index 42cf310..b0d5eef 100644 --- a/nearest_correlation_matrices/ncm_nag.ipynb +++ b/nearest_correlation_matrices/ncm_nag.ipynb @@ -276,8 +276,8 @@ "source": [ "def cov_bar(P):\n", " \"\"\"Returns an approximate sample covariance matrix\"\"\"\n", - " # P.shape returns a tuple (m, n) that we unpack to m and n\n", - " m, n = P.shape\n", + " # P.shape returns a tuple (m, n) that we unpack to _m and n\n", + " _m, n = P.shape # pylint: disable=unused-variable\n", " # Initialize an n-by-n zero matrix\n", " S = np.zeros((n, n))\n", " for i in range(n): \n", @@ -484,7 +484,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Sorted eigenvalues of X [-0.0000 -0.0000 0.0380 0.1731 0.6894 1.7117 1.9217 3.4661 ]\n" + "Sorted eigenvalues of X [-0.0000 0.0000 0.0380 0.1731 0.6894 1.7117 1.9217 3.4661 ]\n" ] } ], @@ -653,7 +653,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Sorted eigenvalues of X [0.0010-0.0000j 0.0010+0.0000j 0.0305+0.0000j 0.1646+0.0000j 0.6764+0.0000j 1.7716+0.0000j 1.8910+0.0000j 3.4639+0.0000j ]\n" + "Sorted eigenvalues of X [0.0010 0.0010 0.0305 0.1646 0.6764 1.7716 1.8910 3.4639 ]\n" ] } ], @@ -829,7 +829,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Sorted eigenvalues of X [0.0010 0.0010 0.0375 0.1734 0.6882 1.7106 1.9224 3.4660 ]\n" + "Sorted eigenvalues of X [0.0010-0.0000j 0.0010+0.0000j 0.0375+0.0000j 0.1734+0.0000j 0.6882+0.0000j 1.7106+0.0000j 1.9224+0.0000j 3.4660+0.0000j ]\n" ] } ], diff --git a/random_number_generation/rand_corr_mat.ipynb b/random_number_generation/rand_corr_mat.ipynb index 2077a02..0a4a937 100644 --- a/random_number_generation/rand_corr_mat.ipynb +++ b/random_number_generation/rand_corr_mat.ipynb @@ -120,9 +120,7 @@ "metadata": {}, "outputs": [], "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "from naginterfaces.library import rand as nag_rand" + "import pandas as pd" ] }, { @@ -274,7 +272,7 @@ "outputs": [], "source": [ "seed_pd = [1]\n", - "statecomm_pd = nag_rand.init_repeat(1,seed_pd)" + "statecomm_pd = nirand.init_repeat(1,seed_pd)" ] }, { @@ -417,7 +415,7 @@ "metadata": {}, "outputs": [], "source": [ - "c_df = nag_rand.matrix_corr(df[0],statecomm_pd)" + "c_df = nirand.matrix_corr(df[0],statecomm_pd)" ] }, { diff --git a/roots/Anderson_Acceleration_Poisson.ipynb b/roots/Anderson_Acceleration_Poisson.ipynb index b5867fc..f062db6 100644 --- a/roots/Anderson_Acceleration_Poisson.ipynb +++ b/roots/Anderson_Acceleration_Poisson.ipynb @@ -268,7 +268,7 @@ "\n", "x0 = init_problem(50)\n", "plt.title('Initial conditions of our example problem on a 50 x 50 grid')\n", - "plt.imshow(x0);" + "_ = plt.imshow(x0)" ] }, { @@ -352,7 +352,7 @@ "class solverinfo:\n", " \"\"\"A class used to get information to/from a solver\n", " \"\"\"\n", - " def __init__(self, w=1):\n", + " def __init__(self, _w=1):\n", " self.iterations = 0\n", " self.w = 1 # Used for SOR and ignored for everything else\n", "\n", @@ -414,7 +414,7 @@ "jacobi_sol = solve_poisson(u, tol, jacobi_info, jacobi)\n", "print(f\"Gauss-Seidel on a {N} by {N} grid\")\n", "print(f\"Solution found in {jacobi_info.iterations} iterations\")\n", - "plt.imshow(jacobi_sol);" + "_ = plt.imshow(jacobi_sol)" ] }, { @@ -446,7 +446,7 @@ "Ex, Ey = np.gradient(jacobi_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "plt.imshow(E)\n", - "plt.title('Electric Field');" + "_ = plt.title('Electric Field')" ] }, { @@ -525,7 +525,7 @@ "Ex, Ey = np.gradient(gs_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "axes[1].imshow(E)\n", - "axes[1].set_title('Electric Field');" + "_ = axes[1].set_title('Electric Field')" ] }, { @@ -624,7 +624,7 @@ "Ex, Ey = np.gradient(SOR_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "axes[1].imshow(E)\n", - "axes[1].set_title('Electric Field');" + "_ = axes[1].set_title('Electric Field')" ] }, { @@ -678,7 +678,7 @@ "Ex, Ey = np.gradient(SOR_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "axes[1].imshow(E)\n", - "axes[1].set_title('Electric Field');" + "_ = axes[1].set_title('Electric Field')" ] }, { @@ -715,7 +715,7 @@ " SOR_info = solverinfo()\n", " SOR_info.w = w\n", " tol = 1e-9\n", - " SOR_sol = solve_poisson(u, tol, SOR_info, SOR)\n", + " _ = solve_poisson(u, tol, SOR_info, SOR)\n", " return SOR_info.iterations\n", "\n", "w = np.arange(1.0, 1.99, 0.01)\n", @@ -723,7 +723,7 @@ "plt.plot(w, iterations)\n", "plt.title('Number of iterations vs SOR parameter')\n", "plt.xlabel('w')\n", - "plt.ylabel('Iterations');" + "_ = plt.ylabel('Iterations')" ] }, { @@ -744,7 +744,7 @@ "outputs": [], "source": [ "@jit\n", - "def jacobi(x, source, solverinfo):\n", + "def jacobi(x, source, solverinfo): # pylint: disable=function-redefined\n", " \"\"\"Performs one iteration of the jacobi method\n", " \n", " Arguments:\n", @@ -796,7 +796,7 @@ "class NAG_solverinfo:\n", " \"\"\"A class used to get information to/from a solver\n", " \"\"\"\n", - " def __init__(self, N=50, w=1):\n", + " def __init__(self, N=50, _w=1):\n", " self.iterations = 0\n", " self.w = 1 # Used for SOR and ignored for everything else\n", " self.source = np.zeros((N, N))" @@ -826,7 +826,7 @@ " # the boundary condition that x = 0 at the edges.\n", " for i in range(1, N - 1):\n", " for j in range(1, N - 1):\n", - " nextx[j, i] = 0.25 * (x[j+1, i] + x[j, i+1] + x[j-1, i] + x[j, i-1]) + 0.25*h**2*solverinfo.source[j, i]\n", + " nextx[j, i] = 0.25 * (x[j+1, i] + x[j, i+1] + x[j-1, i] + x[j, i-1]) + 0.25*h**2*solverinfo.source[j, i]\n", " solverinfo.iterations += 1\n", " nextx -= x # NAG requires this rather than nextx itself\n", " nextx.shape = N*N # Make nextx 1D since that's what NAG needs\n", @@ -895,7 +895,7 @@ "Ex, Ey = np.gradient(NAG_jacobi_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "axes[1].imshow(E)\n", - "axes[1].set_title('Electric Field');" + "_ = axes[1].set_title('Electric Field')" ] }, { @@ -952,7 +952,7 @@ " NAG_jacobi_info = NAG_solverinfo()\n", " NAG_jacobi_info.source = source(N)\n", " tol = 1e-9\n", - " NAG_jacobi_sol, fvec = roots.sys_func_aa(NAG_jacobi, x0, tol, eps, m, data=NAG_jacobi_info)\n", + " _ = roots.sys_func_aa(NAG_jacobi, x0, tol, eps, m, data=NAG_jacobi_info)\n", " return NAG_jacobi_info.iterations" ] }, @@ -980,7 +980,7 @@ "plt.plot(mlist, iterations)\n", "plt.title('Anderson Accelerated Jacobi\\nNumber of iterations vs m')\n", "plt.xlabel('m')\n", - "plt.ylabel('Iterations');" + "_ = plt.ylabel('Iterations')" ] }, { @@ -1035,7 +1035,7 @@ "Ex, Ey = np.gradient(NAG_jacobi_sol)\n", "E = np.sqrt(Ex**2+Ey**2) # Magnitude of Electric field\n", "axes[1].imshow(E)\n", - "axes[1].set_title('Electric Field');" + "_ = axes[1].set_title('Electric Field')" ] }, { @@ -1153,14 +1153,14 @@ "metadata": {}, "outputs": [], "source": [ - "def find_best_m(m):\n", + "def find_best_m(m): # pylint: disable=function-redefined\n", " N = 100\n", " x0 = init_problem(N)\n", " x0.shape = N*N\n", " NAG_gs_info = NAG_solverinfo()\n", " NAG_gs_info.source = source(N)\n", " tol = 1e-9\n", - " NAG_gs_sol, fvec = roots.sys_func_aa(NAG_gauss_seidel, x0, tol, eps, m, data=NAG_gs_info)\n", + " _ = roots.sys_func_aa(NAG_gauss_seidel, x0, tol, eps, m, data=NAG_gs_info)\n", " return NAG_gs_info.iterations" ] }, @@ -1200,10 +1200,10 @@ " facecolor=\"black\", width=0.5,\n", " headwidth=4, shrink=0.1)\n", "\n", - "plt.annotate(\n", + "_ = plt.annotate(\n", " \"Best SOR result\", xy=(arrow_x, arrow_y),\n", " xytext=(label_x, label_y),\n", - " arrowprops=arrow_properties);" + " arrowprops=arrow_properties)" ] }, { @@ -1331,7 +1331,7 @@ " NAG_SOR_info.source = source(N)\n", " NAG_SOR_info.w = w\n", " tol = 1e-9\n", - " NAG_SOR_sol, fvec = roots.sys_func_aa(NAG_SOR, x0, tol, eps, m, data=NAG_SOR_info)\n", + " _ = roots.sys_func_aa(NAG_SOR, x0, tol, eps, m, data=NAG_SOR_info)\n", " return NAG_SOR_info.iterations" ] }, diff --git a/special_functions/mathieu_functions.ipynb b/special_functions/mathieu_functions.ipynb index 1219326..dc193de 100644 --- a/special_functions/mathieu_functions.ipynb +++ b/special_functions/mathieu_functions.ipynb @@ -91,7 +91,6 @@ } ], "source": [ - "import scipy as sp\n", "sp.__version__" ] }, diff --git a/time_series_analysis/cp_pelt.ipynb b/time_series_analysis/cp_pelt.ipynb index beb1afc..5b97cc3 100644 --- a/time_series_analysis/cp_pelt.ipynb +++ b/time_series_analysis/cp_pelt.ipynb @@ -968,7 +968,7 @@ " '(FX data from www.macrotrends.net)\\n'\n", " 'Showing change points determined in the mean')\n", "plt.legend(handles=[vl, hl], loc='upper right')\n", - "plt.show();" + "plt.show()" ] } ], diff --git a/time_series_analysis/inhom_iema.ipynb b/time_series_analysis/inhom_iema.ipynb index 7eb566c..936c5e8 100644 --- a/time_series_analysis/inhom_iema.ipynb +++ b/time_series_analysis/inhom_iema.ipynb @@ -944,7 +944,7 @@ "plt.ylabel('Value')\n", "plt.suptitle('Exponential Moving Averages')\n", "plt.title(r'3 $\\tau$' + ' values applied to simulated data', fontsize=10)\n", - "plt.show();" + "plt.show()" ] }, { From ec4c0d9fe4521a8697cf5f9cf7c8465204ac3ffb Mon Sep 17 00:00:00 2001 From: A Date: Tue, 6 Oct 2020 14:40:47 +0100 Subject: [PATCH 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b/local_optimization/BXNL/Readme.md @@ -6,7 +6,7 @@ Data fitting and calibrating parameters of complex numerical models is one of th problems found in numerous industries such as physics, space exploration, simulations, engineering, amongs many others. [NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems, [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)). It offers a significant variety of algorithms and regularisation techniques. -The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small- to mid-scale (100s to 1000s of parameters) bound-constrained nonlinear least-squares problems +The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small to medium sized fitting problems (up to 1000s of parameters) bound-constrained nonlinear least-squares problems and is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook](./notebooks/orbit_ex.ipynb)). The task is to find the optimal orbit path given a variety of measurements for which the orbit has to approximatly pass-by. 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zi##V&yOHN$nn!q8Fn!UQh({kc8?RbMo)0j26?sl3Es^JB*0RSHnY@ZTCzDr^=Va0x zc@E|pMV^z%tH^UQc@=q1CVi3TWYQOTPUd#^`~dUZiaaON7>Yb6vzDj_nA(Uu=XUZS z@|;W_M4ppLOXNA2>lS%Frt@e_BZ zAC>0_3XD^EPBnW%5yX7 zTb1W#)VC_n&FIUj^K&uHk5zeYMh{lyxtX;@JuvRoM&-G; Date: Wed, 14 Oct 2020 11:30:56 +0100 Subject: [PATCH 057/182] Update README.md --- local_optimization/FOAS/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index 59dbe55..b1f592b 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -52,7 +52,7 @@ It illustrates the agressive steps taken by the [Conjugate Gradient method](http Beale function solved using e04kf and L-BFGS-B -**Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star in the. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. +**Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. # References From 194c965ffcc05154fafb317b4a3de336823aa08d Mon Sep 17 00:00:00 2001 From: shuanghuabai Date: Thu, 29 Oct 2020 15:58:25 +0000 Subject: [PATCH 058/182] add qcqp notebook and add note for socp notebook --- .../SOCP/portfolio_optimization_qcqp.ipynb | 709 + .../portfolio_optimization_using_socp.ipynb | 18 +- .../static/portfolio_optimization_qcqp.html | 13933 ++++++++++++++++ .../static/portfolio_optimization_qcqp.pdf | Bin 0 -> 256920 bytes .../portfolio_optimization_using_socp.html | 16 +- .../portfolio_optimization_using_socp.pdf | Bin 294539 -> 297213 bytes 6 files changed, 14673 insertions(+), 3 deletions(-) create mode 100644 local_optimization/SOCP/portfolio_optimization_qcqp.ipynb create mode 100644 local_optimization/SOCP/static/portfolio_optimization_qcqp.html create mode 100644 local_optimization/SOCP/static/portfolio_optimization_qcqp.pdf diff --git a/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb new file mode 100644 index 0000000..b7ba23e --- /dev/null +++ b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb @@ -0,0 +1,709 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Quadratically constrained quadratic programming and its applications in portfolio optimization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Correct Rendering of this notebook\n", + "\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "\n", + "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", + "\n", + "# Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Quadratically constrained quadratic programming (QCQP) is a type of optimization problem in which both the objective function and the constraints involve quadratic functions. A general QCQP problem has the following form\n", + "\\begin{equation}\n", + "\\begin{array}{ll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{minimize}} & \\frac{1}{2}x^TP_0x+q_0^Tx+r_0\\\\[0.6ex]\n", + "\\mbox{subject to} & \\frac{1}{2}x^TP_ix+q_i^Tx+r_i\\leq0,\\quad i=1,\\ldots,p.\n", + "\\end{array}\n", + "\\end{equation}\n", + "It appears in applications such as modern portfolio theory, machine learning, engineering and control. Convex QCQP is usually handled through conic optimization, or, more precisely, second-order cone programming (SOCP) due to its computational efficiency and ability to detect infeasibility. However, using SOCP to solve convex QCQP is nontrivial task which requires extra amount of effort to transform problem data and add auxiliary variables. In this notebook, we are going to demonstrate how to use the *NAG Optimization Modelling Suite* in the NAG Library to define and solve QCQP in portfolio optimization." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data Preparation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We consider daily prices for the 30 stocks in the DJIA from March 2018 to March 2019. In practice, the estimation of the mean return $r$ and covariance $V$ is often a nontrivial task. In this notebook, we estimate those entities using simple sample estimates." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Import necessary libraries\n", + "import pickle as pkl\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Load stock price data from stock_price.plk\n", + "# Stock_price: dict = ['close_price': [data], 'date_index': [data]]\n", + "stock_price = stock_price = pkl.load(open('./data/stock_price.pkl', 'rb'))\n", + "close_price = stock_price['close_price']\n", + "date_index = stock_price['date_index']" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Size of data, m: number of observations, n: number of stocks\n", + "m = len(date_index)\n", + "n = len(close_price)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Extract stock closing prices to a numpy array\n", + "data = np.zeros(shape=(m, n))\n", + "i = 0\n", + "for stock in close_price:\n", + " data[:,i] = close_price[stock]\n", + " plt.plot(np.arange(m), data[:,i])\n", + " i += 1\n", + "# Plot closing prices\n", + "plt.xlabel('Time (days)')\n", + "plt.ylabel('Closing price ($)')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For each stock $i$, we first estimate the $j$th daily relative return as $$relative~return_{i,j} = \\frac{closing~price_{i,j+1}-closing~price_{i,j}}{closing~price_{i,j}}.$$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Relative return\n", + "rel_rtn = np.zeros(shape=(m-1, n))\n", + "for j in range(m-1):\n", + " rel_rtn[j,:] = np.divide(data[j+1,:] - data[j,:], data[j,:])\n", + "# Plot relative return\n", + "for i in range(n):\n", + " plt.plot(np.arange(m-1),rel_rtn[:,i])\n", + "plt.xlabel('Time (days)')\n", + "plt.ylabel('Relative return')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Simply take arithmetic mean of each column of relative return to get mean return $r$ for each stock, followed by estimating covariance $V$ using numpy." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# Mean return\n", + "r = np.zeros(n)\n", + "r = rel_rtn.sum(axis=0)\n", + "r = r / (m-1)\n", + "# Covariance matrix\n", + "V = np.cov(rel_rtn.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Classic Mean-Variance Model\n", + "## Efficient Frontier" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One of the major goals of portfolio management is to achieve a certain level of return under a specific risk measurement. Here we demonstrate how to use NAG Library to build efficient frontier by solving classical Markowitz model with long-only constraint (meaning, buy to hold and short selling is not allowed):\n", + "\\begin{equation}\\label{MV_model}\n", + "\\begin{array}{ll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{minimize}} & -r^Tx+\\mu x^TVx\\\\[0.6ex]\n", + "\\mbox{subject to} & e^Tx = 1,\\\\[0.6ex]\n", + " & x\\geq0,\n", + "\\end{array}\n", + "\\end{equation}\n", + "where $e\\in\\Re^n$ is vector of all ones and $\\mu$ is a scalar controling trade-off between return and risk. Note one could build the efficient frontier by varying $\\mu$ from $0$ to a certain value." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# Import the NAG Library\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt\n", + "from naginterfaces.library import lapackeig\n", + "# Import necessary math libraries\n", + "from scipy.sparse import coo_matrix\n", + "import math as mt\n", + "import warnings as wn" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# Input for quadratic objective\n", + "# Sparsity pattern of upper triangular V\n", + "irowq, icolq = np.nonzero(np.triu(V))\n", + "v_val = V[irowq, icolq]\n", + "# Convert to 1-based\n", + "irowq = irowq + 1\n", + "icolq = icolq + 1\n", + "# Sparsity pattern of r, which is actually dense in this application\n", + "idxr = np.arange(1, n+1)\n", + "\n", + "# Input for linear constraint: e'x = 1\n", + "irowa = np.full(n, 1, dtype=int)\n", + "icola = np.arange(1, n+1)\n", + "a = np.full(n, 1.0, dtype=float)\n", + "bl = np.full(1, 1.0, dtype=float)\n", + "bu = np.full(1, 1.0, dtype=float)\n", + "\n", + "# Input for bound constraint: x >= 0\n", + "blx = np.zeros(n)\n", + "bux = np.full(n, 1.e20, float)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The input data is ready, we can easily build the efficient frontier as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# Set step for mu\n", + "step = 2001\n", + "\n", + "# Initialize output data: absolute risk and return\n", + "ab_risk = np.empty(0, float)\n", + "ab_rtn = np.empty(0, float)\n", + "\n", + "for mu in np.linspace(0.0, 2000.0, step):\n", + " # Create problem handle\n", + " handle = opt.handle_init(n)\n", + " \n", + " # Set quadratic objective function\n", + " # In qcqp standard form q should be 2*mu*V\n", + " q = 2.0 * mu * v_val\n", + " idqc = -1\n", + " opt.handle_set_qconstr(handle, 0.0, idqc, idxr, -r, irowq, icolq, q)\n", + " \n", + " # Set linear constraint e'x = 1\n", + " opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)\n", + " \n", + " # Set bound constraint\n", + " opt.handle_set_simplebounds(handle, blx, bux)\n", + " \n", + " # Set options\n", + " for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print File = -1',\n", + " 'SOCP Scaling = A'\n", + " ]:\n", + " opt.handle_opt_set(handle, option)\n", + " \n", + " # Call socp interior point solver\n", + " # Mute warnings and do not count results from warnings\n", + " wn.simplefilter('error', utils.NagAlgorithmicWarning)\n", + " try:\n", + " slt = opt.handle_solve_socp_ipm(handle)\n", + "\n", + " # Compute risk and return from the portfolio\n", + " ab_risk = np.append(ab_risk, mt.sqrt(slt.x[0:n].dot(V.dot(slt.x[0:n]))))\n", + " ab_rtn = np.append(ab_rtn, r.dot(slt.x[0:n]))\n", + " except utils.NagAlgorithmicWarning:\n", + " pass\n", + " \n", + " # Destroy the handle:\n", + " opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the result\n", + "plt.plot(ab_risk*100.0, ab_rtn*100.0)\n", + "plt.ylabel('Total Expected Return (%)')\n", + "plt.xlabel('Absolute Risk (%)')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Maximizing the Sharpe ratio" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Sharpe ratio is defined as the ratio of return of portfolio and standard deviation of the portfolio's excess return. It is usually used to measure the efficiency of a portfolio. Find the most efficient portfolio is equivalent to solve the following optimization problem.\n", + "\\begin{equation}\\label{sr_model}\n", + "\\begin{array}{ll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{minimize}} & \\frac{\\sqrt{x^TVx}}{r^Tx}\\\\[0.6ex]\n", + "\\mbox{subject to} & e^Tx = 1,\\\\[0.6ex]\n", + " & x\\geq0.\n", + "\\end{array}\n", + "\\end{equation}\n", + "By replacing $x$ with $\\frac{y}{\\lambda}, \\lambda\\gt0$, model (\\ref{sr_model}) is equivalent to\n", + "\\begin{equation}\\label{sr_model_eq}\n", + "\\begin{array}{ll}\n", + "\\underset{y\\in\\Re^n, \\lambda\\in\\Re}{\\mbox{minimize}} & y^TVy\\\\[0.6ex]\n", + "\\mbox{subject to} & e^Ty = \\lambda,\\\\[0.6ex]\n", + " & r^Ty=1, \\\\\n", + " & y\\geq0, \\\\\n", + " & \\lambda\\geq0.\n", + "\\end{array}\n", + "\\end{equation}\n", + "Problem (\\ref{sr_model_eq}) is similar to problem (\\ref{MV_model}) in the sense that they both have a quadratic objective function and linear constraints." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Input for linear constraint: e'y = lambda\n", + "irowa = np.full(n+1, 1, dtype=int)\n", + "icola = np.arange(1, n+2)\n", + "a = np.append(np.full(n, 1.0, dtype=float), -1.0)\n", + "bl = np.zeros(1)\n", + "bu = np.zeros(1)\n", + "\n", + "# Inpute for linear constraint: r'y = 1\n", + "irowa = np.append(irowa, np.full(n, 2, dtype=int))\n", + "icola = np.append(icola, np.arange(1, n+1))\n", + "a = np.append(a, r)\n", + "bl = np.append(bl, 1.0)\n", + "bu = np.append(bu, 1.0)\n", + "\n", + "# Input for bound constraint: x >= 0\n", + "blx = np.zeros(n+1)\n", + "bux = np.full(n+1, 1.e20, float)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can call the NAG SOCP solver as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# Create problem handle\n", + "handle = opt.handle_init(n+1)\n", + "\n", + "# Set quadratic objective function\n", + "# In qcqp standard form q should be 2*V\n", + "q = 2.0 * v_val\n", + "idqc = -1\n", + "opt.handle_set_qconstr(handle, 0.0, idqc, irowq=irowq, icolq=icolq, q=q)\n", + "\n", + "# Set linear constraints\n", + "opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)\n", + " \n", + "# Set bound constraint\n", + "opt.handle_set_simplebounds(handle, blx, bux)\n", + " \n", + "# Set options\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print File = -1',\n", + " 'SOCP Scaling = A'\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + " \n", + "# Call socp interior point solver\n", + "slt = opt.handle_solve_socp_ipm(handle)\n", + "\n", + "sr_risk = mt.sqrt(slt.x[0:n].dot(V.dot(slt.x[0:n])))/slt.x[n]\n", + "sr_rtn = r.dot(slt.x[0:n])/slt.x[n]\n", + "sr_x = slt.x[0:n]/slt.x[n]\n", + "\n", + "# Destroy the handle:\n", + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot result.\n", + "plt.plot(ab_risk*100.0, ab_rtn*100.0, label='Efficient frontier')\n", + "plt.plot([sr_risk*100], [sr_rtn*100], 'rs', label='Portfolio with maximum Sharpe ratio')\n", + "plt.plot([sr_risk*100, 0.0], [sr_rtn*100, 0.0], 'r-', label='Capital market line')\n", + "plt.axis([min(ab_risk*100), max(ab_risk*100), min(ab_rtn*100), max(ab_rtn*100)])\n", + "plt.ylabel('Total Expected Return (%)')\n", + "plt.xlabel('Absolute Risk (%)')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Portfolio optimization with tracking-error constraint" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To avoid taking unnecessary risk when beating a benchmark, the investors commonly impose a limit on the volatility of the deviation of the active portfolio from the benchmark, which is also known as tracking-error volatility (TEV) \\cite{J03}. The model to build efficient frontier in excess-return space is\n", + "\\begin{equation}\\label{er_tev}\n", + "\\begin{array}{ll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{maximize}} & r^Tx\\\\\n", + "\\mbox{subject to} & e^Tx = 0,\\\\\n", + " & x^TVx\\leq tev,\n", + "\\end{array}\n", + "\\end{equation}\n", + "where $tev$ is a limit on the track-error. Roll \\cite{R92} noted that problem (\\ref{er_tev}) is totally independent of the benchmark and leads to the unpalatable result that the active portfolio has systematically higher risk than the benchmark and is not optimal. Therefore, in this section we solve a more advanced model by taking absolute risk into account as follows.\n", + "\\begin{equation}\\label{tev_model}\n", + "\\begin{array}{ll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{minimize}} & -r^Tx+\\mu (x+b)^TV(x+b)\\\\\n", + "\\mbox{subject to} & e^Tx = 0,\\\\\n", + " & x^TVx\\leq tev,\\\\\n", + " & x+b\\geq0,\n", + "\\end{array}\n", + "\\end{equation}\n", + "where $b$ is a benchmark portfolio. In this demonstration, it is generated synthetically. Note here we use the same covariance matrix $V$ for tev and absolute risk measurement for demonstration purpose. In practice one could use different covariance matrices from different markets." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# Generate a benchmark portfolio from efficient portfolio that maximiz the Sharpe ratio\n", + "# Perturb x\n", + "b = sr_x + 1.e-1\n", + "# Normalize b\n", + "b = b/sum(b)\n", + "\n", + "# Set limit on tracking-error\n", + "tev = 0.000002\n", + "\n", + "# Compute risk and return at the benchmark\n", + "b_risk = mt.sqrt(b.dot(V.dot(b)))\n", + "b_rtn = r.dot(b)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# Input for linear constraint: e'x = 0\n", + "irowa = np.full(n, 1, dtype=int)\n", + "icola = np.arange(1, n+1)\n", + "a = np.full(n, 1.0, dtype=float)\n", + "bl = np.zeros(1)\n", + "bu = np.zeros(1)\n", + "\n", + "# Input for bound constraint: x >= -b\n", + "blx = -b\n", + "bux = np.full(n, 1.e20, float)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize output data: TEV risk and return\n", + "tev_risk = np.empty(0, float)\n", + "tev_rtn = np.empty(0, float)\n", + "\n", + "for mu in np.linspace(0.0, 2000.0, step):\n", + " # Create problem handle\n", + " handle = opt.handle_init(n)\n", + " \n", + " # Set quadratic objective function\n", + " # In qcqp standard form q should be 2*mu*V\n", + " q = 2.0 * mu * v_val\n", + " r_mu = 2.0*mu*V.dot(b)-r\n", + " idqc = -1\n", + " opt.handle_set_qconstr(handle, 0.0, idqc, idxr, r_mu, irowq, icolq, q)\n", + " \n", + " # Set quadratic constraint\n", + " # In qcqp standard form q should be 2*V\n", + " q = 2.0 * v_val\n", + " idqc = 0\n", + " opt.handle_set_qconstr(handle, -tev, idqc, irowq=irowq, icolq=icolq, q=q)\n", + " \n", + " # Set linear constraint e'x = 1\n", + " opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)\n", + " \n", + " # Set bound constraint\n", + " opt.handle_set_simplebounds(handle, blx, bux)\n", + " \n", + " # Set options\n", + " for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print File = -1',\n", + " 'SOCP Scaling = A'\n", + " ]:\n", + " opt.handle_opt_set(handle, option)\n", + " \n", + " # Call socp interior point solver\n", + " # Mute warnings and do not count results from warnings\n", + " wn.simplefilter('error', utils.NagAlgorithmicWarning)\n", + " try:\n", + " slt = opt.handle_solve_socp_ipm(handle)\n", + "\n", + "# Compute risk and return from the portfolio\n", + " tev_risk = np.append(tev_risk, mt.sqrt((slt.x[0:n]+b).dot(V.dot(slt.x[0:n]+b))))\n", + " tev_rtn = np.append(tev_rtn, r.dot(slt.x[0:n]+b))\n", + " except utils.NagAlgorithmicWarning:\n", + " pass\n", + " \n", + " # Destroy the handle:\n", + " opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the result\n", + "plt.figure(figsize=(7.5, 5.5))\n", + "plt.plot(ab_risk*100.0, ab_rtn*100.0, label='Classic efficient frontier')\n", + "plt.plot([sr_risk*100], [sr_rtn*100], 'rs', label='Portfolio with maximum Sharpe ratio')\n", + "plt.plot([sr_risk*100, 0.0], [sr_rtn*100, 0.0], 'r-', label='Capital market line')\n", + "plt.plot(b_risk*100, b_rtn*100, 'r*', label='Benchmark portfolio')\n", + "plt.plot(tev_risk*100.0, tev_rtn*100.0, 'seagreen', label='Efficient frontier with tev constraint')\n", + "\n", + "plt.axis([min(ab_risk*100), max(ab_risk*100), min(tev_rtn*100), max(ab_rtn*100)])\n", + "plt.ylabel('Total Expected Return (%)')\n", + "plt.xlabel('Absolute Risk (%)')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Conclusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook, we demonstrated how to use NAG Library to solve various quadratic models in portfolio optimization. Conic optimization is usually a good choice to solve convex QCQP. It is worth pointing out that the versatility of SOCP is not just limited to the QCQP models mentioned here. It covers a lot more problems and constraints. For example, DeMiguel et al. \\cite{DGNU09} discussed portfolio optimization with norm constraint, which can be easily transformed into an SOCP problem. We refer readers to the NAG Library documentation \\cite{NAGDOC} on SOCP solver and \\cite{AG03, LVBL98} for more details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# References\n", + "\n", + "[1] Jorion Philippe, ``_Portfolio optimization with tracking-error constraints_'', Financial Analysts Journal, vol. 59, number 5, pp. 70--82, 2003.\n", + "\n", + "[2] Roll Richard, ``_A mean/variance analysis of tracking error_'', The Journal of Portfolio Management, vol. 18, number 4, pp. 13--22, 1992.\n", + "\n", + "[3] DeMiguel Victor, Garlappi Lorenzo, Nogales Francisco J et al., ``_A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms_'', Management science, vol. 55, number 5, pp. 798--812, 2009.\n", + "\n", + "[4] Numerical Algorithms Group, ``_NAG documentation_'', 2019. [online](https://www.nag.com/numeric/fl/nagdoc_latest/html/frontmatter/manconts.html)\n", + "\n", + "[5] Alizadeh Farid and Goldfarb Donald, ``_Second-order cone programming_'', Mathematical programming, vol. 95, number 1, pp. 3--51, 2003.\n", + "\n", + "[6] Lobo Miguel Sousa, Vandenberghe Lieven, Boyd Stephen et al., ``_Applications of second-order cone programming_'', Linear algebra and its applications, vol. 284, number 1-3, pp. 193--228, 1998.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.1" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "number", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb index 968792e..510ac04 100644 --- a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb @@ -15,8 +15,22 @@ "\n", "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", "\n", - "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_using_socp.pdf).\n", + "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_using_socp.pdf)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Note for the users of the NAG Library Mark $27.1$ onwards\n", "\n", + "At Mark $27.1$ of the NAG Library, NAG introduced two new additions to help users easily define a Quadratically Constrained Quadratic Programming (QCQP) problem. All the models in this notebook then can be solved in a much simpler way without the need of a reformulation or any extra effort. It's recommended that the users of the NAG Library Mark $27.1$ or newer should look at the [notebook on QCQP instead](./portfolio_optimization_qcqp.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "# Introduction" ] }, @@ -1168,7 +1182,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.1" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/static/portfolio_optimization_qcqp.html b/local_optimization/SOCP/static/portfolio_optimization_qcqp.html new file mode 100644 index 0000000..d0531e6 --- /dev/null +++ b/local_optimization/SOCP/static/portfolio_optimization_qcqp.html @@ -0,0 +1,13933 @@ + + + + + + + + + + + + + + + + +portfolio_optimization_qcqp + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+

Quadratically constrained quadratic programming and its applications in portfolio optimization

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+

Introduction

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Quadratically constrained quadratic programming (QCQP) is a type of optimization problem in which both the objective function and the constraints involve quadratic functions. A general QCQP problem has the following form

+\begin{equation} +\begin{array}{ll} +\underset{x\in\Re^n}{\mbox{minimize}} & \frac{1}{2}x^TP_0x+q_0^Tx+r_0\\[0.6ex] +\mbox{subject to} & \frac{1}{2}x^TP_ix+q_i^Tx+r_i\leq0,\quad i=1,\ldots,p. +\end{array} +\end{equation}

It appears in applications such as modern portfolio theory, machine learning, engineering and control. Convex QCQP is usually handled through conic optimization, or, more precisely, second-order cone programming (SOCP) due to its computational efficiency and ability to detect infeasibility. However, using SOCP to solve convex QCQP is nontrivial task which requires extra amount of effort to transform problem data and add auxiliary variables. In this notebook, we are going to demonstrate how to use the NAG Optimization Modelling Suite in the NAG Library to define and solve QCQP in portfolio optimization.

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+

Data Preparation

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We consider daily prices for the 30 stocks in the DJIA from March 2018 to March 2019. In practice, the estimation of the mean return $r$ and covariance $V$ is often a nontrivial task. In this notebook, we estimate those entities using simple sample estimates.

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+
In [1]:
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+
+
# Import necessary libraries
+import pickle as pkl
+import numpy as np
+import matplotlib.pyplot as plt
+
+ +
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+ +
+
+
+
In [3]:
+
+
+
# Load stock price data from stock_price.plk
+# Stock_price: dict = ['close_price': [data], 'date_index': [data]]
+stock_price = stock_price = pkl.load(open('./data/stock_price.pkl', 'rb'))
+close_price = stock_price['close_price']
+date_index = stock_price['date_index']
+
+ +
+
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+ +
+
+
+
In [4]:
+
+
+
# Size of data, m: number of observations, n: number of stocks
+m = len(date_index)
+n = len(close_price)
+
+ +
+
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+ +
+
+
+
In [5]:
+
+
+
# Extract stock closing prices to a numpy array
+data = np.zeros(shape=(m, n))
+i = 0
+for stock in close_price:
+    data[:,i] = close_price[stock]
+    plt.plot(np.arange(m), data[:,i])
+    i += 1
+# Plot closing prices
+plt.xlabel('Time (days)')
+plt.ylabel('Closing price ($)')
+plt.show()
+
+ +
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+ +
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+ + +
+ +
+ + + + +
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For each stock $i$, we first estimate the $j$th daily relative return as $$relative~return_{i,j} = \frac{closing~price_{i,j+1}-closing~price_{i,j}}{closing~price_{i,j}}.$$

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In [6]:
+
+
+
# Relative return
+rel_rtn = np.zeros(shape=(m-1, n))
+for j in range(m-1):
+    rel_rtn[j,:] = np.divide(data[j+1,:] - data[j,:], data[j,:])
+# Plot relative return
+for i in range(n):
+    plt.plot(np.arange(m-1),rel_rtn[:,i])
+plt.xlabel('Time (days)')
+plt.ylabel('Relative return')
+plt.show()
+
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+ + +
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Simply take arithmetic mean of each column of relative return to get mean return $r$ for each stock, followed by estimating covariance $V$ using numpy.

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In [7]:
+
+
+
# Mean return
+r = np.zeros(n)
+r = rel_rtn.sum(axis=0)
+r = r / (m-1)
+# Covariance matrix
+V = np.cov(rel_rtn.T)
+
+ +
+
+
+ +
+
+
+
+

Classic Mean-Variance Model

Efficient Frontier

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+

One of the major goals of portfolio management is to achieve a certain level of return under a specific risk measurement. Here we demonstrate how to use NAG Library to build efficient frontier by solving classical Markowitz model with long-only constraint (meaning, buy to hold and short selling is not allowed):

+\begin{equation}\label{MV_model} +\begin{array}{ll} +\underset{x\in\Re^n}{\mbox{minimize}} & -r^Tx+\mu x^TVx\\[0.6ex] +\mbox{subject to} & e^Tx = 1,\\[0.6ex] + & x\geq0, +\end{array} +\end{equation}

where $e\in\Re^n$ is vector of all ones and $\mu$ is a scalar controling trade-off between return and risk. Note one could build the efficient frontier by varying $\mu$ from $0$ to a certain value.

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In [8]:
+
+
+
# Import the NAG Library
+from naginterfaces.base import utils
+from naginterfaces.library import opt
+from naginterfaces.library import lapackeig
+# Import necessary math libraries
+from scipy.sparse import coo_matrix
+import math as mt
+import warnings as wn
+
+ +
+
+
+ +
+
+
+
In [9]:
+
+
+
# Input for quadratic objective
+# Sparsity pattern of upper triangular V
+irowq, icolq = np.nonzero(np.triu(V))
+v_val = V[irowq, icolq]
+# Convert to 1-based
+irowq = irowq + 1
+icolq = icolq + 1
+# Sparsity pattern of r, which is actually dense in this application
+idxr = np.arange(1, n+1)
+
+# Input for linear constraint: e'x = 1
+irowa = np.full(n, 1, dtype=int)
+icola = np.arange(1, n+1)
+a = np.full(n, 1.0, dtype=float)
+bl = np.full(1, 1.0, dtype=float)
+bu = np.full(1, 1.0, dtype=float)
+
+# Input for bound constraint: x >= 0
+blx = np.zeros(n)
+bux = np.full(n, 1.e20, float)
+
+ +
+
+
+ +
+
+
+
+

The input data is ready, we can easily build the efficient frontier as follows.

+ +
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+
In [10]:
+
+
+
# Set step for mu
+step = 2001
+
+# Initialize output data: absolute risk and return
+ab_risk = np.empty(0, float)
+ab_rtn = np.empty(0, float)
+
+for mu in np.linspace(0.0, 2000.0, step):
+    # Create problem handle
+    handle = opt.handle_init(n)
+    
+    # Set quadratic objective function
+    # In qcqp standard form q should be 2*mu*V
+    q = 2.0 * mu * v_val
+    idqc = -1
+    opt.handle_set_qconstr(handle, 0.0, idqc, idxr, -r, irowq, icolq, q)
+    
+    # Set linear constraint e'x = 1
+    opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)
+    
+    # Set bound constraint
+    opt.handle_set_simplebounds(handle, blx, bux)
+    
+    # Set options
+    for option in [
+            'Print Options = NO',
+            'Print Level = 1',
+            'Print File = -1',
+            'SOCP Scaling = A'
+    ]:
+        opt.handle_opt_set(handle, option)
+        
+    # Call socp interior point solver
+    # Mute warnings and do not count results from warnings
+    wn.simplefilter('error', utils.NagAlgorithmicWarning)
+    try:
+        slt = opt.handle_solve_socp_ipm(handle)
+
+        # Compute risk and return from the portfolio
+        ab_risk = np.append(ab_risk, mt.sqrt(slt.x[0:n].dot(V.dot(slt.x[0:n]))))
+        ab_rtn = np.append(ab_rtn, r.dot(slt.x[0:n]))
+    except utils.NagAlgorithmicWarning:
+        pass
+    
+    # Destroy the handle:
+    opt.handle_free(handle)
+
+ +
+
+
+ +
+
+
+
In [11]:
+
+
+
# plot the result
+plt.plot(ab_risk*100.0, ab_rtn*100.0)
+plt.ylabel('Total Expected Return (%)')
+plt.xlabel('Absolute Risk (%)')
+plt.show()
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
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+ +
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+
+
+

Maximizing the Sharpe ratio

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+

The Sharpe ratio is defined as the ratio of return of portfolio and standard deviation of the portfolio's excess return. It is usually used to measure the efficiency of a portfolio. Find the most efficient portfolio is equivalent to solve the following optimization problem.

+\begin{equation}\label{sr_model} +\begin{array}{ll} +\underset{x\in\Re^n}{\mbox{minimize}} & \frac{\sqrt{x^TVx}}{r^Tx}\\[0.6ex] +\mbox{subject to} & e^Tx = 1,\\[0.6ex] + & x\geq0. +\end{array} +\end{equation}

By replacing $x$ with $\frac{y}{\lambda}, \lambda\gt0$, model (\ref{sr_model}) is equivalent to

+\begin{equation}\label{sr_model_eq} +\begin{array}{ll} +\underset{y\in\Re^n, \lambda\in\Re}{\mbox{minimize}} & y^TVy\\[0.6ex] +\mbox{subject to} & e^Ty = \lambda,\\[0.6ex] + & r^Ty=1, \\ + & y\geq0, \\ + & \lambda\geq0. +\end{array} +\end{equation}

Problem (\ref{sr_model_eq}) is similar to problem (\ref{MV_model}) in the sense that they both have a quadratic objective function and linear constraints.

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+
In [12]:
+
+
+
# Input for linear constraint: e'y = lambda
+irowa = np.full(n+1, 1, dtype=int)
+icola = np.arange(1, n+2)
+a = np.append(np.full(n, 1.0, dtype=float), -1.0)
+bl = np.zeros(1)
+bu = np.zeros(1)
+
+# Inpute for linear constraint: r'y = 1
+irowa = np.append(irowa, np.full(n, 2, dtype=int))
+icola = np.append(icola, np.arange(1, n+1))
+a = np.append(a, r)
+bl = np.append(bl, 1.0)
+bu = np.append(bu, 1.0)
+
+# Input for bound constraint: x >= 0
+blx = np.zeros(n+1)
+bux = np.full(n+1, 1.e20, float)
+
+ +
+
+
+ +
+
+
+
+

Now we can call the NAG SOCP solver as follows.

+ +
+
+
+
+
+
In [13]:
+
+
+
# Create problem handle
+handle = opt.handle_init(n+1)
+
+# Set quadratic objective function
+# In qcqp standard form q should be 2*V
+q = 2.0 * v_val
+idqc = -1
+opt.handle_set_qconstr(handle, 0.0, idqc, irowq=irowq, icolq=icolq, q=q)
+
+# Set linear constraints
+opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)
+    
+# Set bound constraint
+opt.handle_set_simplebounds(handle, blx, bux)
+    
+# Set options
+for option in [
+        'Print Options = NO',
+        'Print Level = 1',
+        'Print File = -1',
+        'SOCP Scaling = A'
+]:
+    opt.handle_opt_set(handle, option)
+        
+# Call socp interior point solver
+slt = opt.handle_solve_socp_ipm(handle)
+
+sr_risk = mt.sqrt(slt.x[0:n].dot(V.dot(slt.x[0:n])))/slt.x[n]
+sr_rtn = r.dot(slt.x[0:n])/slt.x[n]
+sr_x = slt.x[0:n]/slt.x[n]
+
+# Destroy the handle:
+opt.handle_free(handle)
+
+ +
+
+
+ +
+
+
+
In [14]:
+
+
+
# plot result.
+plt.plot(ab_risk*100.0, ab_rtn*100.0, label='Efficient frontier')
+plt.plot([sr_risk*100], [sr_rtn*100], 'rs', label='Portfolio with maximum Sharpe ratio')
+plt.plot([sr_risk*100, 0.0], [sr_rtn*100, 0.0], 'r-', label='Capital market line')
+plt.axis([min(ab_risk*100), max(ab_risk*100), min(ab_rtn*100), max(ab_rtn*100)])
+plt.ylabel('Total Expected Return (%)')
+plt.xlabel('Absolute Risk (%)')
+plt.legend()
+plt.show()
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
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+
+
+

Portfolio optimization with tracking-error constraint

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+
+
+
+
+
+

To avoid taking unnecessary risk when beating a benchmark, the investors commonly impose a limit on the volatility of the deviation of the active portfolio from the benchmark, which is also known as tracking-error volatility (TEV) \cite{J03}. The model to build efficient frontier in excess-return space is

+\begin{equation}\label{er_tev} +\begin{array}{ll} +\underset{x\in\Re^n}{\mbox{maximize}} & r^Tx\\ +\mbox{subject to} & e^Tx = 0,\\ + & x^TVx\leq tev, +\end{array} +\end{equation}

where $tev$ is a limit on the track-error. Roll \cite{R92} noted that problem (\ref{er_tev}) is totally independent of the benchmark and leads to the unpalatable result that the active portfolio has systematically higher risk than the benchmark and is not optimal. Therefore, in this section we solve a more advanced model by taking absolute risk into account as follows.

+\begin{equation}\label{tev_model} +\begin{array}{ll} +\underset{x\in\Re^n}{\mbox{minimize}} & -r^Tx+\mu (x+b)^TV(x+b)\\ +\mbox{subject to} & e^Tx = 0,\\ + & x^TVx\leq tev,\\ + & x+b\geq0, +\end{array} +\end{equation}

where $b$ is a benchmark portfolio. In this demonstration, it is generated synthetically. Note here we use the same covariance matrix $V$ for tev and absolute risk measurement for demonstration purpose. In practice one could use different covariance matrices from different markets.

+ +
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+
+
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+
In [15]:
+
+
+
# Generate a benchmark portfolio from efficient portfolio that maximiz the Sharpe ratio
+# Perturb x
+b = sr_x + 1.e-1
+# Normalize b
+b = b/sum(b)
+
+# Set limit on tracking-error
+tev = 0.000002
+
+# Compute risk and return at the benchmark
+b_risk = mt.sqrt(b.dot(V.dot(b)))
+b_rtn = r.dot(b)
+
+ +
+
+
+ +
+
+
+
In [16]:
+
+
+
# Input for linear constraint: e'x = 0
+irowa = np.full(n, 1, dtype=int)
+icola = np.arange(1, n+1)
+a = np.full(n, 1.0, dtype=float)
+bl = np.zeros(1)
+bu = np.zeros(1)
+
+# Input for bound constraint: x >= -b
+blx = -b
+bux = np.full(n, 1.e20, float)
+
+ +
+
+
+ +
+
+
+
In [17]:
+
+
+
# Initialize output data: TEV risk and return
+tev_risk = np.empty(0, float)
+tev_rtn = np.empty(0, float)
+
+for mu in np.linspace(0.0, 2000.0, step):
+    # Create problem handle
+    handle = opt.handle_init(n)
+    
+    # Set quadratic objective function
+    # In qcqp standard form q should be 2*mu*V
+    q = 2.0 * mu * v_val
+    r_mu = 2.0*mu*V.dot(b)-r
+    idqc = -1
+    opt.handle_set_qconstr(handle, 0.0, idqc, idxr, r_mu, irowq, icolq, q)
+    
+    # Set quadratic constraint
+    # In qcqp standard form q should be 2*V
+    q = 2.0 * v_val
+    idqc = 0
+    opt.handle_set_qconstr(handle, -tev, idqc, irowq=irowq, icolq=icolq, q=q)
+    
+    # Set linear constraint e'x = 1
+    opt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)
+    
+    # Set bound constraint
+    opt.handle_set_simplebounds(handle, blx, bux)
+    
+    # Set options
+    for option in [
+            'Print Options = NO',
+            'Print Level = 1',
+            'Print File = -1',
+            'SOCP Scaling = A'
+    ]:
+        opt.handle_opt_set(handle, option)
+        
+    # Call socp interior point solver
+    # Mute warnings and do not count results from warnings
+    wn.simplefilter('error', utils.NagAlgorithmicWarning)
+    try:
+        slt = opt.handle_solve_socp_ipm(handle)
+
+#       Compute risk and return from the portfolio
+        tev_risk = np.append(tev_risk, mt.sqrt((slt.x[0:n]+b).dot(V.dot(slt.x[0:n]+b))))
+        tev_rtn = np.append(tev_rtn, r.dot(slt.x[0:n]+b))
+    except utils.NagAlgorithmicWarning:
+        pass
+    
+    # Destroy the handle:
+    opt.handle_free(handle)
+
+ +
+
+
+ +
+
+
+
In [18]:
+
+
+
# Plot the result
+plt.figure(figsize=(7.5, 5.5))
+plt.plot(ab_risk*100.0, ab_rtn*100.0, label='Classic efficient frontier')
+plt.plot([sr_risk*100], [sr_rtn*100], 'rs', label='Portfolio with maximum Sharpe ratio')
+plt.plot([sr_risk*100, 0.0], [sr_rtn*100, 0.0], 'r-', label='Capital market line')
+plt.plot(b_risk*100, b_rtn*100, 'r*', label='Benchmark portfolio')
+plt.plot(tev_risk*100.0, tev_rtn*100.0, 'seagreen', label='Efficient frontier with tev constraint')
+
+plt.axis([min(ab_risk*100), max(ab_risk*100), min(tev_rtn*100), max(ab_rtn*100)])
+plt.ylabel('Total Expected Return (%)')
+plt.xlabel('Absolute Risk (%)')
+plt.legend()
+plt.show()
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+

Conclusion

+
+
+
+
+
+
+

In this notebook, we demonstrated how to use NAG Library to solve various quadratic models in portfolio optimization. Conic optimization is usually a good choice to solve convex QCQP. It is worth pointing out that the versatility of SOCP is not just limited to the QCQP models mentioned here. It covers a lot more problems and constraints. For example, DeMiguel et al. \cite{DGNU09} discussed portfolio optimization with norm constraint, which can be easily transformed into an SOCP problem. We refer readers to the NAG Library documentation \cite{NAGDOC} on SOCP solver and \cite{AG03, LVBL98} for more details.

+ +
+
+
+
+
+
+

References

[1] Jorion Philippe, ``Portfolio optimization with tracking-error constraints'', Financial Analysts Journal, vol. 59, number 5, pp. 70--82, 2003.

+

[2] Roll Richard, ``A mean/variance analysis of tracking error'', The Journal of Portfolio Management, vol. 18, number 4, pp. 13--22, 1992.

+

[3] DeMiguel Victor, Garlappi Lorenzo, Nogales Francisco J et al., ``A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms'', Management science, vol. 55, number 5, pp. 798--812, 2009.

+

[4] Numerical Algorithms Group, ``NAG documentation'', 2019. online

+

[5] Alizadeh Farid and Goldfarb Donald, ``Second-order cone programming'', Mathematical programming, vol. 95, number 1, pp. 3--51, 2003.

+

[6] Lobo Miguel Sousa, Vandenberghe Lieven, Boyd Stephen et al., ``Applications of second-order cone programming'', Linear algebra and its applications, vol. 284, number 1-3, pp. 193--228, 1998.

+ +
+
+
+
+
+
In [ ]:
+
+
+
 
+
+ +
+
+
+ +
+
+
+ + diff --git a/local_optimization/SOCP/static/portfolio_optimization_qcqp.pdf b/local_optimization/SOCP/static/portfolio_optimization_qcqp.pdf new file mode 100644 index 0000000000000000000000000000000000000000..dfcb20edc3d4d8d8779d91801a9ce88a943fbb6e GIT binary patch literal 256920 zcmb5Vb9iM@(=QmSV|IMvq+{Do$LZL%ZQC}wW7|$Twr$(ioPNLi%pH7lXXbg%AM32W z_S#jo3csq_n@nCrjFyp(6^?BG`r;Xmi4(v8ur;uNs!OQt!`-kw8d*h={i!qw~y8{>mtMzg#j}{IH!^g z(qi+BV@W{k(W%JpKRhaq7$A=1<((au(1G~o$uqZLv@qmRtG1!TM{hE7Jw!9or`x&i ztMTbo-|;a?Lr!HGpld^bwU<>#N8fIi6l>hN@?}@(e7(etdlNdtW$}z&sr|BRo~rcviFA>6kow3Fqg?QhYuSDe>IJLbG>-3P z-#ahu1Yd&3J`>7!9aYv|ih;9i`o}Wbv}8SVsHv)mwK=$Rl1V$&f}CPw#w!aDnfHzC zZBKT1#g{F{D-T!tLia(Vbm|zvNgY*f_3{qqyv%|K#|_nxpVzBM(ujE4aH>&()zed1 z?u%2e*Y!LX=63;x1H*^Wt{WXWhg|OyP-QT2^42wklg+4)kKEngD&aS7Xq>=`1CFwwsTA9Xs_+A#UmJc8(iNqR=V&~qbnjAYd{gj{?StK9 zUxUe&d~KuOf{NmG@@PoidaN2$8$4&+nRYej!QYm!<|%T z#5oASOAjbo*8|{-Vi5`d&8yo%Cjz&*cmfGekX8eHk;`}iqLb^+6K+eHUJko$&3>Wh zcSte%dt7&QT7b`@>Ip#G$}XDnyw6Isg71c!vmy>OHiK$e;5{bwbWPxBA(DZ#*q8$LW0pzCmaYBoTrH}8rVg_e`yj(eZzxkk={zN zUbAWK%5*G^QV$yy-XRJs*XYsv>9(oQ?4N|VCNafjHF-_anb4n-h}R^Ih}(qEwkY_u zX>gDP{`5UCW|cqb2(Kq=zs5m*LKKv0;eHKyM3l%>Ud$IEOqUG+hn4+cJRUWOOO5_0 zXZ=AA7%l|WQX`DzwS(sHp7G=FSiwfyL*}{(h~RdcT=(??SBT3%tHy#IjS#(tNZHy| z&FCWD___7|exZW5Yd#GveUpL;uj<*P;gcb7h6G!bUeoJPToOQ{t>+16|)X zbK10$al%lO;k4`jXY!O&D9LKlu9nnjLjhlRXL(3L86E`xqP`dL~*4V%( z3wvv$^y#zF$fQ~;i$4Cthp$}W^!5>ia>}PSXB{b{y)p}`gF10j{ze-Pfq1UUgI=`B z*{qGHGM92B3}B&4kgsCWP7ccyye;BQzw4oOh@AG6Ie>ru*O~6_OjM7Wp;Gi2Nzs6V zwZ>J}T8jY5vV{)YQ{HpCptEv>EgFC2e6KCz@r4in%5#OKrG6_P_U>&7;Wp zY*IB|HCd_9BC=_j>qicd} z-Hwo0>VNHr^%^5P-+svU)-pq;hDF5rjC#sOhjF1s5x9xR^!-9bAzaUA&$lFB93wBk z(Jehk=B*R^DSF<{$EI4%jR6J0U7{A8f<8n?&79WICuZrFzs^5HLzK15^=M6vst@;z z;zHVgu<4>+g!^~0t4mdLfK*X-jlAenBQ)yirt3FpFN=#y#|-^RRcF;9QXTJBy&ClD zkc;-N(qXdT#1wDihtvDpxR6|R?S_jTwSFAbYN>cE$F;YGNBv}^ z5~WKKi+kaA@wWXbma4?xOofJ6#RBeAHHzcH=_M zrY*Q0&L$LM(zS3+K_we%BrTe7wZ6Ta=L&1N@R)U?wB5{CsxlMVSXpUFKL)YuOCln+ zxd^-r9nN6qM$5>*ULIMgE-!zCC|b-X%uZ6Khn;CLu~OXVTn;DtLy@~)#%MW~M~h+O zBNAj++?^;*?jvSgU<77oT$V#)=v+G_>NH2}3~nHqg?@SY`6l%rjdar_SJW|5;d}Y|``h|{UOyMVY3A##`r1)4s1&M& zZOA!cGr24PczvywAm5UgLzP?AvQxt3COSvF4Jg*>BV!fJ!MQ*4d_*i12V02A-_kI+ z@(95o!Wn%;ke~=Vjkps35IzHAyXv4wkf&3k zI6yRjWPxBXD%JfX%|$*t6pYPaOld+)IP)x3o_li@6Y$%6fx*p}MT8Cd?BMMnlyJuq zX>Y6dNI04VKEF3qX9|Sy8;1;aB1*@AO=-j;y{~7pAcS0=tKRzkb1!CcJ-FU#`FZPT zUAl|zH$mGg&Sh*#Z$?q-*I)X(ZDZ<7%JmRP?Z5Ks>&>Eu_l(-x2`9pGGE~Hy*_doo z7l`evmIU+8P*H;nit|`@WFxh?L!III(S7``B2gzA^4@R*Mr~P;5pEd@+ zadSQ=#%N}_fB41o4Ve`}6;I1My2d-5L>5fAD=dA+<{O{;0M6^c>(J8~B@P7@y&W2O z@K_2a&Zcn1RqnF(q4ufwTcEG6#_b=t0r(Lr6 zg_=k75{Uu6j={MwiC^`7NE3-78=)74s+DgAAPSF-vRKY%>0E8ik%M z(>7=4C|^%%&wOgEIyYiMT}fw~VXAq*at7Y`R$<?w1o?n82l* zKC4};n{Hja(+EOS4(hE+U$EcKcC)N6ep3Pks5Z<+A43NhP(ryf5okwRNfgg)(m z)~7)m@Nwa-4`PW^1SUd58~0tIm^M;C{?)U9>>Y@PCR>YBrbY(mM`IM&iT0=xgr zUF+#M{44#@?RT?a8Mk?~T=F;S_f9YGqA}u_AWiL*{x43$o9^G+I#|EGMmb}@evg3p zKJjCzgh#^}+Zg?iyaG7-mx(Yl|Id`gp|QAwzB|2;xs#*3v4gO!wVkbv zv5gZP2k`2@{6=2i!P*g+`TSoO066|@Cr1F|zk##0jpKiwB=2BsWNzqW>i}Tl zy0`c*?T&Jew5IMjpAdXL=}-ayFu)%%r-ihjZIK2d#3j`)kl)=TY3N>PcvuRejN;}W zeJR6M06PJ-${NHNOShkQiKee^#d7N!em!_QH%ZS6TtN>F>2-UPApV>}gNHy+VUm1F#77w^F-(0e00C*qY#lb9tChjiNHBGyu z_sj14PQtcm%MK;%Dhia*4tW|~JLbX_S{NLKB<>Va=}QX`zFmqE_S60#So8yd0DyqP z2!Mbg|93+nev#=#{FO^b+Fa$xHWC|{)wXjVE<#VXUDbc6RLpmoXiIZjve(@?a9z3ej$oP4R$< z-el!t*S~LwnKSk#P29N;8;0NuMEg z-+0+L{^TVOEQAdVXQ}up3t`utlnXfMQjj=)ukp1q;96uk%jICe+IbW~U^`6yT=?Z% zHw{j{CPrlUv{M9?(D|*l$Yofa|s)?>S6u~`p=*OSE-;qeV4gVq$)I5VmmH_@NKla z`y=JU{EDY@3)IDd-D)Z`u7O72UF+@I8TnsRqI3Mi)jJ`t_g@8EWoU6Jt06hrN6|&2@VUTi~G0C9xbr zQoryKK8C=6%uZ{iIDZ4!3AY^U{%mrW1NW!sqdsG%WZ^@A(V`#EnHrJR>J3gO33#y9 z+^L6xc}Gs_U1FW1R^tDy=_-rAn33dHq+}&0&U6&ukVETg(qMH`{N6)SMZh#xo zlUs+o@1x0?^;|C;=|oiP35~xV88&cvmq{tz%Ve zyO&|~eIlw#e|`aFDB)Sx5bBCMZe|p4hs31D9VYWQvLJr zkQHz(EI+6|d>+Mv4^c6~7XNGPx!5chfVmT}N$UcW}L5n$^c@1LV2 za4ZZF8pw~4&}TK+-1abnP>KWb@o#!Aw9&Nl__i2HMLXFV20wz$N%0_7Sx|L;NMPqVR4tXU)mMjK2ubH8XnaDSKo7s40LM40>IS_B0v#u z&R=mtLZlRvTx_Kwu(*Q)oo<^fZ!yrHA%HrIbKvuy!a#WdpGFiQ@0wJ&

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Correct Rendering of this notebook

This notebook makes use of the latex_envs Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html

The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the pdf version instead.

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+

Note for the users of the NAG Library Mark $27.1$ onwards

At Mark $27.1$ of the NAG Library, NAG introduced two new additions to help users easily define a Quadratically Constrained Quadratic Programming (QCQP) problem. All the models in this notebook then can be solved in a much simpler way without the need of a reformulation or any extra effort. It's recommended that the users of the NAG Library Mark $27.1$ or newer should look at the notebook on QCQP instead.

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zwXim}#dvIo?Xd%P#4gwgJ7ZVuhTSn42Vf8Eh5fNFj>dsF3Mrbbj<58~*>qi&iaYnsFX#|&2=3VWTxEj~udfbScaVu`eo#Jjf z|Fm1Hy|+Jl@BH!JU*LW4-up1d`)HQ;@&8Y^N8FP)+PlQPh}7O6_6+U4;$H97P7C{+ z_5pF9zGxp2_c>nskOcW@9%vtzAb)l3qY_k((moY-iuMT!s)_d5uoJXTOVHt~_5}$# z_S8NnK|%xVOJQ%-z9_+{4F9j5lFgWZ19hS<3T19&b98cLVQmU!Ze(v_Y6^37VRCeM Ua%E-;GC4CgGdBt)B}Gq03g%&84FCWD From 766ced53b5bf95ce1772bc6140f1eb4dc2140047 Mon Sep 17 00:00:00 2001 From: Shuanghua <32490707+shuanghuabai@users.noreply.github.com> Date: Thu, 29 Oct 2020 22:15:08 +0000 Subject: [PATCH 059/182] Update Readme.md --- local_optimization/SOCP/Readme.md | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/local_optimization/SOCP/Readme.md b/local_optimization/SOCP/Readme.md index a3f331b..382ce52 100644 --- a/local_optimization/SOCP/Readme.md +++ b/local_optimization/SOCP/Readme.md @@ -23,7 +23,7 @@ This directory contains demonstrations using NAG's SOCP solver in Python. * [A classification example using NAG's SOCP from CVXPY](./cvxpy_classification.ipynb) -## Portfolio Optimization using Second Order Cone Programming (SOCP) +## Portfolio Optimization as Quadratically Constrained Quadratic Programming (QCQP) This demonstration is a walk-through of modelling techniques in portfolio optimization using second-order cone programming in the NAG Library. Models in portfolio optimization include @@ -31,7 +31,13 @@ This demonstration is a walk-through of modelling techniques in portfolio optimi * quadratically constrained quadratic programming (tev portfolio) * optimization with objective of fraction of quadratic and linear (the Sharpe ratio). -General functions are enclosed for users to get the principle idea on SOCP reformulation. They provide one of the ways to build and solve their problems using NAG's SOCP solver and could be copy and paste into a model and reuse repeatedly. +NAG provides two functions for users to easily define quadratic objective and constraints. Then the second-order cone programming solver can be called directly to solve the problem without any extra effort on reformulation. + +* [portfolio_optimization_qcqp.ipynb](./portfolio_optimization_qcqp.ipynb) Jupyter notebook +* [portfolio_optimization_qcqp.pdf](./static/portfolio_optimization_qcqp.pdf) Static pdf version +* [portfolio_optimization_qcqp.html](./static/portfolio_optimization_qcqp.html) Static html version + +Users can also transform their QCQP problem into second-order cone programming model by hand. In the following notebook two general functions are enclosed for users to get the principle idea on SOCP reformulation. * [portfolio_optimization_using_socp.ipynb](./portfolio_optimization_using_socp.ipynb) Jupyter notebook * [portfolio_optimization_using_socp.pdf](./static/portfolio_optimization_using_socp.pdf) Static pdf version From 792a41df20e07ec5dfbd9634bdc2375c2c7ad5ee Mon Sep 17 00:00:00 2001 From: Mat Cross Date: Wed, 4 Nov 2020 19:40:50 +0000 Subject: [PATCH 060/182] Updated for MK27.1. --- .../quantile_linreg_easy.ipynb | 4 +- .../dim2_spline_ts_sctr.ipynb | 4 +- .../web_site_classification_using_nnmf.ipynb | 2 +- global_optimization/PSO_demo.ipynb | 6 +- global_optimization/SQP_multistart.ipynb | 2 +- global_optimization/bnd_mcs_solve.ipynb | 4 +- linear_algebra/real_toeplitz_solve.ipynb | 62 ++-- local_optimization/DFO_noisy.ipynb | 180 ++++++++++-- local_optimization/FOAS/rosenbrock2d.ipynb | 85 +++--- local_optimization/LP_demo.ipynb | 43 ++- local_optimization/SDP/NCM_SDP.ipynb | 270 ++++++++++++++---- .../SDP/matrix_completion.ipynb | 270 ++++++++++++++---- .../SDP/theta_optimization.ipynb | 270 ++++++++++++++---- .../SOCP/cvxpy_classification.ipynb | 28 +- .../portfolio_optimization_using_socp.ipynb | 2 +- local_optimization/SOCP/robust_lp.ipynb | 30 +- local_optimization/SOCP/simple_SOCP.ipynb | 8 +- .../bounds_quasi_func_easy.ipynb | 72 ++++- local_optimization/christmas_demo.ipynb | 4 +- multivariate_methods/k-means.ipynb | 2 +- nearest_correlation_matrices/ncm_nag.ipynb | 2 +- operations_research/nag_rugby_tsm.ipynb | 2 +- random_number_generation/rand_corr_mat.ipynb | 2 +- roots/Anderson_Acceleration_Poisson.ipynb | 2 +- special_functions/mathieu_functions.ipynb | 4 +- time_series_analysis/cp_pelt.ipynb | 4 +- time_series_analysis/inhom_iema.ipynb | 4 +- 27 files changed, 1044 insertions(+), 324 deletions(-) diff --git a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb index 22f2e52..308dd71 100644 --- a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb +++ b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb @@ -6,7 +6,7 @@ "source": [ "# Quantile Regression\n", "\n", - "The NAG function [`correg.quantile_linreg_easy`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.correg.html#naginterfaces.library.correg.quantile_linreg_easy) can be used to model the conditional $\\tau$-th quantile of a dependent variable against one or more independent or explanatory variables.\n", + "The NAG function [`correg.quantile_linreg_easy`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.correg.quantile_linreg_easy.html) can be used to model the conditional $\\tau$-th quantile of a dependent variable against one or more independent or explanatory variables.\n", "\n", "Whereas the method of least squares results in estimates of the conditional mean of the response (dependent) variable, quantile regression gives estimates of the conditional median (or any other quantile) of the response variable.\n", "\n", @@ -1012,7 +1012,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb index 813613a..6dced1c 100644 --- a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb +++ b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb @@ -923,7 +923,7 @@ "source": [ "Now, how do we go about fitting a nice, smooth surface through those scattered points?\n", "\n", - "The NAG Library supplies a very configurable function (based on the TSFIT package of Davydov and Zeilfelder) for fitting a continuously differentiable ($C^1$ or $C^2$) surface to scattered data: [`fit.dim2_spline_ts_sctr`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.fit.html#naginterfaces.library.fit.dim2_spline_ts_sctr).\n", + "The NAG Library supplies a very configurable function (based on the TSFIT package of Davydov and Zeilfelder) for fitting a continuously differentiable ($C^1$ or $C^2$) surface to scattered data: [`fit.dim2_spline_ts_sctr`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.fit.dim2_spline_ts_sctr.html).\n", "\n", "We need to choose a granularity for the triangulation that the function will use" ] @@ -1896,7 +1896,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/dimension_reduction/web_site_classification_using_nnmf.ipynb b/dimension_reduction/web_site_classification_using_nnmf.ipynb index 039eb77..0848b68 100644 --- a/dimension_reduction/web_site_classification_using_nnmf.ipynb +++ b/dimension_reduction/web_site_classification_using_nnmf.ipynb @@ -815,7 +815,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/global_optimization/PSO_demo.ipynb b/global_optimization/PSO_demo.ipynb index a610786..ede91d8 100644 --- a/global_optimization/PSO_demo.ipynb +++ b/global_optimization/PSO_demo.ipynb @@ -101,7 +101,7 @@ " \n", " return objf, vecout\n", "\n", - "We will explore the meaning of all of these arguments later (or you can skip to the [full documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.html#naginterfaces.library.glopt.bnd_pso) for details) but for now, all we need to worry about is the input vector `in` and the input/output vectors `objf` and `vecout`\n", + "We will explore the meaning of all of these arguments later (or you can skip to the [full documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.bnd_pso.html) for details) but for now, all we need to worry about is the input vector `in` and the input/output vectors `objf` and `vecout`\n", "\n", "* `x` contains a vector of co-ordinates of the N-dimensional point where we wish to evaluate the objective function \n", "* `objf` contains the value of the objective function at the point `x`\n", @@ -312,7 +312,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Switching the warning off doesn't mean we shouldn't worry about what's going on and you should refer to [The documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.html#naginterfaces.library.glopt.bnd_pso) for the meaning of the various `inform` values. \n", + "Switching the warning off doesn't mean we shouldn't worry about what's going on and you should refer to [The documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.bnd_pso.html) for the meaning of the various `inform` values. \n", "\n", "In the example above, `inform=2` which means that the standard deviation of the location of all the particles in the swarm is below the set threshold (‘Swarm Standard Deviation’). We may or may not choose to worry about this. Since we know we have found the global minimum in this example, we will ignore it" ] @@ -393,7 +393,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/global_optimization/SQP_multistart.ipynb b/global_optimization/SQP_multistart.ipynb index ac4937f..c2f3847 100644 --- a/global_optimization/SQP_multistart.ipynb +++ b/global_optimization/SQP_multistart.ipynb @@ -211,7 +211,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/global_optimization/bnd_mcs_solve.ipynb b/global_optimization/bnd_mcs_solve.ipynb index ea3a070..c290070 100644 --- a/global_optimization/bnd_mcs_solve.ipynb +++ b/global_optimization/bnd_mcs_solve.ipynb @@ -5,7 +5,7 @@ "metadata": {}, "source": [ "# Global Optimization\n", - "Finding the absolute maximum or minimum value of a function can be hard. For problems with a few tens of variables and only bound constraints the NAG solver [`glopt.bnd_mcs_solve`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.html#naginterfaces.library.glopt.bnd_mcs_solve) for multi-level coordinate search (from Huyer and Neumaier) is an effective routine.\n", + "Finding the absolute maximum or minimum value of a function can be hard. For problems with a few tens of variables and only bound constraints the NAG solver [`glopt.bnd_mcs_solve`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.glopt.bnd_mcs_solve.html) for multi-level coordinate search (from Huyer and Neumaier) is an effective routine.\n", "\n", "For a quick demonstration of `glopt.bnd_mcs_solve` we find the global minimum of the two-dimensional 'peaks' function, which (in a suitable form for the solver's `objfun` argument) is" ] @@ -267,7 +267,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/linear_algebra/real_toeplitz_solve.ipynb b/linear_algebra/real_toeplitz_solve.ipynb index cc71868..c10f2ad 100644 --- a/linear_algebra/real_toeplitz_solve.ipynb +++ b/linear_algebra/real_toeplitz_solve.ipynb @@ -202,39 +202,39 @@ "\n", "### Real matrices\n", "\n", - "* [library.linsys.real_toeplitz_solve](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.linsys.html#naginterfaces.library.linsys.real_toeplitz_solve) Solution of **real symmetric positive definite Toeplitz** system of linear equations.\n", - "* [library.lapacklin.dgbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dgbsv) Computes the solution to a **real banded** system of linear equations.\n", - "* [library.lapacklin.dsgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dsgesv) Computes the solution to a **real** system of linear equations using **mixed precision arithmetic**.\n", - "* [library.lapacklin.dsysv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dsysv) Computes the solution to a **real symmetric** system of linear equations.\n", - "* [library.lapacklin.dspsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dspsv) Computes the solution to a **real symmetric** system of linear equations, **packed storage**.\n", - "* [library.lapacklin.dpbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dpbsv) Computes the solution to a **real symmetric positive definite banded** system of linear equations.\n", - "* [library.lapacklin.dposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dposv) Computes the solution to a **real symmetric positive definite** system of linear equations.\n", - "* [library.lapacklin.dppsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dppsv) Computes the solution to a **real symmetric** positive definite system of linear equations, **packed storage**.\n", - "* [library.lapacklin.dsposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dsposv) Computes the solution to a **real symmetric positive definite** system of linear equations using **mixed precision arithmetic**.\n", - "* [library.lapacklin.dptsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dptsv) Computes the solution to a **real symmetric positive definite tridiagonal** system of linear equations.\n", - "* [library.lapacklin.dtbtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dtbtrs) Solution of **real band triangular** system of linear equations, **multiple right-hand sides**.\n", - "* [library.lapacklin.dtrtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dtrtrs) Solution of **real triangular** system of **linear equations, multiple right-hand sides**.\n", - "* [library.lapacklin.dtptrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dtptrs) Solution of **real triangular** system of linear equations, **multiple right-hand sides, packed storage**.\n", - "* [library.lapacklin.dgtsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.dgtsv) Computes the solution to a **real tridiagonal** system of linear equations.\n", + "* [library.linsys.real_toeplitz_solve](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.linsys.real_toeplitz_solve.html) Solution of **real symmetric positive definite Toeplitz** system of linear equations.\n", + "* [library.lapacklin.dgbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dgbsv.html) Computes the solution to a **real banded** system of linear equations.\n", + "* [library.lapacklin.dsgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dsgesv.html) Computes the solution to a **real** system of linear equations using **mixed precision arithmetic**.\n", + "* [library.lapacklin.dsysv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dsysv.html) Computes the solution to a **real symmetric** system of linear equations.\n", + "* [library.lapacklin.dspsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dspsv.html) Computes the solution to a **real symmetric** system of linear equations, **packed storage**.\n", + "* [library.lapacklin.dpbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dpbsv.html) Computes the solution to a **real symmetric positive definite banded** system of linear equations.\n", + "* [library.lapacklin.dposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dposv.html) Computes the solution to a **real symmetric positive definite** system of linear equations.\n", + "* [library.lapacklin.dppsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dppsv.html) Computes the solution to a **real symmetric** positive definite system of linear equations, **packed storage**.\n", + "* [library.lapacklin.dsposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dsposv.html) Computes the solution to a **real symmetric positive definite** system of linear equations using **mixed precision arithmetic**.\n", + "* [library.lapacklin.dptsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dptsv.html) Computes the solution to a **real symmetric positive definite tridiagonal** system of linear equations.\n", + "* [library.lapacklin.dtbtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dtbtrs.html) Solution of **real band triangular** system of linear equations, **multiple right-hand sides**.\n", + "* [library.lapacklin.dtrtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dtrtrs.html) Solution of **real triangular** system of **linear equations, multiple right-hand sides**.\n", + "* [library.lapacklin.dtptrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dtptrs.html) Solution of **real triangular** system of linear equations, **multiple right-hand sides, packed storage**.\n", + "* [library.lapacklin.dgtsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dgtsv.html) Computes the solution to a **real tridiagonal** system of linear equations.\n", "\n", "### Complex matrices\n", "\n", - "* [library.lapacklin.zgbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zgbsv) Computes the solution to a **complex banded** system of linear equations.\n", - "* [library.lapacklin.zhesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zhesv) Computes the solution to a **complex Hermitian** system of linear equations.\n", - "* [library.lapacklin.zhpsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zhpsv) Computes the solution to **complex Hermitian** of linear equations, **packed storage.**\n", - "* [library.lapacklin.zpbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zpbsv) Computes the solution to a **complex Hermitian positive definite banded** system of linear equations.\n", - "* [library.lapacklin.zposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zposv) Computes the solution to a **complex Hermitian positive definite** system of linear equations.\n", - "* [library.lapacklin.zppsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zppsv) Computes the solution to a **complex Hermitian positive definite** system of linear equations, **packed storage**.\n", - "* [library.lapacklin.zcposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zcposv) Computes the solution to a **complex Hermitian positive definite** system of linear equations using **mixed precision** arithmetic.\n", - "* [library.lapacklin.zptsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zptsv) Computes the solution to a **complex Hermitian positive definite tridiagonal** system of linear equations.\n", - "* [library.lapacklin.zgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zgesv) Computes the solution to a **complex** system of linear equations.\n", - "* [library.lapacklin.zcgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zcgesv) Computes the solution to a **complex** system of linear equations using **mixed precision** arithmetic.\n", - "* [library.lapacklin.zsysv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zsysv) Computes the solution to a **complex symmetric** system of linear equations. \n", - "* [library.lapacklin.zspsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zspsv) Computes the solution to a **complex symmetric** system of linear equations, **packed storage**.\n", - "* [ibrary.lapacklin.ztbtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.ztbtrs) Solution of **complex band triangular** system of linear equations, **multiple right-hand sides**.\n", - "* [library.lapacklin.ztrtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.ztrtrs) Solution of **complex triangular** system of linear equations, **multiple right-hand sides**.\n", - "* [library.lapacklin.ztptrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.ztptrs) Solution of **complex triangular** system of linear equations, **multiple right-hand sides**, **packed storage**.\n", - "* [library.lapacklin.zgtsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.html#naginterfaces.library.lapacklin.zgtsv) Computes the solution to a **complex tridiagonal** system of linear equations.\n" + "* [library.lapacklin.zgbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zgbsv.html) Computes the solution to a **complex banded** system of linear equations.\n", + "* [library.lapacklin.zhesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zhesv.html) Computes the solution to a **complex Hermitian** system of linear equations.\n", + "* [library.lapacklin.zhpsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zhpsv.html) Computes the solution to **complex Hermitian** of linear equations, **packed storage.**\n", + "* [library.lapacklin.zpbsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zpbsv.html) Computes the solution to a **complex Hermitian positive definite banded** system of linear equations.\n", + "* [library.lapacklin.zposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zposv.html) Computes the solution to a **complex Hermitian positive definite** system of linear equations.\n", + "* [library.lapacklin.zppsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zppsv.html) Computes the solution to a **complex Hermitian positive definite** system of linear equations, **packed storage**.\n", + "* [library.lapacklin.zcposv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zcposv.html) Computes the solution to a **complex Hermitian positive definite** system of linear equations using **mixed precision** arithmetic.\n", + "* [library.lapacklin.zptsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zptsv.html) Computes the solution to a **complex Hermitian positive definite tridiagonal** system of linear equations.\n", + "* [library.lapacklin.zgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zgesv.html) Computes the solution to a **complex** system of linear equations.\n", + "* [library.lapacklin.zcgesv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zcgesv.html) Computes the solution to a **complex** system of linear equations using **mixed precision** arithmetic.\n", + "* [library.lapacklin.zsysv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zsysv.html) Computes the solution to a **complex symmetric** system of linear equations. \n", + "* [library.lapacklin.zspsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zspsv.html) Computes the solution to a **complex symmetric** system of linear equations, **packed storage**.\n", + "* [ibrary.lapacklin.ztbtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.ztbtrs.html) Solution of **complex band triangular** system of linear equations, **multiple right-hand sides**.\n", + "* [library.lapacklin.ztrtrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.ztrtrs.html) Solution of **complex triangular** system of linear equations, **multiple right-hand sides**.\n", + "* [library.lapacklin.ztptrs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.ztptrs.html) Solution of **complex triangular** system of linear equations, **multiple right-hand sides**, **packed storage**.\n", + "* [library.lapacklin.zgtsv](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.zgtsv.html) Computes the solution to a **complex tridiagonal** system of linear equations.\n" ] } ], @@ -254,7 +254,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/local_optimization/DFO_noisy.ipynb b/local_optimization/DFO_noisy.ipynb index d82e08b..750f9ce 100644 --- a/local_optimization/DFO_noisy.ipynb +++ b/local_optimization/DFO_noisy.ipynb @@ -334,7 +334,7 @@ " opt.handle_opt_set(handle, optstr)\n", " # Call the solver\n", " try:\n", - " _ = opt.handle_solve_dfno(handle, objfun, xstart, data=data, io_manager=iom)\n", + " _ = opt.handle_solve_dfno(handle, xstart, objfun=objfun, data=data, io_manager=iom)\n", " except utils.NagCallbackTerminateWarning as _e:\n", " pass\n", " # print results\n", @@ -548,7 +548,7 @@ "text": [ "Help on function handle_solve_dfno in module naginterfaces.library.opt:\n", "\n", - "handle_solve_dfno(handle, objfun, x, monit=None, data=None, io_manager=None)\n", + "handle_solve_dfno(handle, x, objfun=None, monit=None, data=None, io_manager=None)\n", " Direct communication derivative-free (DFO) solver for a nonlinear\n", " objective function with bounded variables.\n", " \n", @@ -563,19 +563,32 @@ " For full information please refer to the NAG Library document for\n", " e04jd\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04jdf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04jdf.html\n", " \n", " Parameters\n", " ----------\n", " handle : Handle\n", - " The handle to the problem. It needs to be initialized by\n", - " ``handle_init`` and **must not** be changed before the call to\n", - " ``handle_solve_dfno``.\n", + " The handle to the problem. It needs to be initialized (e.g., by\n", + " ``handle_init``) and to hold a problem formulation compatible\n", + " with ``handle_solve_dfno``. It **must not** be changed between\n", + " calls to the NAG optimization modelling suite.\n", + " \n", + " x : float, array-like, shape (nvar)\n", + " x_0, the initial estimates of the variables, x.\n", + " \n", + " objfun : None or callable (fx, inform) = objfun(x, inform,\n", + " data=None), optional\n", + " Note: if this argument is None then a NAG-supplied facility will\n", + " be used.\n", " \n", - " objfun : callable (fx, inform) = objfun(x, inform, data=None)\n", " `objfun` calculates the value of the objective function f(x) at\n", " a specified point x.\n", " \n", + " If there is no nonlinear objective (e.g., ``handle_set_linobj``\n", + " or ``handle_set_quadobj`` was called to define a linear or\n", + " quadratic objective function), `objfun` will never be called by\n", + " ``handle_solve_dfno`` and may be None.\n", + " \n", " Parameters\n", " ~~~~~~~~~~\n", " x : float, ndarray, shape (nvar)\n", @@ -610,9 +623,6 @@ " return the best available point as well as the solve\n", " statistics.\n", " \n", - " x : float, array-like, shape (nvar)\n", - " x_0, the initial estimates of the variables x.\n", - " \n", " monit : None or callable monit(x, rinfo, stats, data=None), optional\n", " Note: if this argument is None then a NAG-supplied facility will\n", " be used.\n", @@ -653,7 +663,7 @@ " Returns\n", " -------\n", " x : float, ndarray, shape (nvar)\n", - " The final values of the variables x.\n", + " The final values of the variables, x.\n", " \n", " rinfo : float, ndarray, shape (100)\n", " Optimal objective value and various indicators at monitoring\n", @@ -997,11 +1007,10 @@ " The problem is already being solved.\n", " \n", " (`errno` 4)\n", - " The information supplied does not match with that previously\n", - " stored.\n", + " On entry, nvar = **, expected value = **.\n", " \n", - " On entry, nvar = ** must match that given during\n", - " initialization of the `handle`, i.e., **.\n", + " Constraint: nvar must match the current number of variables\n", + " of the model in the `handle`.\n", " \n", " (`errno` 5)\n", " Inconsistent options 'DFO Trust Region Tolerance' rho_end\n", @@ -1043,6 +1052,9 @@ " Growing the interpolation set is not supported for this\n", " solver.\n", " \n", + " (`errno` 7)\n", + " Please provide a proper `objfun` function.\n", + " \n", " Warns\n", " -----\n", " NagAlgorithmicWarning\n", @@ -1106,6 +1118,74 @@ " (`errno` 20)\n", " User requested termination during a monitoring step.\n", " \n", + " Notes\n", + " -----\n", + " ``handle_solve_dfno`` is aimed at minimizing a nonlinear objective\n", + " function subject to bound constraints:\n", + " \n", + " [table omitted]\n", + " \n", + " Here f is a smooth nonlinear function and l_x and u_x are\n", + " n-dimensional vectors defining bounds on the variables.\n", + " \n", + " ``handle_solve_dfno`` serves as a solver for compatible problems\n", + " stored as a handle.\n", + " The handle points to an internal data structure which defines the\n", + " problem and serves as a means of communication for functions in the\n", + " NAG optimization modelling suite.\n", + " To define a compatible problem handle, you must call ``handle_init``\n", + " followed by ``handle_set_nlnobj`` to initialize it and optionally\n", + " call ``handle_set_simplebounds`` to define bounds on the variables.\n", + " If ``handle_set_simplebounds`` is not called, all the variables will\n", + " be considered free by the solver.\n", + " It should be noted that ``handle_solve_dfno`` always assumes that\n", + " the gradient of the objective is dense, therefore, defining a sparse\n", + " structure for the residuals in the call to ``handle_set_nlnobj``\n", + " will have no effect.\n", + " See [the E04 Introduction] for more details about the NAG\n", + " optimization modelling suite.\n", + " \n", + " The solver allows fixing variables with the definition of the\n", + " bounds.\n", + " However, the following constraint must be met in order to be able to\n", + " call the solver:\n", + " \n", + " for all non-fixed variable x_i, the value of u_x(i)-l_x(i) must\n", + " be at least twice the starting trust region radius (see the\n", + " consistency constraint of the option 'DFO Starting Trust\n", + " Region').\n", + " \n", + " The solver is based on a derivative-free trust region framework.\n", + " This type of method is well suited for small to medium-scale\n", + " problems (around 100 variables) for which the derivatives are\n", + " unavailable or not easy to compute, and/or for which the function\n", + " evaluations are expensive or noisy.\n", + " For a detailed description of the algorithm see [Algorithmic\n", + " Details].\n", + " \n", + " The algorithm behaviour and solver strategy can be modified by\n", + " various options (see [Other Parameters]) which can be set by\n", + " ``handle_opt_set`` and ``handle_opt_set_file`` at any time between\n", + " the initialization of the handle by ``handle_init`` and a call to\n", + " the solver.\n", + " The options' names specific for this solver start either with the\n", + " prefix DFO (Derivative-free Optimization) or DFNO (Derivative-free\n", + " Nonlinear Optimization).\n", + " The default values for these options are chosen to work well in the\n", + " general case, but it is recommended you tune them to your particular\n", + " problem.\n", + " In particular, if the objective function is known to be noisy, it is\n", + " highly recommended to set the option 'DFO Noisy Problem' to 'YES'.\n", + " Once the solver has finished, options may be modified for the next\n", + " solve.\n", + " The solver may be called repeatedly with various starting points\n", + " and/or options.\n", + " \n", + " The underlying algorithm implemented for ``handle_solve_dfno`` is\n", + " the same as the one used by ``handle_solve_dfno_rcomm``.\n", + " ``handle_solve_dfno`` serves as a forward communication interface to\n", + " the derivative-free solver for nonlinear objective functions.\n", + " \n", " References\n", " ----------\n", " Cartis, C, Fiala, J, Marteau, B and Roberts, L, 2018, `Improving the\n", @@ -1159,7 +1239,7 @@ " For full information please refer to the NAG Library document for\n", " e04jy\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04jyf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04jyf.html\n", " \n", " Parameters\n", " ----------\n", @@ -1358,6 +1438,72 @@ " No equivalent traditional C interface for this routine exists in the\n", " NAG Library.\n", " \n", + " ``bounds_quasi_func_easy`` is applicable to problems of the form:\n", + " \n", + " MinimizeF(x_1,x_2,...,x_n) subject to l_j <= x_j <= u_j, j =\n", + " 1,2,...,n\n", + " \n", + " when derivatives of F(x) are unavailable.\n", + " \n", + " Special provision is made for problems which actually have no bounds\n", + " on the x_j, problems which have only non-negativity bounds and\n", + " problems in which l_1 = l_2 = ... = l_n and u_1 = u_2 = ... = u_n.\n", + " You must supply a function to calculate the value of F(x) at any\n", + " point x.\n", + " \n", + " From a starting point you supplied there is generated, on the basis\n", + " of estimates of the gradient and the curvature of F(x), a sequence\n", + " of feasible points which is intended to converge to a local minimum\n", + " of the constrained function.\n", + " An attempt is made to verify that the final point is a minimum.\n", + " \n", + " A typical iteration starts at the current point x where n_z (say)\n", + " variables are free from both their bounds.\n", + " The projected gradient vector g_z, whose elements are finite\n", + " difference approximations to the derivatives of F(x) with respect to\n", + " the free variables, is known.\n", + " A unit lower triangular matrix L and a diagonal matrix D (both of\n", + " dimension n_z), such that LDL^T is a positive definite approximation\n", + " of the matrix of second derivatives with respect to the free\n", + " variables (i.e., the projected Hessian) are also held.\n", + " The equations\n", + " \n", + " LDL^Tp_z = -g_z\n", + " \n", + " are solved to give a search direction p_z, which is expanded to an\n", + " n-vector p by an insertion of appropriate zero elements.\n", + " Then alpha is found such that F(x+alpha p) is approximately a\n", + " minimum (subject to the fixed bounds) with respect to alpha; x is\n", + " replaced by x+alpha p, and the matrices L and D are updated so as to\n", + " be consistent with the change produced in the estimated gradient by\n", + " the step alpha p.\n", + " If any variable actually reaches a bound during the search along p,\n", + " it is fixed and n_z is reduced for the next iteration.\n", + " Most iterations calculate g_z using forward differences, but central\n", + " differences are used when they seem necessary.\n", + " \n", + " There are two sets of convergence criteria -- a weaker and a\n", + " stronger.\n", + " Whenever the weaker criteria are satisfied, the Lagrange multipliers\n", + " are estimated for all the active constraints.\n", + " If any Lagrange multiplier estimate is significantly negative, then\n", + " one of the variables associated with a negative Lagrange multiplier\n", + " estimate is released from its bound and the next search direction is\n", + " computed in the extended subspace (i.e., n_z is increased).\n", + " Otherwise minimization continues in the current subspace provided\n", + " that this is practicable.\n", + " When it is not, or when the stronger convergence criteria are\n", + " already satisfied, then, if one or more Lagrange multiplier\n", + " estimates are close to zero, a slight perturbation is made in the\n", + " values of the corresponding variables in turn until a lower function\n", + " value is obtained.\n", + " The normal algorithm is then resumed from the perturbed point.\n", + " \n", + " If a saddle point is suspected, a local search is carried out with a\n", + " view to moving away from the saddle point.\n", + " A local search is also performed when a point is found which is\n", + " thought to be a constrained minimum.\n", + " \n", " References\n", " ----------\n", " Gill, P E and Murray, W, 1976, `Minimization subject to bounds on\n", @@ -1387,7 +1533,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index b801136..55d4b0d 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -33,14 +33,15 @@ "metadata": {}, "outputs": [], "source": [ - "objfun = lambda x, _inform: (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", + "objfun = lambda x, inform: ((1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2, inform)\n", "\n", - "def objgrd(x, fdx, _inform):\n", + "def objgrd(x, fdx, inform):\n", " \"\"\"The objective's gradient.\"\"\"\n", " fdx[:] = [\n", " 2.*x[0] - 400.*x[0]*(x[1]-x[0]**2) - 2.,\n", " 200.*(x[1]-x[0]**2),\n", " ]\n", + " return inform\n", "\n", "\n", "steps = []\n", @@ -160,9 +161,11 @@ "name": "stdout", "output_type": "stream", "text": [ - " -------------------------------------------------------------------------------\n", + "\n", + " ----------------------------------------------------------\n", " E04KF, First order method for bound-constrained problems\n", - " -------------------------------------------------------------------------------\n", + " ----------------------------------------------------------\n", + "\n", " Begin of Options\n", " Print File = 9 * d\n", " Print Level = 2 * U\n", @@ -191,14 +194,12 @@ " Foas Tolerance Norm = Infinity * d\n", " End of Options\n", "\n", - " Problem statistics\n", - " Number of variables 2\n", - " Number of free variables 0\n", - " Number of fixed variables 0\n", - " Number of variables with only lower bound 0\n", - " Number of variables with only upper bound 0\n", - " Number of variables with bounds 2\n", - " Objective type Nonlinear\n", + " Problem Statistics\n", + " No of variables 2\n", + " free (unconstrained) 0\n", + " bounded 2\n", + " Objective function Nonlinear\n", + "\n", "\n", " -------------------------------------------------------------------------------\n", " iters | objective | optim | dir\n", @@ -221,47 +222,51 @@ " 15 1.12429E+00 2.33E+00 2.01E+00\n", " 16 1.01998E+00 5.04E+00 2.02E+00\n", " 17 8.94996E-01 8.97E+00 2.02E+00\n", - " 18 7.06235E-01 1.32E+00 1.11E+00\n", - " 19 5.06072E-01 5.09E+00 1.91E+00\n", + " 18 7.06184E-01 1.32E+00 1.10E+00\n", + " 19 5.06340E-01 5.11E+00 1.91E+00\n", " -------------------------------------------------------------------------------\n", " iters | objective | optim | dir\n", " -------------------------------------------------------------------------------\n", - " 20 3.18869E-01 9.51E-01 3.65E-01\n", - " 21 2.98131E-01 1.03E+00 1.03E+00\n", - " 22 2.48807E-01 2.90E+00 1.74E+00\n", - " 23 2.10033E-01 5.38E+00 1.65E+00\n", - " 24 1.19320E-01 1.40E+00 5.40E-01\n", - " 25 8.38051E-02 4.97E+00 1.77E+00\n", - " 26 6.45222E-02 8.65E-01 8.65E-01\n", - " 27 5.31881E-02 6.17E-01 6.17E-01\n", - " 28 4.20831E-02 7.71E-01 7.71E-01\n", - " 29 4.04842E-02 4.40E-01 4.40E-01\n", - " 30 4.04842E-02 4.40E-01 4.40E-01\n", - " 31 4.01532E-02 2.48E-01 2.48E-01\n", - " 32 4.01532E-02 2.48E-01 2.48E-01\n", - " 33 4.00000E-02 0.00E+00 0.00E+00\n", + " 20 3.21115E-01 1.03E+00 3.67E-01\n", + " 21 2.99551E-01 9.31E-01 9.31E-01\n", + " 22 2.51003E-01 2.68E+00 1.75E+00\n", + " 23 2.14196E-01 4.82E+00 1.66E+00\n", + " 24 1.15236E-01 1.17E+00 3.70E-01\n", + " 25 8.06733E-02 1.98E+00 1.73E+00\n", + " 26 6.60815E-02 4.33E+00 1.79E+00\n", + " 27 5.37636E-02 3.33E+00 1.80E+00\n", + " 28 4.02960E-02 3.44E-01 3.44E-01\n", + " 29 4.02960E-02 3.44E-01 3.44E-01\n", + " 30 4.00937E-02 1.94E-01 1.94E-01\n", + " 31 4.00937E-02 1.94E-01 1.94E-01\n", + " 32 4.00000E-02 0.00E+00 0.00E+00\n", " -------------------------------------------------------------------------------\n", " Status: converged, an optimal solution was found\n", " -------------------------------------------------------------------------------\n", " Value of the objective 4.00000E-02\n", " Norm of inactive gradient 0.00000E+00\n", " Norm of projected direction 0.00000E+00\n", - " Iterations 33\n", - " Function evaluations 80\n", + " Iterations 32\n", + " Function evaluations 75\n", " FD func. evaluations 0\n", - " Gradient evaluations 40\n", + " Gradient evaluations 36\n", " NPG function calls 18\n", " NPG gradient calls 3\n", " CG function calls 9\n", " CG gradient calls 5\n", - " LCG function calls 53\n", - " LCG gradient calls 32\n", + " LCG function calls 48\n", + " LCG gradient calls 28\n", " -------------------------------------------------------------------------------\n", "\n", - " Variables:\n", - " idx lower bound value upper bound gradient\n", - " 1 -1.00000E+00 8.00000E-01 8.00000E-01 -4.00000E-01\n", - " 2 -2.00000E+00 6.40000E-01 2.00000E+00 0.00000E+00\n" + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -1.00000E+00 8.00000E-01 8.00000E-01\n", + " 2 -2.00000E+00 6.40000E-01 2.00000E+00\n", + "\n", + " Box bounds dual variables:\n", + " idx Lower bound Value Upper bound Value\n", + " 1 -1.00000E+00 0.00000E+00 8.00000E-01 4.00000E-01\n", + " 2 -2.00000E+00 0.00000E+00 2.00000E+00 0.00000E+00\n" ] } ], @@ -334,7 +339,7 @@ "j = y_m[0]\n", "for i in range(0, 101):\n", " for j in range(0, 101):\n", - " z_m[i, j] = objfun([x_m[i], y_m[j]], 0)\n", + " z_m[i, j], _inform = objfun([x_m[i], y_m[j]], 1)\n", "nb = 25\n", "x_box = np.linspace(bl[0], bu[0], nb)\n", "y_box = np.linspace(bl[1], bu[1], nb)\n", @@ -342,7 +347,7 @@ " np.concatenate([bl[1]*np.ones(nb), y_box, bu[1]*np.ones(nb), y_box[::-1]])])\n", "z_box = np.empty(box[0].shape)\n", "for i in range(0, (box[0].size)):\n", - " z_box[i] = objfun([box[0][i], box[1][i]], 0)\n", + " z_box[i], _inform = objfun([box[0][i], box[1][i]], 1)\n", "\n", "X, Y = np.meshgrid(x_m, y_m, indexing='ij')" ] @@ -432,7 +437,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/LP_demo.ipynb b/local_optimization/LP_demo.ipynb index 7aec8b5..99bd3d4 100644 --- a/local_optimization/LP_demo.ipynb +++ b/local_optimization/LP_demo.ipynb @@ -187,40 +187,39 @@ " Lpipm System Formulation = Auto * d\n", " End of Options\n", "\n", - " Original Problem Statistics\n", + " Problem Statistics\n", + " No of variables 5\n", + " free (unconstrained) 0\n", + " bounded 5\n", + " No of lin. constraints 4\n", + " nonzeroes 12\n", + " Objective function Linear\n", "\n", - " Number of variables 5\n", - " Number of constraints 4\n", - " Free variables 0\n", - " Number of nonzeros 12\n", - "\n", - "\n", - " Presolved Problem Statistics\n", - "\n", - " Number of variables 9\n", - " Number of constraints 4\n", - " Free variables 0\n", - " Number of nonzeros 16\n", + " Presolved Problem Measures\n", + " No of variables 9\n", + " free (unconstrained) 0\n", + " No of lin. constraints 4\n", + " nonzeroes 16\n", "\n", "\n", " ------------------------------------------------------------------------------\n", " it| pobj | dobj | optim | feas | compl | mu | mcc | I\n", " ------------------------------------------------------------------------------\n", - " 0 2.95739E-01 -2.29831E-17 2.38E+00 1.58E-01 2.38E-01 2.9E-01\n", + " 0 2.95739E-01 -1.53220E-17 2.38E+00 1.58E-01 2.38E-01 2.9E-01\n", " 1 3.82786E-02 -2.79688E-01 3.71E-02 6.98E-17 1.91E-02 2.0E-02 0\n", " 2 1.00015E-02 -5.05058E-03 1.88E-03 1.29E-14 9.30E-04 9.4E-04 0\n", - " 3 1.78344E-05 -2.39954E-05 1.86E-16 1.48E-15 2.19E-06 2.2E-06 0\n", - " 4 8.91734E-09 -1.19978E-08 8.80E-17 2.79E-16 1.09E-09 1.1E-09 0\n", - " 5 4.45867E-12 -5.99890E-12 8.35E-17 4.48E-16 5.46E-13 5.5E-13 0\n", + " 3 1.78344E-05 -2.39954E-05 1.83E-16 1.48E-15 2.19E-06 2.2E-06 0\n", + " 4 8.91734E-09 -1.19978E-08 9.23E-17 2.78E-16 1.09E-09 1.1E-09 0\n", + " 5 4.45867E-12 -5.99890E-12 9.02E-17 5.83E-17 5.46E-13 5.5E-13 0\n", " ------------------------------------------------------------------------------\n", " Status: converged, an optimal solution found\n", " ------------------------------------------------------------------------------\n", " Final primal objective value 4.458673E-12\n", " Final dual objective value -5.998898E-12\n", - " Absolute primal infeasibility 2.355139E-16\n", - " Relative primal infeasibility 8.352537E-17\n", - " Absolute dual infeasibility 7.761642E-16\n", - " Relative dual infeasibility 4.476207E-16\n", + " Absolute primal infeasibility 2.543841E-16\n", + " Relative primal infeasibility 5.826594E-17\n", + " Absolute dual infeasibility 1.010318E-16\n", + " Relative dual infeasibility 9.021771E-17\n", " Absolute complementarity gap 2.464120E-12\n", " Relative complementarity gap 5.464522E-13\n", " Iterations 5\n" @@ -268,7 +267,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/local_optimization/SDP/NCM_SDP.ipynb b/local_optimization/SDP/NCM_SDP.ipynb index f2532b9..7c2bff2 100644 --- a/local_optimization/SDP/NCM_SDP.ipynb +++ b/local_optimization/SDP/NCM_SDP.ipynb @@ -220,14 +220,25 @@ "name": "stdout", "output_type": "stream", "text": [ - " E04SV, NLP-SDP Solver (Pennon)\n", - " ------------------------------\n", - " Number of variables 3 [eliminated 0]\n", - " simple linear nonlin\n", - " (Standard) inequalities 0 0 0\n", - " (Standard) equalities 0 0\n", - " Matrix inequalities 1 0 [dense 1, sparse 0]\n", - " [max dimension 4]\n", + "\n", + " --------------------------------\n", + " E04SV, NLP-SDP Solver (Pennon)\n", + " --------------------------------\n", + "\n", + " Problem Statistics\n", + " No of variables 3\n", + " bounds not defined\n", + " No of lin. constraints 0\n", + " nonzeroes 0\n", + " No of matrix inequal. 1\n", + " detected matrix inq. 1\n", + " linear 1\n", + " nonlinear 0\n", + " max. dimension 4\n", + " detected normal inq. 0\n", + " linear 0\n", + " nonlinear 0\n", + " Objective function Quadratic\n", "\n", " --------------------------------------------------------------\n", " it| objective | optim | feas | compl | pen min |inner\n", @@ -428,28 +439,29 @@ " ``handle_opt_set``, ``handle_opt_get``.\n", " \n", " ``handle_solve_pennon`` is a solver from the NAG optimization\n", - " modelling suite for problems such as, quadratic programming (QP),\n", - " linear semidefinite programming (SDP) and semidefinite programming\n", + " modelling suite for problems such as, Quadratic Programming (QP),\n", + " linear Semidefinite Programming (SDP) and semidefinite programming\n", " with bilinear matrix inequalities (BMI-SDP).\n", " \n", " For full information please refer to the NAG Library document for\n", " e04sv\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04svf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04svf.html\n", " \n", " Parameters\n", " ----------\n", " handle : Handle\n", - " The handle to the problem. It needs to be initialized by\n", - " ``handle_init`` and **must not** be changed before the call to\n", - " ``handle_solve_pennon``.\n", + " The handle to the problem. It needs to be initialized (e.g., by\n", + " ``handle_init``) and to hold a problem formulation compatible\n", + " with ``handle_solve_pennon``. It **must not** be changed between\n", + " calls to the NAG optimization modelling suite.\n", " \n", " x : float, array-like, shape (nvar)\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", " > 0.\n", " \n", " If 'Initial X' = 'USER' (the default), x^0, the initial estimate\n", - " of the variables x, otherwise `x` need not be set.\n", + " of the variables x; otherwise, `x` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -461,7 +473,7 @@ " \n", " `On intermediate entry`: if set to 0, solving the current\n", " problem is terminated and the function returns `errno` = 20;\n", - " otherwise the function continues.\n", + " otherwise, the function continues.\n", " \n", " u : None or float, array-like, shape (nnzu), optional\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", @@ -477,7 +489,7 @@ " Note: if nnzu = 0, `u` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), u^0, the\n", - " initial estimate of the Lagrangian multipliers u, otherwise `u`\n", + " initial estimate of the Lagrangian multipliers u; otherwise, `u`\n", " need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", @@ -500,8 +512,8 @@ " If nnzua = 0, `ua` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), U^0, the\n", - " initial estimate of the matrix Lagrangian multipliers U,\n", - " otherwise `ua` need not be set.\n", + " initial estimate of the matrix Lagrangian multipliers U;\n", + " otherwise, `ua` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -722,7 +734,7 @@ " Constraint: 'Inner Stop Criteria' = 'HEURISTIC' or 'STRICT'.\n", " \n", " 'Inner Stop Tolerance' : float\n", - " Default = 10^(-2)\n", + " Default = 10^-2\n", " \n", " This option sets the required precision alpha^0 for the first\n", " inner problem solved by [Algorithm 2].\n", @@ -836,7 +848,7 @@ " reaching the requested accuracy on the feasibility.\n", " Under normal circumstances, the default value is recommended.\n", " \n", - " Constraint: epsilon <= 'P Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'P Min' <= 10^-2.\n", " \n", " 'Pmat Min' : float\n", " Default = sqrt(epsilon)\n", @@ -845,7 +857,7 @@ " option P_min.\n", " The same advice applies.\n", " \n", - " Constraint: epsilon <= 'Pmat Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'Pmat Min' <= 10^-2.\n", " \n", " 'Preference' : str\n", " Default = 'SPEED'\n", @@ -951,7 +963,7 @@ " Constraint: 'Stop Criteria' = 'SOFT' or 'STRICT'.\n", " \n", " 'Stop Tolerance 1' : float\n", - " Default = max(10^(-6), sqrt(epsilon))\n", + " Default = max(10^-6, sqrt(epsilon))\n", " \n", " This option defines epsilon_1 used as a tolerance for the\n", " relative duality gap (0) and the relative precision (1), see\n", @@ -960,7 +972,7 @@ " Constraint: 'Stop Tolerance 1' > epsilon.\n", " \n", " 'Stop Tolerance 2' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This option sets the value epsilon_2 which is used for\n", " optimality (2) and complementarity (4) tests from KKT conditions\n", @@ -971,7 +983,7 @@ " Constraint: 'Stop Tolerance 2' > epsilon.\n", " \n", " 'Stop Tolerance Feasibility' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This argument places an acceptance limit on the feasibility of\n", " the solution (3), epsilon_feas.\n", @@ -1053,17 +1065,14 @@ " This solver does not support the model defined in the\n", " handle.\n", " \n", - " (`errno` 2)\n", - " This solver does not support fixed variables.\n", - " \n", " (`errno` 3)\n", - " A different solver from the suite has already been used.\n", + " The problem is already being solved.\n", " \n", " (`errno` 4)\n", " On entry, nvar = **, expected value = **.\n", " \n", - " Constraint: nvar must match the value given during\n", - " initialization of `handle`.\n", + " Constraint: nvar must match the current number of variables\n", + " of the model in the `handle`.\n", " \n", " (`errno` 5)\n", " On entry, nnzu = **.\n", @@ -1108,25 +1117,6 @@ " (`errno` 21)\n", " The current starting point is unusable.\n", " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Inner iteration limit has been reached.\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Limited progress in the inner subproblem triggered a stop\n", - " (heuristic inner stop criteria).\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Line search or another internal component failed.\n", - " \n", " (`errno` 51)\n", " The problem was found to be infeasible during preprocessing.\n", " \n", @@ -1159,9 +1149,187 @@ " \n", " The requested accuracy is not achieved.\n", " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Inner iteration limit has been reached.\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Limited progress in the inner subproblem triggered a stop\n", + " (heuristic inner stop criteria).\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Line search or another internal component failed.\n", + " \n", " (`errno` 24)\n", " Unable to make progress, the algorithm was stopped.\n", " \n", + " Notes\n", + " -----\n", + " ``handle_solve_pennon`` serves as a solver for compatible problems\n", + " stored as a handle.\n", + " The handle points to an internal data structure which defines the\n", + " problem and serves as a means of communication for functions in the\n", + " NAG optimization modelling suite.\n", + " First, the problem handle is initialized by calling ``handle_init``.\n", + " Then some of the functions ``handle_set_linobj``,\n", + " ``handle_set_quadobj``, ``handle_set_simplebounds``,\n", + " ``handle_set_linconstr``, ``handle_set_linmatineq`` or\n", + " ``handle_set_quadmatineq`` may be used to formulate the objective\n", + " function, (standard) constraints and matrix constraints of the\n", + " problem.\n", + " Once the problem is fully set, the handle may be passed to the\n", + " solver.\n", + " When the handle is no longer needed, ``handle_free`` should be\n", + " called to destroy it and deallocate the memory held within.\n", + " See [the E04 Introduction] for more details about the NAG\n", + " optimization modelling suite.\n", + " \n", + " Problems which can be defined this way are, for example, (generally\n", + " nonconvex) Quadratic Programming (QP)\n", + " \n", + " [table omitted]\n", + " \n", + " linear semidefinite programming problems (SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " or semidefinite programming problems with bilinear matrix\n", + " inequalities (BMI-SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " Here c, l_x and u_x are n-dimensional vectors, H is a symmetric n*n\n", + " matrix, l_B, u_B are m_B-dimensional vectors, B is a general m_B*n\n", + " rectangular matrix and A_i^k, Q_ij^k are symmetric matrices.\n", + " The expression S⪰0 stands for a constraint on eigenvalues of a\n", + " symmetric matrix S, namely, all the eigenvalues should be\n", + " non-negative, i.e., the matrix should be positive semidefinite.\n", + " See relevant functions in the suite for more details on the problem\n", + " formulation.\n", + " \n", + " The solver is based on a generalized Augmented Lagrangian method\n", + " with a suitable choice of standard and matrix penalty functions.\n", + " For a detailed description of the algorithm see [Algorithmic\n", + " Details].\n", + " Under standard assumptions on the problem (Slater constraint\n", + " qualification, boundedness of the objective function on the feasible\n", + " set, see Stingl (2006) for details) the algorithm converges to a\n", + " local solution.\n", + " In case of convex problems such as linear SDP or convex QP, this is\n", + " the global solution.\n", + " The solver is suitable for both small dense and large-scale sparse\n", + " problems.\n", + " \n", + " The algorithm behaviour and solver strategy can be modified by\n", + " various options (see [Other Parameters]) which can be set by\n", + " ``handle_opt_set`` and ``handle_opt_set_file`` anytime between the\n", + " initialization of the handle by ``handle_init`` and a call to the\n", + " solver.\n", + " Once the solver has finished, options may be modified for the next\n", + " solve.\n", + " The solver may be called repeatedly with various starting points\n", + " and/or options.\n", + " \n", + " There are several options with a multiple choice where the default\n", + " choice is 'AUTO' (for example, 'Hessian Density').\n", + " This value means that the decision over the option is left to the\n", + " solver based on the structure of the problem.\n", + " Option getter ``handle_opt_get`` can be called to retrieve the\n", + " choice of these options as well as on any other options.\n", + " \n", + " Option 'Task' may be used to switch the problem to maximization or\n", + " to ignore the objective function and find only a feasible point.\n", + " \n", + " Option 'Monitor Frequency' may be used to turn on the monitor mode\n", + " of the solver.\n", + " The solver invoked in this mode pauses regularly even before the\n", + " optimal point is found to allow monitoring the progress from the\n", + " calling program.\n", + " All the important error measures and statistics are available in the\n", + " calling program which may terminate the solver early if desired (see\n", + " argument `inform`).\n", + " \n", + " Structure of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " The algorithm works internally with estimates of both the decision\n", + " variables, denoted by x, and the Lagrangian multipliers (dual\n", + " variables) for standard and matrix constraints, denoted by u and U,\n", + " respectively.\n", + " You may provide initial estimates, request approximations during the\n", + " run (the monitor mode turned on) and obtain the final values.\n", + " The Lagrangian multipliers are split into two arrays, the\n", + " multipliers u for (standard) constraints are stored in array `u` and\n", + " multipliers U for matrix constraints in array `ua`.\n", + " Both arrays need to conform to the structure of the constraints.\n", + " \n", + " If the simple bounds were defined (``handle_set_simplebounds`` was\n", + " successfully called), the first 2n elements of `u` belong to the\n", + " corresponding Lagrangian multipliers, interleaving a multiplier for\n", + " the lower and for the upper bound for each x_i.\n", + " If any of the bounds were set to infinity, the corresponding\n", + " Lagrangian multipliers are set to 0 and may be ignored.\n", + " \n", + " Similarly, the following 2m_B elements of `u` belong to multipliers\n", + " for the linear constraints, if formulated by\n", + " ``handle_set_linconstr``.\n", + " The organization is the same, i.e., the multipliers for each\n", + " constraint for the lower and upper bounds are alternated and zeroes\n", + " are used for any missing (infinite bound) constraint.\n", + " \n", + " A Lagrangian multiplier for a matrix constraint (one block) of\n", + " dimension d*d is a dense symmetric matrix of the same dimension.\n", + " All multipliers U are stored next to each other in array `ua` in the\n", + " same order as the matrix constraints were defined by\n", + " ``handle_set_linmatineq`` and ``handle_set_quadmatineq``.\n", + " The lower triangle of each is stored in the packed column order (see\n", + " [the F07 Introduction]).\n", + " For example, if there are four matrix constraints of dimensions 7,\n", + " 3, 1, 1, the dimension of array `ua` should be 36.\n", + " The first 28 elements (d_1*(d_1+1)/2) belong to the packed lower\n", + " triangle of U_1, followed by six elements of U_2 and one element for\n", + " each U_3 and U_4.\n", + " \n", + " Approximation of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " By the nature of the algorithm, all inequality Lagrangian multiplier\n", + " u,U are always kept positive during the computational process.\n", + " This applies even to Lagrangian multipliers of inactive constraints\n", + " at the solution.\n", + " They will only be close to zero although they would normally be\n", + " equal to zero exactly.\n", + " This is one of the major differences between results from solvers\n", + " based on the active set method (such as ``qpconvex2_sparse_solve``)\n", + " and others, such as, ``handle_solve_pennon`` or interior point\n", + " methods.\n", + " As a consequence, the initial estimate of the multipliers (if\n", + " provided) might be adjusted by the solver to be sufficiently\n", + " positive, also the estimates returned during the intermediate exits\n", + " might only be a very crude approximation to their final values as\n", + " they do not satisfy all the Karush--Kuhn--Tucker (KKT) conditions.\n", + " \n", + " Another difference is that ``qpconvex2_sparse_solve`` merges\n", + " multipliers for both lower and upper inequality into one element\n", + " whose sign determines the inequality because there can be at most\n", + " one active constraint and multiplier for the inactive is exact zero.\n", + " Negative multipliers are associated with the upper bounds and\n", + " positive with the lower bounds.\n", + " On the other hand, ``handle_solve_pennon`` works with both\n", + " multipliers at the same time so they are returned in two elements,\n", + " one for the lower bound, the other for the upper bound (see\n", + " [Structure of the Lagrangian Multipliers]).\n", + " An equivalent result can be achieved by subtracting the upper bound\n", + " multiplier from the lower one.\n", + " This holds even when equalities are interpreted as two inequalities\n", + " (see option 'Transform Constraints').\n", + " \n", " References\n", " ----------\n", " Ben--Tal, A and Zibulevsky, M, 1997, `Penalty/barrier multiplier\n", @@ -1221,7 +1389,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SDP/matrix_completion.ipynb b/local_optimization/SDP/matrix_completion.ipynb index 0f035e9..48d6196 100644 --- a/local_optimization/SDP/matrix_completion.ipynb +++ b/local_optimization/SDP/matrix_completion.ipynb @@ -293,14 +293,25 @@ "name": "stdout", "output_type": "stream", "text": [ - " E04SV, NLP-SDP Solver (Pennon)\n", - " ------------------------------\n", - " Number of variables 196 [eliminated 0]\n", - " simple linear nonlin\n", - " (Standard) inequalities 0 0 0\n", - " (Standard) equalities 0 0\n", - " Matrix inequalities 1 0 [dense 1, sparse 0]\n", - " [max dimension 21]\n", + "\n", + " --------------------------------\n", + " E04SV, NLP-SDP Solver (Pennon)\n", + " --------------------------------\n", + "\n", + " Problem Statistics\n", + " No of variables 196\n", + " bounds not defined\n", + " No of lin. constraints 0\n", + " nonzeroes 0\n", + " No of matrix inequal. 1\n", + " detected matrix inq. 1\n", + " linear 1\n", + " nonlinear 0\n", + " max. dimension 21\n", + " detected normal inq. 0\n", + " linear 0\n", + " nonlinear 0\n", + " Objective function Linear\n", "\n", " --------------------------------------------------------------\n", " it| objective | optim | feas | compl | pen min |inner\n", @@ -441,28 +452,29 @@ " ``handle_opt_set``, ``handle_opt_get``.\n", " \n", " ``handle_solve_pennon`` is a solver from the NAG optimization\n", - " modelling suite for problems such as, quadratic programming (QP),\n", - " linear semidefinite programming (SDP) and semidefinite programming\n", + " modelling suite for problems such as, Quadratic Programming (QP),\n", + " linear Semidefinite Programming (SDP) and semidefinite programming\n", " with bilinear matrix inequalities (BMI-SDP).\n", " \n", " For full information please refer to the NAG Library document for\n", " e04sv\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04svf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04svf.html\n", " \n", " Parameters\n", " ----------\n", " handle : Handle\n", - " The handle to the problem. It needs to be initialized by\n", - " ``handle_init`` and **must not** be changed before the call to\n", - " ``handle_solve_pennon``.\n", + " The handle to the problem. It needs to be initialized (e.g., by\n", + " ``handle_init``) and to hold a problem formulation compatible\n", + " with ``handle_solve_pennon``. It **must not** be changed between\n", + " calls to the NAG optimization modelling suite.\n", " \n", " x : float, array-like, shape (nvar)\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", " > 0.\n", " \n", " If 'Initial X' = 'USER' (the default), x^0, the initial estimate\n", - " of the variables x, otherwise `x` need not be set.\n", + " of the variables x; otherwise, `x` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -474,7 +486,7 @@ " \n", " `On intermediate entry`: if set to 0, solving the current\n", " problem is terminated and the function returns `errno` = 20;\n", - " otherwise the function continues.\n", + " otherwise, the function continues.\n", " \n", " u : None or float, array-like, shape (nnzu), optional\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", @@ -490,7 +502,7 @@ " Note: if nnzu = 0, `u` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), u^0, the\n", - " initial estimate of the Lagrangian multipliers u, otherwise `u`\n", + " initial estimate of the Lagrangian multipliers u; otherwise, `u`\n", " need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", @@ -513,8 +525,8 @@ " If nnzua = 0, `ua` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), U^0, the\n", - " initial estimate of the matrix Lagrangian multipliers U,\n", - " otherwise `ua` need not be set.\n", + " initial estimate of the matrix Lagrangian multipliers U;\n", + " otherwise, `ua` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -735,7 +747,7 @@ " Constraint: 'Inner Stop Criteria' = 'HEURISTIC' or 'STRICT'.\n", " \n", " 'Inner Stop Tolerance' : float\n", - " Default = 10^(-2)\n", + " Default = 10^-2\n", " \n", " This option sets the required precision alpha^0 for the first\n", " inner problem solved by [Algorithm 2].\n", @@ -849,7 +861,7 @@ " reaching the requested accuracy on the feasibility.\n", " Under normal circumstances, the default value is recommended.\n", " \n", - " Constraint: epsilon <= 'P Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'P Min' <= 10^-2.\n", " \n", " 'Pmat Min' : float\n", " Default = sqrt(epsilon)\n", @@ -858,7 +870,7 @@ " option P_min.\n", " The same advice applies.\n", " \n", - " Constraint: epsilon <= 'Pmat Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'Pmat Min' <= 10^-2.\n", " \n", " 'Preference' : str\n", " Default = 'SPEED'\n", @@ -964,7 +976,7 @@ " Constraint: 'Stop Criteria' = 'SOFT' or 'STRICT'.\n", " \n", " 'Stop Tolerance 1' : float\n", - " Default = max(10^(-6), sqrt(epsilon))\n", + " Default = max(10^-6, sqrt(epsilon))\n", " \n", " This option defines epsilon_1 used as a tolerance for the\n", " relative duality gap (0) and the relative precision (1), see\n", @@ -973,7 +985,7 @@ " Constraint: 'Stop Tolerance 1' > epsilon.\n", " \n", " 'Stop Tolerance 2' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This option sets the value epsilon_2 which is used for\n", " optimality (2) and complementarity (4) tests from KKT conditions\n", @@ -984,7 +996,7 @@ " Constraint: 'Stop Tolerance 2' > epsilon.\n", " \n", " 'Stop Tolerance Feasibility' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This argument places an acceptance limit on the feasibility of\n", " the solution (3), epsilon_feas.\n", @@ -1066,17 +1078,14 @@ " This solver does not support the model defined in the\n", " handle.\n", " \n", - " (`errno` 2)\n", - " This solver does not support fixed variables.\n", - " \n", " (`errno` 3)\n", - " A different solver from the suite has already been used.\n", + " The problem is already being solved.\n", " \n", " (`errno` 4)\n", " On entry, nvar = **, expected value = **.\n", " \n", - " Constraint: nvar must match the value given during\n", - " initialization of `handle`.\n", + " Constraint: nvar must match the current number of variables\n", + " of the model in the `handle`.\n", " \n", " (`errno` 5)\n", " On entry, nnzu = **.\n", @@ -1121,25 +1130,6 @@ " (`errno` 21)\n", " The current starting point is unusable.\n", " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Inner iteration limit has been reached.\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Limited progress in the inner subproblem triggered a stop\n", - " (heuristic inner stop criteria).\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Line search or another internal component failed.\n", - " \n", " (`errno` 51)\n", " The problem was found to be infeasible during preprocessing.\n", " \n", @@ -1172,9 +1162,187 @@ " \n", " The requested accuracy is not achieved.\n", " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Inner iteration limit has been reached.\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Limited progress in the inner subproblem triggered a stop\n", + " (heuristic inner stop criteria).\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Line search or another internal component failed.\n", + " \n", " (`errno` 24)\n", " Unable to make progress, the algorithm was stopped.\n", " \n", + " Notes\n", + " -----\n", + " ``handle_solve_pennon`` serves as a solver for compatible problems\n", + " stored as a handle.\n", + " The handle points to an internal data structure which defines the\n", + " problem and serves as a means of communication for functions in the\n", + " NAG optimization modelling suite.\n", + " First, the problem handle is initialized by calling ``handle_init``.\n", + " Then some of the functions ``handle_set_linobj``,\n", + " ``handle_set_quadobj``, ``handle_set_simplebounds``,\n", + " ``handle_set_linconstr``, ``handle_set_linmatineq`` or\n", + " ``handle_set_quadmatineq`` may be used to formulate the objective\n", + " function, (standard) constraints and matrix constraints of the\n", + " problem.\n", + " Once the problem is fully set, the handle may be passed to the\n", + " solver.\n", + " When the handle is no longer needed, ``handle_free`` should be\n", + " called to destroy it and deallocate the memory held within.\n", + " See [the E04 Introduction] for more details about the NAG\n", + " optimization modelling suite.\n", + " \n", + " Problems which can be defined this way are, for example, (generally\n", + " nonconvex) Quadratic Programming (QP)\n", + " \n", + " [table omitted]\n", + " \n", + " linear semidefinite programming problems (SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " or semidefinite programming problems with bilinear matrix\n", + " inequalities (BMI-SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " Here c, l_x and u_x are n-dimensional vectors, H is a symmetric n*n\n", + " matrix, l_B, u_B are m_B-dimensional vectors, B is a general m_B*n\n", + " rectangular matrix and A_i^k, Q_ij^k are symmetric matrices.\n", + " The expression S⪰0 stands for a constraint on eigenvalues of a\n", + " symmetric matrix S, namely, all the eigenvalues should be\n", + " non-negative, i.e., the matrix should be positive semidefinite.\n", + " See relevant functions in the suite for more details on the problem\n", + " formulation.\n", + " \n", + " The solver is based on a generalized Augmented Lagrangian method\n", + " with a suitable choice of standard and matrix penalty functions.\n", + " For a detailed description of the algorithm see [Algorithmic\n", + " Details].\n", + " Under standard assumptions on the problem (Slater constraint\n", + " qualification, boundedness of the objective function on the feasible\n", + " set, see Stingl (2006) for details) the algorithm converges to a\n", + " local solution.\n", + " In case of convex problems such as linear SDP or convex QP, this is\n", + " the global solution.\n", + " The solver is suitable for both small dense and large-scale sparse\n", + " problems.\n", + " \n", + " The algorithm behaviour and solver strategy can be modified by\n", + " various options (see [Other Parameters]) which can be set by\n", + " ``handle_opt_set`` and ``handle_opt_set_file`` anytime between the\n", + " initialization of the handle by ``handle_init`` and a call to the\n", + " solver.\n", + " Once the solver has finished, options may be modified for the next\n", + " solve.\n", + " The solver may be called repeatedly with various starting points\n", + " and/or options.\n", + " \n", + " There are several options with a multiple choice where the default\n", + " choice is 'AUTO' (for example, 'Hessian Density').\n", + " This value means that the decision over the option is left to the\n", + " solver based on the structure of the problem.\n", + " Option getter ``handle_opt_get`` can be called to retrieve the\n", + " choice of these options as well as on any other options.\n", + " \n", + " Option 'Task' may be used to switch the problem to maximization or\n", + " to ignore the objective function and find only a feasible point.\n", + " \n", + " Option 'Monitor Frequency' may be used to turn on the monitor mode\n", + " of the solver.\n", + " The solver invoked in this mode pauses regularly even before the\n", + " optimal point is found to allow monitoring the progress from the\n", + " calling program.\n", + " All the important error measures and statistics are available in the\n", + " calling program which may terminate the solver early if desired (see\n", + " argument `inform`).\n", + " \n", + " Structure of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " The algorithm works internally with estimates of both the decision\n", + " variables, denoted by x, and the Lagrangian multipliers (dual\n", + " variables) for standard and matrix constraints, denoted by u and U,\n", + " respectively.\n", + " You may provide initial estimates, request approximations during the\n", + " run (the monitor mode turned on) and obtain the final values.\n", + " The Lagrangian multipliers are split into two arrays, the\n", + " multipliers u for (standard) constraints are stored in array `u` and\n", + " multipliers U for matrix constraints in array `ua`.\n", + " Both arrays need to conform to the structure of the constraints.\n", + " \n", + " If the simple bounds were defined (``handle_set_simplebounds`` was\n", + " successfully called), the first 2n elements of `u` belong to the\n", + " corresponding Lagrangian multipliers, interleaving a multiplier for\n", + " the lower and for the upper bound for each x_i.\n", + " If any of the bounds were set to infinity, the corresponding\n", + " Lagrangian multipliers are set to 0 and may be ignored.\n", + " \n", + " Similarly, the following 2m_B elements of `u` belong to multipliers\n", + " for the linear constraints, if formulated by\n", + " ``handle_set_linconstr``.\n", + " The organization is the same, i.e., the multipliers for each\n", + " constraint for the lower and upper bounds are alternated and zeroes\n", + " are used for any missing (infinite bound) constraint.\n", + " \n", + " A Lagrangian multiplier for a matrix constraint (one block) of\n", + " dimension d*d is a dense symmetric matrix of the same dimension.\n", + " All multipliers U are stored next to each other in array `ua` in the\n", + " same order as the matrix constraints were defined by\n", + " ``handle_set_linmatineq`` and ``handle_set_quadmatineq``.\n", + " The lower triangle of each is stored in the packed column order (see\n", + " [the F07 Introduction]).\n", + " For example, if there are four matrix constraints of dimensions 7,\n", + " 3, 1, 1, the dimension of array `ua` should be 36.\n", + " The first 28 elements (d_1*(d_1+1)/2) belong to the packed lower\n", + " triangle of U_1, followed by six elements of U_2 and one element for\n", + " each U_3 and U_4.\n", + " \n", + " Approximation of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " By the nature of the algorithm, all inequality Lagrangian multiplier\n", + " u,U are always kept positive during the computational process.\n", + " This applies even to Lagrangian multipliers of inactive constraints\n", + " at the solution.\n", + " They will only be close to zero although they would normally be\n", + " equal to zero exactly.\n", + " This is one of the major differences between results from solvers\n", + " based on the active set method (such as ``qpconvex2_sparse_solve``)\n", + " and others, such as, ``handle_solve_pennon`` or interior point\n", + " methods.\n", + " As a consequence, the initial estimate of the multipliers (if\n", + " provided) might be adjusted by the solver to be sufficiently\n", + " positive, also the estimates returned during the intermediate exits\n", + " might only be a very crude approximation to their final values as\n", + " they do not satisfy all the Karush--Kuhn--Tucker (KKT) conditions.\n", + " \n", + " Another difference is that ``qpconvex2_sparse_solve`` merges\n", + " multipliers for both lower and upper inequality into one element\n", + " whose sign determines the inequality because there can be at most\n", + " one active constraint and multiplier for the inactive is exact zero.\n", + " Negative multipliers are associated with the upper bounds and\n", + " positive with the lower bounds.\n", + " On the other hand, ``handle_solve_pennon`` works with both\n", + " multipliers at the same time so they are returned in two elements,\n", + " one for the lower bound, the other for the upper bound (see\n", + " [Structure of the Lagrangian Multipliers]).\n", + " An equivalent result can be achieved by subtracting the upper bound\n", + " multiplier from the lower one.\n", + " This holds even when equalities are interpreted as two inequalities\n", + " (see option 'Transform Constraints').\n", + " \n", " References\n", " ----------\n", " Ben--Tal, A and Zibulevsky, M, 1997, `Penalty/barrier multiplier\n", @@ -1234,7 +1402,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SDP/theta_optimization.ipynb b/local_optimization/SDP/theta_optimization.ipynb index 3b3a07c..9cc33ce 100644 --- a/local_optimization/SDP/theta_optimization.ipynb +++ b/local_optimization/SDP/theta_optimization.ipynb @@ -165,14 +165,25 @@ "name": "stdout", "output_type": "stream", "text": [ - " E04SV, NLP-SDP Solver (Pennon)\n", - " ------------------------------\n", - " Number of variables 16 [eliminated 0]\n", - " simple linear nonlin\n", - " (Standard) inequalities 0 0 0\n", - " (Standard) equalities 0 0\n", - " Matrix inequalities 1 0 [dense 1, sparse 0]\n", - " [max dimension 10]\n", + "\n", + " --------------------------------\n", + " E04SV, NLP-SDP Solver (Pennon)\n", + " --------------------------------\n", + "\n", + " Problem Statistics\n", + " No of variables 16\n", + " bounds not defined\n", + " No of lin. constraints 0\n", + " nonzeroes 0\n", + " No of matrix inequal. 1\n", + " detected matrix inq. 1\n", + " linear 1\n", + " nonlinear 0\n", + " max. dimension 10\n", + " detected normal inq. 0\n", + " linear 0\n", + " nonlinear 0\n", + " Objective function Linear\n", "\n", " --------------------------------------------------------------\n", " it| objective | optim | feas | compl | pen min |inner\n", @@ -282,28 +293,29 @@ " ``handle_opt_set``, ``handle_opt_get``.\n", " \n", " ``handle_solve_pennon`` is a solver from the NAG optimization\n", - " modelling suite for problems such as, quadratic programming (QP),\n", - " linear semidefinite programming (SDP) and semidefinite programming\n", + " modelling suite for problems such as, Quadratic Programming (QP),\n", + " linear Semidefinite Programming (SDP) and semidefinite programming\n", " with bilinear matrix inequalities (BMI-SDP).\n", " \n", " For full information please refer to the NAG Library document for\n", " e04sv\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04svf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04svf.html\n", " \n", " Parameters\n", " ----------\n", " handle : Handle\n", - " The handle to the problem. It needs to be initialized by\n", - " ``handle_init`` and **must not** be changed before the call to\n", - " ``handle_solve_pennon``.\n", + " The handle to the problem. It needs to be initialized (e.g., by\n", + " ``handle_init``) and to hold a problem formulation compatible\n", + " with ``handle_solve_pennon``. It **must not** be changed between\n", + " calls to the NAG optimization modelling suite.\n", " \n", " x : float, array-like, shape (nvar)\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", " > 0.\n", " \n", " If 'Initial X' = 'USER' (the default), x^0, the initial estimate\n", - " of the variables x, otherwise `x` need not be set.\n", + " of the variables x; otherwise, `x` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -315,7 +327,7 @@ " \n", " `On intermediate entry`: if set to 0, solving the current\n", " problem is terminated and the function returns `errno` = 20;\n", - " otherwise the function continues.\n", + " otherwise, the function continues.\n", " \n", " u : None or float, array-like, shape (nnzu), optional\n", " Note: intermediate stops take place only if 'Monitor Frequency'\n", @@ -331,7 +343,7 @@ " Note: if nnzu = 0, `u` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), u^0, the\n", - " initial estimate of the Lagrangian multipliers u, otherwise `u`\n", + " initial estimate of the Lagrangian multipliers u; otherwise, `u`\n", " need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", @@ -354,8 +366,8 @@ " If nnzua = 0, `ua` will not be referenced.\n", " \n", " If 'Initial U' = 'USER' (the default is 'AUTOMATIC'), U^0, the\n", - " initial estimate of the matrix Lagrangian multipliers U,\n", - " otherwise `ua` need not be set.\n", + " initial estimate of the matrix Lagrangian multipliers U;\n", + " otherwise, `ua` need not be set.\n", " \n", " `On intermediate entry`: the input is ignored.\n", " \n", @@ -576,7 +588,7 @@ " Constraint: 'Inner Stop Criteria' = 'HEURISTIC' or 'STRICT'.\n", " \n", " 'Inner Stop Tolerance' : float\n", - " Default = 10^(-2)\n", + " Default = 10^-2\n", " \n", " This option sets the required precision alpha^0 for the first\n", " inner problem solved by [Algorithm 2].\n", @@ -690,7 +702,7 @@ " reaching the requested accuracy on the feasibility.\n", " Under normal circumstances, the default value is recommended.\n", " \n", - " Constraint: epsilon <= 'P Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'P Min' <= 10^-2.\n", " \n", " 'Pmat Min' : float\n", " Default = sqrt(epsilon)\n", @@ -699,7 +711,7 @@ " option P_min.\n", " The same advice applies.\n", " \n", - " Constraint: epsilon <= 'Pmat Min' <= 10^(-2).\n", + " Constraint: epsilon <= 'Pmat Min' <= 10^-2.\n", " \n", " 'Preference' : str\n", " Default = 'SPEED'\n", @@ -805,7 +817,7 @@ " Constraint: 'Stop Criteria' = 'SOFT' or 'STRICT'.\n", " \n", " 'Stop Tolerance 1' : float\n", - " Default = max(10^(-6), sqrt(epsilon))\n", + " Default = max(10^-6, sqrt(epsilon))\n", " \n", " This option defines epsilon_1 used as a tolerance for the\n", " relative duality gap (0) and the relative precision (1), see\n", @@ -814,7 +826,7 @@ " Constraint: 'Stop Tolerance 1' > epsilon.\n", " \n", " 'Stop Tolerance 2' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This option sets the value epsilon_2 which is used for\n", " optimality (2) and complementarity (4) tests from KKT conditions\n", @@ -825,7 +837,7 @@ " Constraint: 'Stop Tolerance 2' > epsilon.\n", " \n", " 'Stop Tolerance Feasibility' : float\n", - " Default = max(10^(-7), sqrt(epsilon))\n", + " Default = max(10^-7, sqrt(epsilon))\n", " \n", " This argument places an acceptance limit on the feasibility of\n", " the solution (3), epsilon_feas.\n", @@ -907,17 +919,14 @@ " This solver does not support the model defined in the\n", " handle.\n", " \n", - " (`errno` 2)\n", - " This solver does not support fixed variables.\n", - " \n", " (`errno` 3)\n", - " A different solver from the suite has already been used.\n", + " The problem is already being solved.\n", " \n", " (`errno` 4)\n", " On entry, nvar = **, expected value = **.\n", " \n", - " Constraint: nvar must match the value given during\n", - " initialization of `handle`.\n", + " Constraint: nvar must match the current number of variables\n", + " of the model in the `handle`.\n", " \n", " (`errno` 5)\n", " On entry, nnzu = **.\n", @@ -962,25 +971,6 @@ " (`errno` 21)\n", " The current starting point is unusable.\n", " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Inner iteration limit has been reached.\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Limited progress in the inner subproblem triggered a stop\n", - " (heuristic inner stop criteria).\n", - " \n", - " (`errno` 23)\n", - " The inner subproblem could not be solved to the required\n", - " accuracy.\n", - " \n", - " Line search or another internal component failed.\n", - " \n", " (`errno` 51)\n", " The problem was found to be infeasible during preprocessing.\n", " \n", @@ -1013,9 +1003,187 @@ " \n", " The requested accuracy is not achieved.\n", " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Inner iteration limit has been reached.\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Limited progress in the inner subproblem triggered a stop\n", + " (heuristic inner stop criteria).\n", + " \n", + " (`errno` 23)\n", + " The inner subproblem could not be solved to the required\n", + " accuracy.\n", + " \n", + " Line search or another internal component failed.\n", + " \n", " (`errno` 24)\n", " Unable to make progress, the algorithm was stopped.\n", " \n", + " Notes\n", + " -----\n", + " ``handle_solve_pennon`` serves as a solver for compatible problems\n", + " stored as a handle.\n", + " The handle points to an internal data structure which defines the\n", + " problem and serves as a means of communication for functions in the\n", + " NAG optimization modelling suite.\n", + " First, the problem handle is initialized by calling ``handle_init``.\n", + " Then some of the functions ``handle_set_linobj``,\n", + " ``handle_set_quadobj``, ``handle_set_simplebounds``,\n", + " ``handle_set_linconstr``, ``handle_set_linmatineq`` or\n", + " ``handle_set_quadmatineq`` may be used to formulate the objective\n", + " function, (standard) constraints and matrix constraints of the\n", + " problem.\n", + " Once the problem is fully set, the handle may be passed to the\n", + " solver.\n", + " When the handle is no longer needed, ``handle_free`` should be\n", + " called to destroy it and deallocate the memory held within.\n", + " See [the E04 Introduction] for more details about the NAG\n", + " optimization modelling suite.\n", + " \n", + " Problems which can be defined this way are, for example, (generally\n", + " nonconvex) Quadratic Programming (QP)\n", + " \n", + " [table omitted]\n", + " \n", + " linear semidefinite programming problems (SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " or semidefinite programming problems with bilinear matrix\n", + " inequalities (BMI-SDP)\n", + " \n", + " [table omitted]\n", + " \n", + " Here c, l_x and u_x are n-dimensional vectors, H is a symmetric n*n\n", + " matrix, l_B, u_B are m_B-dimensional vectors, B is a general m_B*n\n", + " rectangular matrix and A_i^k, Q_ij^k are symmetric matrices.\n", + " The expression S⪰0 stands for a constraint on eigenvalues of a\n", + " symmetric matrix S, namely, all the eigenvalues should be\n", + " non-negative, i.e., the matrix should be positive semidefinite.\n", + " See relevant functions in the suite for more details on the problem\n", + " formulation.\n", + " \n", + " The solver is based on a generalized Augmented Lagrangian method\n", + " with a suitable choice of standard and matrix penalty functions.\n", + " For a detailed description of the algorithm see [Algorithmic\n", + " Details].\n", + " Under standard assumptions on the problem (Slater constraint\n", + " qualification, boundedness of the objective function on the feasible\n", + " set, see Stingl (2006) for details) the algorithm converges to a\n", + " local solution.\n", + " In case of convex problems such as linear SDP or convex QP, this is\n", + " the global solution.\n", + " The solver is suitable for both small dense and large-scale sparse\n", + " problems.\n", + " \n", + " The algorithm behaviour and solver strategy can be modified by\n", + " various options (see [Other Parameters]) which can be set by\n", + " ``handle_opt_set`` and ``handle_opt_set_file`` anytime between the\n", + " initialization of the handle by ``handle_init`` and a call to the\n", + " solver.\n", + " Once the solver has finished, options may be modified for the next\n", + " solve.\n", + " The solver may be called repeatedly with various starting points\n", + " and/or options.\n", + " \n", + " There are several options with a multiple choice where the default\n", + " choice is 'AUTO' (for example, 'Hessian Density').\n", + " This value means that the decision over the option is left to the\n", + " solver based on the structure of the problem.\n", + " Option getter ``handle_opt_get`` can be called to retrieve the\n", + " choice of these options as well as on any other options.\n", + " \n", + " Option 'Task' may be used to switch the problem to maximization or\n", + " to ignore the objective function and find only a feasible point.\n", + " \n", + " Option 'Monitor Frequency' may be used to turn on the monitor mode\n", + " of the solver.\n", + " The solver invoked in this mode pauses regularly even before the\n", + " optimal point is found to allow monitoring the progress from the\n", + " calling program.\n", + " All the important error measures and statistics are available in the\n", + " calling program which may terminate the solver early if desired (see\n", + " argument `inform`).\n", + " \n", + " Structure of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " The algorithm works internally with estimates of both the decision\n", + " variables, denoted by x, and the Lagrangian multipliers (dual\n", + " variables) for standard and matrix constraints, denoted by u and U,\n", + " respectively.\n", + " You may provide initial estimates, request approximations during the\n", + " run (the monitor mode turned on) and obtain the final values.\n", + " The Lagrangian multipliers are split into two arrays, the\n", + " multipliers u for (standard) constraints are stored in array `u` and\n", + " multipliers U for matrix constraints in array `ua`.\n", + " Both arrays need to conform to the structure of the constraints.\n", + " \n", + " If the simple bounds were defined (``handle_set_simplebounds`` was\n", + " successfully called), the first 2n elements of `u` belong to the\n", + " corresponding Lagrangian multipliers, interleaving a multiplier for\n", + " the lower and for the upper bound for each x_i.\n", + " If any of the bounds were set to infinity, the corresponding\n", + " Lagrangian multipliers are set to 0 and may be ignored.\n", + " \n", + " Similarly, the following 2m_B elements of `u` belong to multipliers\n", + " for the linear constraints, if formulated by\n", + " ``handle_set_linconstr``.\n", + " The organization is the same, i.e., the multipliers for each\n", + " constraint for the lower and upper bounds are alternated and zeroes\n", + " are used for any missing (infinite bound) constraint.\n", + " \n", + " A Lagrangian multiplier for a matrix constraint (one block) of\n", + " dimension d*d is a dense symmetric matrix of the same dimension.\n", + " All multipliers U are stored next to each other in array `ua` in the\n", + " same order as the matrix constraints were defined by\n", + " ``handle_set_linmatineq`` and ``handle_set_quadmatineq``.\n", + " The lower triangle of each is stored in the packed column order (see\n", + " [the F07 Introduction]).\n", + " For example, if there are four matrix constraints of dimensions 7,\n", + " 3, 1, 1, the dimension of array `ua` should be 36.\n", + " The first 28 elements (d_1*(d_1+1)/2) belong to the packed lower\n", + " triangle of U_1, followed by six elements of U_2 and one element for\n", + " each U_3 and U_4.\n", + " \n", + " Approximation of the Lagrangian Multipliers\n", + " ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n", + " By the nature of the algorithm, all inequality Lagrangian multiplier\n", + " u,U are always kept positive during the computational process.\n", + " This applies even to Lagrangian multipliers of inactive constraints\n", + " at the solution.\n", + " They will only be close to zero although they would normally be\n", + " equal to zero exactly.\n", + " This is one of the major differences between results from solvers\n", + " based on the active set method (such as ``qpconvex2_sparse_solve``)\n", + " and others, such as, ``handle_solve_pennon`` or interior point\n", + " methods.\n", + " As a consequence, the initial estimate of the multipliers (if\n", + " provided) might be adjusted by the solver to be sufficiently\n", + " positive, also the estimates returned during the intermediate exits\n", + " might only be a very crude approximation to their final values as\n", + " they do not satisfy all the Karush--Kuhn--Tucker (KKT) conditions.\n", + " \n", + " Another difference is that ``qpconvex2_sparse_solve`` merges\n", + " multipliers for both lower and upper inequality into one element\n", + " whose sign determines the inequality because there can be at most\n", + " one active constraint and multiplier for the inactive is exact zero.\n", + " Negative multipliers are associated with the upper bounds and\n", + " positive with the lower bounds.\n", + " On the other hand, ``handle_solve_pennon`` works with both\n", + " multipliers at the same time so they are returned in two elements,\n", + " one for the lower bound, the other for the upper bound (see\n", + " [Structure of the Lagrangian Multipliers]).\n", + " An equivalent result can be achieved by subtracting the upper bound\n", + " multiplier from the lower one.\n", + " This holds even when equalities are interpreted as two inequalities\n", + " (see option 'Transform Constraints').\n", + " \n", " References\n", " ----------\n", " Ben--Tal, A and Zibulevsky, M, 1997, `Penalty/barrier multiplier\n", @@ -1075,7 +1243,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/cvxpy_classification.ipynb b/local_optimization/SOCP/cvxpy_classification.ipynb index df06d26..71dc38f 100644 --- a/local_optimization/SOCP/cvxpy_classification.ipynb +++ b/local_optimization/SOCP/cvxpy_classification.ipynb @@ -227,20 +227,22 @@ " Socp Stop Tolerance 2 = 1.05367E-08 * d\n", " Socp System Formulation = Auto * d\n", " End of Options\n", - " Original Problem Statistics\n", "\n", - " Number of variables 32\n", - " Number of linear constraints 176\n", - " Number of nonzeros 2432\n", - " Number of cones 1\n", + " Problem Statistics\n", + " No of variables 32\n", + " bounds not defined\n", + " No of lin. constraints 176\n", + " nonzeroes 2432\n", + " No of quad.constraints 0\n", + " No of cones 1\n", + " biggest cone size 16\n", + " Objective function Linear\n", "\n", - "\n", - " Presolved Problem Statistics\n", - "\n", - " Number of variables 191\n", - " Number of linear constraints 175\n", - " Number of nonzeros 2590\n", - " Number of cones 1\n", + " Presolved Problem Measures\n", + " No of variables 191\n", + " No of lin. constraints 175\n", + " nonzeroes 2590\n", + " No of cones 1\n", "\n", "\n", " ------------------------------------------------------------------------\n", @@ -369,7 +371,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb index 510ac04..9919a82 100644 --- a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb @@ -1182,7 +1182,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.1" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/robust_lp.ipynb b/local_optimization/SOCP/robust_lp.ipynb index cd0673b..d131125 100644 --- a/local_optimization/SOCP/robust_lp.ipynb +++ b/local_optimization/SOCP/robust_lp.ipynb @@ -401,20 +401,22 @@ "naginterfaces.base.opt.handle_solve_socp_ipm: E04PT, Interior point method for SOCP problems\n", "naginterfaces.base.opt.handle_solve_socp_ipm: ------------------------------------------------\n", "naginterfaces.base.opt.handle_solve_socp_ipm:\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Original Problem Statistics\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: Problem Statistics\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of variables 17\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: free (unconstrained) 9\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: bounded 8\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of lin. constraints 10\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: nonzeroes 89\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of quad.constraints 0\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of cones 1\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: biggest cone size 9\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: Objective function Linear\n", "naginterfaces.base.opt.handle_solve_socp_ipm:\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of variables 17\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of linear constraints 10\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of nonzeros 89\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of cones 1\n", - "naginterfaces.base.opt.handle_solve_socp_ipm:\n", - "naginterfaces.base.opt.handle_solve_socp_ipm:\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Presolved Problem Statistics\n", - "naginterfaces.base.opt.handle_solve_socp_ipm:\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of variables 17\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of linear constraints 10\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of nonzeros 89\n", - "naginterfaces.base.opt.handle_solve_socp_ipm: Number of cones 1\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: Presolved Problem Measures\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of variables 17\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of lin. constraints 10\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: nonzeroes 89\n", + "naginterfaces.base.opt.handle_solve_socp_ipm: No of cones 1\n", "naginterfaces.base.opt.handle_solve_socp_ipm:\n", "naginterfaces.base.opt.handle_solve_socp_ipm:\n", "naginterfaces.base.opt.handle_solve_socp_ipm: ------------------------------------------------------------------------\n", @@ -573,7 +575,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/simple_SOCP.ipynb b/local_optimization/SOCP/simple_SOCP.ipynb index 09eb643..42b5fe0 100644 --- a/local_optimization/SOCP/simple_SOCP.ipynb +++ b/local_optimization/SOCP/simple_SOCP.ipynb @@ -194,11 +194,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "\n", - " ------------------------------------------------\n", - " E04PT, Interior point method for SOCP problems\n", - " ------------------------------------------------\n", - "\n", + " E04PT, Interior point method for SOCP problems\n", " Status: converged, an optimal solution found\n", " Final primal objective value -1.951817E+01\n", " Final dual objective value -1.951817E+01\n" @@ -298,7 +294,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/bounds_quasi_func_easy.ipynb b/local_optimization/bounds_quasi_func_easy.ipynb index 51020b5..9088f29 100644 --- a/local_optimization/bounds_quasi_func_easy.ipynb +++ b/local_optimization/bounds_quasi_func_easy.ipynb @@ -15,7 +15,7 @@ "One can see from the HTML documentation at https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.html that the relevant algorithmic submodule for (local) optimization is ``opt``.\n", "\n", "Studying the `opt` Functionality Index confirms that the relevant optimization solver to call is\n", - "``bounds_quasi_func_easy``. The HTML documentation for this solver is at https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.bounds_quasi_func_easy.\n", + "``bounds_quasi_func_easy``. The HTML documentation for this solver is at https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.bounds_quasi_func_easy.html.\n", "\n", "The optimization solver may be imported directly if desired" ] @@ -64,7 +64,7 @@ " For full information please refer to the NAG Library document for\n", " e04jy\n", " \n", - " https://www.nag.com/numeric/nl/nagdoc_27/flhtml/e04/e04jyf.html\n", + " https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/e04/e04jyf.html\n", " \n", " Parameters\n", " ----------\n", @@ -263,6 +263,72 @@ " No equivalent traditional C interface for this routine exists in the\n", " NAG Library.\n", " \n", + " ``bounds_quasi_func_easy`` is applicable to problems of the form:\n", + " \n", + " MinimizeF(x_1,x_2,...,x_n) subject to l_j <= x_j <= u_j, j =\n", + " 1,2,...,n\n", + " \n", + " when derivatives of F(x) are unavailable.\n", + " \n", + " Special provision is made for problems which actually have no bounds\n", + " on the x_j, problems which have only non-negativity bounds and\n", + " problems in which l_1 = l_2 = ... = l_n and u_1 = u_2 = ... = u_n.\n", + " You must supply a function to calculate the value of F(x) at any\n", + " point x.\n", + " \n", + " From a starting point you supplied there is generated, on the basis\n", + " of estimates of the gradient and the curvature of F(x), a sequence\n", + " of feasible points which is intended to converge to a local minimum\n", + " of the constrained function.\n", + " An attempt is made to verify that the final point is a minimum.\n", + " \n", + " A typical iteration starts at the current point x where n_z (say)\n", + " variables are free from both their bounds.\n", + " The projected gradient vector g_z, whose elements are finite\n", + " difference approximations to the derivatives of F(x) with respect to\n", + " the free variables, is known.\n", + " A unit lower triangular matrix L and a diagonal matrix D (both of\n", + " dimension n_z), such that LDL^T is a positive definite approximation\n", + " of the matrix of second derivatives with respect to the free\n", + " variables (i.e., the projected Hessian) are also held.\n", + " The equations\n", + " \n", + " LDL^Tp_z = -g_z\n", + " \n", + " are solved to give a search direction p_z, which is expanded to an\n", + " n-vector p by an insertion of appropriate zero elements.\n", + " Then alpha is found such that F(x+alpha p) is approximately a\n", + " minimum (subject to the fixed bounds) with respect to alpha; x is\n", + " replaced by x+alpha p, and the matrices L and D are updated so as to\n", + " be consistent with the change produced in the estimated gradient by\n", + " the step alpha p.\n", + " If any variable actually reaches a bound during the search along p,\n", + " it is fixed and n_z is reduced for the next iteration.\n", + " Most iterations calculate g_z using forward differences, but central\n", + " differences are used when they seem necessary.\n", + " \n", + " There are two sets of convergence criteria -- a weaker and a\n", + " stronger.\n", + " Whenever the weaker criteria are satisfied, the Lagrange multipliers\n", + " are estimated for all the active constraints.\n", + " If any Lagrange multiplier estimate is significantly negative, then\n", + " one of the variables associated with a negative Lagrange multiplier\n", + " estimate is released from its bound and the next search direction is\n", + " computed in the extended subspace (i.e., n_z is increased).\n", + " Otherwise minimization continues in the current subspace provided\n", + " that this is practicable.\n", + " When it is not, or when the stronger convergence criteria are\n", + " already satisfied, then, if one or more Lagrange multiplier\n", + " estimates are close to zero, a slight perturbation is made in the\n", + " values of the corresponding variables in turn until a lower function\n", + " value is obtained.\n", + " The normal algorithm is then resumed from the perturbed point.\n", + " \n", + " If a saddle point is suspected, a local search is carried out with a\n", + " view to moving away from the saddle point.\n", + " A local search is also performed when a point is found which is\n", + " thought to be a constrained minimum.\n", + " \n", " References\n", " ----------\n", " Gill, P E and Murray, W, 1976, `Minimization subject to bounds on\n", @@ -1280,7 +1346,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/local_optimization/christmas_demo.ipynb b/local_optimization/christmas_demo.ipynb index 644fe39..4555735 100644 --- a/local_optimization/christmas_demo.ipynb +++ b/local_optimization/christmas_demo.ipynb @@ -367,7 +367,7 @@ "outputs": [], "source": [ "# Main callback function for the MINLP solver\n", - "def objfun_h02da(mode, varcon, x, objgrd, _nstate, data):\n", + "def objfun_h02da(mode, _varcon, x, objgrd, _nstate, data):\n", " objmip = x[0]**2 + x[0] + np.cos(2*np.pi*x[1])**2 + 0.5*x[1]\n", " data.npts = data.npts + 1\n", " data.pts.append((x[0], x[1]))\n", @@ -588,7 +588,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/multivariate_methods/k-means.ipynb b/multivariate_methods/k-means.ipynb index 3b342b1..9f46006 100644 --- a/multivariate_methods/k-means.ipynb +++ b/multivariate_methods/k-means.ipynb @@ -114,7 +114,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/nearest_correlation_matrices/ncm_nag.ipynb b/nearest_correlation_matrices/ncm_nag.ipynb index b0d5eef..9797e34 100644 --- a/nearest_correlation_matrices/ncm_nag.ipynb +++ b/nearest_correlation_matrices/ncm_nag.ipynb @@ -1138,7 +1138,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "nbpresent": { "slides": { diff --git a/operations_research/nag_rugby_tsm.ipynb b/operations_research/nag_rugby_tsm.ipynb index 4816b1c..9129ac6 100644 --- a/operations_research/nag_rugby_tsm.ipynb +++ b/operations_research/nag_rugby_tsm.ipynb @@ -376,7 +376,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/random_number_generation/rand_corr_mat.ipynb b/random_number_generation/rand_corr_mat.ipynb index 0a4a937..d3b0d86 100644 --- a/random_number_generation/rand_corr_mat.ipynb +++ b/random_number_generation/rand_corr_mat.ipynb @@ -621,7 +621,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/roots/Anderson_Acceleration_Poisson.ipynb b/roots/Anderson_Acceleration_Poisson.ipynb index f062db6..708c7ba 100644 --- a/roots/Anderson_Acceleration_Poisson.ipynb +++ b/roots/Anderson_Acceleration_Poisson.ipynb @@ -1454,7 +1454,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/special_functions/mathieu_functions.ipynb b/special_functions/mathieu_functions.ipynb index dc193de..adc5f06 100644 --- a/special_functions/mathieu_functions.ipynb +++ b/special_functions/mathieu_functions.ipynb @@ -102,7 +102,7 @@ { "data": { "text/plain": [ - "'27.0.2.0'" + "'27.1.0.0'" ] }, "execution_count": 3, @@ -132,7 +132,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/time_series_analysis/cp_pelt.ipynb b/time_series_analysis/cp_pelt.ipynb index 5b97cc3..7360aa5 100644 --- a/time_series_analysis/cp_pelt.ipynb +++ b/time_series_analysis/cp_pelt.ipynb @@ -6,7 +6,7 @@ "source": [ "# Change Point Analysis\n", "\n", - "Change points are time points at which some feature of a data set changes. For detecting change points in a univariate time series we can use [`tsa.cp_pelt`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.html#naginterfaces.library.tsa.cp_pelt).\n", + "Change points are time points at which some feature of a data set changes. For detecting change points in a univariate time series we can use [`tsa.cp_pelt`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.cp_pelt.html).\n", "\n", "Consider the following time series, showing the EUR/GBP exchange rate between January 1999 and February 2020 (numbers indicate Euros per Pound, with FX data from www.macrotrends.net)" ] @@ -988,7 +988,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/time_series_analysis/inhom_iema.ipynb b/time_series_analysis/inhom_iema.ipynb index 936c5e8..d81b735 100644 --- a/time_series_analysis/inhom_iema.ipynb +++ b/time_series_analysis/inhom_iema.ipynb @@ -27,7 +27,7 @@ "\n", "The value of $\\nu$ depends on the method of interpolation chosen.\n", "\n", - "See the NAG Library for Python documentation for the further details on this function: [NAG Library for Python docs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.html#naginterfaces.library.tsa.inhom_iema)" + "See the NAG Library for Python documentation for the further details on this function: [NAG Library for Python docs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.inhom_iema.html)" ] }, { @@ -1018,7 +1018,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.5" } }, "nbformat": 4, From 17b1b61b6c2f9af99248074dd293718d1c513522 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 6 Nov 2020 07:31:47 +0000 Subject: [PATCH 061/182] Update link to leaflet info --- local_optimization/BXNL/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index 4a63757..12e31d7 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -23,7 +23,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook # More Info - 1. [BXNL information leaflet]() + 1. [BXNL information leaflet](https://www.nag.com/content/faster-data-fitting-solver) 2. [BXNL in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) 3. [BXNL documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] From e51cff6b690e111c99eb53ce687465f9a76a202e Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Fri, 13 Nov 2020 15:30:29 -0600 Subject: [PATCH 062/182] new implied volatility notebook --- special_functions/opt_imp_vol/graphs.PNG | Bin 0 -> 101498 bytes .../opt_imp_vol/imp_vol_demo.ipynb | 300 ++++++++++++++++++ special_functions/opt_imp_vol/impvolsurf.png | Bin 0 -> 439262 bytes 3 files changed, 300 insertions(+) create mode 100644 special_functions/opt_imp_vol/graphs.PNG create mode 100644 special_functions/opt_imp_vol/imp_vol_demo.ipynb create 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0000000..0f28161 --- /dev/null +++ b/special_functions/opt_imp_vol/imp_vol_demo.ipynb @@ -0,0 +1,300 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fast Implied Volatilities using the NAG Library" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Black-Scholes formula for the price of a European call option is\n", + "\n", + "$$P = S_0\\Phi\\left(\\frac{\\ln\\left(\\frac{S_0}{K}\\right)+\\left[r+\\frac{\\sigma^2}{2}\\right]T}{\\sigma\\sqrt{T}}\\right) - Ke^{-rT}\\Phi\\left(\\frac{\\ln\\left(\\frac{S_0}{K}\\right)+\\left[r-\\frac{\\sigma^2}{2}\\right]T}{\\sigma\\sqrt{T}}\\right),$$\n", + "\n", + "where $T$ is the time to maturity, $S_0$ is the spot price of the underlying asset, $K$ is the strike price, $r$ is\n", + "the interest rate and $\\sigma$ is the volatility. A similar formula applies for European put options.\n", + "\n", + "An important problem in finance is to compute the implied volatility, $σ$, given values for $T$, $K$, $S_0$,\n", + "$r$ and $P$. An explicit formula for $\\sigma$ is not available. Furthermore, $\\sigma$ cannot be directly measured from\n", + "financial data. Instead, it must be computed using a numerical approximation. Typically, multiple values\n", + "of the input data are provided, so the Black-Scholes formula must be solved many times.\n", + "\n", + "As shown in the figure below, the volatility surface (a three-dimensional plot of how the volatility varies\n", + "according to the price and time to maturity) can be highly curved. This makes accurately computing\n", + "the implied volatility a difficult problem.\n", + "\n", + "\n", + "\n", + "Before introducing our new NAG Library routine, let’s demonstrate how one might naively\n", + "compute implied volatilities using a general purpose root finder. First we need to import a few things:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import time\n", + "from naginterfaces.library import rand, roots, specfun" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's generate some input data using a random number generator from the NAG Library:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "n = 10000 # This is the number of volatilities we will be computing\n", + "statecomm = rand.init_nonrepeat(1)\n", + "p = rand.dist_uniform(n, 3.9, 5.8, statecomm)\n", + "k = rand.dist_uniform(n, 271.5, 272.0, statecomm)\n", + "s0 = rand.dist_uniform(n, 259.0, 271.0, statecomm)\n", + "t = rand.dist_uniform(n, 0.016, 0.017, statecomm)\n", + "r = rand.dist_uniform(n, 0.017, 0.018, statecomm)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have chosen the limits of the various uniform distributions above to ensure the input data takes\n", + "sensible values.\n", + "\n", + "There are various standard root finding techniques that we could use to compute implied volatilities,\n", + "a common example being bisection. The NAG Library routine ```contfn_cntin```, is a general\n", + "purpose root finder based on the secant method. It uses a *callback*, with data passed in via a communication object:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def black_scholes(sigma, data):\n", + " try:\n", + " price = specfun.opt_bsm_price('C', [data['k']], data['s0'], [data['t']], sigma, data['r'], 0.0)\n", + " except:\n", + " price = np.zeros((1,1))\n", + " return price[0, 0] - data['p']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " ```contfn_cntin``` operates on scalars, so we need to call the routine\n", + "once for every volatility we want to compute. We will time the computation and count how many errors are caught:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using a general purpose root finder:\n", + " Time taken: 44.848 seconds\n", + " There were 3 failures\n" + ] + } + ], + "source": [ + "data = {}\n", + "errorcount = 0\n", + "tic = time.perf_counter()\n", + "for i in range(n):\n", + " data['p'] = p[i]\n", + " data['k'] = k[i]\n", + " data['s0'] = s0[i]\n", + " data['t'] = t[i]\n", + " data['r'] = r[i]\n", + " try:\n", + " sigma = roots.contfn_cntin(0.15, black_scholes, 1.0e-14, 0.0, 500, data)\n", + " if sigma < 0.0:\n", + " errorcount += 1\n", + " except:\n", + " errorcount += 1\n", + "toc = time.perf_counter() \n", + "print('Using a general purpose root finder:')\n", + "print(' Time taken: {0:.3f} seconds'.format(toc-tic))\n", + "print(' There were {} failures'.format(errorcount))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can a bespoke implied volatility routine do better? Our new routine at Mark 27.1 is called ```opt_imp_vol```. We call it as follows:\n", + "\n", + "```sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=2)```\n", + "\n", + "The return argument ```ivalid``` is an array recording any data points for which the volatility could not be computed. The argument ```mode``` allows us to select which algorithm to use – more on that in a moment, but\n", + "for now we choose ```mode=2```. This selects the algorithm of Jäckel (2015), a very accurate method based\n", + "on third order Householder iterations.\n", + "\n", + "Here is the call surrounded by some timing code:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "omp_imp_vol with mode = 2 (Jäckel algorithm):\n", + " Time taken: 0.00792 seconds\n", + " There were 0 failures\n" + ] + } + ], + "source": [ + "tic = time.perf_counter()\n", + "sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=2)\n", + "toc = time.perf_counter()\n", + "print('omp_imp_vol with mode = 2 (Jäckel algorithm):')\n", + "print(' Time taken: {0:.5f} seconds'.format(toc-tic))\n", + "print(' There were {} failures'.format(np.count_nonzero(ivalid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The new routine is several orders of magnitude faster than the root finder, with no failures reported. We could try\n", + "tweaking the convergence parameters and iteration limits in ```nag_roots_contfn_cntin```, and we could certainly\n", + "improve the way data is passed through the callback, but we are unlikely to match the\n", + "performance of ```opt_imp_vol```.\n", + "\n", + "Recently NAG embarked upon a collaboration with mathematicians at Queen Mary University of\n", + "London, who have been developing an alternative algorithm for computing implied volatilities. The new\n", + "algorithm (based on Glau et. al. (2018)) uses Chebyshev interpolation to remove branching and give\n", + "increased SIMD performance. We access it by setting ```mode=1``` in the call to ```opt_imp_vol```:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "omp_imp_vol with mode = 2 (Glau algorithm):\n", + " Time taken: 0.00740 seconds\n", + " There were 0 failures\n" + ] + } + ], + "source": [ + "tic = time.perf_counter()\n", + "sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=1)\n", + "toc = time.perf_counter()\n", + "print('omp_imp_vol with mode = 2 (Glau algorithm):')\n", + "print(' Time taken: {0:.5f} seconds'.format(toc-tic))\n", + "print(' There were {} failures'.format(np.count_nonzero(ivalid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Depending on your system, you should find that, for similar accuracy, there is a modest speedup over the Jäckel algorithm. Our numerical experiments have shown that for very small arrays (containing fewer than 100 elements) the Jäckel algorithm actually\n", + "outperforms that of Glau et.al., but for larger arrays the converse is true. As vector units continue\n", + "to improve in the future, we expect the performance of the highly vectorizable Glau et.al. approach to\n", + "improve similarly.\n", + "\n", + "So far, we have been computing implied volatilities with a relative accuracy as close as possible to\n", + "double precision. However, in some applications implied volatilities are only required with a few decimal\n", + "places of precision. One advantage of the Glau et.al. algorithm is that it can be run in a lower accuracy\n", + "mode, aiming only for seven decimal places of accuracy. This is accessed by setting ```mode=0``` in the call\n", + "to ```opt_imp_vol```. It roughly doubles the speed of the routine:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "omp_imp_vol with mode = 2 (lower accuracy Glau algorithm):\n", + " Time taken: 0.00391 seconds\n", + " There were 0 failures\n" + ] + } + ], + "source": [ + "tic = time.perf_counter()\n", + "sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=0)\n", + "toc = time.perf_counter()\n", + "print('omp_imp_vol with mode = 2 (lower accuracy Glau algorithm):')\n", + "print(' Time taken: {0:.5f} seconds'.format(toc-tic))\n", + "print(' There were {} failures'.format(np.count_nonzero(ivalid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The charts below summarize the results, using timings collected on an Intel Skylake machine. We can see that the Glau et.al. algorithm outperforms the Jäckel algorithm for large arrays but not for small arrays. Note that the general purpose root finder\n", + "is omitted here as it is so much slower ```opt_imp_vol```.\n", + "\n", + "\n", + "In summary, NAG’s new state-of-the art algorithm can be run in three different modes, according to\n", + "the length of the input arrays and the required accuracy. For more information, and to access the NAG\n", + "Library, go to: https://www.nag.co.uk/content/nag-library.\n", + "\n", + "### References\n", + "\n", + "P. Jäckel (2015). Let’s be rational. *Wilmott* 2015, 40-53.\n", + "\n", + "K. Glau, P. Herold, D. B. Madan, C. Pötz (2019). The Chebyshev method for the implied volatility.\n", + "*Journal of Computational Finance*, 23(3)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/special_functions/opt_imp_vol/impvolsurf.png b/special_functions/opt_imp_vol/impvolsurf.png new file mode 100644 index 0000000000000000000000000000000000000000..20b4c230b347a6fb8dec1ccfbaa063024e28e802 GIT binary patch literal 439262 zcmd?RX;@QN_dXoNp^mgzYZZmo9>78s3IYNGTCI2(RS01o6ch-9$Rr7q6BetY2P2b! z17iXSGEX5m(#R+f!i)+sg@6!3m_q*h#8&kAeR;pX_UiRepOCZ9+H0?MuY28VM;|vc z+_-N0It&K05k7Y0BnGp(4TD+r^Ea!(-^k77;lcl`JbTFW5C-!kX8oeeD)8Swoj!Kb 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special_functions/opt_imp_vol/imp_vol_demo.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/special_functions/opt_imp_vol/imp_vol_demo.ipynb b/special_functions/opt_imp_vol/imp_vol_demo.ipynb index 0f28161..4958f7f 100644 --- a/special_functions/opt_imp_vol/imp_vol_demo.ipynb +++ b/special_functions/opt_imp_vol/imp_vol_demo.ipynb @@ -25,7 +25,7 @@ "\n", "As shown in the figure below, the volatility surface (a three-dimensional plot of how the volatility varies\n", "according to the price and time to maturity) can be highly curved. This makes accurately computing\n", - "the implied volatility a difficult problem.\n", + "the implied volatility a difficult problem.\n",/PNG "\n", "\n", "\n", @@ -261,7 +261,7 @@ "source": [ "The charts below summarize the results, using timings collected on an Intel Skylake machine. We can see that the Glau et.al. algorithm outperforms the Jäckel algorithm for large arrays but not for small arrays. Note that the general purpose root finder\n", "is omitted here as it is so much slower ```opt_imp_vol```.\n", - "\n", + "\n", "\n", "In summary, NAG’s new state-of-the art algorithm can be run in three different modes, according to\n", "the length of the input arrays and the required accuracy. For more information, and to access the NAG\n", From ec7acaba9f6f515b479bd71e013c65c10055686a Mon Sep 17 00:00:00 2001 From: Mike Croucher Date: Mon, 16 Nov 2020 11:37:16 +0000 Subject: [PATCH 064/182] Update imp_vol_demo.ipynb --- special_functions/opt_imp_vol/imp_vol_demo.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/special_functions/opt_imp_vol/imp_vol_demo.ipynb b/special_functions/opt_imp_vol/imp_vol_demo.ipynb index 4958f7f..a28af75 100644 --- a/special_functions/opt_imp_vol/imp_vol_demo.ipynb +++ b/special_functions/opt_imp_vol/imp_vol_demo.ipynb @@ -25,7 +25,7 @@ "\n", "As shown in the figure below, the volatility surface (a three-dimensional plot of how the volatility varies\n", "according to the price and time to maturity) can be highly curved. This makes accurately computing\n", - "the implied volatility a difficult problem.\n",/PNG + "the implied volatility a difficult problem.\n", "\n", "\n", "\n", From 0e36e8ce1e22bc7a9d150eb867444e2e979e8a19 Mon Sep 17 00:00:00 2001 From: Ben Date: Wed, 25 Nov 2020 13:42:54 +0100 Subject: [PATCH 065/182] new optimisation modelling suite examples --- local_optimization/handle_disable_ex.ipynb | 365 +++++++++++++++++++ local_optimization/production_planning.ipynb | 295 +++++++++++++++ 2 files changed, 660 insertions(+) create mode 100644 local_optimization/handle_disable_ex.ipynb create mode 100644 local_optimization/production_planning.ipynb diff --git a/local_optimization/handle_disable_ex.ipynb b/local_optimization/handle_disable_ex.ipynb new file mode 100644 index 0000000..ace45ee --- /dev/null +++ b/local_optimization/handle_disable_ex.ipynb @@ -0,0 +1,365 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Removing outliers from a calibration problem with the NAG optimisation suite\n", + "\n", + "## Correct Rendering of this notebook\n", + "\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "\n", + "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", + "\n", + "## Calibration problem\n", + "\n", + "Consider a simple calibration problem where we want to fit the 5 parameters of a model $f$ to some given data points. The model is of the form:\n", + "$$\n", + "\\min_{x\\in\\mathbb{R}^5} \\sum_{i=1}^{30}\\left( f(t_i, x) - y_i \\right)^2\n", + "$$\n", + "where $x=[a,b,c,d,\\omega]$ are the parameters to fit and $f(t, x) = at^2 + bt+ c + d\\sin(\\omega t)$ is the model.\n", + "\n", + "### Data\n", + "\n", + "The initial data points $\\{(t_i, y_i)\\}$ were simulated using \n", + "$$(a=0.3,b=1.0,c=0.01,d=0.2,\\omega =5.0)$$\n", + "with $t_i$ uniformly spread in $\\left[-1.0,1.0\\right]$ and $y_i=f(t_i,x)+\\epsilon_i$ where $\\epsilon_i$ is random noise.\n", + "\n", + "Two of those points ($y_{10}$ and $y_{20}$) were modified to emulate the presence of outilers." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import pickle\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "\n", + "# load the simulated data containing 2 outliers\n", + "data = pickle.load(open('nlnlsq_data.pck', 'rb'))\n", + "nres = len(data['y'])\n", + "\n", + "# plot the data points and the true function used to generate them\n", + "f_true = lambda t : 0.3*t**2 + t + 0.01 + 0.2*math.sin(5.0*t) \n", + "plt.plot(data['t'], data['y'], '*')\n", + "t = np.linspace(-1.0,1.0, num=200)\n", + "y = [f_true(x) for x in t]\n", + "plt.plot(t, y)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set up the calibration problem\n", + "\n", + "Start by defining the callbacks that will be used by the solver to determine the quality of the fit with any given set of parameters $x$." + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": {}, + "outputs": [], + "source": [ + "def lsqfun(x, nres, inform, data):\n", + " \"\"\"\n", + " Objective function callback passed to the least squares solver.\n", + " \"\"\"\n", + " rx = np.zeros(nres)\n", + " t = data['t']\n", + " y = data['y']\n", + " for i in range(nres):\n", + " rx[i] = (\n", + " x[0]*t[i]**2 + x[1]*t[i] + x[2] + x[3]*np.sin(x[4]*t[i]) - y[i]\n", + " )\n", + " return rx, inform" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [], + "source": [ + "def lsqgrd(x, nres, rdx, inform, data):\n", + " \"\"\"\n", + " Computes the Jacobian of the least square residuals.\n", + " \"\"\"\n", + " n = len(x)\n", + " t = data['t']\n", + " for i in range(nres):\n", + " rdx[i*n+0] = t[i]**2\n", + " rdx[i*n+1] = t[i]\n", + " rdx[i*n+2] = 1.0\n", + " rdx[i*n+3] = np.sin(x[4]*t[i])\n", + " rdx[i*n+4] = x[3]*t[i]*np.cos(x[4]*t[i])\n", + " return rdx, inform" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initialize the NAG 'handle' with the problem dimensions and some optional parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [], + "source": [ + "from naginterfaces.library import opt\n", + "from naginterfaces.base import utils\n", + "\n", + "nvar = 5\n", + "# Initialize the Optimization model handle with the number of variables\n", + "handle = opt.handle_init(nvar)\n", + "\n", + "# Define a dense nonlinear least-squares objective function\n", + "opt.handle_set_nlnls(handle, nres)\n", + "\n", + "# Set some optional parameters to control the output of the solver\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Print Solution = X',\n", + " 'Bxnl Iteration Limit = 100',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + " \n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solve the problem with outliers" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GG, Nonlinear least squares method for bound-constrained problems\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 1.05037E+00\n", + " Norm of gradient 8.78014E-06\n", + " Norm of scaled gradient 6.05781E-06\n", + " Norm of step 1.47886E-01\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf 3.61301E-01 inf\n", + " 2 -inf 9.10227E-01 inf\n", + " 3 -inf 3.42138E-03 inf\n", + " 4 -inf -6.08965E+00 inf\n", + " 5 -inf 6.24881E-04 inf\n" + ] + } + ], + "source": [ + "# Call the solver\n", + "x = np.ones(nvar, dtype=float)\n", + "res = opt.handle_solve_bxnl(handle, lsqfun, lsqgrd, x, nres, data=data,\n", + " io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can plot the model with the fitted parameters and see the influence of outliers:" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the data points and the fitted function\n", + "x = res.x\n", + "f_out = lambda t : x[0]*t**2 + x[1]*t + x[2] + x[3]*math.sin(x[4]*t) \n", + "plt.plot(data['t'], data['y'], '*')\n", + "y = [f_out(z) for z in t]\n", + "plt.plot(t, y)\n", + "plt.savefig(\"outlier_fit.png\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Remove the outliers and solve again" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GG, Nonlinear least squares method for bound-constrained problems\n", + " Status: converged, an optimal solution was found\n", + " Value of the objective 5.96811E-02\n", + " Norm of gradient 1.19914E-06\n", + " Norm of scaled gradient 3.47087E-06\n", + " Norm of step 3.49256E-06\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf 3.53888E-01 inf\n", + " 2 -inf 1.06575E+00 inf\n", + " 3 -inf 1.91383E-03 inf\n", + " 4 -inf 2.17299E-01 inf\n", + " 5 -inf 5.17660E+00 inf\n" + ] + } + ], + "source": [ + "# Disable the two outlier residuals\n", + "opt.handle_disable(handle, comp='NLS', idx=[10, 20])\n", + "\n", + "# Solve the problem again\n", + "x = np.ones(nvar, dtype=float)\n", + "res = opt.handle_solve_bxnl(handle, lsqfun, lsqgrd, x, nres, data=data,\n", + " io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The fitted function is much closer to the data!" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the data points and the fitted function\n", + "x = res.x\n", + "f_fit = lambda t : x[0]*t**2 + x[1]*t + x[2] + x[3]*math.sin(x[4]*t) \n", + "plt.plot(data['t'], data['y'], '*')\n", + "y = [f_fit(z) for z in t]\n", + "plt.plot(t, y)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": {}, + "outputs": [], + "source": [ + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/local_optimization/production_planning.ipynb b/local_optimization/production_planning.ipynb new file mode 100644 index 0000000..c336b2b --- /dev/null +++ b/local_optimization/production_planning.ipynb @@ -0,0 +1,295 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Edit and solve different variants of a production-planning problem\n", + "\n", + "## Correct Rendering of this notebook\n", + "\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "\n", + "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", + "\n", + "## Problem description\n", + "We consider a situation where a factory can manufacture two different chemicals $A_1$ and $A_2$. The goal for the factory is to determine the quantities $x_1$ and $x_2$ of each chemical to maximize profit under the following circumstances:\n", + "- a unit of $A_1$ weighs 40kg and a unit of $A_2$ weighs 80kg;\n", + "- the total daily production cannot exceed 16000kg to match the transport capabilities;\n", + "- the factory generates \\\\$2 profit for each unit of $A_1$ and \\\\$4.5 profit for each unit of $A_2$;\n", + "- both products need to use the same machine as part of their respective processes; a unit of A1 requires 1.2 minutes of machine time while a unit of $A_2$ requires 3 minutes; the machine can only function for 1500 minutes daily;\n", + "- a unit of $A_1$ uses 6 square metres of packing material while a unit of $A_2$ uses 10 square metres; 6000 square metres of packing materials are available each day;\n", + "- production of $A_2$ is limited to 100 units per day.\n", + "\n", + "Note that since the chemicals are considered fluid, the quantities $x_1$ and $x_2$ are not limited to integer values.\\\\\n", + "\n", + "The problem can be formulated as a linear program:\n", + "\\vspace{0.1cn}\n", + "\\begin{equation*}\n", + "\\begin{array}{lll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{maximize}} & 2x_1+4.5x_2&\\\\[0.6ex]\n", + "\\mbox{subject to} & 1.2x_1 + 3x_2 \\leq 1500, &\\text{ (machine time constraint)} \\\\[0.6ex]\n", + " & 6x_1+10x_2 \\leq 6000, & \\text{ (packaging material constraint)} \\\\[0.6ex]\n", + " & 40x_1+80x_2 \\leq 16000, & \\text{ (transport constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_1, & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_1 \\leq 100 & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + "\\end{array}\n", + "\\end{equation*}" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04MT, Interior point method for LP problems\n", + " Status: converged, an optimal solution found\n", + " Final primal objective value 8.500000E+02\n", + " Final dual objective value 8.500000E+02\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 2.00000E+02 inf\n", + " 2 0.00000E+00 1.00000E+02 1.00000E+02\n" + ] + } + ], + "source": [ + "# Define and solve the linear program with the NAG optimization modelling suite\n", + "\n", + "from naginterfaces.library import opt\n", + "from naginterfaces.base import utils\n", + "\n", + "infbnd = 1.0e20\n", + " \n", + "# Initialize the Optimization model handle with the number of variables\n", + "handle = opt.handle_init(2)\n", + "\n", + "# Define a linear objective function\n", + "opt.handle_set_linobj(handle, cvec=[2.0, 4.5])\n", + "\n", + "# Box constraints\n", + "opt.handle_set_simplebounds(\n", + " handle,\n", + " bl=[0.0, 0.0],\n", + " bu=[infbnd, 100])\n", + "\n", + "# Set the linear constraints\n", + "opt.handle_set_linconstr(\n", + " handle,\n", + " bl=[-infbnd, -infbnd, -infbnd],\n", + " bu=[1500.0, 6000.0, 16000.0],\n", + " irowb=[1, 1, 2, 2, 3, 3],\n", + " icolb=[1, 2, 1, 2, 1, 2],\n", + " b=[1.2, 3.0, 6.0, 10.0, 40.0, 80.0]\n", + ")\n", + "\n", + "# Set some alogorithmic options\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + " 'Task = Max',\n", + " 'Print Solution = X',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)\n", + "\n", + "# Solve the problem\n", + "res = opt.handle_solve_lp_ipm(handle, io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimal repartition is to produce 200 units of $A_1$ and 100 units of $A_2$ for a total profit of 850\\\\$.\n", + "\n", + "### Plant expansion: a new chemical $A_3$ can be produced \n", + "\n", + "The following data is available for $A_3$:\n", + "- a unit of $A_3$ takes 5 minutes on the common machine;\n", + "- a unit of $A_3$ takes 12 square metres of packaging material;\n", + "- a unit of $A_3$ weighs 120kg;\n", + "- a unit of $A_3$ generates \\\\$7 profit;\n", + "- production of $A_3$ is limited to 50 units per day.\n", + "\n", + "The problem becomes:\n", + "\\vspace{0.1cn}\n", + "\\begin{equation*}\n", + "\\begin{array}{lll}\n", + "\\underset{x\\in\\Re^n}{\\mbox{maximize}} & 2x_1+4.5x_2+7x_3&\\\\[0.6ex]\n", + "\\mbox{subject to} & 1.2x_1 + 3x_2 + 5x_3 \\leq 1500, &\\text{ (machine time constraint)} \\\\[0.6ex]\n", + " & 6x_1+10x_2+12x_3 \\leq 6000, & \\text{ (packaging material constraint)} \\\\[0.6ex]\n", + " & 40x_1+80x_2+120x_3 \\leq 16000, & \\text{ (transport constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_1, & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_1 \\leq 100 & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_3 \\leq 50 & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + "\\end{array}\n", + "\\end{equation*}" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04MT, Interior point method for LP problems\n", + " Status: converged, an optimal solution found\n", + " Final primal objective value 9.000000E+02\n", + " Final dual objective value 9.000000E+02\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 5.00000E+01 inf\n", + " 2 0.00000E+00 1.00000E+02 1.00000E+02\n", + " 3 0.00000E+00 5.00000E+01 5.00000E+01\n" + ] + } + ], + "source": [ + "# Edit the problem to account for the new plant capacity\n", + "# add a variable\n", + "opt.handle_add_vars(handle, nadd=1)\n", + "\n", + "# Box Constraint on the new variable\n", + "opt.handle_set_bound(handle, comp='X', idx=3, bli=0.0, bui=50.0)\n", + "\n", + "# Add the linear objective component\n", + "opt.handle_set_linobj_coeff(handle, idxci=3, ci=7.0)\n", + "\n", + "# Add linear constraints coefficients\n", + "opt.handle_set_linconstr_coeff(handle, idlc=1, icolbj=3, bij=5.0)\n", + "opt.handle_set_linconstr_coeff(handle, idlc=2, icolbj=3, bij=12.0)\n", + "opt.handle_set_linconstr_coeff(handle, idlc=3, icolbj=3, bij=120.0)\n", + "\n", + "# Solve the problem again\n", + "res = opt.handle_solve_lp_ipm(handle, io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The new optimum is to produce 50 units of $A_1$, 100 units of $A_2$ and 50 units of $A_3$ for a total profit of 900\\\\$.\n", + "\n", + "### New regulation: additional constraint\n", + "\n", + "At a later date, regulation changes require that products $A_2$ and $A_3$ follow a rigorous quality assurance test before being sent to market. Now the factory is only able to process a total of 100 units per day which amounts to adding the following constraint to our linear program:\n", + "\\begin{equation*}\n", + "\\begin{array}{ll}\n", + " x_2+x_3 \\leq 100 & \\text{ (regulation constraint)} \\\\[0.6ex]\n", + "\\end{array}\n", + "\\end{equation*}" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04MT, Interior point method for LP problems\n", + " Status: converged, an optimal solution found\n", + " Final primal objective value 8.750000E+02\n", + " Final dual objective value 8.750000E+02\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 0.00000E+00 1.50000E+02 inf\n", + " 2 0.00000E+00 5.00000E+01 1.00000E+02\n", + " 3 0.00000E+00 5.00000E+01 5.00000E+01\n" + ] + } + ], + "source": [ + "# Add a linear constraint\n", + "opt.handle_set_linconstr(\n", + " handle,\n", + " bl=[-infbnd],\n", + " bu=[100.0],\n", + " irowb=[1, 1],\n", + " icolb=[2, 3],\n", + " b=[1.0, 1.0]\n", + ")\n", + "\n", + "# Solve the problem again\n", + "res = opt.handle_solve_lp_ipm(handle, io_manager=iom)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the new regulation, maximum profit of 875\\\\$ can be achived by producing 150 units of $A_1$, 50 units of $A_2$ and 50 units of $A_3$." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} From cff5cca017da2e0e14491b01e51d6d0f7a491e9d Mon Sep 17 00:00:00 2001 From: Ben Date: Wed, 25 Nov 2020 13:51:24 +0100 Subject: [PATCH 066/182] added data file for data fitting example --- local_optimization/nlnlsq_data.pck | Bin 0 -> 572 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 local_optimization/nlnlsq_data.pck diff --git a/local_optimization/nlnlsq_data.pck b/local_optimization/nlnlsq_data.pck new file mode 100644 index 0000000000000000000000000000000000000000..353830bd2cd9c650a5651fd33a992479fa7dbaf8 GIT binary patch literal 572 zcmZo*nQF+y00y;FGLsaNqv{BILgR?P-q7cQ*98?|(f_aQV(eDfj&^6Q!!B z39fM8|6E7ezvz&u`~D~2!7TUvj}DmtnE~$mAN1M+_1$&f57Y`|U2)%k!)@NvmdtnV z`$47wh1~a_1Mwp~-1i>?8(ibQe;3f)|q|Xhj_Wi-5weUsXdI9kWjhjw|;}B z;$`>!52th%pOEBp-+!~_`^=gUFQEVKX)n4j8x54&y1|Y+8W>>rv)`}=tnCAesI0wo zNA$P*{(BYoeNG8|1d7NVkXs!i?{5FtLG5}hs}C^bPR~F0-sK-Kz^1FnpIu<(zWeCbY0zhbrTX6P_KRIId_RWHakoFJAmRPp8yHRx7JOSMwob_1 z{$Zn8`dr4tKyw-;lp Date: Fri, 11 Dec 2020 19:41:52 -0600 Subject: [PATCH 067/182] added link to docs --- special_functions/opt_imp_vol/imp_vol_demo.ipynb | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/special_functions/opt_imp_vol/imp_vol_demo.ipynb b/special_functions/opt_imp_vol/imp_vol_demo.ipynb index a28af75..81c152c 100644 --- a/special_functions/opt_imp_vol/imp_vol_demo.ipynb +++ b/special_functions/opt_imp_vol/imp_vol_demo.ipynb @@ -272,8 +272,19 @@ "P. Jäckel (2015). Let’s be rational. *Wilmott* 2015, 40-53.\n", "\n", "K. Glau, P. Herold, D. B. Madan, C. Pötz (2019). The Chebyshev method for the implied volatility.\n", - "*Journal of Computational Finance*, 23(3)." + "*Journal of Computational Finance*, 23(3).\n", + "\n", + "### NAG Library for Python Setup\n", + "\n", + "Find instructions to install the NAG Library for Python in the documentation here: https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { From 89eeaafbee79002679797990884e04de5af992a4 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 26 Jan 2021 13:19:36 +0000 Subject: [PATCH 068/182] Update Readme.md --- local_optimization/Readme.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index d93803d..db535ce 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -1,4 +1,8 @@ -# Local Optimization Examples +![NAG Logo](../nag_logo.png) + +# Local Optimization + +# Content * [Second Order Cone Programming (SOCP)](./SOCP/) * [First order active set CG (FOAS)](./FOAS) From f34dfca409eb56294cfc904bd1ead614e25213c9 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 26 Jan 2021 13:57:03 +0000 Subject: [PATCH 069/182] Rename local_optimization/DFO_noisy.ipynb to local_optimization/DFO/DFO_noisy.ipynb --- local_optimization/{ => DFO}/DFO_noisy.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename local_optimization/{ => DFO}/DFO_noisy.ipynb (100%) diff --git a/local_optimization/DFO_noisy.ipynb b/local_optimization/DFO/DFO_noisy.ipynb similarity index 100% rename from local_optimization/DFO_noisy.ipynb rename to local_optimization/DFO/DFO_noisy.ipynb From bbaac965353138ad0e0cccf287f1f4a29bbc81fe Mon Sep 17 00:00:00 2001 From: Andrew Sajo Date: Tue, 26 Jan 2021 14:17:01 +0000 Subject: [PATCH 070/182] Move files into directories --- local_optimization/{ => DFO}/animation.mp4 | Bin local_optimization/{ => Modelling}/LP_demo.ipynb | 0 .../{ => Modelling}/christmas_demo.ipynb | 0 .../{ => Modelling}/handle_disable_ex.ipynb | 0 local_optimization/{ => Modelling}/nlnlsq_data.pck | Bin .../{ => Modelling}/production_planning.ipynb | 0 .../{ => Notebooks}/bounds_quasi_func_easy.ipynb | 0 7 files changed, 0 insertions(+), 0 deletions(-) rename local_optimization/{ => DFO}/animation.mp4 (100%) rename local_optimization/{ => Modelling}/LP_demo.ipynb (100%) rename local_optimization/{ => Modelling}/christmas_demo.ipynb (100%) rename local_optimization/{ => Modelling}/handle_disable_ex.ipynb (100%) rename local_optimization/{ => Modelling}/nlnlsq_data.pck (100%) rename local_optimization/{ => Modelling}/production_planning.ipynb (100%) rename local_optimization/{ => Notebooks}/bounds_quasi_func_easy.ipynb (100%) diff --git a/local_optimization/animation.mp4 b/local_optimization/DFO/animation.mp4 similarity index 100% rename from local_optimization/animation.mp4 rename to local_optimization/DFO/animation.mp4 diff --git a/local_optimization/LP_demo.ipynb b/local_optimization/Modelling/LP_demo.ipynb similarity index 100% rename from local_optimization/LP_demo.ipynb rename to local_optimization/Modelling/LP_demo.ipynb diff --git a/local_optimization/christmas_demo.ipynb b/local_optimization/Modelling/christmas_demo.ipynb similarity index 100% rename from local_optimization/christmas_demo.ipynb rename to local_optimization/Modelling/christmas_demo.ipynb diff --git a/local_optimization/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb similarity index 100% rename from local_optimization/handle_disable_ex.ipynb rename to local_optimization/Modelling/handle_disable_ex.ipynb diff --git a/local_optimization/nlnlsq_data.pck b/local_optimization/Modelling/nlnlsq_data.pck similarity index 100% rename from local_optimization/nlnlsq_data.pck rename to local_optimization/Modelling/nlnlsq_data.pck diff --git a/local_optimization/production_planning.ipynb b/local_optimization/Modelling/production_planning.ipynb similarity index 100% rename from local_optimization/production_planning.ipynb rename to local_optimization/Modelling/production_planning.ipynb diff --git a/local_optimization/bounds_quasi_func_easy.ipynb b/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb similarity index 100% rename from local_optimization/bounds_quasi_func_easy.ipynb rename to local_optimization/Notebooks/bounds_quasi_func_easy.ipynb From d72c6a46a86d3c10812eb2fe1dd7046180d3f9ed Mon Sep 17 00:00:00 2001 From: Andrew Sajo Date: Tue, 26 Jan 2021 15:08:29 +0000 Subject: [PATCH 071/182] Add images folder --- local_optimization/images/dfo_calib.png | Bin 0 -> 77417 bytes local_optimization/images/wingsection.png | Bin 0 -> 276738 bytes 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 local_optimization/images/dfo_calib.png create mode 100644 local_optimization/images/wingsection.png diff 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HcmV?d00001 From 4a89481ed0d7967e3aad078b71f63ce4c2e6750b Mon Sep 17 00:00:00 2001 From: A Date: Tue, 26 Jan 2021 17:24:25 +0000 Subject: [PATCH 072/182] Update Readme.md Mayor updated to landing page --- local_optimization/Readme.md | 135 ++++++++++++++++++++++++++++++++++- 1 file changed, 133 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index db535ce..36c4529 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -1,6 +1,21 @@ -![NAG Logo](../nag_logo.png) +[![NAG Logo](../nag_logo.png)](https://www.nag.com) -# Local Optimization +# Local Optimization + +Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html). + +If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). + + +

+ + + +
DFO Calibration example           Optimization example of a wing section
+ +**Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, +red line shows the final solution. (right) Optimization of a wing section: red represent the baseline, center section in yellow +shows an overall improvement of 13% while the rightmost section in green/blue shows a further 33% improvement. # Content @@ -8,6 +23,122 @@ * [First order active set CG (FOAS)](./FOAS) * [Nonlinear Least-Squares (BXNL)](./BXNL) * [Semi-Definite Programming (SDP)](./SDP/) +* [Derivative-Free Optimization (DFO)](./DFO/) +* [Tips and Tricks in modelling](./modelling) + +## Examples (Remove) * [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) * [Linear Programming Demo](./LP_demo.ipynb) * [Model-based derivative free optimization](./DFO_noisy.ipynb) + +# How to install the NAG Library for Python + +In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). + +### Step 1. Downloading and Installing (`pip`) +Installing the Library is done using the `pip` package manager, fire-up a terminal and create a Python 3 virtual environment where to install and test the Library +```{bash} +guest@nag-37:~$ python3 -m venv nag3 +guest@nag-37:~$ . nag3/bin/activate +(nag3) guest@nag-37:~$ +``` + +```{bash} +(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces +``` +or if you have Intel MKL, then use +```{bash} +(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces +``` +for Intel MKL-enabled NAG Library. + +### Step 2. Getting a Trial License +The next step is to get the licensing info (**product code** and **KUSARI ID**) and request a lincense. From the same virtual terminal +```{bash} +(nag3) andrews@olney:~$ python -m naginterfaces.kusari +``` +The output should be similar to +``` +The NAG Library for Python on this platform uses +underlying Library NLL6I271VL. +This Library has been installed as part of the package +and it requires a valid licence key. +No such key could be validated: +the key may not have been installed correctly or +it may have expired. +The Kusari licence-check utility reports the following: +User: guest +Directory: /home/guest +NAG_KUSARI_FILE="" +File /home/guest/nag.key does not exist +------------------------------------------------------------------------------- +Error: Licence not found; this product requires a key for NLL6I271VL +The above information has been generated on machine olney.nag.co.uk +For information on how to obtain a licence, please see +https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html +KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd" +``` +The **two** important bits are the + + 1. **product code** shown as **`underlying Library NLL6I271VL.`** which identifies the lincense to request, and + + 2. **Kusary ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd"`** which idenfies the machine you are running the library on. + + **Note** the **product code** might be different while the **Kusari ID** _will_ be different for your case. + + With these, you are set to [contact NAG and request a trial license](https://www.nag.com/content/software-trials?product=NAG%20Library). + + The trial licence is a plain text chunk similar to + ``` + NLL6I271VL TRIAL "Xu+++XjvgmyemlussawO0+++++" "++++vylBNlEagiaouoce----" & +& "k5kissm+n+++++eyhH5gabf" + ``` + So copy and save the text into the file `/home/guest/nag.key`. + + The final step is to make sure the licence is valid and the library is working as expected + +### Step 3. Testing the Library +The last step is to make sure the licence was correctly stored and that the library is working correctly. From the same virtual terminal re-run kusary +```{bash} +(nag3) andrews@olney:~$ python -m naginterfaces.kusari +``` +This time the output should be similar to +``` +``` +Let's try some other more interesting example ([list of optimization examples](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#examples)) + +This command runs the example for the [FOAS (First-Order Active set method) solver and minimizes the Rosenbrock 2D function](./FOAS). +``` +python -m naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex +``` + +### Running more examples + +All examples may be executed sequentially by running +``` +python -m naginterfaces.library.examples +``` +To display the full list of example source files on disk, but not run them, execute +``` +python -m naginterfaces.library.examples --locate +``` +Run +``` +python -m naginterfaces.library.examples --help +``` +to see any additional usage. + + + +# Useful links + +* [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) +* [NAG Library Optimization (Chapter E04) Introduction](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) +* [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) +* [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree) +* [Request a Trial Licence](https://www.nag.com/content/software-trials?product=NAG%20Library) +* [kurari license module documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) + + From 781b9e613f2c6128b1eaaf77e2929c5672813a50 Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Tue, 26 Jan 2021 15:03:28 -0600 Subject: [PATCH 073/182] Revert "Update Readme.md" --- local_optimization/Readme.md | 135 +---------------------------------- 1 file changed, 2 insertions(+), 133 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 36c4529..db535ce 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -1,21 +1,6 @@ -[![NAG Logo](../nag_logo.png)](https://www.nag.com) +![NAG Logo](../nag_logo.png) -# Local Optimization - -Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html). - -If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). - - - - - - -
DFO Calibration example           Optimization example of a wing section
- -**Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, -red line shows the final solution. (right) Optimization of a wing section: red represent the baseline, center section in yellow -shows an overall improvement of 13% while the rightmost section in green/blue shows a further 33% improvement. +# Local Optimization # Content @@ -23,122 +8,6 @@ shows an overall improvement of 13% while the rightmost section in green/blue sh * [First order active set CG (FOAS)](./FOAS) * [Nonlinear Least-Squares (BXNL)](./BXNL) * [Semi-Definite Programming (SDP)](./SDP/) -* [Derivative-Free Optimization (DFO)](./DFO/) -* [Tips and Tricks in modelling](./modelling) - -## Examples (Remove) * [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) * [Linear Programming Demo](./LP_demo.ipynb) * [Model-based derivative free optimization](./DFO_noisy.ipynb) - -# How to install the NAG Library for Python - -In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). - -### Step 1. Downloading and Installing (`pip`) -Installing the Library is done using the `pip` package manager, fire-up a terminal and create a Python 3 virtual environment where to install and test the Library -```{bash} -guest@nag-37:~$ python3 -m venv nag3 -guest@nag-37:~$ . nag3/bin/activate -(nag3) guest@nag-37:~$ -``` - -```{bash} -(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces -``` -or if you have Intel MKL, then use -```{bash} -(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces -``` -for Intel MKL-enabled NAG Library. - -### Step 2. Getting a Trial License -The next step is to get the licensing info (**product code** and **KUSARI ID**) and request a lincense. From the same virtual terminal -```{bash} -(nag3) andrews@olney:~$ python -m naginterfaces.kusari -``` -The output should be similar to -``` -The NAG Library for Python on this platform uses -underlying Library NLL6I271VL. -This Library has been installed as part of the package -and it requires a valid licence key. -No such key could be validated: -the key may not have been installed correctly or -it may have expired. -The Kusari licence-check utility reports the following: -User: guest -Directory: /home/guest -NAG_KUSARI_FILE="" -File /home/guest/nag.key does not exist -------------------------------------------------------------------------------- -Error: Licence not found; this product requires a key for NLL6I271VL -The above information has been generated on machine olney.nag.co.uk -For information on how to obtain a licence, please see -https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html -KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd" -``` -The **two** important bits are the - - 1. **product code** shown as **`underlying Library NLL6I271VL.`** which identifies the lincense to request, and - - 2. **Kusary ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd"`** which idenfies the machine you are running the library on. - - **Note** the **product code** might be different while the **Kusari ID** _will_ be different for your case. - - With these, you are set to [contact NAG and request a trial license](https://www.nag.com/content/software-trials?product=NAG%20Library). - - The trial licence is a plain text chunk similar to - ``` - NLL6I271VL TRIAL "Xu+++XjvgmyemlussawO0+++++" "++++vylBNlEagiaouoce----" & -& "k5kissm+n+++++eyhH5gabf" - ``` - So copy and save the text into the file `/home/guest/nag.key`. - - The final step is to make sure the licence is valid and the library is working as expected - -### Step 3. Testing the Library -The last step is to make sure the licence was correctly stored and that the library is working correctly. From the same virtual terminal re-run kusary -```{bash} -(nag3) andrews@olney:~$ python -m naginterfaces.kusari -``` -This time the output should be similar to -``` -``` -Let's try some other more interesting example ([list of optimization examples](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#examples)) - -This command runs the example for the [FOAS (First-Order Active set method) solver and minimizes the Rosenbrock 2D function](./FOAS). -``` -python -m naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex -``` - -### Running more examples - -All examples may be executed sequentially by running -``` -python -m naginterfaces.library.examples -``` -To display the full list of example source files on disk, but not run them, execute -``` -python -m naginterfaces.library.examples --locate -``` -Run -``` -python -m naginterfaces.library.examples --help -``` -to see any additional usage. - - - -# Useful links - -* [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) -* [NAG Library Optimization (Chapter E04) Introduction](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) -* [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) -* [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree) -* [Request a Trial Licence](https://www.nag.com/content/software-trials?product=NAG%20Library) -* [kurari license module documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) - - From fe258bea08d8e92b276249cab5170d87f1db3687 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 08:59:48 +0000 Subject: [PATCH 074/182] Update Readme.md Further updates to Kusari --- local_optimization/Readme.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 36c4529..28db8f1 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -52,10 +52,10 @@ or if you have Intel MKL, then use ``` for Intel MKL-enabled NAG Library. -### Step 2. Getting a Trial License +### Step 2. Getting a Trial Licence The next step is to get the licensing info (**product code** and **KUSARI ID**) and request a lincense. From the same virtual terminal ```{bash} -(nag3) andrews@olney:~$ python -m naginterfaces.kusari +(nag3) guest@nag-37:~$ python -m naginterfaces.kusari ``` The output should be similar to ``` @@ -86,7 +86,7 @@ The **two** important bits are the **Note** the **product code** might be different while the **Kusari ID** _will_ be different for your case. - With these, you are set to [contact NAG and request a trial license](https://www.nag.com/content/software-trials?product=NAG%20Library). + With these, you are set to [contact NAG and request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library). The trial licence is a plain text chunk similar to ``` @@ -98,7 +98,7 @@ The **two** important bits are the The final step is to make sure the licence is valid and the library is working as expected ### Step 3. Testing the Library -The last step is to make sure the licence was correctly stored and that the library is working correctly. From the same virtual terminal re-run kusary +The last step is to make sure the licence was correctly stored and that the library is working correctly. From the same virtual terminal re-run Kusary licence module ```{bash} (nag3) andrews@olney:~$ python -m naginterfaces.kusari ``` @@ -135,9 +135,9 @@ to see any additional usage. * [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) * [NAG Library Optimization (Chapter E04) Introduction](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) * [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) -* [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree) -* [Request a Trial Licence](https://www.nag.com/content/software-trials?product=NAG%20Library) -* [kurari license module documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) +* [Decision Tree for selecting the right optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree) +* [Request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library) +* [Kusari licence module Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) From 261cb1d76a6a6997682d3c077e7d74e5973ec50e Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 09:48:03 +0000 Subject: [PATCH 076/182] Doc anchors --- local_optimization/Readme.md | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 3fa608c..176387d 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -1,6 +1,6 @@ [![NAG Logo](../nag_logo.png)](https://www.nag.com) -# Local Optimization +# Local Optimization
Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html). @@ -17,13 +17,13 @@ If you are already familiar with NAG's optimization offering and just need to fi red line shows the final solution. (right) Optimization of a wing section: red represent the baseline, center section in yellow shows an overall improvement of 13% while the rightmost section in green/blue shows a further 33% improvement. -# Content +# Content -* [How to install the NAG Library for Python]() -* [How to run the Jupyter Notebooks]() -* [Useful links]() +* [How to install the NAG Library for Python](#install) +* [How to run the Jupyter notebook examples](#jupyter) +* [Useful links](#links) -## Repository +### Repository * [Second Order Cone Programming (SOCP)](./SOCP/) * [First order active set CG (FOAS)](./FOAS/) @@ -32,12 +32,12 @@ shows an overall improvement of 13% while the rightmost section in green/blue sh * [Derivative-Free Optimization (DFO)](./DFO/) * [Tips and Tricks in modelling](./modelling/) -## Examples (Remove) +### Examples (Remove) * [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) * move this into modelling [Linear Programming Demo](./LP_demo.ipynb) * move this into DFO [Model-based derivative free optimization](./DFO_noisy.ipynb) -# How to install the NAG Library for Python +# How to install the NAG Library for Python In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). @@ -145,9 +145,9 @@ python -m naginterfaces.library.examples ``` Run `python -m naginterfaces.library.examples --help` to see any additional usage. - +# How to run the Jupyter notebook examples -# Useful links +# Useful links * [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) * [NAG Library Optimization (Chapter E04) Introduction](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) @@ -156,6 +156,8 @@ Run `python -m naginterfaces.library.examples --help` to see any additional usag * [Request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library) * [Kusari licence module Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) + +**[Back to Top](#top)** From 5fa79ad45ee393223520c4b9a15a0fa1c6029aad Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 09:53:58 +0000 Subject: [PATCH 077/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 176387d..aa3edd2 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -2,7 +2,7 @@ # Local Optimization -Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html). +Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) on this repository. If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). From fc8be91a7a33f93ed20d9bd36bd5b7c256c1f4ec Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 11:22:52 +0000 Subject: [PATCH 078/182] Add badges --- local_optimization/Readme.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index aa3edd2..c7e5cdf 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -147,6 +147,15 @@ Run `python -m naginterfaces.library.examples --help` to see any additional usag # How to run the Jupyter notebook examples +This section briefly illustrates how to setup a host in order to open and run the [Jupyter notebooks](https://jupyter.org/) provided in this repository. +Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting it is advisable to read [Jupyter's installation guide](). + +You can [view a static render of the notebooks using Jupiter's nbviewer here](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/) +[![Jupyter](https://img.shields.io/badge/launch-nbviewer-blue?logo=jupyter&logoColor=white)](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/). +Alternatively, use [Binder](https://mybinder.org/) to view a [render of the notebooks here](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD) +[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD) + + # Useful links * [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) From a109fbf8cb6ab36a67f9d67d2834a954392cf26c Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 11:53:49 +0000 Subject: [PATCH 079/182] Update Readme.md --- local_optimization/Readme.md | 42 +++++++++++++++++++++++++++++++----- 1 file changed, 37 insertions(+), 5 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index c7e5cdf..aaa4c90 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -145,15 +145,47 @@ python -m naginterfaces.library.examples ``` Run `python -m naginterfaces.library.examples --help` to see any additional usage. + + # How to run the Jupyter notebook examples This section briefly illustrates how to setup a host in order to open and run the [Jupyter notebooks](https://jupyter.org/) provided in this repository. -Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting it is advisable to read [Jupyter's installation guide](). +Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting it is advisable to read [Jupyter's installation page](https://jupyter.org/install.html). + +You can [view a static render of the notebooks using Jupyter's nbviewer here](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/) +[![Jupyter](https://img.shields.io/badge/launch-nbviewer-blue?logo=jupyter&logoColor=white)](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/) +or alternatively use [Binder](https://mybinder.org/) to [view them here](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD) +[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD). + + +### Installing Jupyter +To install jupyter, launch a terminal and activate the virtual environment used to install the NAG Library for Python +```{bash} +guest@nag-37:~$ . nag3/bin/activate +(nag3) guest@nag-37:~$ pip install notebook +Collecting notebook + Downloading https://files.pythonhosted.org/packages/74/19/50cd38acf22e33370d01fef764355f1e3517f6e12b4fceb8d434ece4f8fd/notebook-6.2.0-py3-none-any.whl (9.5MB) + 100% |████████████████████████████████| 9.5MB 115kB/s +Collecting argon2-cffi (from notebook) +... +Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwidth-0.2.5 +``` +This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example +### Running the notebook examples +Once `pip` finished to install `notebook` all the dependencies, it is time start up the notebook interface +```{bash} +(nag3) guest@nag-37:~$ jupyter-notebook +[I 05:13:44.313 NotebookApp] Serving notebooks from local directory: /home/guest +[I 05:13:44.313 NotebookApp] 0 active kernels +[I 05:13:44.313 NotebookApp] The Jupyter Notebook is running at: http://localhost:8888/ +[I 05:13:44.313 NotebookApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation). +``` +This command will fire-up your web browser and launch the notebook service. Use the gui interface to open up any of the notebooks provided in this repository + + + + -You can [view a static render of the notebooks using Jupiter's nbviewer here](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/) -[![Jupyter](https://img.shields.io/badge/launch-nbviewer-blue?logo=jupyter&logoColor=white)](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/). -Alternatively, use [Binder](https://mybinder.org/) to view a [render of the notebooks here](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD) -[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/numericalalgorithmsgroup/NAGPythonExamples/HEAD) # Useful links From 7c60eefcacd1ea27b69995451e7d39e7a9b4aba7 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 12:02:53 +0000 Subject: [PATCH 080/182] Update Readme.md --- local_optimization/Readme.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index aaa4c90..3486cb4 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -152,14 +152,14 @@ Run `python -m naginterfaces.library.examples --help` to see any additional usag This section briefly illustrates how to setup a host in order to open and run the [Jupyter notebooks](https://jupyter.org/) provided in this repository. Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting it is advisable to read [Jupyter's installation page](https://jupyter.org/install.html). -You can [view a static render of the notebooks using Jupyter's nbviewer here](https://nbviewer.jupyter.org/github/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/) + -### Installing Jupyter -To install jupyter, launch a terminal and activate the virtual environment used to install the NAG Library for Python +### Installing Jupyter notebook +To install Jupyter, launch a terminal and activate the virtual environment used to install the NAG Library for Python ```{bash} guest@nag-37:~$ . nag3/bin/activate (nag3) guest@nag-37:~$ pip install notebook From 395fd1792a5e3c5b4aa587f6c9248b2b1097bfda Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 12:03:59 +0000 Subject: [PATCH 081/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 3486cb4..daacaf0 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -172,7 +172,7 @@ Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwid ``` This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example ### Running the notebook examples -Once `pip` finished to install `notebook` all the dependencies, it is time start up the notebook interface +Once `pip` finished to install `notebook` and all the dependencies, it is time start up the notebook interface ```{bash} (nag3) guest@nag-37:~$ jupyter-notebook [I 05:13:44.313 NotebookApp] Serving notebooks from local directory: /home/guest From 026aed0856a5b37b7f80eaca2cd80fb397aa60d1 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 12:43:54 +0000 Subject: [PATCH 082/182] Update Readme.md --- local_optimization/Readme.md | 25 +++++++++++++++++-------- 1 file changed, 17 insertions(+), 8 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index daacaf0..80f6ede 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -162,7 +162,7 @@ or alternatively use [Binder](https://mybinder.org/) to [view them here](https:/ To install Jupyter, launch a terminal and activate the virtual environment used to install the NAG Library for Python ```{bash} guest@nag-37:~$ . nag3/bin/activate -(nag3) guest@nag-37:~$ pip install notebook +(nag3) guest@nag-37:~$ pip install notebook matplotlib Collecting notebook Downloading https://files.pythonhosted.org/packages/74/19/50cd38acf22e33370d01fef764355f1e3517f6e12b4fceb8d434ece4f8fd/notebook-6.2.0-py3-none-any.whl (9.5MB) 100% |████████████████████████████████| 9.5MB 115kB/s @@ -172,15 +172,24 @@ Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwid ``` This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example ### Running the notebook examples -Once `pip` finished to install `notebook` and all the dependencies, it is time start up the notebook interface +Once `pip` finished to install `notebook` and all the dependencies, it is time to grab a copy of the notebook of interest and start up the notebook interface. +In this example we download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) file `rosenbrock2d.ipynb` into the current working directory ```{bash} -(nag3) guest@nag-37:~$ jupyter-notebook -[I 05:13:44.313 NotebookApp] Serving notebooks from local directory: /home/guest -[I 05:13:44.313 NotebookApp] 0 active kernels -[I 05:13:44.313 NotebookApp] The Jupyter Notebook is running at: http://localhost:8888/ -[I 05:13:44.313 NotebookApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation). +(nag3) guest@nag-37:~$ curl -O https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/local_optimization/FOAS/rosenbrock2d.ipynb + % Total % Received % Xferd Average Speed Time Time Time Current + Dload Upload Total Spent Left Speed +100 61961 100 61961 0 0 382k 0 --:--:-- --:--:-- --:--:-- 382k ``` -This command will fire-up your web browser and launch the notebook service. Use the gui interface to open up any of the notebooks provided in this repository +and open it using `jupyter-notebook` +```{bash} +(nag3) guest@nag-37:~$ jupyter-notebook rosenbrock2d.ipynb +[I 12:24:07.336 NotebookApp] Serving notebooks from local directory: /home/guest +[I 12:24:07.336 NotebookApp] Jupyter Notebook 6.2.0 is running at: +[I 12:24:07.336 NotebookApp] http://localhost:8888/?token=f1836a06799a92f25ef9966439bf3491b2f0960dcb51806d +... +``` +This command will fire-up your web browser and launch the web gui and open the `rosenbrock2d.ipynb` notebook and should have an output similar to +![Notebook screenshot](Notebooks/screenshot.png) From e52eeecb3335f3797034789d87291b510f123e2f Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 12:44:21 +0000 Subject: [PATCH 083/182] Add files via upload --- local_optimization/Notebooks/screenshot.png | Bin 0 -> 108759 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 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z>4f;z)!~m>|4l#Bxx?Vp^}Vhy)`oX5&_Ux3)Mijchg@W!0O1Ot53jPGT%@)@Ah1M8p#!Pf109vpD2>n!=w#Du{c2xthMYk#{d~T z+JV|Pfn=jSG2|Y=^SJ{-hX?U}b+Z8$^CWXK#jUex$Fxe<4l@l-RAAZ3ciV3yq~;9L zLKkuTMh?HOB&nc2^J$JRV`-KYVT|G#%jHMzguc;#!(jc7}gEpczy$J_3#7AYm8 zcm<%1nUs{|*f@ofgLfEbf1;k1PE&edeb?feWEChH#e;wHfF~>Insa6*Q?$c9Ku28{UKO(&y5}O;bD`k&U z#GYZU?Cr`?izxgV*A{)roo}9?$w|0e-Pqt)^^&r)rJag&9J-lsY*b&5P>^pGC082^?-_( z@g!dSgaU+JfKm5wpw<9{vtT!^2U7RD=&tX{X{7_{(hi1gU5DxCsH*@aixe+;Ed(kX zez6~kA|xA+P@xC_q5@{pemqDNE;}iOSL0H&NW(ovP+&>mSZe7YsD)orQDy^P0J}-L zymYlm-z-o7yu41t;1g3oQ5P^M-fvw)Z}(z<6^^_{u!ae3UCPVGEd#0POOW9`5`XR4kTgYgzAgaD zdfMfrC`CiyYIB=5tN-&c2f!mR)FOoh)Vlc9Oc1Lm?wdE+PVD6&9(E|on+086Xc-w@ zgm1gurgirsbJ_RFWLBCsD_i1@SgA>;8w>$2vd(5mWUQ3&c7G(E0yh~Y7PpLsY~DNZ z1|ndfR2CR`l_){>-&Yj|-7cAxzvTn2E_$Y>!w`L_SCPhlr#b-rb+F$HTn35nwjbea zw{Q0v-Q_g+z!cRK-;`j%zb;iX!maJ z!73`^k65EL=+Te4{m Date: Wed, 27 Jan 2021 12:45:04 +0000 Subject: [PATCH 084/182] Update Readme.md --- local_optimization/Readme.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 80f6ede..9f3e906 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -189,6 +189,8 @@ and open it using `jupyter-notebook` ... ``` This command will fire-up your web browser and launch the web gui and open the `rosenbrock2d.ipynb` notebook and should have an output similar to + + ![Notebook screenshot](Notebooks/screenshot.png) From 64decf9554c9a82c035a713ebac2a2add1b7d6a1 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:10:11 +0000 Subject: [PATCH 085/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 9f3e906..12e9ed2 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -188,7 +188,7 @@ and open it using `jupyter-notebook` [I 12:24:07.336 NotebookApp] http://localhost:8888/?token=f1836a06799a92f25ef9966439bf3491b2f0960dcb51806d ... ``` -This command will fire-up your web browser and launch the web gui and open the `rosenbrock2d.ipynb` notebook and should have an output similar to +This command will fire-up your web browser and open the `rosenbrock2d.ipynb` notebook, the window should be similar to ![Notebook screenshot](Notebooks/screenshot.png) From aca6c886168441b18e71867683f6b936fc26c434 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:15:17 +0000 Subject: [PATCH 086/182] Update Readme.md --- local_optimization/Readme.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 12e9ed2..7ce9629 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -170,10 +170,10 @@ Collecting argon2-cffi (from notebook) ... Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwidth-0.2.5 ``` -This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example +This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example. ### Running the notebook examples -Once `pip` finished to install `notebook` and all the dependencies, it is time to grab a copy of the notebook of interest and start up the notebook interface. -In this example we download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) file `rosenbrock2d.ipynb` into the current working directory +To run an example, grab a copy of the notebook of interest and start up the notebook interface. +First, in this example we download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) file `rosenbrock2d.ipynb` into the current directory ```{bash} (nag3) guest@nag-37:~$ curl -O https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/local_optimization/FOAS/rosenbrock2d.ipynb % Total % Received % Xferd Average Speed Time Time Time Current From d0f58b7f0d22135ee6a5addf9a16c74163d3b010 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:16:49 +0000 Subject: [PATCH 087/182] Update Readme.md --- local_optimization/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 7ce9629..03491f3 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -173,14 +173,14 @@ Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwid This indicates that Jupyter was successfully installed. The next section shows how to start the notebok interface and open an example. ### Running the notebook examples To run an example, grab a copy of the notebook of interest and start up the notebook interface. -First, in this example we download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) file `rosenbrock2d.ipynb` into the current directory +For example, download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) notebook `rosenbrock2d.ipynb` into the current directory ```{bash} (nag3) guest@nag-37:~$ curl -O https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/local_optimization/FOAS/rosenbrock2d.ipynb % Total % Received % Xferd Average Speed Time Time Time Current Dload Upload Total Spent Left Speed 100 61961 100 61961 0 0 382k 0 --:--:-- --:--:-- --:--:-- 382k ``` -and open it using `jupyter-notebook` +and now open it using `jupyter-notebook` ```{bash} (nag3) guest@nag-37:~$ jupyter-notebook rosenbrock2d.ipynb [I 12:24:07.336 NotebookApp] Serving notebooks from local directory: /home/guest From 74d52bd39fdc683016b30fc6286c52e62b4848d9 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:19:28 +0000 Subject: [PATCH 088/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 03491f3..64eb1c5 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -2,7 +2,7 @@ # Local Optimization -Here you will find a variety of resources (mostly Python notebooks) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) on this repository. +Here you will find a variety of resources (mostly [Jupyter notebooks](https://jupyter.org/)) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) on this repository. If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). From 7a55b2ee8591e842b09367ea723cd2e9f6356f75 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:20:57 +0000 Subject: [PATCH 089/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 64eb1c5..249a483 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -2,7 +2,7 @@ # Local Optimization -Here you will find a variety of resources (mostly [Jupyter notebooks](https://jupyter.org/)) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) on this repository. +Here you will find a variety of resources (mostly [Jupyter notebooks](https://jupyter.org/)) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [NAG Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) of this `Readme`. If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). From 11be5e08c06cb05c0e7a2750a1c5220406ae4007 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:26:19 +0000 Subject: [PATCH 090/182] Update Readme.md --- local_optimization/Readme.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 249a483..486d585 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -14,8 +14,9 @@ If you are already familiar with NAG's optimization offering and just need to fi **Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, -red line shows the final solution. (right) Optimization of a wing section: red represent the baseline, center section in yellow -shows an overall improvement of 13% while the rightmost section in green/blue shows a further 33% improvement. +red line shows the final solution. (right) Optimization of a wing section struct: red represent the baseline design, center section in yellow +shows a design with an overall improvement of 13% while the rightmost section in green/blue shows design with a further 33% improvement. Improvement metric is +based on weight and strengh of the design. # Content From 5b19d5ce2743401079843752a48691f214a55503 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:27:19 +0000 Subject: [PATCH 091/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 486d585..9b615f6 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -16,7 +16,7 @@ If you are already familiar with NAG's optimization offering and just need to fi **Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, red line shows the final solution. (right) Optimization of a wing section struct: red represent the baseline design, center section in yellow shows a design with an overall improvement of 13% while the rightmost section in green/blue shows design with a further 33% improvement. Improvement metric is -based on weight and strengh of the design. +based on weight and strengh of the piece. # Content From 10f123e0ba7465e50c7e1796c33e6254b501878b Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:29:35 +0000 Subject: [PATCH 092/182] Update Readme.md --- local_optimization/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 9b615f6..4f82898 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -42,14 +42,14 @@ based on weight and strengh of the piece. In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). -### Step 1. Downloading and installing (`pip`) +### Step 1. Downloading and installing Installing the NAG Library is done using the `pip` package manager, fire-up a terminal and create a Python 3 virtual environment where to install and test the NAG Library ```{bash} guest@nag-37:~$ python3 -m venv nag3 guest@nag-37:~$ . nag3/bin/activate (nag3) guest@nag-37:~$ ``` - +Now use `pip` to install the NAG Library for Python ```{bash} (nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces ``` From f0ae5374166ef0ad456d04201bde78a43707e166 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:31:50 +0000 Subject: [PATCH 093/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 4f82898..2d46f55 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -93,7 +93,7 @@ NAG_KUSARI_FILE="" File /home/guest/nag.key does not exist ------------------------------------------------------------------------------- Error: Licence not found; this product requires a key for NLL6I271VL -The above information has been generated on machine olney.nag.co.uk +The above information has been generated on machine nag-37 For information on how to obtain a licence, please see https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd" From c149ec353667524407b3513eb6a3fac962963603 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:32:56 +0000 Subject: [PATCH 094/182] Update Readme.md --- local_optimization/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 2d46f55..1bf562f 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -102,9 +102,9 @@ The **two** important bits are the 1. **product code** shown as **`underlying Library NLL6I271VL.`** which identifies the licence to request, and - 2. **Kusary ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd"`** which identifies the host you are running the library on. + 2. **KUSARI ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd"`** which identifies the host you are running the library on. - **Note** that the **product code** and **Kusari ID** can be different from the previous example. + **Note** that the **product code** and **KUSARI ID** can be different from the previous example. With these, you are set to [contact NAG and request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library). From aee7d884afc90c5d10c51d9027fb87c86b7b4255 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:35:22 +0000 Subject: [PATCH 095/182] Update Readme.md --- local_optimization/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 1bf562f..e17737a 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -96,13 +96,13 @@ Error: Licence not found; this product requires a key for NLL6I271VL The above information has been generated on machine nag-37 For information on how to obtain a licence, please see https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html -KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd" +KUSARI ID = "ADLXt-adEclJLmvnxlrU2sseteZoo,RopA-Ld" ``` The **two** important bits are the 1. **product code** shown as **`underlying Library NLL6I271VL.`** which identifies the licence to request, and - 2. **KUSARI ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrYfsseteZoo,mRLd"`** which identifies the host you are running the library on. + 2. **KUSARI ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrU2sseteZoo,RopA-Ld"`** which identifies the host you are running the library on. **Note** that the **product code** and **KUSARI ID** can be different from the previous example. From e8a532ae785cdda164390ea4a69c891d6d3b0ddb Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:39:22 +0000 Subject: [PATCH 096/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index e17737a..7e7c433 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -117,7 +117,7 @@ The **two** important bits are the The final step is to make sure the licence is valid and the library is working as expected. ### Step 3. Testing the NAG Library -The last step is to make sure the licence was correctly stored and that the NAG Library is working correctly. From the same virtual terminal re-run the Kusary licence module +The last step is to make sure the licence was correctly stored and that the NAG Library is working correctly. From the same virtual terminal re-run the Kusari licence module ```{bash} (nag3) guest@nag-37:~$ python -m naginterfaces.kusari ``` From 4410aba3a07f1f4413986717382db606d38190c8 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:42:59 +0000 Subject: [PATCH 097/182] Update Readme.md --- local_optimization/Readme.md | 18 ++++++++++++++++-- 1 file changed, 16 insertions(+), 2 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 7e7c433..aa943c4 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -130,9 +130,23 @@ Now let's try a more interesting example ([list of optimization examples](https: This command runs the example for the [FOAS (First-Order Active set method) solver and minimizes the Rosenbrock 2D function](./FOAS). ``` -python -m naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex +(nag3) guest@nag-37:~$ python -m naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex ``` -The source code of the previous example can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/_modules/naginterfaces/library/examples/opt/handle_solve_bounds_foas_ex.html#main). +Should generate an outputsimilar to +```{bash} +Trying: + main() +Expecting: + naginterfaces.library.opt.handle_solve_bounds_foas Python Example Results. + Minimizing a bound-constrained Rosenbrock problem. + E04KF, First order method for bound-constrained problems +... + Status: converged, an optimal solution was found + Value of the objective 4.00000E-02 + ... +ok +``` +indicating that the example was successfully executed. The source code can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/_modules/naginterfaces/library/examples/opt/handle_solve_bounds_foas_ex.html#main). ### Running more examples From b0ea05d0024929acdcaabc83a7ca4effd6f6164d Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 14:44:58 +0000 Subject: [PATCH 098/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index aa943c4..777fb36 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -165,7 +165,7 @@ Run `python -m naginterfaces.library.examples --help` to see any additional usag # How to run the Jupyter notebook examples This section briefly illustrates how to setup a host in order to open and run the [Jupyter notebooks](https://jupyter.org/) provided in this repository. -Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting it is advisable to read [Jupyter's installation page](https://jupyter.org/install.html). +Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting, it is advised to read [Jupyter's installation page](https://jupyter.org/install.html). From 77cc5dd7ae88cf264e2083a087c9aac4947a64b6 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 15:06:16 +0000 Subject: [PATCH 101/182] Update Readme.md --- local_optimization/SOCP/Readme.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/local_optimization/SOCP/Readme.md b/local_optimization/SOCP/Readme.md index 6372a22..ad6cddd 100644 --- a/local_optimization/SOCP/Readme.md +++ b/local_optimization/SOCP/Readme.md @@ -1,3 +1,5 @@ +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) + # Second Order Cone Programming [Second Order Cone Programming (SOCP)](https://en.wikipedia.org/wiki/Second-order_cone_programming) is convex optimization which extends linear programming (LP) with second-order (Lorentz or the ice cream) cones. Search region of the solution is the intersection of an affine From a9b3e72e272f285dbf2f9dfcb00bfed2fcaee5be Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 15:16:53 +0000 Subject: [PATCH 102/182] Update README.md Updated Header, Footer and links to Python Lib --- local_optimization/FOAS/README.md | 23 +++++++++++++++-------- 1 file changed, 15 insertions(+), 8 deletions(-) diff --git a/local_optimization/FOAS/README.md b/local_optimization/FOAS/README.md index b1f592b..fbceeba 100644 --- a/local_optimization/FOAS/README.md +++ b/local_optimization/FOAS/README.md @@ -1,6 +1,8 @@ -[![NAG](https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) -# First-order active-set method (FOAS) [`handle_solve_bounds_foas (e04kf)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) +# First-order active-set method (FOAS) +[[`handle_solve_bounds_foas`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) | [`e04kff`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) | +[`e04kfc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) ] Implementations of first-order methods not only are ubiquitous and have a widespread use, they have also demonstrated to endure the challenges of ever-growing problems sizes imposed by the industry. Most notable are applications in statistics, e.g. parameter calibration for log-linear models, conditional random fields (L2-regularisation) or logistic multi-class regression, amongs many other. First-order methods and the Conjugate Gradient method inparticular have been a research subject for well over 50 years and continue to be improved. @@ -17,13 +19,13 @@ The following example illustrates the simple usage of FOAS to solve the bound-co **Figure 1.** 2D Rosenbrock function, (left) the minimum is shown as a yellow dot at x=(1,1). On the right a bound constrained version showing with a purple dotted line a path towards the constrained solution point on the border. -# More information +## More information 1. [FOAS information page](https://www.nag.com/content/limited-memory-nonlinear-conjugate-gradient-solver) 2. [FOAS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) 3. [FOAS documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) [ [C](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html) | [Fortran](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) ] 4. Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] -# A modern replacement for NAG solver [`uncon_conjgrd_comp` (`e04dg`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) +## A modern replacement for NAG solver [`uncon_conjgrd_comp` (`e04dg`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) One of the main design objectives for `handle_solve_bounds_foas` (`e04kf`) was to provide a modern and attractive replacement for the CG solver `e04dg` introduced in Mark 12. While this solver was targeted for unconstrained NLPs, `e04kf` has been extended with an active-set method in order to solve bound-constrained NLPs. More recent and modern methods have been incorporated into `e04kf` making it much faster than `e04dg`. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers `e04kf` and `e04dg`. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations. @@ -36,15 +38,16 @@ More recent and modern methods have been incorporated into `e04kf` making it muc **Figure 2.** Performance profiles comparing solvers `e04kf` and `e04dg`. In the time plot on the left, higher line indicates faster solver. For the center and right plots higher line represent less functions (NF) or gradients (NG) calls. For all three plots it can be seen that `e04kf` is 40% faster in time and requires less function and gradient calls. -# Migrating from [`uncon_conjgrd_comp (e04dg)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) (Mark 26.x) to [`handle_solve_bounds_foas (e04kf)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html) (Mark 27+) +## Migrating from Marks 25 and 26 to Mark 27 -Notes and comments on migrating your code to the new FOAS solver: +Notes and comments on migrating your code from [`uncon_conjgrd_comp (e04dg)`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html) to the new FOAS solver [`handle_solve_bounds_foas`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bounds_foas) ([`e04kff`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html), +[`e04kfc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html)): * [Python](migration/migration_e04dg_e04kf.ipynb) * [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf) * [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc) -# Beale's function +## Beale's function This example compares the steps taken by FOAS and L-BFGS-B 3.0 to find the solution point to [Beale's function](https://en.wikipedia.org/wiki/Test_functions_for_optimization). It is a classic nonconvex test function used to benchmark nonlinear optimization solvers. Both solvers are used to find a minimum to the function and are started at the same initial point (2, 2). The following figure shows an animation of the steps taken by each solver to find a minimum to the function. @@ -54,7 +57,7 @@ It illustrates the agressive steps taken by the [Conjugate Gradient method](http **Figure 3.** Contour plots for Beale's function (thin blue lines), and the steps taken by FOAS (red) and L-BFGS-B 3.0 (blue) to find the minimum of Beale's funtion at (3, 0.5) marked with a magenta star. It can be seen that FOAS by the 8th step provides a reasonable approximation to the solution point while L-BFGS-B is still relatively far from it. -# References +## References * Hager W W and Zhang H (2005) _A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search_. SIAM J. Optim. 16(1) 170–192 * Hager W W and Zhang H (2006a) _Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent_. ACM Trans. Math. Software 32(1) 113–137 @@ -64,4 +67,8 @@ It illustrates the agressive steps taken by the [Conjugate Gradient method](http +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) From 031828f9b30b7f617b1c632af65b35b8f1631b17 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 15:29:27 +0000 Subject: [PATCH 103/182] Update Readme.md --- local_optimization/BXNL/Readme.md | 15 ++++++++++++--- 1 file changed, 12 insertions(+), 3 deletions(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index 12e31d7..bf46583 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -1,10 +1,13 @@ -[![NAG](https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/nag_logo.png)](https://www.nag.co.uk) +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) # Nonlinear Least-Squares Trust-Region Method (BXNL) +[[`handle_solve_bxnl`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) | [`e04ggf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) | +[`e04ggc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ] + Data fitting and calibrating parameters of complex numerical models is one of the most common problems found in numerous industries such as physics, space exploration, simulations, engineering, amongs many others. -[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems, [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)). It offers a significant variety of algorithms and regularisation techniques. +[NAG](https://www.nag.co.uk/) introduces to the [NAG Library at Mark 27.1](https://www.nag.co.uk/content/nag-library) a novel [nonlinear least-square](https://en.wikipedia.org/wiki/Non-linear_least_squares) [trust-region solver](https://en.wikipedia.org/wiki/Trust_region) for unconstrained or bound-constrained fitting problems, [`handle_solve_bxnl`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) ([`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html)). It offers a significant variety of algorithms and regularisation techniques. The solver [`e04gg`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) is aimed at small to medium sized fitting problems (up to 1000s of parameters) bound-constrained nonlinear least-squares problems and is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers. @@ -25,7 +28,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook # More Info 1. [BXNL information leaflet](https://www.nag.com/content/faster-data-fitting-solver) 2. [BXNL in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) - 3. [BXNL documentation page](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] + 3. [BXNL Python documentation page](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bxnl.html#naginterfaces.library.opt.handle_solve_bxnl) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] # Unfolding Nuclear Track Data @@ -96,4 +99,10 @@ represent less functions and gradients calls. * Adachi S, Iwata S, Nakatsukasa Y, and Takeda A (2015) _Solving the trust region subproblem by a generalized eigenvalue problem_. Technical report, METR 2015-14. Mathematical Engineering, The University of Tokyo https://www.keisu.t.u-tokyo.ac.jp/data/2015/METR15-14.pdf * Conn A R, Gould N I M and Toint Ph L (2000) _Trust Region Methods_. SIAM, Philadephia + + +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) From e5a26f12ed8b86b943bf1bf8906ded78a1e7bc4f Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 15:31:40 +0000 Subject: [PATCH 104/182] Update Readme.md --- local_optimization/BXNL/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index bf46583..640ad4d 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -28,7 +28,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook # More Info 1. [BXNL information leaflet](https://www.nag.com/content/faster-data-fitting-solver) 2. [BXNL in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_bxnl) - 3. [BXNL Python documentation page](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bxnl.html#naginterfaces.library.opt.handle_solve_bxnl) [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] + 3. Examples [[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_disable_ex.main), [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ggc.html#example), [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ggf.html#example)] # Unfolding Nuclear Track Data From db295e3bd8535c82875ae5cf8d902c83517b0eb4 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 15:37:26 +0000 Subject: [PATCH 105/182] Update Readme.md --- local_optimization/SDP/Readme.md | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/local_optimization/SDP/Readme.md b/local_optimization/SDP/Readme.md index 01a6c1e..f41b68e 100644 --- a/local_optimization/SDP/Readme.md +++ b/local_optimization/SDP/Readme.md @@ -1,7 +1,20 @@ +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) + # Semi-Definite Programming (SDP) +[[`handle_solve_pennon`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_pennon.html#naginterfaces.library.opt.handle_solve_pennon) | [`e04svf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04svf.html) | +[`e04svc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04svc.html) ] + + Linear semidefinite programming can be viewed as a generalization of linear programming. While keeping many good properties of LP (such as the duality theory and solvability in polynomial time), SDP introduces a new highly nonlinear type of constraint – matrix inequality. It is an inequality on the eigenvalues of a matrix which depends on the decision variables. Typically, the matrix inequality is written in the form to request all eigenvalues of the matrix to be non-negative, thus the matrix is to be positive semidefinite * [Matrix completion using Semi-Definite Programming (SDP)](./matrix_completion.ipynb) * [Nearest correlation matrix using Semi-Definite Programming (SDP)](./NCM_SDP.ipynb) * [Compute the Lovasz number of a graph using Semi-Definite Programming (SDP)](./theta_optimization.ipynb) + + + +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) From 64b9ccd8b7ab89ccfc6fcba82bed4e5edf79f484 Mon Sep 17 00:00:00 2001 From: Andrew Sajo Date: Wed, 27 Jan 2021 15:40:47 +0000 Subject: [PATCH 106/182] Moved screenshot to images --- .../{Notebooks => images}/screenshot.png | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename local_optimization/{Notebooks => 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00:00:00 2001 From: A Date: Wed, 27 Jan 2021 16:37:57 +0000 Subject: [PATCH 108/182] Create Readme.md --- local_optimization/DFO/Readme.md | 71 ++++++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 local_optimization/DFO/Readme.md diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md new file mode 100644 index 0000000..1d247fe --- /dev/null +++ b/local_optimization/DFO/Readme.md @@ -0,0 +1,71 @@ +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) + +# Derivative-Free Optimization (DFO) + +* Calibration: Derivative Nonlinear least squares (DFLS) +[[`handle_solve_dfls`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls) | +[`e04fff`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04fff.html) | +[`e04ffc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ffc.html) ] + + * Derivative-Free Nonlinear Optimization (DFNO) + [[`handle_solve_dfno`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfno) | + [`e04jdf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04jdf.html) | +[`e04jdc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04jdc.html) ] + +DFO solvers are aimed at optimizing _black box_ models and can handle either calibration (nonlinear least squares) problems +or problems with a generic objective function. + +Optimizing complex numerical models is one of the most common problems found in the industry (finance, multi-physics simulations, +engineering, etc.). To solve these optimization problems with a standard optimization algorithm such as +[Gauss–Newton](https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm) (for +problems with a nonlinear least squares structure) or +[CG](https://en.wikipedia.org/wiki/Conjugate_gradient_method) (for unstructured nonlinear objective) requires good estimates +of the model's derivatives. + +If exact derivatives are easy to compute then using derivative-based methods is preferable. However, explicitly writing the derivatives +or applying [AD methods](https://www.nag.com/content/algorithmic-differentiation-software) might be impossible if the model is a black box. +The alternative, estimating derivatives via [finite differences](https://en.wikipedia.org/wiki/Finite_difference#Relation_with_derivatives), +can quickly become impractical or too computationally expensive. + + +![2 steps of DFO algorithm](animation.gif) +**Figure 1.** Animation showing 2 iterations of a model-based DFO algorithm [`handle_solve_dfls`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls). + + +## Poster + + + + +
A 2019 poster discussing NAG's DFO/DFLS functionality +is available on the NAG website. +DFO Poster thumbnail
+ +## Example + +The Jupyter notebook showcases the optimization of noisy problems where the objective function is not deterministic. +The example discuses and illustrates the advantages of using a DFO solver instead of a derivative-based solver using +finite difference estimations for the gradient. + + * [Noisy problem notebook.](DFO_noisy.ipynb) + +## More information + * [Informative Leaflet] + * [DFO in the NAG Library for Python] + * Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] + +## References + +* C. Cartis, J. Fiala, B. Marteau, and L. Roberts (2019) _Improving the Flexibility and robustness of + model-based derivative-free optimization solvers_. ACM Transactions On Numerical Software. +* C. Cartis and L. Roberts (2017) _A derivative-free Gauss–Newton method_. Mathematical Programming Computation. +* Powell M. J. D. (2009) _The BOBYQA algorithm for bound constrained optimization without derivatives_. Report DAMTP 2009/NA06 University of Cambridge. + + + +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) + From 7415dd08c98f6c4cca0814727f88f3956284770e Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 16:38:27 +0000 Subject: [PATCH 109/182] Update Readme.md --- local_optimization/DFO/Readme.md | 1 + 1 file changed, 1 insertion(+) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 1d247fe..66db526 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -29,6 +29,7 @@ can quickly become impractical or too computationally expensive. ![2 steps of DFO algorithm](animation.gif) + **Figure 1.** Animation showing 2 iterations of a model-based DFO algorithm [`handle_solve_dfls`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls). From 5c3e699c96de0af4ef6396ae369dcf92d4847f9f Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 16:51:43 +0000 Subject: [PATCH 110/182] Update Readme.md --- local_optimization/DFO/Readme.md | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 66db526..23d4c54 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -52,9 +52,19 @@ finite difference estimations for the gradient. * [Noisy problem notebook.](DFO_noisy.ipynb) ## More information - * [Informative Leaflet] - * [DFO in the NAG Library for Python] - * Examples [ [Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html#example) | [Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) ] + + * [Informative Leaflet](https://www.nag.com/content/derivative-free-optimization-dfo) + + * Blog post from the OptCorner [The price of derivatives - Derivative-free Optimization](https://www.nag.com/blog/optcorner-price-derivatives-derivative-free-optimization) + + * [DFO/DFLS in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls) + + * Examples [ [Python example](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfls_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ffc.html#example) | [Fortran 90 example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04fff.html#example) ] + + * [DFO/DFNO in the NAG Library for Python](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfno) + + * Examples [ [Python example](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main) | [C example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04jdc.html#example) | [Fortran 90 example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04jdf.html#example) ] + ## References From 2896258b02d83f8dd371e4ccf00ab87b9320accb Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 16:55:03 +0000 Subject: [PATCH 111/182] Update Readme.md --- local_optimization/DFO/Readme.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 23d4c54..8393dbc 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -2,18 +2,19 @@ # Derivative-Free Optimization (DFO) -* Calibration: Derivative Nonlinear least squares (DFLS) +DFO solvers are aimed at optimizing _black box_ models and can handle either calibration (nonlinear least squares) problems (DFLS) +or problems with a generic objective function (DFNO). + +* Calibration: DFLS (Derivative Nonlinear least squares) [[`handle_solve_dfls`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls) | [`e04fff`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04fff.html) | [`e04ffc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04ffc.html) ] - * Derivative-Free Nonlinear Optimization (DFNO) + * DFNO (Derivative-Free Nonlinear Optimization) [[`handle_solve_dfno`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfno) | [`e04jdf`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04jdf.html) | [`e04jdc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04jdc.html) ] -DFO solvers are aimed at optimizing _black box_ models and can handle either calibration (nonlinear least squares) problems -or problems with a generic objective function. Optimizing complex numerical models is one of the most common problems found in the industry (finance, multi-physics simulations, engineering, etc.). To solve these optimization problems with a standard optimization algorithm such as From 428316bc4cd345cd4e514c4f2ede62ef6fe63e2f Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:00:51 +0000 Subject: [PATCH 112/182] Update Readme.md --- local_optimization/DFO/Readme.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 8393dbc..c0b168a 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -22,12 +22,17 @@ engineering, etc.). To solve these optimization problems with a standard optimiz problems with a nonlinear least squares structure) or [CG](https://en.wikipedia.org/wiki/Conjugate_gradient_method) (for unstructured nonlinear objective) requires good estimates of the model's derivatives. - If exact derivatives are easy to compute then using derivative-based methods is preferable. However, explicitly writing the derivatives or applying [AD methods](https://www.nag.com/content/algorithmic-differentiation-software) might be impossible if the model is a black box. The alternative, estimating derivatives via [finite differences](https://en.wikipedia.org/wiki/Finite_difference#Relation_with_derivatives), can quickly become impractical or too computationally expensive. +NAG's model-based DFO solvers for DFLS and DFNO present a number of attractive features: + + * Proved resilience to noise. + * Solvers are able to start making progress with as few as two objective evaluations; + * Integrated to the NAG Optimization Modeling Suite with simple interfaces for the solvers and related routines; + * Optional reverse communication interface ![2 steps of DFO algorithm](animation.gif) From cd700900f1ac37258269d09148349bd03aa2af66 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:01:41 +0000 Subject: [PATCH 113/182] Update Readme.md --- local_optimization/DFO/Readme.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index c0b168a..881dd6b 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -29,10 +29,10 @@ can quickly become impractical or too computationally expensive. NAG's model-based DFO solvers for DFLS and DFNO present a number of attractive features: - * Proved resilience to noise. - * Solvers are able to start making progress with as few as two objective evaluations; - * Integrated to the NAG Optimization Modeling Suite with simple interfaces for the solvers and related routines; - * Optional reverse communication interface + * Proved resilience to noise, + * Solvers are able to start making progress with as few as two objective evaluations, + * Integrated to the NAG Optimization Modeling Suite with simple interfaces for the solvers and related routines, + * Optional reverse communication interface. ![2 steps of DFO algorithm](animation.gif) From f57c3e37e22f4df1f27cff2d48c2757eda4ed282 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:06:55 +0000 Subject: [PATCH 114/182] Update Readme.md --- local_optimization/Readme.md | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 72ce261..1f00dd6 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -33,10 +33,8 @@ based on weight and strengh of the piece. * [Derivative-Free Optimization (DFO)](./DFO/) * [Tips and Tricks in modelling](./modelling/) -### Examples (Remove) +### Examples (FIXME: Remove section) * [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) -* move this into modelling [Linear Programming Demo](./LP_demo.ipynb) -* move this into DFO [Model-based derivative free optimization](./DFO_noisy.ipynb) # How to install the NAG Library for Python From e9b86354bdecfba1b443ae8c12b9a56cbd854a53 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:15:29 +0000 Subject: [PATCH 115/182] Create Readme.md --- local_optimization/Notebooks/Readme.md | 15 +++++++++++++++ 1 file changed, 15 insertions(+) create mode 100644 local_optimization/Notebooks/Readme.md diff --git a/local_optimization/Notebooks/Readme.md b/local_optimization/Notebooks/Readme.md new file mode 100644 index 0000000..ece2ee9 --- /dev/null +++ b/local_optimization/Notebooks/Readme.md @@ -0,0 +1,15 @@ +[![NAG Logo](../nag_logo.png)](https://www.nag.com) + +# Local Optimization Jupyter notebooks + + * [Example on minimizing the generalized Rosenbrock function](bounds_quasi_func_easy.ipynb) + using [bounds_quasi_func_easy](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.bounds_quasi_func_easy.html). + + + + + +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) From 7b04211feb6c40a7f389d324848f696ccc077d1d Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:17:01 +0000 Subject: [PATCH 116/182] Update Readme.md --- local_optimization/Notebooks/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Notebooks/Readme.md b/local_optimization/Notebooks/Readme.md index ece2ee9..9850f1e 100644 --- a/local_optimization/Notebooks/Readme.md +++ b/local_optimization/Notebooks/Readme.md @@ -1,4 +1,4 @@ -[![NAG Logo](../nag_logo.png)](https://www.nag.com) +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) # Local Optimization Jupyter notebooks From 826eba4826c6683b81304bb2337b46295e1c2a9e Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:22:23 +0000 Subject: [PATCH 117/182] Update Readme.md --- local_optimization/Readme.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 1f00dd6..85522cb 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -32,6 +32,8 @@ based on weight and strengh of the piece. * [Semi-Definite Programming (SDP)](./SDP/) * [Derivative-Free Optimization (DFO)](./DFO/) * [Tips and Tricks in modelling](./modelling/) +* [Assortment of example notebooks](./Notebooks) ![Jupyter](https://img.shields.io/badge/NAG-Work in progress-yellow) + ### Examples (FIXME: Remove section) * [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) From f799c0d33a98c8ca8d078f45422ac82769815353 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:23:06 +0000 Subject: [PATCH 118/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 85522cb..43259fb 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -31,7 +31,7 @@ based on weight and strengh of the piece. * [Nonlinear Least-Squares (BXNL)](./BXNL) * [Semi-Definite Programming (SDP)](./SDP/) * [Derivative-Free Optimization (DFO)](./DFO/) -* [Tips and Tricks in modelling](./modelling/) +* [Tips and Tricks in modelling](./Modelling/) * [Assortment of example notebooks](./Notebooks) ![Jupyter](https://img.shields.io/badge/NAG-Work in progress-yellow) From 5345296b0f2cca1399d7a818a3f317cec620573f Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:23:59 +0000 Subject: [PATCH 119/182] Update Readme.md --- local_optimization/Readme.md | 3 --- 1 file changed, 3 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 43259fb..333de5c 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -35,9 +35,6 @@ based on weight and strengh of the piece. * [Assortment of example notebooks](./Notebooks) ![Jupyter](https://img.shields.io/badge/NAG-Work in progress-yellow) -### Examples (FIXME: Remove section) -* [Minimizing the generalized Rosenbrock function using bound constrained optimization](./bounds_quasi_func_easy.ipynb) - # How to install the NAG Library for Python In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). From 10e8f3ce2df350f24e0fecfc5d10545fe7474cc4 Mon Sep 17 00:00:00 2001 From: A Date: Wed, 27 Jan 2021 17:27:48 +0000 Subject: [PATCH 120/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 333de5c..7e73dbd 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -206,7 +206,7 @@ and now open it using `jupyter-notebook` This command will fire-up your web browser and open the `rosenbrock2d.ipynb` notebook, the window should be similar to -![Notebook screenshot](Notebooks/screenshot.png) +![Notebook screenshot](images/screenshot.png) From 812cc47cb80b7da26fe0a48dd4a2033f9d0ce745 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 10:15:00 +0000 Subject: [PATCH 121/182] Update Readme.md --- local_optimization/DFO/Readme.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 881dd6b..1c2ccbb 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -25,13 +25,14 @@ of the model's derivatives. If exact derivatives are easy to compute then using derivative-based methods is preferable. However, explicitly writing the derivatives or applying [AD methods](https://www.nag.com/content/algorithmic-differentiation-software) might be impossible if the model is a black box. The alternative, estimating derivatives via [finite differences](https://en.wikipedia.org/wiki/Finite_difference#Relation_with_derivatives), -can quickly become impractical or too computationally expensive. +can quickly become impractical or too computationally expensive. Under these circumstances, an attractive optimization solver that does not +require the user to provide any derivatives is the model-based DFO solver. NAG's model-based DFO solvers for DFLS and DFNO present a number of attractive features: * Proved resilience to noise, * Solvers are able to start making progress with as few as two objective evaluations, - * Integrated to the NAG Optimization Modeling Suite with simple interfaces for the solvers and related routines, + * Integrated to the [NAG Optimization Modeling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html#optsuite) with simple interfaces for the solvers and related routines, * Optional reverse communication interface. ![2 steps of DFO algorithm](animation.gif) From c7aa1aa71c8d51618221d93aea128ed5eb7f2822 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 10:29:02 +0000 Subject: [PATCH 122/182] Update Readme.md --- local_optimization/DFO/Readme.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 1c2ccbb..3191fe6 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -1,9 +1,9 @@ [![NAG Logo](../../nag_logo.png)](https://www.nag.com) -# Derivative-Free Optimization (DFO) +# Derivative-Free Optimization ([DFO](https://en.wikipedia.org/wiki/Derivative-free_optimization)) -DFO solvers are aimed at optimizing _black box_ models and can handle either calibration (nonlinear least squares) problems (DFLS) -or problems with a generic objective function (DFNO). +[DFO](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#derivatives) solvers are aimed at optimizing _black box_ models and can handle either [calibration (nonlinear least squares)](https://en.wikipedia.org/wiki/Non-linear_least_squares) problems (DFLS) +or [problems with a generic objective function](https://en.wikipedia.org/wiki/Nonlinear_programming) (DFNO). * Calibration: DFLS (Derivative Nonlinear least squares) [[`handle_solve_dfls`](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.opt.handle_solve_dfls) | @@ -28,7 +28,7 @@ The alternative, estimating derivatives via [finite differences](https://en.wiki can quickly become impractical or too computationally expensive. Under these circumstances, an attractive optimization solver that does not require the user to provide any derivatives is the model-based DFO solver. -NAG's model-based DFO solvers for DFLS and DFNO present a number of attractive features: +NAG's model-based [DFO](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#derivatives) [solvers for DFLS and DFNO]() present a number of attractive features: * Proved resilience to noise, * Solvers are able to start making progress with as few as two objective evaluations, From cdd7cd405588ed628b4d9d450bdea0107368efa6 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 10:29:38 +0000 Subject: [PATCH 123/182] Update Readme.md --- local_optimization/DFO/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 3191fe6..052f135 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -1,6 +1,6 @@ [![NAG Logo](../../nag_logo.png)](https://www.nag.com) -# Derivative-Free Optimization ([DFO](https://en.wikipedia.org/wiki/Derivative-free_optimization)) +# Derivative-Free Optimization ([DFO](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#derivatives)) [DFO](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#derivatives) solvers are aimed at optimizing _black box_ models and can handle either [calibration (nonlinear least squares)](https://en.wikipedia.org/wiki/Non-linear_least_squares) problems (DFLS) or [problems with a generic objective function](https://en.wikipedia.org/wiki/Nonlinear_programming) (DFNO). From 0a2339a41c77eb8da40d032f533c0327d20025f2 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 11:22:47 +0000 Subject: [PATCH 124/182] Create Readme.md --- local_optimization/Modelling/Readme.md | 37 ++++++++++++++++++++++++++ 1 file changed, 37 insertions(+) create mode 100644 local_optimization/Modelling/Readme.md diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md new file mode 100644 index 0000000..6e7b81a --- /dev/null +++ b/local_optimization/Modelling/Readme.md @@ -0,0 +1,37 @@ +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) + +# Modelling Optimization Problems + +In this folder you will find notebook examples, tips and tricks related to modeling optimization problems. + +* **Christmas Special** [How to decorate your Christmas tree (Notebook)](christmas_demo.ipynb) + or view the [Blog-post](https://www.nag.com/blog/optcorner-christmas-edition). + + See how optimization can help to decorate a Christmas tree... + +* **Demo** [Linear Programming (LP)](LP_demo.ipynb). + + Tiny and Cute LP problem... +* **Demo** [Nonlinear calibration (data fitting)](handle_disable_ex.ipynb). + + This demo shows useful features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) in [Nonlinear Least-squares]() problem. +* **Demo** [Production Planning](production_planning.ipynb). + + Optimal production planning showcasing features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite). + +# Useful Links +* [Background to Optimization Methods](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#algorithms) +* [Nag Blog](https://www.nag.com/content/nag-blog) + + + + + +# Obtaining the NAG Library for Python + + * Instructions on [how to install the NAG Library for Python](../Readme.md#install) + * Instructions on [how to run the Jupyter notebooks in the Repository](../Readme.md#jupyter) From 494b8bf7b64a3f428a79c585e05761c7b597bbce Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 11:24:39 +0000 Subject: [PATCH 125/182] Add files via upload --- local_optimization/images/nlls.png | Bin 0 -> 10472 bytes local_optimization/images/xmas_tree.png | Bin 0 -> 8049 bytes 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 local_optimization/images/nlls.png create mode 100644 local_optimization/images/xmas_tree.png diff --git a/local_optimization/images/nlls.png b/local_optimization/images/nlls.png new file mode 100644 index 0000000000000000000000000000000000000000..363962432db3ed8d67b05bf2045742d9928049a8 GIT binary patch literal 10472 zcmZvC2RK|^*EUA4K@eR=4WhS@C^1?@@1h2i=)Jd5qeP8pQ6D8b(MvE|B#aWCC}Eh1 z2tvjr%3zfLc;5H>-|xTv*L9iU?6db?XP>q1wbs2>vZ1~f4J8{T0RaJxjyA-YfPgR- z`1^#M6!=8TpbLR7V*iIarsTj+1i5n(@IQr*wv|5t0TsjbFX0?A>KwSJ5TIchVB!r8 z2zK;yA@Fnz@bT~t@Nj*~6XfFO@9OO(EhZ%L-dV%~nw#B;e{CKC|w 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z8#Sl!kQYhFp1$2lPS89B7RNYvPrNP$e991a41{%Bo@lG5mc%l(fC`zzdWKZBS@zaK zd_jH{$e7OUh-TxdHLVp1;1M7a`DkVq94rZGR^B~?09R+=deEi0)!O;y`?2I{bq$kpG4ZAU}AnYw2{@I#>ql{qH7!~>B_`hOC;e|eQbP#+P)Dm@}S4&2j%LEmWDKmH%-5Eo7W literal 0 HcmV?d00001 From f2181f7339b40e57b09c0183f77c4642afea1608 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 11:32:40 +0000 Subject: [PATCH 126/182] Update Readme.md --- local_optimization/Modelling/Readme.md | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md index 6e7b81a..6c37235 100644 --- a/local_optimization/Modelling/Readme.md +++ b/local_optimization/Modelling/Readme.md @@ -6,8 +6,13 @@ In this folder you will find notebook examples, tips and tricks related to model * **Christmas Special** [How to decorate your Christmas tree (Notebook)](christmas_demo.ipynb) or view the [Blog-post](https://www.nag.com/blog/optcorner-christmas-edition). + + + +
See how optimization can help to decorate a Christmas tree... +Xmas Tree Plot
- See how optimization can help to decorate a Christmas tree... * **Demo** [Linear Programming (LP)](LP_demo.ipynb). @@ -15,6 +20,15 @@ In this folder you will find notebook examples, tips and tricks related to model * **Demo** [Nonlinear calibration (data fitting)](handle_disable_ex.ipynb). This demo shows useful features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) in [Nonlinear Least-squares]() problem. + + + + +
This demo shows useful features of the NAG Optimization Modelling Suite (NOMS) in a Nonlinear Least-squares problem. +Data fitting Plot
+ + * **Demo** [Production Planning](production_planning.ipynb). Optimal production planning showcasing features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite). From 686cdc694a00cc9d7b29b3b431b680b0cd6f817a Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 11:35:49 +0000 Subject: [PATCH 127/182] Update Readme.md --- local_optimization/Modelling/Readme.md | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md index 6c37235..25dd503 100644 --- a/local_optimization/Modelling/Readme.md +++ b/local_optimization/Modelling/Readme.md @@ -7,10 +7,12 @@ In this folder you will find notebook examples, tips and tricks related to model * **Christmas Special** [How to decorate your Christmas tree (Notebook)](christmas_demo.ipynb) or view the [Blog-post](https://www.nag.com/blog/optcorner-christmas-edition). - + +width="100" height="100px" alt="Xmas Tree Plot"/> + +
See how optimization can help to decorate a Christmas tree... Xmas Tree PlotSee how optimization can help to decorate a Christmas tree...
@@ -22,10 +24,12 @@ width="362" height="248px" alt="Xmas Tree Plot"/> This demo shows useful features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) in [Nonlinear Least-squares]() problem. - +width="100" height="80px" alt="Data fitting Plot"/> + + +
This demo shows useful features of the NAG Optimization Modelling Suite (NOMS) in a Nonlinear Least-squares problem. Data fitting PlotThis demo shows useful features of the NAG Optimization Modelling Suite (NOMS) in a Nonlinear Least-squares problem.
From 37bf004216a162a338bd668589f5fccfb288ad62 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 28 Jan 2021 11:36:28 +0000 Subject: [PATCH 128/182] Update Readme.md --- local_optimization/Modelling/Readme.md | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md index 25dd503..2c5ddc1 100644 --- a/local_optimization/Modelling/Readme.md +++ b/local_optimization/Modelling/Readme.md @@ -19,10 +19,7 @@ width="100" height="100px" alt="Xmas Tree Plot"/> * **Demo** [Linear Programming (LP)](LP_demo.ipynb). Tiny and Cute LP problem... -* **Demo** [Nonlinear calibration (data fitting)](handle_disable_ex.ipynb). - - This demo shows useful features of the [NAG Optimization Modelling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) in [Nonlinear Least-squares]() problem. - +* **Demo** [Nonlinear calibration (data fitting)](handle_disable_ex.ipynb).
Date: Fri, 29 Jan 2021 14:59:18 +0100 Subject: [PATCH 129/182] small edits of the Readmes --- local_optimization/DFO/Readme.md | 4 ++-- local_optimization/Readme.md | 3 +-- 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/local_optimization/DFO/Readme.md b/local_optimization/DFO/Readme.md index 052f135..9460b19 100644 --- a/local_optimization/DFO/Readme.md +++ b/local_optimization/DFO/Readme.md @@ -30,8 +30,8 @@ require the user to provide any derivatives is the model-based DFO solver. NAG's model-based [DFO](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#derivatives) [solvers for DFLS and DFNO]() present a number of attractive features: - * Proved resilience to noise, - * Solvers are able to start making progress with as few as two objective evaluations, + * Proved resilient to noise, + * The least-square solver is able to start making progress with as few as two objective evaluations, * Integrated to the [NAG Optimization Modeling Suite (NOMS)](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html#optsuite) with simple interfaces for the solvers and related routines, * Optional reverse communication interface. diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 7e73dbd..922a46f 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -52,11 +52,10 @@ Now use `pip` to install the NAG Library for Python ```{bash} (nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces ``` -or if you have Intel MKL, then use +or if you prefer the version of the package that relies on Intel MKLfor optimized linear algebra routines, then use ```{bash} (nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces ``` -for Intel MKL-enabled NAG Library. The output should be similar to ```{bash} From f05353cf6c0690383d7e89bf96c2117c9fb791c4 Mon Sep 17 00:00:00 2001 From: Ben Date: Fri, 29 Jan 2021 15:29:38 +0100 Subject: [PATCH 130/182] typo and small paragraph in notebook linking to installation instructions --- local_optimization/Readme.md | 2 +- local_optimization/SOCP/simple_SOCP.ipynb | 11 +++++++++++ 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 922a46f..b5d7c1e 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -52,7 +52,7 @@ Now use `pip` to install the NAG Library for Python ```{bash} (nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces ``` -or if you prefer the version of the package that relies on Intel MKLfor optimized linear algebra routines, then use +or if you prefer the version of the package that relies on Intel MKL for optimized linear algebra routines, then use ```{bash} (nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces ``` diff --git a/local_optimization/SOCP/simple_SOCP.ipynb b/local_optimization/SOCP/simple_SOCP.ipynb index 42b5fe0..d652874 100644 --- a/local_optimization/SOCP/simple_SOCP.ipynb +++ b/local_optimization/SOCP/simple_SOCP.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, From 1ea965f005ea77e30bfe8ae700e5f0665ede7301 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 29 Jan 2021 14:37:35 +0000 Subject: [PATCH 131/182] Update Readme.md --- local_optimization/Readme.md | 20 +++++++++++++++++++- 1 file changed, 19 insertions(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index 407cf8c..b5d7c1e 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -1,4 +1,22 @@ -![NAG Logo](../nag_logo.png) +[![NAG Logo](../nag_logo.png)](https://www.nag.com) + +# Local Optimization + +Here you will find a variety of resources (mostly [Jupyter notebooks](https://jupyter.org/)) related to the use of our optimization routines and modelling suite. If you are new to NAG's optimization solvers we highly recomment to read the [E04 chapter](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04intro.html) of the [NAG](https://www.nag.com) Library which is dedicated to local optimization. While if you are new to NAG Library for Python we encourage to review the [NAG Python documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) and read the sections on [How to install the NAG Library for Python](#install) and [How to run the Jupyter notebook examples](#jupyter) of this `Readme`. + +If you are already familiar with NAG's optimization offering and just need to find the right solver to use for your problem, then we recommend reviewing the [Optimization Index](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html) or the [Decision Tree for selecting the right Optimization solver](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#dtree). + + + + + + +
DFO Calibration example           Optimization example of a wing section
+ +**Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, +red line shows the final solution. (right) Optimization of a wing section struct: red represent the baseline design, center section in yellow +shows a design with an overall improvement of 13% while the rightmost section in green/blue shows design with a further 33% improvement. Improvement metric is +based on weight and strengh of the piece. # Content From c98b89d2f2ba9686d0ede43d44846943bc0ce02a Mon Sep 17 00:00:00 2001 From: Ben Date: Fri, 29 Jan 2021 18:26:30 +0100 Subject: [PATCH 132/182] added section on library installation on all notebooks --- .../BXNL/notebooks/orbit_ex.ipynb | 13 ++++++++- .../BXNL/notebooks/simple_BXNL.ipynb | 13 ++++++++- local_optimization/DFO/DFO_noisy.ipynb | 29 +++++++++++++++++++ local_optimization/FOAS/rosenbrock2d.ipynb | 11 +++++++ local_optimization/Modelling/LP_demo.ipynb | 29 +++++++++++++++++++ .../Modelling/christmas_demo.ipynb | 29 +++++++++++++++++++ .../Modelling/handle_disable_ex.ipynb | 11 +++++++ .../Modelling/production_planning.ipynb | 11 +++++++ .../Notebooks/bounds_quasi_func_easy.ipynb | 29 +++++++++++++++++++ local_optimization/SDP/NCM_SDP.ipynb | 15 ++++++++-- .../SDP/matrix_completion.ipynb | 11 +++++++ .../SDP/theta_optimization.ipynb | 15 ++++++++-- .../SOCP/cvxpy_classification.ipynb | 15 ++++++++-- .../SOCP/portfolio_optimization_qcqp.ipynb | 17 +++++++++-- .../portfolio_optimization_using_socp.ipynb | 11 +++++++ local_optimization/SOCP/robust_lp.ipynb | 19 +++++++++--- 16 files changed, 263 insertions(+), 15 deletions(-) diff --git a/local_optimization/BXNL/notebooks/orbit_ex.ipynb b/local_optimization/BXNL/notebooks/orbit_ex.ipynb index e290bbd..e1f376e 100644 --- a/local_optimization/BXNL/notebooks/orbit_ex.ipynb +++ b/local_optimization/BXNL/notebooks/orbit_ex.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -362,7 +373,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb index 5c49cde..49a5d80 100644 --- a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb +++ b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -526,7 +537,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.6" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/DFO/DFO_noisy.ipynb b/local_optimization/DFO/DFO_noisy.ipynb index 750f9ce..289e7d6 100644 --- a/local_optimization/DFO/DFO_noisy.ipynb +++ b/local_optimization/DFO/DFO_noisy.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "code", "execution_count": 1, @@ -1534,6 +1545,24 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false } }, "nbformat": 4, diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index 55d4b0d..3e332b0 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/local_optimization/Modelling/LP_demo.ipynb b/local_optimization/Modelling/LP_demo.ipynb index 99bd3d4..4835a32 100644 --- a/local_optimization/Modelling/LP_demo.ipynb +++ b/local_optimization/Modelling/LP_demo.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -268,6 +279,24 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false } }, "nbformat": 4, diff --git a/local_optimization/Modelling/christmas_demo.ipynb b/local_optimization/Modelling/christmas_demo.ipynb index 4555735..4ecae93 100644 --- a/local_optimization/Modelling/christmas_demo.ipynb +++ b/local_optimization/Modelling/christmas_demo.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -589,6 +600,24 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false } }, "nbformat": 4, diff --git a/local_optimization/Modelling/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb index ace45ee..034348e 100644 --- a/local_optimization/Modelling/handle_disable_ex.ipynb +++ b/local_optimization/Modelling/handle_disable_ex.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/local_optimization/Modelling/production_planning.ipynb b/local_optimization/Modelling/production_planning.ipynb index c336b2b..d8d3d63 100644 --- a/local_optimization/Modelling/production_planning.ipynb +++ b/local_optimization/Modelling/production_planning.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb b/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb index 9088f29..5578976 100644 --- a/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb +++ b/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1347,6 +1358,24 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false } }, "nbformat": 4, diff --git a/local_optimization/SDP/NCM_SDP.ipynb b/local_optimization/SDP/NCM_SDP.ipynb index 7c2bff2..875b386 100644 --- a/local_optimization/SDP/NCM_SDP.ipynb +++ b/local_optimization/SDP/NCM_SDP.ipynb @@ -18,15 +18,26 @@ "# Nearest correlation matrix using Semi-Definite Programming (SDP)\n", "## Correct Rendering of this notebook\n", "\n", - "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing the NAG library and running this notebook\n", "\n", - "## Introduction" + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Introduction\n", + "\n", "We start with a matrix $G$ that is not quite a correlation matrix:\n", "\\begin{bmatrix}\n", "1 & -1 & 0 & 0\\\\\n", diff --git a/local_optimization/SDP/matrix_completion.ipynb b/local_optimization/SDP/matrix_completion.ipynb index 48d6196..9069f98 100644 --- a/local_optimization/SDP/matrix_completion.ipynb +++ b/local_optimization/SDP/matrix_completion.ipynb @@ -1,5 +1,16 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "code", "execution_count": 1, diff --git a/local_optimization/SDP/theta_optimization.ipynb b/local_optimization/SDP/theta_optimization.ipynb index 9cc33ce..e0efc2d 100644 --- a/local_optimization/SDP/theta_optimization.ipynb +++ b/local_optimization/SDP/theta_optimization.ipynb @@ -21,15 +21,26 @@ "\n", "## Correct Rendering of this notebook\n", "\n", - "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing the NAG library and running this notebook\n", "\n", - "## Introduction" + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Introduction\n", + "\n", "The Lovasz number allows to compute an upper bound on the Shannon capacity of a graph $G$ (the maximum size of independent sets of vertices in G). While the complexity of computing the Shannon capacity is not known, the Lovasz number can be efficiently computed in polynomial time via SDP. \n", "\n", "Start by defining a graph $G = (V, E)$" diff --git a/local_optimization/SOCP/cvxpy_classification.ipynb b/local_optimization/SOCP/cvxpy_classification.ipynb index 71dc38f..0ae1273 100644 --- a/local_optimization/SOCP/cvxpy_classification.ipynb +++ b/local_optimization/SOCP/cvxpy_classification.ipynb @@ -13,15 +13,26 @@ "source": [ "## Correct Rendering of this notebook\n", "\n", - "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing the NAG library and running this notebook\n", "\n", - "## Introduction" + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Introduction\n", + "\n", "In this notebook, we demonstrate how NAG second-order conic programming (SOCP) solver can be used to find a quartic polynomial\n", "\\vspace{0.1cm}\n", "\\begin{equation}\\label{poly}\n", diff --git a/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb index b7ba23e..541f315 100644 --- a/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb @@ -15,15 +15,26 @@ "\n", "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", "\n", - "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", + "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", "\n", - "# Introduction" + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "# Introduction\n", + "\n", "Quadratically constrained quadratic programming (QCQP) is a type of optimization problem in which both the objective function and the constraints involve quadratic functions. A general QCQP problem has the following form\n", "\\begin{equation}\n", "\\begin{array}{ll}\n", @@ -683,7 +694,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.1" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb index 9919a82..504b1e1 100644 --- a/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_using_socp.ipynb @@ -18,6 +18,17 @@ "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_using_socp.pdf)." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", + "\n", + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." + ] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/local_optimization/SOCP/robust_lp.ipynb b/local_optimization/SOCP/robust_lp.ipynb index d131125..c935cb1 100644 --- a/local_optimization/SOCP/robust_lp.ipynb +++ b/local_optimization/SOCP/robust_lp.ipynb @@ -13,15 +13,26 @@ "source": [ "# Correct Rendering of this notebook\n", "\n", - "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG library and running this notebook\n", "\n", - "## Introduction" + "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "\n", + "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Introduction\n", + "\n", "We consider a classic portfolio problem with loss risk constraints:\n", "\\vspace{0.1cn}\n", "\\begin{equation}\\label{prob}\n", @@ -561,9 +572,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python" + "name": "python3" }, "language_info": { "codemirror_mode": { From 340bf02cb6a38446a0135fb9daa499f5e1664c41 Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Wed, 3 Feb 2021 18:15:55 -0600 Subject: [PATCH 133/182] Update README.md more detail in library and Jupyter setup instructions --- README.md | 197 +++++++++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 181 insertions(+), 16 deletions(-) diff --git a/README.md b/README.md index cb4d799..d3144e7 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,14 @@ -![NAG Logo](./nag_logo.png) +![NAG Logo](./nag_logo.png) -# Examples using the NAG Library for Python +# Content + +* [Examples using the NAG Library for Python](#examples) +* [How to install the NAG Library for Python](#install) +* [How to run the Jupyter notebook examples](#jupyter) +* [List of Chapters in the NAG Library for Python](#chapters) +* [Useful links](#links) + +# Examples using the NAG Library for Python This repository contains examples and demonstrations using the [NAG Library for Python](https://www.nag.com/nag-library-python). The NAG Library for Python contains 1900+ functions spanning many areas of numerical computing and data science. @@ -29,34 +37,181 @@ In addition to those presented here, The NAG Library for Python ships with a set python -m naginterfaces.library.examples --locate ``` -## NAG Library for Python installation +# How to install the NAG Library for Python -The NAG Library for Python comes in two versions. One is linked to the Intel MKL for improved linear algebra performance on x86 architectures and the other is linked to NAG's self contained linear algebra libraries. +In this section we illustrate how to install the NAG Library for Python, request a Trial Licence and make sure the Library is working. Details and further information regarding the installation can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). -When using Intel or AMD CPUs we recommend the use of the Intel MKL version of the NAG Library for Python. +**Note** Before starting make sure you have access to a host that has Python 3 (3.4 or more recent). -Install using the following command +### Step 1. Downloading and installing +Installing the NAG Library is done using the `pip` package manager, fire-up a terminal and create a Python 3 virtual environment where to install and test the NAG Library +```{bash} +guest@nag-37:~$ python3 -m venv nag3 +guest@nag-37:~$ . nag3/bin/activate +(nag3) guest@nag-37:~$ +``` +Now use `pip` to install the NAG Library for Python +```{bash} +(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_nag naginterfaces +``` +or if you prefer the version of the package that relies on Intel MKL for optimized linear algebra routines, then use +```{bash} +(nag3) guest@nag-37:~$ python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces +``` +The output should be similar to +```{bash} +Collecting naginterfaces + Downloading https://www.nag.com/downloads/py/naginterfaces_nag/naginterfaces/naginterfaces-27.1.0.0-py2.py3-none-linux_x86_64.whl (55.8MB) + 100% |████████████████████████████████| 55.8MB 21kB/s +Collecting numpy>=1.15 (from naginterfaces) + Downloading https://files.pythonhosted.org/packages/45/b2/6c7545bb7a38754d63048c7696804a0d947328125d81bf12beaa692c3ae3/numpy-1.19.5-cp36-cp36m-manylinux1_x86_64.whl (13.4MB) + 100% |████████████████████████████████| 13.4MB 70kB/s +Installing collected packages: numpy, naginterfaces +Successfully installed naginterfaces-27.1.0.0 numpy-1.19.5 ``` -python -m pip install --extra-index-url https://www.nag.com/downloads/py/naginterfaces_mkl naginterfaces +The output indicates that the installation was successful. + +### Step 2. Getting a trial licence +The next step is to get the licensing info (**product code** and **KUSARI ID**) and use it to request a licence. From the same virtual terminal, try +```{bash} +(nag3) guest@nag-37:~$ python -m naginterfaces.kusari +``` +The output should be similar to ``` +The NAG Library for Python on this platform uses +underlying Library NLL6I271VL. +This Library has been installed as part of the package +and it requires a valid licence key. +No such key could be validated: +the key may not have been installed correctly or +it may have expired. +The Kusari licence-check utility reports the following: +User: guest +Directory: /home/guest +NAG_KUSARI_FILE="" +File /home/guest/nag.key does not exist +------------------------------------------------------------------------------- +Error: Licence not found; this product requires a key for NLL6I271VL +The above information has been generated on machine nag-37 +For information on how to obtain a licence, please see +https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html +KUSARI ID = "ADLXt-adEclJLmvnxlrU2sseteZoo,RopA-Ld" +``` +The **two** important bits are the -## Obtaining a license + 1. **product code** shown as **`underlying Library NLL6I271VL.`** which identifies the licence to request, and + + 2. **KUSARI ID** shown as **`KUSARI ID = "ADLXt-adEclJLmvnxlrU2sseteZoo,RopA-Ld"`** which identifies the host you are running the library on. + + **Note** that the **product code** and **KUSARI ID** can be different from the previous example. + + With these, you are set to [contact NAG and request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library). + + The trial licence is a plain text chunk similar to + ``` + NLL6I271V TRIAL 2021/01/27 "RverXn0Pc-Ib?ctdgF=Wpis2j7I" + ``` + Save or copy the text into the file `/home/guest/nag.key`. + + The final step is to make sure the licence is valid and the library is working as expected. + +### Step 3. Testing the NAG Library +The last step is to make sure the licence was correctly stored and that the NAG Library is working correctly. From the same virtual terminal re-run the Kusari licence module +```{bash} +(nag3) guest@nag-37:~$ python -m naginterfaces.kusari +``` +This time the output should be similar to +``` +Licence available; the required NLL6I271VL licence key for this product is valid +TRIAL licence, 27 days remaining (licence from file) +``` +Now let's try a more interesting example ([list of optimization examples](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#examples)) -Before you can use the NAG Library for Python, you'll need a license. Free trial licenses are available! +This command runs the example for the [FOAS (First-Order Active set method) solver and minimizes the Rosenbrock 2D function](./FOAS). +``` +(nag3) guest@nag-37:~$ python -m naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex +``` +Should generate an outputsimilar to +```{bash} +Trying: + main() +Expecting: + naginterfaces.library.opt.handle_solve_bounds_foas Python Example Results. + Minimizing a bound-constrained Rosenbrock problem. + E04KF, First order method for bound-constrained problems +... + Status: converged, an optimal solution was found + Value of the objective 4.00000E-02 + ... +ok +``` +indicating that the example was successfully executed. The source code can be found [here](https://www.nag.com/numeric/py/nagdoc_latest/_modules/naginterfaces/library/examples/opt/handle_solve_bounds_foas_ex.html#main). -Run the following command to begin the licensing process and email [support@nag.com](mailto:support@nag.com) if you have any problems. +### Running more examples +To display the full list of example source files on disk, but not run them, execute ``` -# This will launch a license request GUI on windows -# On Mac and Linux, it gives the information you need to send to support@nag.com to request a trial license -python -m naginterfaces.kusari +python -m naginterfaces.library.examples --locate ``` +All examples may be executed sequentially by running +``` +python -m naginterfaces.library.examples +``` +Run `python -m naginterfaces.library.examples --help` to see any additional usage. + + -* More detailed installation instructions are [available in the official documentation](https://www.nag.com/numeric/py/nagdoc_latest/readme.html#installation). -* More detailed license management instructions are available at [https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) +# How to run the Jupyter notebook examples -## List of Chapters in the NAG Library for Python +This section briefly illustrates how to setup a host in order to open and run the [Jupyter notebooks](https://jupyter.org/) provided in this repository. +Before running the notebooks make sure the [NAG Library is installed and working](#install). Before starting, it is advised to read [Jupyter's installation page](https://jupyter.org/install.html). + + + + +### Installing Jupyter notebook +To install Jupyter, launch a terminal and activate the virtual environment used to install the NAG Library for Python +```{bash} +guest@nag-37:~$ . nag3/bin/activate +(nag3) guest@nag-37:~$ pip install notebook matplotlib +Collecting notebook + Downloading https://files.pythonhosted.org/packages/74/19/50cd38acf22e33370d01fef764355f1e3517f6e12b4fceb8d434ece4f8fd/notebook-6.2.0-py3-none-any.whl (9.5MB) + 100% |████████████████████████████████| 9.5MB 115kB/s +Collecting argon2-cffi (from notebook) +... +Successfully installed jupyter-client-6.1.11 jupyterlab-pygments-0.1.2 ... wcwidth-0.2.5 +``` +This indicates that Jupyter and matplotlib were successfully installed. The next section shows how to start the notebok interface and open an example. + +### Running the notebook examples +To run an example, grab a copy of the notebook of interest and start up the notebook interface. +For example, download the [Rosenbrock 2D optimization example](./FOAS/rosenbrock2d.ipynb) notebook `rosenbrock2d.ipynb` into the current directory +```{bash} +(nag3) guest@nag-37:~$ curl -O https://raw.githubusercontent.com/numericalalgorithmsgroup/NAGPythonExamples/master/local_optimization/FOAS/rosenbrock2d.ipynb + % Total % Received % Xferd Average Speed Time Time Time Current + Dload Upload Total Spent Left Speed +100 61961 100 61961 0 0 382k 0 --:--:-- --:--:-- --:--:-- 382k +``` +and now open it using `jupyter-notebook` +```{bash} +(nag3) guest@nag-37:~$ jupyter-notebook rosenbrock2d.ipynb +[I 12:24:07.336 NotebookApp] Serving notebooks from local directory: /home/guest +[I 12:24:07.336 NotebookApp] Jupyter Notebook 6.2.0 is running at: +[I 12:24:07.336 NotebookApp] http://localhost:8888/?token=f1836a06799a92f25ef9966439bf3491b2f0960dcb51806d +... +``` +This command will fire-up your web browser and open the `rosenbrock2d.ipynb` notebook, the window should be similar to + + +![Notebook screenshot](images/screenshot.png) + + + +# List of Chapters in the NAG Library for Python The following links take you to the relevant section in the official documentation @@ -108,3 +263,13 @@ The following links take you to the relevant section in the official documentati * [library.univar](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.univar.html) - Univariate Estimation * [library.wav](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.wav.html) - Wavelet Transforms * [library.zeros](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.zeros.html) - Zeros of Polynomials + + +# Useful links + +* [NAG Library for Python Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) +* [Request a trial licence](https://www.nag.com/content/software-trials?product=NAG%20Library) +* [Kusari licence module Documentation](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.kusari.html#kusari) + + +**[Back to Top](#top)** From c5925f69444a8f0ccd8323e7ad9e9cab4335ab91 Mon Sep 17 00:00:00 2001 From: A Date: Fri, 5 Feb 2021 11:27:55 +0000 Subject: [PATCH 134/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index b5d7c1e..fb7cc46 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -42,7 +42,7 @@ In this section we illustrate how to install the NAG Library for Python, request **Note** Before starting make sure you have access to a host that has Python 3 (3.4 or more recent). ### Step 1. Downloading and installing -Installing the NAG Library is done using the `pip` package manager, fire-up a terminal and create a Python 3 virtual environment where to install and test the NAG Library +Installing the NAG Library is done using the `pip` package manager, fire-up a terminal with [Bash](https://www.gnu.org/software/bash/) and create a Python 3 virtual environment where to install and test the NAG Library ```{bash} guest@nag-37:~$ python3 -m venv nag3 guest@nag-37:~$ . nag3/bin/activate From 298712be6f32f8589aaa17d46f301106dffd0529 Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Fri, 5 Feb 2021 13:54:11 -0600 Subject: [PATCH 135/182] typo correction in output --- .../opt_imp_vol/imp_vol_demo.ipynb | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/special_functions/opt_imp_vol/imp_vol_demo.ipynb b/special_functions/opt_imp_vol/imp_vol_demo.ipynb index 81c152c..e08dbb3 100644 --- a/special_functions/opt_imp_vol/imp_vol_demo.ipynb +++ b/special_functions/opt_imp_vol/imp_vol_demo.ipynb @@ -110,8 +110,8 @@ "output_type": "stream", "text": [ "Using a general purpose root finder:\n", - " Time taken: 44.848 seconds\n", - " There were 3 failures\n" + " Time taken: 51.561 seconds\n", + " There were 4 failures\n" ] } ], @@ -162,7 +162,7 @@ "output_type": "stream", "text": [ "omp_imp_vol with mode = 2 (Jäckel algorithm):\n", - " Time taken: 0.00792 seconds\n", + " Time taken: 0.01415 seconds\n", " There were 0 failures\n" ] } @@ -200,8 +200,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "omp_imp_vol with mode = 2 (Glau algorithm):\n", - " Time taken: 0.00740 seconds\n", + "omp_imp_vol with mode = 1 (Glau algorithm):\n", + " Time taken: 0.01770 seconds\n", " There were 0 failures\n" ] } @@ -210,7 +210,7 @@ "tic = time.perf_counter()\n", "sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=1)\n", "toc = time.perf_counter()\n", - "print('omp_imp_vol with mode = 2 (Glau algorithm):')\n", + "print('omp_imp_vol with mode = 1 (Glau algorithm):')\n", "print(' Time taken: {0:.5f} seconds'.format(toc-tic))\n", "print(' There were {} failures'.format(np.count_nonzero(ivalid)))" ] @@ -240,8 +240,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "omp_imp_vol with mode = 2 (lower accuracy Glau algorithm):\n", - " Time taken: 0.00391 seconds\n", + "omp_imp_vol with mode = 0 (lower accuracy Glau algorithm):\n", + " Time taken: 0.01556 seconds\n", " There were 0 failures\n" ] } @@ -250,7 +250,7 @@ "tic = time.perf_counter()\n", "sigma, ivalid = specfun.opt_imp_vol('C', p, k, s0, t, r, mode=0)\n", "toc = time.perf_counter()\n", - "print('omp_imp_vol with mode = 2 (lower accuracy Glau algorithm):')\n", + "print('omp_imp_vol with mode = 0 (lower accuracy Glau algorithm):')\n", "print(' Time taken: {0:.5f} seconds'.format(toc-tic))\n", "print(' There were {} failures'.format(np.count_nonzero(ivalid)))" ] From fb883258a67ababfb425717780b6beca3600ff82 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 9 Feb 2021 14:23:20 +0000 Subject: [PATCH 136/182] Update Readme.md --- local_optimization/Readme.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index fb7cc46..cb16d63 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -10,13 +10,12 @@ If you are already familiar with NAG's optimization offering and just need to fi - +
DFO Calibration example            Optimization example of a wing sectionNonlinear least-squares callibration example (distribution unfolding)
**Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, -red line shows the final solution. (right) Optimization of a wing section struct: red represent the baseline design, center section in yellow -shows a design with an overall improvement of 13% while the rightmost section in green/blue shows design with a further 33% improvement. Improvement metric is -based on weight and strengh of the piece. +red line shows the final solution. (right) Nonlinear least-squares fitting example, experimental data histogram (blue bars) is fitted with an +aggregated model (green curve) and unfolded models (blue and red curves). Optimal parameter values are reported in the legend, for more details see [here](./BXNL/Readme.md). # Content From 1b98c9bde5e036840211abcf25f9b2e38a7d72e1 Mon Sep 17 00:00:00 2001 From: A Date: Tue, 9 Feb 2021 14:26:25 +0000 Subject: [PATCH 137/182] Update Readme.md --- local_optimization/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/Readme.md b/local_optimization/Readme.md index cb16d63..304ee0e 100644 --- a/local_optimization/Readme.md +++ b/local_optimization/Readme.md @@ -15,7 +15,7 @@ If you are already familiar with NAG's optimization offering and just need to fi **Figure 1.** Applied optimization examples. (left) DFO nonlinear least-square calibration for the Kowalik and Osborne function, red line shows the final solution. (right) Nonlinear least-squares fitting example, experimental data histogram (blue bars) is fitted with an -aggregated model (green curve) and unfolded models (blue and red curves). Optimal parameter values are reported in the legend, for more details see [here](./BXNL/Readme.md). +aggregated model (green curve) while the unfolded models are the blue and red curves. 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f5db2aa5d17e526f73576b26244db7676dd32447 Mon Sep 17 00:00:00 2001 From: Christos Date: Tue, 23 Feb 2021 12:47:29 +0200 Subject: [PATCH 139/182] Fixed links --- local_optimization/BXNL/Readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/BXNL/Readme.md b/local_optimization/BXNL/Readme.md index 640ad4d..1a3e2cb 100644 --- a/local_optimization/BXNL/Readme.md +++ b/local_optimization/BXNL/Readme.md @@ -22,7 +22,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook

**Figure 1.** Example of a NLLS orbital data fitting. - Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 254.90 units wich is withing the suggested tolerance. Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help). + Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 254.90 units wich is withing the suggested tolerance. Image credit: [Image of Earth](https://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](https://pics.eumetsat.int/viewer/index.html#help). # More Info From e57fc05ab9b27db66d06a52f9b9412205e984544 Mon Sep 17 00:00:00 2001 From: Christos Date: Tue, 23 Feb 2021 12:52:45 +0200 Subject: [PATCH 140/182] Fixed image link --- local_optimization/BXNL/notebooks/simple_BXNL.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb index 49a5d80..2393fff 100644 --- a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb +++ b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb @@ -43,7 +43,7 @@ "etched nuclear track data to a convoluted distribution. A target\n", "sheet is scanned and track diameters (red wedges in\n", "the following Figure 1) are recorded into a histogram and a mixed Normal and log-Normal model is to be fitted to the experimental histogram (see Figure 2).\n", - "![PADC](tracks.png)\n" + "![PADC](../images/tracks.png)\n" ] }, { @@ -560,4 +560,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file From 217deedf36956854b8c32057c44ad8ea27e58ad6 Mon Sep 17 00:00:00 2001 From: Christos Date: Tue, 9 Mar 2021 15:25:38 +0200 Subject: [PATCH 141/182] Fixed objfun function based on the new structure of handle_solve_bounds_foas --- .../migration/migration_e04dg_e04kf.ipynb | 42 +++++++++---------- 1 file changed, 20 insertions(+), 22 deletions(-) diff --git a/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb b/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb index 5bc5c7b..ec88954 100644 --- a/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb +++ b/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb @@ -53,10 +53,10 @@ "outputs": [], "source": [ "# Define user call-backs for E04KF\n", - "def objfun_e04kf(x, _inform, _data=None): \n", + "def objfun_e04kf(x, inform, _data=None): \n", " \"\"\"Return the objective function value\"\"\"\n", " objf = (1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2\n", - " return objf\n", + " return objf, inform\n", "\n", "def objgrd_e04kf(x, fdx, inform, _data=None):\n", " \"\"\"The objective's gradient. Note that fdx has to be updated IN-PLACE\"\"\"\n", @@ -92,24 +92,24 @@ "execution_count": 5, "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Solution: \n", - " [1.00000676 1.00001354]\n" - ] - }, { "name": "stderr", "output_type": "stream", "text": [ - "/home/andrews/ni3dev/lib/python3.5/site-packages/ipykernel_launcher.py:2: NagDeprecatedWarning: (NAG Python function naginterfaces.library.opt.uncon_conjgrd_comp)\n", + ":2: NagDeprecatedWarning: (NAG Python function naginterfaces.library.opt.uncon_conjgrd_comp)\n", "This function is deprecated.\n", "The following advice is given for making a replacement:\n", "Please use handle_solve_bounds_foas instead.\n", "See also https://www.nag.com/numeric/py/nagdoc_latest/replace.html\n", - " \n" + " slv = opt.uncon_conjgrd_comp(objfun_e04dg, x, comm, io_manager=iom)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Solution: \n", + " [1.00000676 1.00001354]\n" ] } ], @@ -135,18 +135,16 @@ "name": "stdout", "output_type": "stream", "text": [ - " -------------------------------------------------------------------------------\n", - " E04KF, First order method for bound-constrained problems\n", - " -------------------------------------------------------------------------------\n", + " E04KF, First order method for bound-constrained problems\n", "\n", " Status: converged, an optimal solution was found\n", " Value of the objective 2.12807E-15\n", " Norm of gradient 3.67342E-08\n", "\n", - " Variables:\n", - " idx lower bound value upper bound gradient\n", - " 1 -inf 1.00000E+00 inf -1.87204E-08\n", - " 2 -inf 1.00000E+00 inf -3.67342E-08\n" + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf 1.00000E+00 inf\n", + " 2 -inf 1.00000E+00 inf\n" ] } ], @@ -166,9 +164,9 @@ " 'Print Level = 1', # print details of each iteration (screen)\n", "]:\n", " opt.handle_opt_set(handle, option)\n", - "\n", + " \n", "# Solve the problem and print the solution\n", - "opt.handle_solve_bounds_foas(handle, x, objfun=objfun_e04kf, objgrd=objgrd_e04kf, \n", + "opt.handle_solve_bounds_foas(handle, x, objfun=objfun_e04kf, objgrd=objgrd_e04kf,\n", " io_manager=iom)\n", "\n", "# Destroy the handle and free allocated memory\n", @@ -192,7 +190,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, From 5b303c6bbab9e43366dc0f2dd2994ba16adc8543 Mon Sep 17 00:00:00 2001 From: Mat Cross Date: Mon, 29 Mar 2021 12:57:03 +0100 Subject: [PATCH 142/182] Dealt with some pylint and matplotlib deprecation issues. --- curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb | 6 ++++-- global_optimization/PSO_demo.ipynb | 3 ++- local_optimization/FOAS/rosenbrock2d.ipynb | 5 +---- local_optimization/Notebooks/bounds_quasi_func_easy.ipynb | 3 ++- local_optimization/SOCP/portfolio_optimization_qcqp.ipynb | 2 -- roots/Anderson_Acceleration_Poisson.ipynb | 3 ++- 6 files changed, 11 insertions(+), 11 deletions(-) diff --git a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb index 6dced1c..a8bc96e 100644 --- a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb +++ b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb @@ -905,7 +905,7 @@ "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm\n", "fig = plt.figure()\n", - "ax = Axes3D(fig)\n", + "ax = Axes3D(fig, auto_add_to_figure=False)\n", "ax.grid(False)\n", "ax.set_title('Scattered data points from the Franke Function')\n", "ax.set_xlabel(r'$\\mathit{x}$')\n", @@ -914,6 +914,7 @@ "ax.azim = -20\n", "ax.elev = 20\n", "res = ax.scatter(x, y, f, marker='x')\n", + "fig.add_axes(ax)\n", "plt.show()" ] }, @@ -1865,7 +1866,7 @@ ], "source": [ "fig = plt.figure()\n", - "ax = Axes3D(fig)\n", + "ax = Axes3D(fig, auto_add_to_figure=False)\n", "ax.grid(False)\n", "ax.plot_wireframe(X, Y, z_m, color='red', linewidths=0.4)\n", "ax.contour(X, Y, z_m, 15, offset=-1.2, cmap=cm.jet)\n", @@ -1876,6 +1877,7 @@ "ax.azim = -20\n", "ax.elev = 20\n", "res = ax.scatter(x, y, f, marker='x')\n", + "fig.add_axes(ax)\n", "plt.show()" ] } diff --git a/global_optimization/PSO_demo.ipynb b/global_optimization/PSO_demo.ipynb index ede91d8..baadbbf 100644 --- a/global_optimization/PSO_demo.ipynb +++ b/global_optimization/PSO_demo.ipynb @@ -60,7 +60,7 @@ "Z = ackley(X, Y)\n", "\n", "fig = plt.figure(figsize=(20,10))\n", - "ax = Axes3D(fig)\n", + "ax = Axes3D(fig, auto_add_to_figure=False)\n", "ax.set_xlim3d(-5, 5)\n", "ax.set_ylim3d(-5, 5)\n", "ax.set_zlim3d(0, 15)\n", @@ -69,6 +69,7 @@ "ax.plot_wireframe(X, Y, Z, color='black', lw=0.5, rstride=10, cstride=20)\n", "lev = [0.1, 1, 2, 3, 4, 5, 6, 7, 8, 10]\n", "ax.contour(X, Y, Z, levels=lev, colors='black', linestyles=\"solid\", offset=-1)\n", + "fig.add_axes(ax)\n", "plt.show()" ] }, diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index 3e332b0..024ab76 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -401,11 +401,8 @@ ], "source": [ "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm\n", - "fig = plt.figure()\n", - "ax = Axes3D(fig)\n", - "ax = fig.gca(projection='3d')\n", + "ax = plt.figure().add_subplot(projection='3d')\n", "ax.grid(False)\n", "ax.plot(box[0], box[1], z_box, 'k-', linewidth=1.5)\n", "ax.plot([bl[0], bu[0], bu[0], bl[0], bl[0]], [bl[1], bl[1], bu[1], bu[1], bl[1]], -1.2*np.ones(5), 'k-')\n", diff --git a/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb b/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb index 5578976..e5c5b26 100644 --- a/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb +++ b/local_optimization/Notebooks/bounds_quasi_func_easy.ipynb @@ -1202,7 +1202,7 @@ " Z[j, i] = rosen(np.array([x_i, y_j]))\n", "\n", "fig = plt.figure()\n", - "ax = Axes3D(fig)\n", + "ax = Axes3D(fig, auto_add_to_figure=False)\n", "ax.grid(False)\n", "ax.plot_wireframe(X, Y, Z, color='red', linewidths=0.4)\n", "ax.contour(X, Y, Z, levels=[5, 25, 50, 100, 250, 500, 1000, 1500, 2000, 2500], offset=-3000.0, cmap=cm.jet)\n", @@ -1212,6 +1212,7 @@ "ax.set_zlim3d(-1.0, 10000.0)\n", "ax.azim = -20\n", "ax.elev = 20\n", + "fig.add_axes(ax)\n", "plt.show()" ] }, diff --git a/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb index 541f315..f05f6ff 100644 --- a/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb +++ b/local_optimization/SOCP/portfolio_optimization_qcqp.ipynb @@ -218,9 +218,7 @@ "# Import the NAG Library\n", "from naginterfaces.base import utils\n", "from naginterfaces.library import opt\n", - "from naginterfaces.library import lapackeig\n", "# Import necessary math libraries\n", - "from scipy.sparse import coo_matrix\n", "import math as mt\n", "import warnings as wn" ] diff --git a/roots/Anderson_Acceleration_Poisson.ipynb b/roots/Anderson_Acceleration_Poisson.ipynb index 708c7ba..537bc73 100644 --- a/roots/Anderson_Acceleration_Poisson.ipynb +++ b/roots/Anderson_Acceleration_Poisson.ipynb @@ -7,7 +7,8 @@ "outputs": [], "source": [ "import numpy as np\n", - "from numba import jit, jitclass, float64, int64\n", + "from numba import jit, float64, int64\n", + "from numba.experimental import jitclass\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "np.set_printoptions(precision=16, suppress=True)\n", From 3dbdfc8d71a07b3195001f224c83011be21e7866 Mon Sep 17 00:00:00 2001 From: Edvin Hopkins Date: Thu, 8 Apr 2021 18:30:41 +0100 Subject: [PATCH 143/182] fixes to reflect changes to BBC webpages --- .../web_site_classification_using_nnmf.ipynb | 181 +++++++++--------- 1 file changed, 94 insertions(+), 87 deletions(-) diff --git a/dimension_reduction/web_site_classification_using_nnmf.ipynb b/dimension_reduction/web_site_classification_using_nnmf.ipynb index 0848b68..34c584d 100644 --- a/dimension_reduction/web_site_classification_using_nnmf.ipynb +++ b/dimension_reduction/web_site_classification_using_nnmf.ipynb @@ -80,17 +80,17 @@ "['Kirstjen Nielsen: Walking a tightrope working for Trump - BBC News']\n", "['Trump homes plan at Menie being recommended for approval - BBC News']\n", "['Theresa May at her worst during Brexit speech - Mark Drakeford - BBC News']\n", - "[\"President Trump shows map of 'IS defeat' - BBC News\"]\n", + "['President Trump shows map of 'IS defeat' - BBC News']\n", "['Brexit: What happens now? - BBC News']\n", "['Trump spooks markets with China trade tariffs warning - BBC News']\n", "['A tale of two Trumps: Jair Bolsonaro goes to Washington - BBC News']\n", "['Brexit: Theresa May to formally ask for delay - BBC News']\n", "['Corbyn calls for compromise to avoid no-deal Brexit - BBC News']\n", - "[\"Trump: I didn't get a thank you for McCain funeral - BBC News\"]\n", + "['Trump: I didn't get a thank you for McCain funeral - BBC News']\n", "['Brexit: EU leaders agree Article 50 delay plan - BBC News']\n", "['Trump: Time to recognise Golan Heights as Israeli territory - BBC News']\n", "['Brexit: MPs urged not to travel home alone as tensions rise - BBC News']\n", - "[\"'Cancel Brexit' petition passes 2m signatures on Parliament site - BBC News\"]\n" + "[''Cancel Brexit' petition passes 2m signatures on Parliament site - BBC News']\n" ] } ], @@ -120,7 +120,7 @@ " pagewords = []\n", " paras = re.findall(r'

(.*?)

', f1.read().decode().lower())\n", " f2 = urllib.request.urlopen(link)\n", - " title = re.findall(r'(.*?)', f2.read().decode())\n", + " title = re.findall(r'(.*?)', f2.read().decode())\n", " print(title)\n", " titles.append(title)\n", " for para in paras:\n", @@ -147,26 +147,26 @@ { "data": { "text/plain": [ - "[('a', 32),\n", - " ('the', 29),\n", - " ('to', 16),\n", - " ('uk', 15),\n", - " ('of', 13),\n", + "[('the', 37),\n", + " ('a', 37),\n", + " ('to', 21),\n", + " ('uk', 17),\n", + " ('of', 15),\n", + " ('that', 10),\n", " ('in', 10),\n", - " ('that', 9),\n", + " ('class', 9),\n", + " ('ssrcss', 9),\n", + " ('eu', 9),\n", " ('it', 9),\n", " ('on', 9),\n", - " ('eu', 8),\n", + " ('bbc', 9),\n", + " ('href', 8),\n", " ('would', 8),\n", + " ('an', 7),\n", " ('extension', 7),\n", - " ('href', 7),\n", - " ('class', 7),\n", - " ('story', 7),\n", - " ('body', 7),\n", - " ('link', 7),\n", - " ('an', 6),\n", - " ('article', 6),\n", - " ('50', 6)]" + " ('and', 7),\n", + " ('www', 7),\n", + " ('co', 7)]" ] }, "execution_count": 3, @@ -193,7 +193,7 @@ { "data": { "text/plain": [ - "2186" + "2268" ] }, "execution_count": 4, @@ -216,7 +216,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This list of 2279 words contains many common words such as 'the', 'that' and 'with' which we want to ignore. \n", + "This list of 2268 words contains many common words such as 'the', 'that' and 'with' which we want to ignore. \n", "These unwanted words are commonly referred to as [stopwords](https://en.wikipedia.org/wiki/Stop_words). \n", "The explicit list of stopwords we are going to use in this analysis are defined in the next cell" ] @@ -285,7 +285,7 @@ { "data": { "text/plain": [ - "1795" + "1873" ] }, "execution_count": 8, @@ -332,7 +332,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "1753 distinct words will be used to form the data matrix\n" + "1825 distinct words will be used to form the data matrix\n" ] } ], @@ -364,7 +364,7 @@ "output_type": "stream", "text": [ "Creating data matrix\n", - "Final data matrix has size:(1753, 15)\n" + "Final data matrix has size:(1825, 15)\n" ] } ], @@ -394,12 +394,12 @@ "data": { "text/plain": [ "array([[0., 0., 0., ..., 0., 0., 0.],\n", - " [0., 0., 0., ..., 1., 0., 0.],\n", " [0., 0., 0., ..., 0., 0., 0.],\n", + " [0., 0., 0., ..., 0., 1., 0.],\n", " ...,\n", " [1., 0., 0., ..., 0., 0., 0.],\n", - " [0., 1., 0., ..., 0., 0., 0.],\n", - " [0., 0., 1., ..., 0., 0., 0.]])" + " [1., 0., 0., ..., 0., 0., 0.],\n", + " [0., 0., 0., ..., 0., 0., 0.]])" ] }, "execution_count": 12, @@ -500,12 +500,12 @@ "name": "stderr", "output_type": "stream", "text": [ - ":8: NagAlgorithmicWarning: (NAG Python function naginterfaces.base.matop.real_nmf, code 7:7,99992)\n", + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: NagAlgorithmicWarning: (NAG Python function naginterfaces.base.matop.real_nmf, code 7:7,99992)\n", "** The function has failed to converge after 500 iterations.\n", "** The factorization given by w and h may still be a good enough approximation\n", "** to be useful. Alternatively an improved factorization may be obtained by\n", "** increasing maxit or using different initial choices of w and h.\n", - " w, h = real_nmf(a, k=2, seed=seed, errtol=errtol, maxit=maxit)\n" + " \n" ] } ], @@ -528,7 +528,7 @@ { "data": { "text/plain": [ - "(1753, 2)" + "(1825, 2)" ] }, "execution_count": 15, @@ -577,7 +577,7 @@ "output_type": "stream", "text": [ "norm of residual:\n", - "0.7313733530687229\n" + "0.4996361512168467\n" ] } ], @@ -609,10 +609,10 @@ "text": [ "\n", "The most important words in column 1 of w are:\n", - "['deal', 'brexit', 'parliament', 'delay', 'body', 'story', 'class', 'minister', 'prime', 'vote']\n", + "['quot', 'deal', 'brexit', 'ssrcss', 'class', 'delay', 'parliament', 'minister', 'prime', 'e1no5rhv0']\n", "\n", "The most important words in column 2 of w are:\n", - "['trump', 'president', 'women', 'nielsen', 'border', 'mccain', 'security', 'senator', 'secretary', 'administration']\n" + "['quot', 'trump', 'president', 'women', 'mccain', 'class', 'ssrcss', 'nielsen', 'border', 'security']\n" ] } ], @@ -628,7 +628,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Looking at these lists, you'll hopefully agree that the first column corresponds to Brexit and the second column Trump. It seems that our non-negative matrix factorization has successfully detected the two categories of web page. Let's denote these using the numbers 0 and 1. Can we now use the NMF to accurately categorise the individual pages? To do this we need to look at the coefficients matrix H.\n", + "Looking at these lists, you'll hopefully agree that the first column corresponds to Trump and the second column Brexit. It seems that our non-negative matrix factorization has successfully detected the two categories of web page. Let's denote these using the numbers 0 and 1. Can we now use the NMF to accurately categorise the individual pages? To do this we need to look at the coefficients matrix H.\n", "\n", "We convert h to a pandas dataframe for display purposes" ] @@ -679,52 +679,52 @@ " \n", " \n", " 0\n", - " 12.072\n", - " 7.953e-16\n", - " 2.419\n", - " 19.137\n", - " 7.953e-16\n", - " 4.437\n", - " 1.823\n", - " 0.044\n", - " 3.159e+01\n", - " 7.113e+00\n", - " 7.953e-16\n", - " 15.560\n", - " 4.042\n", - " 1.429\n", - " 2.800e+01\n", + " 1.226e+01\n", + " 1.195e-15\n", + " 5.253\n", + " 50.795\n", + " 1.353\n", + " 6.003e+00\n", + " 5.638\n", + " 10.739\n", + " 76.032\n", + " 1.913e+01\n", + " 1.195e-15\n", + " 34.929\n", + " 1.195e-15\n", + " 4.433\n", + " 5.544e+01\n", " \n", " \n", " 1\n", - " 1.545\n", - " 3.538e+01\n", - " 2.133\n", - " 1.220\n", - " 1.578e+00\n", - " 0.140\n", - " 2.411\n", - " 11.886\n", - " 7.621e-16\n", - " 7.621e-16\n", - " 2.282e+01\n", - " 0.208\n", - " 17.007\n", - " 0.203\n", - " 7.621e-16\n", + " 9.842e-16\n", + " 5.373e+01\n", + " 5.094\n", + " 3.985\n", + " 3.680\n", + " 9.842e-16\n", + " 7.298\n", + " 24.121\n", + " 0.117\n", + " 9.842e-16\n", + " 4.388e+01\n", + " 0.353\n", + " 2.589e+01\n", + " 1.619\n", + " 9.842e-16\n", " \n", " \n", "\n", "" ], "text/plain": [ - " link1 link2 link3 link4 link5 link6 link7 link8 \\\n", - "0 12.072 7.953e-16 2.419 19.137 7.953e-16 4.437 1.823 0.044 \n", - "1 1.545 3.538e+01 2.133 1.220 1.578e+00 0.140 2.411 11.886 \n", + " link1 link2 link3 link4 link5 link6 link7 link8 \\\n", + "0 1.226e+01 1.195e-15 5.253 50.795 1.353 6.003e+00 5.638 10.739 \n", + "1 9.842e-16 5.373e+01 5.094 3.985 3.680 9.842e-16 7.298 24.121 \n", "\n", - " link9 link10 link11 link12 link13 link14 link15 \n", - "0 3.159e+01 7.113e+00 7.953e-16 15.560 4.042 1.429 2.800e+01 \n", - "1 7.621e-16 7.621e-16 2.282e+01 0.208 17.007 0.203 7.621e-16 " + " link9 link10 link11 link12 link13 link14 link15 \n", + "0 76.032 1.913e+01 1.195e-15 34.929 1.195e-15 4.433 5.544e+01 \n", + "1 0.117 9.842e-16 4.388e+01 0.353 2.589e+01 1.619 9.842e-16 " ] }, "execution_count": 19, @@ -762,21 +762,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "Article \"Brexit delay: How is Article 50 extended? - BBC News\" is in category 0 (Trump)\n", - "Article \"Kirstjen Nielsen: Walking a tightrope working for Trump - BBC News\" is in category 1 (Brexit)\n", - "Article \"Trump homes plan at Menie being recommended for approval - BBC News\" is in category 0 (Trump)\n", - "Article \"Theresa May at her worst during Brexit speech - Mark Drakeford - BBC News\" is in category 0 (Trump)\n", - "Article \"President Trump shows map of 'IS defeat' - BBC News\" is in category 1 (Brexit)\n", - "Article \"Brexit: What happens now? - BBC News\" is in category 0 (Trump)\n", - "Article \"Trump spooks markets with China trade tariffs warning - BBC News\" is in category 1 (Brexit)\n", - "Article \"A tale of two Trumps: Jair Bolsonaro goes to Washington - BBC News\" is in category 1 (Brexit)\n", - "Article \"Brexit: Theresa May to formally ask for delay - BBC News\" is in category 0 (Trump)\n", - "Article \"Corbyn calls for compromise to avoid no-deal Brexit - BBC News\" is in category 0 (Trump)\n", - "Article \"Trump: I didn't get a thank you for McCain funeral - BBC News\" is in category 1 (Brexit)\n", - "Article \"Brexit: EU leaders agree Article 50 delay plan - BBC News\" is in category 0 (Trump)\n", - "Article \"Trump: Time to recognise Golan Heights as Israeli territory - BBC News\" is in category 1 (Brexit)\n", - "Article \"Brexit: MPs urged not to travel home alone as tensions rise - BBC News\" is in category 0 (Trump)\n", - "Article \"'Cancel Brexit' petition passes 2m signatures on Parliament site - BBC News\" is in category 0 (Trump)\n" + "Article \"Brexit delay: How is Article 50 extended? - BBC News\" is in category 0 (Brexit)\n", + "Article \"Kirstjen Nielsen: Walking a tightrope working for Trump - BBC News\" is in category 1 (Trump)\n", + "Article \"Trump homes plan at Menie being recommended for approval - BBC News\" is in category 0 (Brexit)\n", + "Article \"Theresa May at her worst during Brexit speech - Mark Drakeford - BBC News\" is in category 0 (Brexit)\n", + "Article \"President Trump shows map of 'IS defeat' - BBC News\" is in category 1 (Trump)\n", + "Article \"Brexit: What happens now? - BBC News\" is in category 0 (Brexit)\n", + "Article \"Trump spooks markets with China trade tariffs warning - BBC News\" is in category 1 (Trump)\n", + "Article \"A tale of two Trumps: Jair Bolsonaro goes to Washington - BBC News\" is in category 1 (Trump)\n", + "Article \"Brexit: Theresa May to formally ask for delay - BBC News\" is in category 0 (Brexit)\n", + "Article \"Corbyn calls for compromise to avoid no-deal Brexit - BBC News\" is in category 0 (Brexit)\n", + "Article \"Trump: I didn't get a thank you for McCain funeral - BBC News\" is in category 1 (Trump)\n", + "Article \"Brexit: EU leaders agree Article 50 delay plan - BBC News\" is in category 0 (Brexit)\n", + "Article \"Trump: Time to recognise Golan Heights as Israeli territory - BBC News\" is in category 1 (Trump)\n", + "Article \"Brexit: MPs urged not to travel home alone as tensions rise - BBC News\" is in category 0 (Brexit)\n", + "Article \"'Cancel Brexit' petition passes 2m signatures on Parliament site - BBC News\" is in category 0 (Brexit)\n" ] } ], @@ -784,7 +784,7 @@ "for i, link in enumerate(links):\n", " category = 0 if h[0,i] > h[1,i] else 1\n", " title = '\"' + (titles[i][0]) + '\"'\n", - " st = 'Article ' + title.ljust(78,' ') + ' is in category ' + str(category) + [\" (Trump)\",\" (Brexit)\"][category]\n", + " st = 'Article ' + title.ljust(78,' ') + ' is in category ' + str(category) + [\" (Brexit)\",\" (Trump)\"][category]\n", " print(st)" ] }, @@ -797,6 +797,13 @@ "* [Presentation on Non-Negative Matrix Factorization](https://www.nag.com/market/non-negative-matrix-factorization.pdf) by the author of the NAG routines **real_nmf** and **real_nmf_rcomm**\n", "* [NAG Blog post on which this notebook is based](https://www.nag.com/content/classifying-web-pages-using-non-negative-matrix-factorization)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -815,7 +822,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.7.3" }, "latex_envs": { "LaTeX_envs_menu_present": true, From bd20f719c176bbbbc878fea7d0962e5fa10d9d3e Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Mon, 12 Apr 2021 09:07:35 -0500 Subject: [PATCH 144/182] Update README.md fixed screenshot --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index d3144e7..6449762 100644 --- a/README.md +++ b/README.md @@ -207,7 +207,7 @@ and now open it using `jupyter-notebook` This command will fire-up your web browser and open the `rosenbrock2d.ipynb` notebook, the window should be similar to -![Notebook screenshot](images/screenshot.png) +![Notebook screenshot](local_optimization/images/screenshot.png) From 83426a97166b5b865ad25fbd89d1386050000711 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 21 Oct 2021 11:22:14 +0100 Subject: [PATCH 145/182] Add (python) examples list --- .../python-nag-opt-solvers-links.md | 93 +++++++++++++++++++ 1 file changed, 93 insertions(+) create mode 100644 local_optimization/python-nag-opt-solvers-links.md diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md new file mode 100644 index 0000000..950804b --- /dev/null +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -0,0 +1,93 @@ +[![NAG Logo](../nag_logo.png)](https://www.nag.com) + +# Local Optimization + +See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html +(modern solvers are identified with "handle_solve" prefix.) + +## LP + +### Sparse LP + + * IPM: e04mt (handle_solve_lp_ipm) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_lp_ipm.html#naginterfaces.library.opt.handle_solve_lp_ipm + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_lp_ipm_ex.main + Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/LP_demo.ipynb + Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/production_planning.ipynb + + * Primal-Simplex AS e04nc (qpconvex2_sparse_solve) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main + +### Dense LP + + * AS e04mf (lp_solve) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lp_solve.html#naginterfaces.library.opt.lp_solve + + * AS e04nc (lsq_lincon_solve) (also solves Convex QP) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve + + +## QP + +### Sparse QP + + * AS e04nq (qpconvex2_sparse_solve) (convex) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve + + * IPM e04st (handle_solve_ipopt) (convex, possibly also nonconvex) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main + +### Convex QCQP + + * Solver of choice: e04pt (SOCP) (handle_solve_socp_ipm) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_socp_ipm.html#naginterfaces.library.opt.handle_solve_socp_ipm + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main + Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/SOCP + +### Dense QP + + * AS e04nf (qp_dense_solve) (convex, possibly also nonconvex) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qp_dense_solve.html#naginterfaces.library.opt.qp_dense_solve + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main + + * AS e04nc (lsq_lincon_solve) (Convex) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve + + +## NLP + +### Sparse + + * AS SQP (FD) e04vh (nlp2_sparse_solve) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp2_sparse_solve.html#naginterfaces.library.opt.nlp2_sparse_solve + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp2_sparse_solve_ex.main + + * IPM (no-FD) e04st (handle_solve_ipopt) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main + + * CG AS (FD) (only bound constraints) (handle_solve_bounds_foas) (also works on dense) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bounds_foas.html#naginterfaces.library.opt.handle_solve_bounds_foas + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main + Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/FOAS + + * DFNO Model-based e04jd (handle_solve_dfno) (no derivatives required, solver of choice is problem is noisy) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_dfno.html#naginterfaces.library.opt.handle_solve_dfno + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main + Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/DFO + + * AS SQP e04ug (nlp1_sparse_solve) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_sparse_solve.html#naginterfaces.library.opt.nlp1_sparse_solve + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_sparse_solve_ex.main + +### Dense + + * AS SQP (FD) e04uc (nlp1_solve) + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_solve.html#naginterfaces.library.opt.nlp1_solve + Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_solve_ex.main + + + + From c0a1fd5830e468da4642c1d656f3113656ed3ad1 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 21 Oct 2021 11:25:35 +0100 Subject: [PATCH 146/182] Update python-nag-opt-solvers-links.md --- .../python-nag-opt-solvers-links.md | 92 +++++++++---------- 1 file changed, 46 insertions(+), 46 deletions(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 950804b..45d73f4 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -9,84 +9,84 @@ See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/nag ### Sparse LP - * IPM: e04mt (handle_solve_lp_ipm) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_lp_ipm.html#naginterfaces.library.opt.handle_solve_lp_ipm - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_lp_ipm_ex.main - Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/LP_demo.ipynb - Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/production_planning.ipynb + * IPM: e04mt (handle_solve_lp_ipm)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_lp_ipm.html#naginterfaces.library.opt.handle_solve_lp_ipm
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_lp_ipm_ex.main
+ Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/LP_demo.ipynb
+ Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/production_planning.ipynb
- * Primal-Simplex AS e04nc (qpconvex2_sparse_solve) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main + * Primal-Simplex AS e04nc (qpconvex2_sparse_solve)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main
### Dense LP - * AS e04mf (lp_solve) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lp_solve.html#naginterfaces.library.opt.lp_solve + * AS e04mf (lp_solve)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lp_solve.html#naginterfaces.library.opt.lp_solve
- * AS e04nc (lsq_lincon_solve) (also solves Convex QP) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve + * AS e04nc (lsq_lincon_solve) (also solves Convex QP)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve
## QP ### Sparse QP - * AS e04nq (qpconvex2_sparse_solve) (convex) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve + * AS e04nq (qpconvex2_sparse_solve) (convex)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve
- * IPM e04st (handle_solve_ipopt) (convex, possibly also nonconvex) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main + * IPM e04st (handle_solve_ipopt) (convex, possibly also nonconvex)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main
-### Convex QCQP +### Convex QCQP (SOCP) - * Solver of choice: e04pt (SOCP) (handle_solve_socp_ipm) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_socp_ipm.html#naginterfaces.library.opt.handle_solve_socp_ipm - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main - Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/SOCP + * Solver of choice: e04pt (SOCP) (handle_solve_socp_ipm)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_socp_ipm.html#naginterfaces.library.opt.handle_solve_socp_ipm
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main
+ Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/SOCP
### Dense QP - * AS e04nf (qp_dense_solve) (convex, possibly also nonconvex) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qp_dense_solve.html#naginterfaces.library.opt.qp_dense_solve - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main + * AS e04nf (qp_dense_solve) (convex, possibly also nonconvex)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qp_dense_solve.html#naginterfaces.library.opt.qp_dense_solve
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main
- * AS e04nc (lsq_lincon_solve) (Convex) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve + * AS e04nc (lsq_lincon_solve) (Convex)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve
## NLP ### Sparse - * AS SQP (FD) e04vh (nlp2_sparse_solve) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp2_sparse_solve.html#naginterfaces.library.opt.nlp2_sparse_solve - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp2_sparse_solve_ex.main + * AS SQP (FD) e04vh (nlp2_sparse_solve)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp2_sparse_solve.html#naginterfaces.library.opt.nlp2_sparse_solve
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp2_sparse_solve_ex.main
- * IPM (no-FD) e04st (handle_solve_ipopt) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main + * IPM (no-FD) e04st (handle_solve_ipopt)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main
- * CG AS (FD) (only bound constraints) (handle_solve_bounds_foas) (also works on dense) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bounds_foas.html#naginterfaces.library.opt.handle_solve_bounds_foas - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main - Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/FOAS + * CG AS (FD) (only bound constraints) (handle_solve_bounds_foas) (also works on dense)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bounds_foas.html#naginterfaces.library.opt.handle_solve_bounds_foas
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main
+ Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/FOAS
- * DFNO Model-based e04jd (handle_solve_dfno) (no derivatives required, solver of choice is problem is noisy) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_dfno.html#naginterfaces.library.opt.handle_solve_dfno - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main - Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/DFO + * DFNO Model-based e04jd (handle_solve_dfno) (no derivatives required, solver of choice is problem is noisy)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_dfno.html#naginterfaces.library.opt.handle_solve_dfno
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main
+ Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/DFO
* AS SQP e04ug (nlp1_sparse_solve) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_sparse_solve.html#naginterfaces.library.opt.nlp1_sparse_solve - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_sparse_solve_ex.main + Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_sparse_solve.html#naginterfaces.library.opt.nlp1_sparse_solve
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_sparse_solve_ex.main
### Dense - * AS SQP (FD) e04uc (nlp1_solve) - Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_solve.html#naginterfaces.library.opt.nlp1_solve - Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_solve_ex.main + * AS SQP (FD) e04uc (nlp1_solve)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_solve.html#naginterfaces.library.opt.nlp1_solve
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_solve_ex.main
From 2f6ec32986d1cf2ed5e223fd20a055a4ba4fff1a Mon Sep 17 00:00:00 2001 From: A Date: Thu, 21 Oct 2021 11:29:01 +0100 Subject: [PATCH 147/182] Update python-nag-opt-solvers-links.md --- .../python-nag-opt-solvers-links.md | 30 +++++++++---------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 45d73f4..b698ff7 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -9,22 +9,22 @@ See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/nag ### Sparse LP - * IPM: e04mt (handle_solve_lp_ipm)
+ * IPM: `e04mt (handle_solve_lp_ipm)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_lp_ipm.html#naginterfaces.library.opt.handle_solve_lp_ipm
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_lp_ipm_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/LP_demo.ipynb
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Modelling/production_planning.ipynb
- * Primal-Simplex AS e04nc (qpconvex2_sparse_solve)
+ * Primal-Simplex AS `e04nc (qpconvex2_sparse_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main
### Dense LP - * AS e04mf (lp_solve)
+ * AS `e04mf (lp_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lp_solve.html#naginterfaces.library.opt.lp_solve
- * AS e04nc (lsq_lincon_solve) (also solves Convex QP)
+ * AS `e04nc (lsq_lincon_solve)` (also solves convex QP)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve
@@ -32,27 +32,27 @@ See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/nag ### Sparse QP - * AS e04nq (qpconvex2_sparse_solve) (convex)
+ * AS `e04nq (qpconvex2_sparse_solve)` (convex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_solve.html#naginterfaces.library.opt.qpconvex2_sparse_solve
- * IPM e04st (handle_solve_ipopt) (convex, possibly also nonconvex)
+ * IPM `e04st (handle_solve_ipopt)` (convex, possibly also nonconvex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main
### Convex QCQP (SOCP) - * Solver of choice: e04pt (SOCP) (handle_solve_socp_ipm)
+ * Solver of choice: `e04pt (handle_solve_socp_ipm)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_socp_ipm.html#naginterfaces.library.opt.handle_solve_socp_ipm
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/SOCP
### Dense QP - * AS e04nf (qp_dense_solve) (convex, possibly also nonconvex)
+ * AS `e04nf (qp_dense_solve)` (convex, possibly also nonconvex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qp_dense_solve.html#naginterfaces.library.opt.qp_dense_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main
- * AS e04nc (lsq_lincon_solve) (Convex)
+ * AS `e04nc (lsq_lincon_solve)` (convex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve
@@ -60,31 +60,31 @@ See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/nag ### Sparse - * AS SQP (FD) e04vh (nlp2_sparse_solve)
+ * AS SQP (FD) `e04vh (nlp2_sparse_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp2_sparse_solve.html#naginterfaces.library.opt.nlp2_sparse_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp2_sparse_solve_ex.main
- * IPM (no-FD) e04st (handle_solve_ipopt)
+ * IPM (no-FD) `e04st (handle_solve_ipopt)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main
- * CG AS (FD) (only bound constraints) (handle_solve_bounds_foas) (also works on dense)
+ * CG AS (FD) (only bound constraints) `e04kf (handle_solve_bounds_foas)` (also works on dense)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bounds_foas.html#naginterfaces.library.opt.handle_solve_bounds_foas
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/FOAS
- * DFNO Model-based e04jd (handle_solve_dfno) (no derivatives required, solver of choice is problem is noisy)
+ * DFNO Model-based `e04jd (handle_solve_dfno)` (no derivatives required, solver of choice is problem is noisy)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_dfno.html#naginterfaces.library.opt.handle_solve_dfno
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/DFO
- * AS SQP e04ug (nlp1_sparse_solve) + * AS SQP `e04ug (nlp1_sparse_solve)` Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_sparse_solve.html#naginterfaces.library.opt.nlp1_sparse_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_sparse_solve_ex.main
### Dense - * AS SQP (FD) e04uc (nlp1_solve)
+ * AS SQP (FD) `e04uc (nlp1_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_solve.html#naginterfaces.library.opt.nlp1_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_solve_ex.main
From fb269c7501ae781c19381533900861dfe7e43087 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 21 Oct 2021 16:54:18 +0100 Subject: [PATCH 148/182] Update python-nag-opt-solvers-links.md --- local_optimization/python-nag-opt-solvers-links.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index b698ff7..bcb72dc 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -2,8 +2,10 @@ # Local Optimization -See full offering of solvers at https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html -(modern solvers are identified with "handle_solve" prefix.) +See full offering of solvers at +https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html
+(https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html) +NOMS solvers are identified with "handle_solve" prefix. ## LP From e266d1451175be6e76cf3a9ccdce61c6c13a8335 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 21 Oct 2021 17:44:23 +0100 Subject: [PATCH 149/182] Update python-nag-opt-solvers-links.md --- local_optimization/python-nag-opt-solvers-links.md | 1 - 1 file changed, 1 deletion(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index bcb72dc..922262b 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -52,7 +52,6 @@ NOMS solvers are identified with "handle_solve" prefix. * AS `e04nf (qp_dense_solve)` (convex, possibly also nonconvex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qp_dense_solve.html#naginterfaces.library.opt.qp_dense_solve
- Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.qpconvex2_sparse_solve_ex.main
* AS `e04nc (lsq_lincon_solve)` (convex)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.lsq_lincon_solve.html#naginterfaces.library.opt.lsq_lincon_solve
From 01cebe4e7e06040733a15c4a3377ed1c3d9fb246 Mon Sep 17 00:00:00 2001 From: A Date: Mon, 25 Oct 2021 14:03:14 +0100 Subject: [PATCH 150/182] Add dense solver python examples --- .../Modelling/dense_lp_solve_ex.py | 66 +++++++++++++++ .../Modelling/dense_qp_solve_ex.py | 82 +++++++++++++++++++ 2 files changed, 148 insertions(+) create mode 100644 local_optimization/Modelling/dense_lp_solve_ex.py create mode 100644 local_optimization/Modelling/dense_qp_solve_ex.py diff --git a/local_optimization/Modelling/dense_lp_solve_ex.py b/local_optimization/Modelling/dense_lp_solve_ex.py new file mode 100644 index 0000000..049546f --- /dev/null +++ b/local_optimization/Modelling/dense_lp_solve_ex.py @@ -0,0 +1,66 @@ +#!/usr/bin/env python + +# Example to solve dense LP problem using (e04mf/lp_solve) + +# Solve the problem +# min cvec^T * x +# subject to bl <= A * x <= bu +# and if present: blx <= x <= bux + +from naginterfaces.library import opt +from naginterfaces.base import utils +import numpy as np + +print('naginterfaces.library.opt.lp_solve Python Example Results.') +print('Solve a small dense LP problem.') + +infty = 1.0E+25 + +# Problem size +n = 7 + +# Number of linear constraints +nclin = 7 + +# Cost vector +cvec = np.array([-0.02, -0.20, -0.20, -0.20, -0.20, 0.04, 0.04]) + +# Block of linear constraints (Matrix A) +a = np.array([ +[ 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00,], +[ 0.15, 0.04, 0.02, 0.04, 0.02, 0.01, 0.03,], +[ 0.03, 0.05, 0.08, 0.02, 0.06, 0.01, 0.00,], +[ 0.02, 0.04, 0.01, 0.02, 0.02, 0.00, 0.00,], +[ 0.02, 0.03, 0.00, 0.00, 0.01, 0.00, 0.00,], +[ 0.70, 0.75, 0.80, 0.75, 0.80, 0.97, 0.00,], +[ 0.02, 0.06, 0.08, 0.12, 0.02, 0.01, 0.97 ] ]) + +# Bounds on the linear constraints +bl = np.array([-0.01, -0.10,-0.01,-0.04,-0.10, -0.01, -0.01, -0.13, -infty, -infty, -infty, -infty, -9.92E-2,-3.0E-3]) +bu = np.array([ 0.01, 0.15, 0.03, 0.02, 0.05, infty, infty, -0.13, -4.9E-3, -6.4E-3, -3.7E-3, -1.2E-3, infty, 2.0E-3]) + +# Initial Guess +x = np.array([-0.01, -0.03, 0.00, -0.01, -0.10, 0.02, 0.01]) + +# Init solver +comm = opt.nlp1_init('lp_solve') + +# Increase printing verbosity +opt.lp_option_string('Print Level = 2', comm) + +# Defile io manager +iom = utils.FileObjManager(locus_in_output=False) + +# Solve the problem +ret = opt.lp_solve(bl, bu, x, comm, a=a, cvec=cvec, istate=None, io_manager=iom) + +# Report the solution and Lagrange multipliers if solved correctly +print('id V Value Lagr Mult') +for id in range(n): + print('{:5} {: 9.3e} {: 9.3e}'.format(id+1, ret.x[id], ret.clamda[id])) + +print('id LC Value Lagr Mult') +for id in range(nclin): + print('{:5} {: 9.3e} {: 9.3e}'.format(n+id+1, ret.ax[id], ret.clamda[n+id])) + +print('Objective value at solution {:0.5f}'.format(ret.obj)) diff --git a/local_optimization/Modelling/dense_qp_solve_ex.py b/local_optimization/Modelling/dense_qp_solve_ex.py new file mode 100644 index 0000000..6ec784f --- /dev/null +++ b/local_optimization/Modelling/dense_qp_solve_ex.py @@ -0,0 +1,82 @@ +#!/usr/bin/env python + +# Example to solve dense QP problem using (e04nf/qp_solve) + +# Solve the dense QP problem defined in https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/e04/e04nff.html#example + +from naginterfaces.library import opt +from naginterfaces.base import utils +import numpy as np + +print('naginterfaces.library.opt.qp_dense_solve Python Example Results.') +print('Solve a small dense QP problem.') + +infty = 1.0E+25 + +# Problem size +n = 7 + +# Number of linear constraints +nclin = 7 + +# Cost vector +cvec = np.array([-0.02, -0.20, -0.20, -0.20, -0.20, 0.04, 0.04]) + +h = np.array([ +[2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,], +[0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0,], +[0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 0.0,], +[0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 0.0,], +[0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0,], +[0.0, 0.0, 0.0, 0.0, 0.0, -2.0, -2.0,], +[0.0, 0.0, 0.0, 0.0, 0.0, -2.0, -2.0 ] ]) + +# Block of linear constraints (Matrix A) +a = np.array([ +[ 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00,], +[ 0.15, 0.04, 0.02, 0.04, 0.02, 0.01, 0.03,], +[ 0.03, 0.05, 0.08, 0.02, 0.06, 0.01, 0.00,], +[ 0.02, 0.04, 0.01, 0.02, 0.02, 0.00, 0.00,], +[ 0.02, 0.03, 0.00, 0.00, 0.01, 0.00, 0.00,], +[ 0.70, 0.75, 0.80, 0.75, 0.80, 0.97, 0.00,], +[ 0.02, 0.06, 0.08, 0.12, 0.02, 0.01, 0.97 ] ]) + +# Bounds on the linear constraints +bl = np.array([-0.01, -0.10,-0.01,-0.04,-0.10, -0.01, -0.01, -0.13, -infty, -infty, -infty, -infty, -9.92E-2,-3.0E-3]) +bu = np.array([ 0.01, 0.15, 0.03, 0.02, 0.05, infty, infty, -0.13, -4.9E-3, -6.4E-3, -3.7E-3, -1.2E-3, infty, 2.0E-3]) + +# Initial Guess +x = np.array([-0.01, -0.03, 0.00, -0.01, -0.10, 0.02, 0.01]) + +# Init solver +comm = opt.nlp1_init('lp_solve') + +# Increase printing verbosity +opt.lp_option_string('Print Level = 2', comm) + +# Defile io manager +iom = utils.FileObjManager(locus_in_output=False) + +# Note for qphess: +# Note: if this argument is None then a NAG-supplied facility will be used. +# In general, you need not provide a version of qphess. +# However, the algorithm of qp_dense_solve requires only the product of H +# or HTH and a vector x; and in some cases you may obtain increased efficiency +# by providing a version of qphess that avoids the need to define the elements +# of the matrices H or HTH explicitly. + +# Solve the problem +ret = opt.qp_dense_solve(bl, bu, h, x, comm, a=a, cvec=cvec, qphess=None, istate=None, data=None, io_manager=None) + +# Report the solution and Lagrange multipliers if solved correctly +print('id V Value Lagr Mult') +for id in range(n): + print('{:5} {: 9.3e} {: 9.3e}'.format(id+1, ret.x[id], ret.clamda[id])) + +print('id LC Value Lagr Mult') +for id in range(nclin): + print('{:5} {: 9.3e} {: 9.3e}'.format(n+id+1, ret.ax[id], ret.clamda[n+id])) + +print('Objective value at solution {:0.5f}'.format(ret.obj)) + +print('Exit from problem afte {:6} iterations.'.format(ret.itera)) From 3ab2a042f0866b541964614203b3cf501777bfb8 Mon Sep 17 00:00:00 2001 From: A Date: Mon, 25 Oct 2021 14:06:01 +0100 Subject: [PATCH 151/182] Update Readme.md --- local_optimization/Modelling/Readme.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md index 2c5ddc1..cdb394e 100644 --- a/local_optimization/Modelling/Readme.md +++ b/local_optimization/Modelling/Readme.md @@ -1,5 +1,11 @@ [![NAG Logo](../../nag_logo.png)](https://www.nag.com) +# Dense Problem Examples +Python examples for dense problems + +* [Linear Programming (LP)](dense_lp_solve.py) +* [Quadratic Programming (QP)](dense_qp_solve.py) + # Modelling Optimization Problems In this folder you will find notebook examples, tips and tricks related to modeling optimization problems. From 4bd5beb75e7dec2baf8d147d93427989bac9105c Mon Sep 17 00:00:00 2001 From: A Date: Mon, 25 Oct 2021 14:06:28 +0100 Subject: [PATCH 152/182] Update Readme.md --- local_optimization/Modelling/Readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/local_optimization/Modelling/Readme.md b/local_optimization/Modelling/Readme.md index cdb394e..fcad86c 100644 --- a/local_optimization/Modelling/Readme.md +++ b/local_optimization/Modelling/Readme.md @@ -3,8 +3,8 @@ # Dense Problem Examples Python examples for dense problems -* [Linear Programming (LP)](dense_lp_solve.py) -* [Quadratic Programming (QP)](dense_qp_solve.py) +* [Linear Programming (LP)](dense_lp_solve_ex.py) +* [Quadratic Programming (QP)](dense_qp_solve_ex.py) # Modelling Optimization Problems From 89f3619a167ab6f8a14a0f1307054e4167ec6d46 Mon Sep 17 00:00:00 2001 From: Andrew Sajo Date: Wed, 26 Jan 2022 16:24:41 +0000 Subject: [PATCH 153/182] Update bxnl notebooks to new interface --- .../BXNL/notebooks/orbit_ex.ipynb | 14 ++++----- .../BXNL/notebooks/simple_BXNL.ipynb | 16 +++++----- .../Modelling/handle_disable_ex.ipynb | 30 +++++++++---------- 3 files changed, 30 insertions(+), 30 deletions(-) diff --git a/local_optimization/BXNL/notebooks/orbit_ex.ipynb b/local_optimization/BXNL/notebooks/orbit_ex.ipynb index e1f376e..c761eba 100644 --- a/local_optimization/BXNL/notebooks/orbit_ex.ipynb +++ b/local_optimization/BXNL/notebooks/orbit_ex.ipynb @@ -41,7 +41,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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miru9G3g4uO0hQcchbfigqARKmoGtcPHF93j5lasHj+OoTLZ8lEg8D0jXdcaTCe3RNsWkxR4DsrksdnOC6zgEoU8Y7O9PXP7oMqqqooQRqqLiBR6KorJn7qCg4Houl9+/zLWr+1N5UmaK7mhAIpnk7R/+Cbfv32FpaZFXnn+JheISNzY/omhW8KYu5cQ8g0EbP5pQzdSYr6xCFOKnu/Q2uyj6BC8zx0bLZmT7/JcfVHn7T14nl8vwL//Fbx2ZyZaPEonnAWmqzqg/QdE0QiUglTPYvLWL67jouk5CNQg+icd1XRRFQdd03MAliiI0TSMIAjRVxfM9Qk1D13QGkzGRouB4Ln7oMxgFECrsrG8TjgK+8a2vc2H1RQa9Lnm9yF5/i0iJUJWQyI5otbrMV+ZZKJ/GOBFgdobsDHyu3W0zsl1QIqxklun00Zqec5RIPA8oCsEdeGgFk7HfIzejsGTm2Lzaw516BKFCGIYoQDadIZlM4jgOo/EIgCAIiKKIiTMlCEOCKCQCoihi6jooqooaKvhBQKPVwPd9Fo4tgKqAF9LZu489spkvrpFOWqw3brHe3uFYzcQdTrl94wa1+SxGuUZ79x7V8iwoHXRXIwgiojDBD36nBHQOcxgfSRLPA/I8F11XmXou5VKNcdBkrlAhX1BgaLBxd0whX+Hj27eIgPF4jOs5VEvl/UCcKWtLa9zdvEcYRiSTJr1hH03TUVQFQ9cwjARje4Lre5h6gn6rw91rtzhxfIntu9e4ufUxy8vnKZ+8yPHSGRQ2mI4mDPwtahkP1VVZ39lmb7fDqbXT5EtFypUs167dpdvp8zs/kHjikHge0NSZEvhQZxPPzZLTDWrZKjo+ej4in9f5yrOv82//7f9Fr99DV1UMXadUKtHtdrnwzLOkzBSDyZD+oM9sbQZNVXE9l6SZAmBi20CErmtEWsRwNOS//vFbhC+dZ69Vx3MCOq0W26l7OJMOvd4uE9+HXI5KJkE2XeT+1lUMTcdKWRRrGZIpjexGmp3tOo7zaJ/X4LBIPA9oOrWZTFzUgsrUH5EKEuxuXsV3JqTTOUwr5Nrty0RhSDGfp1Iuk0lnUD85qfutj2+Rz+ZpNBskDINGs04xX6TZbWNPbQzDwDQMEoaOnjTwfZ/BZMTYGXPjbmr/lTcvoFvfY9TvYCYUNDUknbDoNDYppE6hqjqO42DbKteuX+X5/EX6vR7NVhvd0B75k4IcFonnAbmeS3fYIZHTCKcD7MhD8VR0RaNQWKNjdmmtD6iUK0SBz+zMLJVKhdFwyHg8RtdUNnc2iKKIhGkQ+D6bu1sYCZNsOoOuaZw5eQrLMFFNg+FoSLfeZK6Q5fTSST683WES9tE0m8BRcUiRNBOMhnUSqsdOax1X1XCdIe2uS7MNrd9vEYYRmUwey0riutPDHsZHksTzgIIgoNFdZ7aUJa1opJJZMqbFaLhLa3qPqZdH8SySqRSmrjMZj2krCvfu3SWbzVGr1ji+tIxlWQzHIwq5PEEUcO36DfK5HL/4i19ndW2VYX+EPZnQb3dobu3RH0/o99po0ZCkGeAHHqGvELo+CS1NFEX7LzI02nhTG1OH/rCPooDrOyiqTiKZwrddPDkcOxaJ5wvQ6zUo+hZpR0FRXFQzj6qaOJMhYzfN9sYmnU6bbCZDsVhAmU4plspYlkW9XqfZbqOqCqqmsrO3x0ytRtpK0x8N2Gvt0Zv0abfa2BObxdocupng+sY9qqUWCWOKoQdEQEJXcYIAIp+UEWHoaVx/ShgEqEoWoiZrJ+cpFOawbR/Xddlc3yQI5HS8cRyZeI7SmSA/r2arz6qr4ygqjjpl0N/GD33K6RX6Y49GYw9N10kkErSaLYbjIZVyhdFkjD21SZgJfN8nmHqkUinqzSa6oRMBV65cQVFVxqMRuWwOTVFRDI20pZMvqEymCumUTioCDQU/UMhm8kRKxHTqkUq6jGyHO+sDVpeLPHX2Ka7f2GRi2yhaRKO5c9jD98g6MgfD/fh5uR41o9GY6cCBKIPtaYQBBCjoaoa8VSUMI8IwpNfv0+52caZTMtks9XqdXq/LoN/HmToEQcBwNGQ4HNJutZlOp7TbbZzplFKxRLlcwXVdbt75mIQBVirDfK1MrZCimDHJZhIUsiZmIqJSXcIw02y1J7z7QY+JbbO8YHH91se4gUPKSuC5Nr2uHMsT15GJ51EWhiGbm9so/hQ/MHBCnQiVyaDP3t5dslYGQ9UZDod4vofne6zfv890OmXqOHiex3g8wvM9NE1D13UMXSdpmmQzGdJpi9W1VU6fOYWRMAijkI3dHt0+BGECXU+QtZJYZop82kILHYat+zTaPW7fcXAcKOVMAkVnNHGBiDDyadR3cR+xE4AcJYe62XZUzwQZx+5unePLc1QqZRKmySTosdfus73do9keo6kK2WyWWrVGfzhg0O+RtiymUxvP81EUBddxCYOA+dkFLMtCN3QMQyeXy2EYBjdv3qTT7eAFPiPb4f7uhFIxi64Z6KpCytAY2y4TJ2IwGTGdeEShhqZGrB4r0u4qGJpBFEZ4vsve7vZhD9sj7VDjOapngozDcRzWN3ZJJS2SqSTp7Dwf3rpHt70/uzqKFAI/oN6oUy6XKRaK7NV38QOfMAgxEgkK+f0jUI8tHsP3Pfb29lhcWGBudo5Ov0en22UynqAqKqqq0h/Z+EGRXCqH5zn4gcdw4uD4MA2StPoB+WyOTr9Hsx8ycSckk0miMKTV3GUwGBz2sD3SjswLBo+D7e09qpUKVibP3NwsF89n+Yv3LjMaj9F1DT/wUUKFbreL4ziYpkm5VAXAtid0Oh1Mc396zlNPPUWlWsWburRbbTb3dpjYNqPRCMd1MQyDie3RGYKeMEnqMJ46aIk0ugKRX2CuCkFYpzscsl0fkc1mCDwfVQ25v35PDr1+QEcmnqN0Jsi4XNfl3v0NUhkTJ7JZXjjBKy9/jY+u3mAy2T8K1PN9bGdKFIaM7TFRFJFKWRxbWsKe2Extm93dXQzdYHl5GSNhsrWxwfbmFuPJBNue7E80VWCn2WfsWoz9PCOvRRDlMQtFlhdOkjCrtJttbv7Wm1gpC9udEkURppng9u1rDGWt88COzAsGj9o+zk/TarXZ2qrT6XW4cu0KXuDy1ecvkM2l0TQN2J8xnc3lyOcLpNNpFGBza4swCvnK8xd55unzTJ0pW1tbbG1u4roeCT2BM50SBOEnLyoY2G7Axs4WW5tb9G0D36hxd7NFpOVQdBU/9JgrVdE0lWw6TSmfp9XaY3Nz43AH6TFxZOJ5XERRxMb6Fv3mmOnI5coHH9Futzl79gS5fIYwCgHwfZ8oCkkkEqTTaarVKigKV69dwzANzp8/i+d7JJImVibN/OI8CwsLzM/Pkk6nSaaSJFNJRp5Dvd+nb4d0Bj6KXiLwQzbWN+m2uwREOJ5LwjTo9tvcunVdPp/nC3JkNtseJ57rcu/OfZaWl7GsDDs7O9RqVc6cXqVSLlBvNBlPHDwvRNc1DMPAspIsLizS7/e4ceMm5UqZZ545S9JMEkbQbrZZnJul1Wpw5/46tjMll81gTxTCAFrdDebmZykVcozHY7q9HuP+AHSNTDrFYNBje3Od0Wh02MPz2JB4HpLJZMLW5iYLi4tk0hbD0ZAgCKjVqqTTKfbqLcYTG01VSSYTZDMWxUKGQj7NdDrl/r37bNzf5OLFCzz11FlmZys0my32mrsoqoKm7ken6xoT20ZV9g918H2PdrdNu9tmPBziBROIPOq7W3Jywy+YxPMQjUYjNjc3CIKAMAwYJ1NMp1OKxQLVShGjrxMG7E/WdB0azQa6ZpC2LKxUmkzaotXq0Ov1MAydZDLBsWMLjMYjWq3uJ3PSIqJo/6VuTVXwPI/t7W2GwyGDwYBGo8G9e/fodORgty+axPOQTcYTNjc28FyXSrVCEPioqsJ0OgUUkikT295/lc1Pp8hk0qTTKWZnq5hmAl3X0DSVfr+P7/v4voeqgK6ruK5HFIXomkYum0bXVYbDIY7j0O12aTQabG5uyqbaQyLxfAkcx2FrawvbtqlUq0ynUxKJBIqq4jgOgR8w9gM832cwHBEGIaqqkM6kURSFKIoIw4jJeEK318dxHBRFgShC0ww0VcX3Xba2thiPxwyHQ1qtFo1GA9eVww0eFonnSxIEAc1mk9FoRKlUIpfLkUym0I0EqqqRTJpEUbQ//83zcV0Po9NFVRU81yMCFCD65L5SSRPXcwl8j0hVqNd72J+8idrpdBgOh/Im6EMm8XyJoihiMpkwnU7p9/vkcjnSmQypZAqiAM/T0VQVXdewUon9k4AokDB0omg/Gj/w0TQD19s/2864P8L3PSbjCf1Bn9FwhO/L8TlfBonnEIRhyPCTw7CTSZN0OoNlWSSTSQzDwDAMNE1D0zQUVUXXNCL2z9TjuR6u6+J5Ho7rYE9sxuMx0+n04Pxw4ssh8RyiMAyZTGwmExtVVTEMg0QiQSKRQDd0NFXb37eBT/Z7QnzfP4jHdV0J5hBJPEdEGIY4joPj/M3xNZ+G8ynZhzlaJJ4jTGI52mRumxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEIz63N9447CU4GiQe8bl95zuHvQRHg8QjREwSzwN6UjZh3ngDLl3av8DffP+kPP6/UxRFP+sSRVEUXbp0KVJVNQLk8rculy4d/jLIY/7iLqqqRm+//Xb0Y35qH7LmESIm+TTsGN544yd3mj/dlPne9+D73z+MJfpyfe97h70ER4RstskmjFz+5iKbbUJ8CSSeBySbME8uiecBPQn7OOLvJvEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxCBGTxCNETBKPEDFJPELEJPEIEZPEI0RMEo8QMUk8QsQk8QgRk8QjREwSjxAxSTxCxCTxPERLS0ucPHkSRVEAMAwDwzD+h9uVSiU0Tfs770NVVarVKoZhUCqVDv5/pVJBVff/+crl8k/8fLlc5uTJk2SzWU6fPk06nebs2bOk02lOnz6NZVlf5MN8YsmnYT8kpmny+uuvs7m5SRRFHDt2DNM00XWd9957j3K5TLVapd/v89JLL/HOO+9QKBRoNpt0Oh0cx6HX63Hu3Dlefvllrl+/zszMDG+++SYAr776Krdu3aLT6fDKK68cfL+3t8fa2hrLy8tkMhmazSYnTpzA8zxeeukl6vU6S0tLvPXWW4c8Qo8+WfM8JGEYcvXqVWq1GmfOnOHpp59meXmZZDLJysoKr7zyCjMzM5w7d452u83Jkyd58cUXefbZZ3n99dcP7ufWrVs0m03ef/99xuMxAPl8HlVVee655zh9+jSFQoHz58/z8ssvEwQBm5ubqKrKZDLh3r179Pt9CoUCjUaD+/fvk0wmD2tYHisSz0OiKAqzs7N4noeu64zHY+r1Op7ncfr0aYbDIXfu3KHb7ZLL5TBNk16vx82bN9F1nZWVFRRFIQgC2u02vu/T7XYBeOGFF0gkErRaLVZXV6nX66yvr9Pv9wmCgF/5lV/BMAx2dnZ49tlnKZfLzM/Ps7e3x7PPPsu9e/cOeXQeEz/rc+Y//SD6S5cuRaqqPpTPvX+cL4qiRKqq/sTXH//+77rNmTNnotXV1ahcLv/E/fztr3/7vl588cWoWCxGQKSqaqRp2k9c/+P/fdjjcpQvqqpGb7/9dvRjfmofn2mfZ21tjd/4jd8gDMPPcnMhHlmKonDixInPdtsoin7W9T/zSiGeAMpPu0L2eYSISeIRIiaJR4iYJB4hYpIZBuLIiKKI3Uaft965hpVK8MuvnCOXTR1MbzpqJB5xJERRxIc3t/nH//q73N9uo6DwD/7+8/yb//0foarg+QEKCooKqqIQhNH/EFUURkREqIpCGEX7t1cgjCJ0XSMMwv03nj95y0VTVTQt/sZX7HiiKGI6nWIYBr7v47oupmmiKAphGOL7Pp7nkUwmCYLg4N1y0zSJoghVVQmCgDAMD24TRdHBz6XTaYIgwHEcFEXBsiw8zzv4nUEQkMlkAA7uR9M0bNtG13VSqRSTyQRVVdH1/YfpeR6GYRBFEUEQ4LruwfKmUimiKDr4fZqmoWkaQRAc3Menb475vk8YhqiqiqZpJBIJxuMxmqbhui6ZTObgd34enucB4Ps+QRBgGMbBMiuKgq7rB5NBH0e/+eafcW+rDYCqKTTbI65c32Rxrsi//D9+i5e+cgLPC3j+wnH+yx/+iGNzJTxv/3mTSZtcvrrJqZUaa8s1fvv3/oqXLq5xf6tNKmnwz//BL/Kbv/0Oq8eq3N1scme9yb/6Z3+Prz27Gnt5H2jN87u/+7uUSiXu3r3L+fPn2draOnjyFItFms0m+XwewzC4e/cuiUSCbDZLo9FgYWHh4El54cIF3n33XQaDAb7vH8wGvnz5MsViEVVVMU2Tra0tVFUlm83S6/X4hV/4BWzbZmNjg729PRYXFw/mcV28eJEPPviAVCpFOp3Gtm3++q//mpWVFUzTZGNjg9nZWQzDYHd3l9dee43bt2/jui7b29skk0lKpRK6rnP16lVOnz5NsVhkOBwymUzodDqkUinG4zHnzp3D933a7TZhGPLNb36TbDb7ucfz2rVrbG5u0mg0sCzr4LEbhkGr1eLrX/861Wr1Qf7JjrT+YALsr1lOLFf55ktn0HUNzwv4eL3Br/3yc1y+ukF/aHNnvYkC3Flv4gchtXKWuxstzp6Y49uvnucP//Qq//Dvv8C//j9/m3QqwW69x/vXNtne6/G//qNX+fe/85e8cGHlgZb3gf6M1Wo1dnZ2KJVK+L6PaZrUajV6vR6VSoXl5WUSiQRhGFIsFimXy+i6ztraGru7uyiKwmAwwDRNbNsmnU5Tq9VQFIX19XWy2SyZTIa5uTlM08QwjIMn0+zsLKqqUq/XCYKAubk5dnd3gf13iVVVJYoiXNdlc3OTyWRCrVaj3W7TbDYpl8sYhsHc3NzBWtCyLE6dOsXc3NzBkz8MQ+bm5qjX66TTaTKZDOPxmGq1yvnz56lUKmxsbBysLRRF4ee88fxTWZZFp9OhXC6Ty+UYDAZEUUS9Xj9YCz3OXv+lCxTzFv/bd77J//0b/4xvvXKOlcUKALl0Ck1TURSF967cQ1EU7m+1ma3lWZwr0uyMSCYNysU0g6GNpqlEEfzSS2fYrvf4d//xh2TSJvX2gK3dLpqmPPC+VOwZBp9u+ny6+fLjmxdBEKBp2sFmThAE6Lp+cN2nT+woigjDENM08X3/4Innui66rqPr+sH9w/7m2acTLT/djAIONr1gf5NHVVUSiQSO4xws26ebPJ/+jK7rB8synU5JJBKoqnoQEuyHE4bhwXJomkYYhj/xeD59TL7vo2nawabqTzs+52cJguAnNnF/fLNR07SDPwqPK98P+P0/+YjL1zZImQb/y+vPs7xQxnV9Pry1jaaqzFRyrG+3qZay+EFAOmWiKDAYTXE9H9cLOLUyQ7s7Yraa5/rt/T/SxbxFIZdiMJpiGBqO47NyrPJZFuunFibTc8SREkXRJzv7HPxxOmQSjxAxydw2Ib5oEo8QMUk8QsT0897nOfS9NSGOKlnzCBGTxCNETBKPEDFJPELEJPEIEZPEI0RM/z8IQzNeDD/IagAAAABJRU5ErkJggg==\n", 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" ] @@ -118,8 +118,8 @@ " Computes the Jacobian of the least square residuals.\n", " Simply return rdx[i] = 2r, i = 1, ..., nres.\n", " \"\"\"\n", - " rdx = 2.0*np.ones(nres)*x\n", - " return rdx, inform" + " rdx[:] = 2.0*np.ones(nres)*x[:]\n", + " return inform" ] }, { @@ -236,7 +236,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -319,7 +319,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -359,7 +359,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -373,7 +373,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.9.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb index 2393fff..63839e7 100644 --- a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb +++ b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb @@ -110,7 +110,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -221,7 +221,7 @@ " rdx[i*n+4] = ((d[i] - mu)**2 - sigma**2)/sigma**3 * g\n", " # dg/dAg\n", " rdx[i*n+5] = gaussian(d[i], mu, sigma, 1.0)\n", - " return rdx, inform" + " return inform" ] }, { @@ -396,7 +396,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "4.4421102582032486e-08\n" + "4.4421102582032467e-08\n" ] } ], @@ -420,7 +420,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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atm3bYIdRKVlZWSQkRFYv8JFWJ6tP6Iu0OtVUfZYsWbJHVZtWZt6ISSBt27bl+++Dej9VpaWlpZGamhrsMKpVpNXJ6hP6Iq1ONVUft5+wSrEmLGOMMZViCcQYY0ylWAIxxhhTKRFzDsSYvLw8tmzZQk5OpR4YWaqkpCRWr15d7csNlkirD0Renaq7PvHx8aSkpBAbG1tty7QEYiLGli1bqF+/Pm3btsV9Hke1OXToEPXr16/WZQZTpNUHIq9O1VkfVSUjI4MtW7bQrl27alkmWBOWiSA5OTkkJydXe/IwJtyJCMnJydV+dG4JxEQUSx7GFC8Q3w1LIMYYYyrFEogx1WzmzJmICD//XNXnewXGP/7xjwrPM3XqVCZOnBiAaEw4i5gEsj/zCLMWbAx2GMbw1ltvccopp/DWW29Vy/I8Hk+1LKdQZRKIMcWJmARiTCjIzMzk66+/ZsqUKbz99tsAFBQUcOONN9K1a1eGDx/Oueeey4wZMwD46KOP6Nq1K/369eOmm27i/PPPB2Dy5MlceeWVDBkyhCuvvJLdu3dz8cUXM2DAAAYMGMCCBQsA2L17N8OHD6d79+5ce+21HH/88ezZsweACy64gH79+tG9e3deeOEFACZNmkR2djZDhgzhiiucR4O//vrrDBw4kD59+nD99deTn58PwCuvvELnzp0ZOHCgd33G+LLLeE1E6jmtZ8CWvXx8yY+InjVrFiNGjKBz584kJyezZMkSNm7cSHp6OqtWrWLXrl2ccMIJXH311eTk5HD99dczb9482rVrx2WXXVZkWatWreLrr7+mbt26XH755dx6662ccsop/Prrr5x99tmsXr2ae++9l2HDhvGXv/yFTz75hClTpnjnf/nll2ncuDHZ2dkMGDCAiy++mAcffJCnn36aBQsWUL9+fVavXs0777zDggULiI2N5cYbb+SNN95g+PDh3HPPPSxZsoSkpCROP/10TjzxxIC9pyY8BTSBiMgI4AmcZxu/pKoP+k2vg/Nc335ABjBWVdNF5Argzz5FewF9VXVpIOM1pqreeustbr75ZgDGjRvHW2+9hcfjYcyYMURFRdGiRQtOP/10AH7++Wfat2/vvS7/sssu8x4pAIwaNYq6desC8Pnnn7Nq1SrvtIMHD3qPdt5//30ARowYQaNGjbxlnnzySe+0zZs388svv5CcnFwk3i+++IIlS5YwYMAAALKzs2nWrBnffvstqampNG3qdNI6duxY1q5dW31vlIkIAUsgIhINPAMMx3mY/WIRma2qq3yKXQPsU9WOIjIO+BdOEnkDeMNdTk9gpiUPE+r27t3Ll19+yfLlyxER8vPzEREuvPDCSi3PtyvvgoICFi1aRHx8fLnmTUtL4/PPP+ebb76hXr16pKamFnsPgKoyfvx4/vnPfxYZP3PmzErFbGqXQB6BDATWqeoGABF5GxgN+CaQ0cBk9/UM4GkREb/HVV4GvF3WyvI0l0OefUD13WVpwldpzUyVUZ67gmfMmMGVV17J888/7x132mmn0bhxY9577z3Gjx/P7t27SUtL4/LLL6dLly5s2LCB9PR02rZtyzvvvFPiss866yyeeuop/vxn58B86dKl9OnThyFDhjB9+nTuuOMOPvvsM/bt2wfAgQMHaNSoEfXq1ePnn39m0aJF3mXFxsaSl5cHwBlnnMHo0aO59dZbadasGXv37uXQoUMMGjSIm2++mYyMDBo0aMC7775L7969K/3+mcgUyATSGtjsM7wFGFRSGVX1iMgBIBnY41NmLE6iOYaIXAdcBxDfNp7HNl1H7ic30j6+ffXUoIZkZmaSlpYW7DCqVTDqlJSUxKFDhwKy7Pz8/DKX/frrr3PLLbcUKXfeeeexdu1amjdvTteuXUlJSaF3797Exsbi8Xh45JFHOOuss0hISKBv377k5eVx6NAhjhw5QmxsrHdZ//jHP7j99tvp0aMHHo+HIUOG8Pjjj3P77bdz9dVXM23aNAYOHEjz5s0BGDJkCE8//TRdunShU6dODBgwgMOHD3Po0CEmTJjA4MGD6d27N1OmTOGvf/0rZ555JgUFBcTGxvLwww8zcOBAJk2axKBBg0hKSqJXr17k5uYG7P2tDuX5jMJJIOqTk5NTvd9LVQ3IH3AJznmPwuErgaf9yqwAUnyG1wNNfIYHAcvLs774tvHaY2oPHfn+SC0oKNBwMnfu3GCHUO2CUadVq1YFbNkHDx6s0vyHDh1SVdU9e/Zo+/btdfv27UXGFxQU6O9//3t99NFHK7TcnJwczcvLU1XVhQsXau/evcs1X1XrE4oirU6BqE9x3xHge63k73wgj0C2Am18hlPcccWV2SIiMUASzsn0QuOACl1Mv/HARr7b8R2DWvof7BgTPOeffz779+8nNzeXu+66ixYtWgDw4osvMm3aNHJzcznxxBO5/vrrK7TcX3/9lUsvvZSCggLi4uJ48cUXAxG+McUKZAJZDHQSkXY4iWIccLlfmdnAeOAbnCOWL92MiIhEAZcCp1Z0xV9t+coSiAkpJTUb3Hrrrdx6662VXm6nTp348ccfKz2/MVURsBsJVdUDTAQ+BVYD01V1pYjcJyKj3GJTgGQRWQfcBkzyWcRQYLO6J+ErYuHWhVUL3hhjTJkCeh+Iqn4EfOQ37m6f1znAmBLmTQNOKu+6YiWOGInFo3msP7CeHVk7aJHQonKBG2OMKVPEdGUSI3EcH9/NO7xo+6JSShtjjKmqiEkg0RJD+7q9vMPLdi8LYjTGGBP5IqYvrGiJISW+s3d4xZ4VQYzGhILq7p159JDSbyQUEa644gpef/11wOlFt2XLlgwaNIgPPvigWmOpTomJiWRmZhYZt3//ft58801uvPHGalnH5MmTSUxM5E9/+lOF49q2bRs33XSTtwPKQEhLSyMuLo6TTz652pY5YcIEzj//fC655JJqW+bJJ5/MwoULSU9PZ+HChVx+uf91STUroo5AWsd3QnCeuvXLvl/I9mQHOSpTmyQkJLBixQqys53tbs6cObRu3ToosVS1C/j9+/fz7LPPBmTZFdWqVauAJg9wEsjChRW7+Kam3wfAG2N6ejpvvvlmja/fX8QkkChiiI+qR/sk5y70fM1ndcbqIEdlaptzzz2XDz/8EHA6VvTtYTcrK4urr76agQMHcuKJJzJr1izA+TE49dRT6du3L3379vX+SGzfvp2hQ4fSp08fevTowfz58wFnz7zQjBkzmDBhAuDs8d5www0MGjSI//u//2P9+vWMGDGCfv36ceqpp3ofcLVx40bOOOMMevbsyd/+9rdi6zFp0iTWr19Pnz59+POf/0xaWhqnnnoqo0aNols351xjcd3FA3zyySf07duX3r17c8YZZxyz7BdffJFzzjnHm2gLbdy4kcGDBx8TV3p6Oj169Cj1vUpLS+Occ85h9OjRtG/fnkmTJvHGG28wcOBAevbsyfr16wGK7RY/PT2d5557jscee4w+ffowf/78ErvP9+9m35eqMnHiRLp06cKZZ57Jrl27vNOWLFnCaaedRr9+/Tj77LPZvn07AKmpqdxxxx0MHDiQzp07ez/jlStXkpqaSp8+fejVqxe//PJLkc9+0qRJzJ8/nz59+vDYY48xdOhQli5d6l3fKaecwrJlNdCMX9k7EEPt7/jOnXXm1xv0r/P/qj2m9tAeU3vo1BVTy32HZjDZnejVw/8u25lfb6jWv7IkJCTosmXL9OKLL9bs7Gzt3bu3zp07V8877zxVVf3LX/6ir732mqqq7tu3Tzt16qSZmZmalZWl2dnZqqq6du1a7devn6qqPvzww/rAAw+oqqrH4/HemZyQkOBd57vvvqvjx49XVdXx48freeedpx6PR1VVhw0bpmvXrlVV1UWLFunpp5+uqqojR47U5557TlVVn3766SLLK7Rx40bt3r27d3ju3Llar1493bDh6PuQkZGhqqqHDx/W7t276549e3TXrl2akpLiLVdY5p577tGHHnpIn3rqKR01apTm5OQcs86RI0fqtGnTjonLN5aS3qu5c+dqUlKSbtu2TXNycrRVq1Z69913q6rq448/rjfffLOqql522WU6f/58VVXdtGmTdu3atUh8hUor17dvXz18+PAx8b/33nt65plnqsfj0a1bt2pSUpK+++67mpubq4MHD9Zdu3apqurbb7+tv/3tb1VV9bTTTtPbbrtNVVU//PBDPeOMM1RVdeLEifriiy+qquqRI0e86yt8T3y3K1XVqVOneuu4Zs0a7/viL5zuRK9RUUQD0L1Jd2atd/bsft4bmo8UNZGrV69epKen89Zbb3HuuecWmfbZZ58xe/ZsHn74YcDpl+jXX3+lVatWTJw4kaVLlxIdHe3tNn3AgAFcffXV5OXlccEFF9CnT58y1z9mzBiio6PJzMxk4cKFjBlz9Cr5I0eOALBgwQKmTp0KwJVXXskdd9xRrroNHDjQ2/U8FN9d/O7duxk6dKi3XOPGjb3lX331Vdq0acPMmTOJjY09ZvkLFizgvffeKzWuvLy8Yt8rgL59+9KyZUsAOnTowFlnnQVAz549mTt3LlByt/j+Sivn282+r3nz5nHZZZcRHR1Nq1atGDZsGABr1qxhxYoVDB8+HHD6uCqME+Ciiy4CoF+/fqSnpwMwePBg7r//fjIyMrjooovo1KnTMevzNWbMGO6//34eeughXn75Ze9RaaBFTAJxblyHro27eset2bcmWOGYWmzUqFH86U9/Ii0tjYyMoz3zqCrvvfceXbp0KVJ+8uTJNG/enGXLllFQUODtsn3o0KHMmzePDz/8kAkTJnDbbbdx1VVXISLeef27aC/sAr6goICGDRsWadbw5buM8vLtXr683cX76tmzJ0uXLmXLli1FElFF4nrssceKfa8A4uLivK+joqKoU6eO93Xh+YrydotfWjnf96E8VJXu3bvzzTffFDu9MM7o6GhvnJdffjndu3fnq6++4txzz+X555/3JqTi1KtXj+HDhzNr1iymT5/OkiVLKhRjZUXMOZDCk+edGx29Emvj/o3k5ucGKyRTS1199dXcc8899OxZ9KmIZ599Nk899VRhR6HeLkgOHDhAy5YtiYqK4rXXXvM+UnbTpk00b96c3/3ud1x77bX88MMPADRv3pzVq1dTUFDgPQLw16BBA9q1a8e7774LOD9ihW3iQ4YM8Z6UfuONN4qdv379+qX2BFtSd/EnnXQS8+bNY+NG5wq4vXv3euc58cQTef755xk1ahTbtm07ZplDhgzxPga4pLhKeq/Kq7Bb/EKFCda/viWVK83QoUN55513yM/PZ/v27d6jni5durB7925vAsnLy2PlypWlLmvDhg20a9eOm266idGjR/PTTz8VmV7c53Pttddy0003MWDAgCIPFgukiDkCKZQQm0Cb+m3YfGgzHvWwfv96Tkg+IdhhmSAYPaT6ng1TkW61U1JSuOmmm44Zf9ddd3HLLbfQq1cvCgoKaNeuHR988AE33ngjF198Ma+++iojRozw7uGmpaXx0EMPERsbS2JiIq+++ioADz74IOeffz5Nmzalf//+xTbBgPMj/Pvf/54HHniAvLw8xo0bR+/evXniiScYO3YsTz75JKNHF/ukBJKTkxkyZAg9evTgnHPO4bzzzisyfcSIETz33HOccMIJdOnShZNOcjqNaNq0KS+88AIXXXQRBQUFNGvWjDlz5njnO+WUU3j44Yc577zzmDNnDk2aNPFOe+KJJ7j88sv517/+VWJcJb1X5fXkk0/yhz/8gV69euHxeBg6dCjPPfccI0eO5JJLLmHWrFk89dRTJZYrzYUXXsiXX35Jt27dOO644xg8eDDgHBnNmDGDm266iQMHDuDxeLjlllvo3r17icuaPn0606ZNo06dOrRo0YI777yzyPRevXoRHR1N7969mTBhArfeeiv9+vWjQYMG/Pa3v63Qe1IVUrg3FO46du2pj0yZzegh7bgt7TbmbHI22vtOvo8LO1XuiXA1JS0tjdTU1GCHUa2CUafVq1dzwgmB2VkozwOlwkmk1Qcir04Vrc+2bdtITU3l559/Jiqq+Mal4r4jIrJEVftXJsaIacLy5duMtXafPcfZGBPZXn31VQYNGsTf//73EpNHIERcExYUPZFuV2IZYyLdVVddxVVXXVXj643II5AujY5e5bJm3xoipZnOlM0+a2OKF4jvRkQmkBYJLWgQ1wCAQ7mH2J61PcgRmZoQHx9PRkaGJRFj/KgqGRkZZV6+XFER2YQlInRp3IXFOxYDTjNWq8RWQY7KBFpKSgpbtmxh9+7d1b7snJycav/yBVOk1Qcir07VXZ/4+HhSUlKqbXkQoQkEnGaswgSyZu8ahh1X8k04JjLExsaWeINaVaWlpXHiiScGZNnBEGn1gcirUzjUJyKbsAC6ND56HsSuxDLGmOoXuQnE70S6McaY6hWxCaRDww5Ei9PB4uZDm8nKywpyRMYYE1kCmkBEZISIrBGRdSIyqZjpdUTkHXf6tyLS1mdaLxH5RkRWishyEanQ2aS46DjaJR1tD/9l3y9VqYoxxhg/AUsgIhINPAOcA3QDLhORbn7FrgH2qWpH4DHgX+68McDrwA2q2h1IBfIqGoPdkW6MMYETyKuwBgLrVHUDgIi8DYwGVvmUGQ1Mdl/PAJ4Wpz/ns4CfVHUZgKpmUAldGnfho40fAc6VWP7PyK7OzvaMMaa2CWQCaQ1s9hneAgwqqYyqekTkAJAMdAZURD4FmgJvq+q//VcgItcB1wE0bdoM9v9CWtom7/Qj2Ue8rxdvWkyv+kVX71s2mDIzM0lLSwt2GNUq0upk9Ql9kVancKhPqN4HEgOcAgwADgNfuD1GfuFbSFVfAF4ApzdeGnYi1eeoovvh7jz77rMA7MjfQUFSB6LkaKtdaogcgVhvvKHP6hP6Iq1O4VCfQJ5E3wq08RlOcccVW8Y975EEZOAcrcxT1T2qehj4COhb0QCa1G1C43jnkZrZnmz2eXZWdBHGGGNKEMgEshjoJCLtRCQOGAfM9iszGxjvvr4E+NJ9yPunQE8RqecmltMoeu6kXESkyIn0HUc2llLaGGNMRQQsgaiqB5iIkwxWA9NVdaWI3Ccio9xiU4BkEVkH3AZMcufdBzyKk4SWAj+o6oeVicP3hsIdR9IrVRdjjDHHCug5EFX9CKf5yXfc3T6vc4AxJcz7Os6lvFXSubHPEUiuHYEYY0x1idg70QvZEYgxxgRGqF6FVSW+93t4VIgmhnw87PPsJKfgMPFR9YIYnTHGRIaIPwKJkViaxh3tA9+OQowxpnpEfAIBaF6nrfe1XYlljDHVo1YkkJZxR28Y3JGbHrxAjDEmgtSKBNLCjkCMMaba1Y4E4nMEsjN3EwWaH8RojDEmMtSKBJIY05Dk+GQA8vQIe/N2BDkiY4wJf7UigUDRZ6TbeRBjjKm62pNAitxQaOdBjDGmqmpNAinSpYndC2KMMVVWaxJI10Zdva+3HVkfxEiMMSYy1JoE0i6pHbFSB4CD+Rkc8uwLckTGGBPeak0CiY6KpmWd9t7hbUfWBTEaY4wJf7UmgQC0rtPR+3qrJRBjjKmSWpVAWvkkkG05dh7EGGOqolYlkNbxHbyv7QjEGGOqplYlkCaxrYmTeAAO5e9l1+FdQY7IGGPCV61KIFFS9ET6qoxVQYzGGGPCW0ATiIiMEJE1IrJORCYVM72OiLzjTv9WRNq649uKSLaILHX/nquumHxPpFsCMcaYygvYI21FJBp4BhgObAEWi8hsVfX91b4G2KeqHUVkHPAvYKw7bb2q9qnuuFrFd4ADzuuVGSure/HGGFNrBPIIZCCwTlU3qGou8DYw2q/MaGCa+3oGcIaISABjonWdTt7XqzJWoaqBXJ0xxkSsQCaQ1sBmn+Et7rhiy6iqB+fYINmd1k5EfhSRr0Tk1OoKKjm2FXFSF4A92XvsRLoxxlRSwJqwqmg7cJyqZohIP2CmiHRX1YO+hUTkOuA6gKZNm8H+X0hL2wRZuccssHB8FNAquiXpng0AvPPVO/Sq1yvQ9SlVZmYmaWlpQY2hukVanaw+oS/S6hQO9QlkAtkKtPEZTnHHFVdmi4jEAElAhjrtSkcAVHWJiKwHOgPf+86sqi8ALwB07NpTadiJ1CHtmLXg2O7afce39vQifb+TQAqaF5DaL7VqNa2itLQ0UlODG0N1i7Q6WX1CX6TVKRzqE8gmrMVAJxFpJyJxwDhgtl+Z2cB49/UlwJeqqiLS1D0Jj4i0BzoBG6orsDbxR58Nsmz3suparDHG1CoBOwJRVY+ITAQ+BaKBl1V1pYjcB3yvqrOBKcBrIrIO2IuTZACGAveJSB5QANygqnurK7bj4o927b4yYyV5BXnERsVW1+KNMaZWCOg5EFX9CPjIb9zdPq9zgDHFzPce8F6g4moQk0xSTFMOeHaT7clm7b61dE/uHqjVGWNMRKpVd6L78j0KWbbLmrGMMaaiam0CsfMgxhhTNbU2gRwXf4L3tSUQY4ypuFqbQFrUaUudaOcRt1szt7Ine0+QIzLGmPBSaxNIjMQWOXFu50GMMaZiam0CAejdrLf39dLdS4MXiDHGhKHanUCaHk0gdh7EGGMqxhKIa+WeleTmH9uHljHGmOLV6gTSpG4Tjqt/HAC5Bbks37M8yBEZY0z4qNUJBGBAiwHe14t3LA5iJMYYE15qfQLp17yf9/X3O78vpaQxxhhftT6B+B6BLNu1jLz8vCBGY4wx4aPWJ5AWCS1ISUwBICc/hxUZK4IckTHGhIdyJRAR+a+InCciEZlwfI9Cvt9hzVjGGFMe5U0IzwKXA7+IyIMi0qWsGcJJ/xb9va/tRLoxxpRPuRKIqn6uqlcAfYF04HMRWSgivxWRsH8SU//mRxPI0t1LySuw8yDGGFOWcjdJiUgyMAG4FvgReAInocwJSGQ1qFViK1ontgYg25PNT7t/CnJExhgT+sp7DuR9YD5QDxipqqNU9R1V/SOQGMgAa8rgVoO9rxduWxjESIwxJjyU9wjkRVXtpqr/VNXtACJSB0BV+5c+a3gY3PJoAlm0bVEQIzHGmPBQ3gTyQDHjvqnOQIJtUMtBRLkXma3IWMGBIweCHJExxoS2UhOIiLQQkX5AXRE5UUT6un+pOM1ZpRKRESKyRkTWicikYqbXEZF33Onfikhbv+nHiUimiPypQrWqhKQ6Sd7ngxRoAd9u/zbQqzTGmLBW1hHI2cDDQArwKPCI+3cbcGdpM4pINPAMcA7QDbhMRLr5FbsG2KeqHYHHgH/5TX8U+LjsalQP3/Mg32yPqAMsY4ypdjGlTVTVacA0EblYVd+r4LIHAutUdQOAiLwNjAZW+ZQZDUx2X88AnhYRUVUVkQuAjUBWBddbIbMWbPS+Lshu5329cOtCVBURCeTqjTEmbJWaQETkN6r6OtBWRG7zn66qj5Yye2tgs8/wFmBQSWVU1SMiB4BkEckB7gCGAyU2X4nIdcB1AE2bNoP9v5CWtgmyjn2uR3Hj/ce10WjqSB2O6BG2ZW3j3c/fpVlss1KqWD0yMzNJS0sL+HpqUqTVyeoT+iKtTuFQn1ITCJDg/q/pS3UnA4+pamZpRwCq+gLwAkDHrj2Vhp1IHdKuyFFFoeLG+4+LBk6udzJzN88FIKdVDqndU6talzKlpaWRmhr49dSkSKuT1Sf0RVqdwqE+ZTVhPe/+v7cSy94KtPEZTnHHFVdmi4jEAElABs6RyiUi8m+gIVAgIjmq+nQl4qiQ01JO8yaQeVvmcVX3qwK9SmOMCUvlvZHw3yLSQERiReQLEdktIr8pY7bFQCcRaSciccA4YLZfmdnAePf1JcCX6jhVVduqalvgceAfNZE8AE5NOdX7esnOJRzKPVQTqzXGmLBT3vtAzlLVg8D5OH1hdQT+XNoMquoBJgKfAquB6aq6UkTuE5FRbrEpOOc81uFc2XXMpb41rVm9ZnRLdi4W86iHBdsWBDkiY4wJTWWdA/Evdx7wrqoeKM/VSar6EfCR37i7fV7nAGPKWMbkcsZYbVJTUlmV4VwsNm/zPEa0HVHTIRhjTMgr7xHIByLyM9AP+EJEmgI5gQsruIa2Gep9PX/rfPIL8oMYjTHGhKbyduc+CTgZ6K+qeTj3ZowOZGDBdELjE2hatykA+4/sZ9nuZUGOyBhjQk9FnjDYFRgrIlfhnPA+KzAhBV+URJHaJtU7PGdT2PdYb4wx1a68V2G9htOlySnAAPcvInrhLcnw44d7X8/ZNIcCLQhiNMYYE3rKexK9P9BNVTWQwYSS/i3607BOQ/Yf2c/OwztZvmc5vZv2DnZYxhgTMsrbhLUCaBHIQEJNbFQsw44b5h3+LP2zIEZjjDGhp7wJpAmwSkQ+FZHZhX+BDCwUnHX80dM8czbNoRYdgBljTJnK24Q1OZBBhKqBLQfSIK4BB3MPsj1rOyv2rKBn057BDssYY0JCeS/j/QrnDvRY9/Vi4IcAxhUS/Jux7GosY4w5qrxXYf0O53kdz7ujWgMzAxRTSPG9GuuT9E/saixjjHGV9xzIH4AhwEEAVf0FCPyDMkLA4JaDSaqTBMD2rO0s2bkkyBEZY0xoKG8COaKq3icvuV2v14ozyrHRsUX6wpq9PuKvHTDGmHIpbwL5SkTuBOqKyHDgXeB/gQsrtIzqMMr7+rP0z8j2ZAcxGmOMCQ3lTSCTgN3AcuB6nB52/xaooEJNzyY9adugLQCHPYf54tcvghuQMcaEgPJehVWAc9L8RlW9RFVfrE13pYtIkaOQ/62vNQdfxhhTolITiDgmi8geYA2wxn0a4d2lzReJzm9/PoLzDJRF2xexM2tnkCMyxpjgKusI5Facq68GqGpjVW2M87zyISJya8CjCyEtE1sysMVAAAq0gP9tsKMQY0ztVlYCuRK4TFU3Fo5Q1Q3Ab4CrAhlYKBrd8egjUGasnWEPmjLG1GplJZBYVd3jP1JVdwOxgQkp+GYt2Fjkr9Dw44d77wnZmrnVnpdujKnVykoguZWcFpHiY+K5oMMF3uHpa6YHLxhjjAmyshJIbxE5WMzfIaDMXgVFZISIrBGRdSIyqZjpdUTkHXf6tyLS1h0/UESWun/LROTCStWuGhUejTTKHOwdN2/LPLZmbg1iVMYYEzylJhBVjVbVBsX81VfVUpuwRCQaeAY4B+gGXCYi3fyKXQPsU9WOwGPAv9zxK3Cev94HGAE87979HnRN4lrRoW4fABRlxtoZwQ3IGGOCpCLPRK+ogcA6Vd3gdoPyNjDar8xoYJr7egZwhoiIqh5WVY87Pp4Q6zZlUNI53tf//eW/5ObXutY8Y4xBAnU/oIhcAoxQ1Wvd4SuBQao60afMCrfMFnd4vVtmj4gMAl4GjgeuVNX3i1nHdcB1AE2bNuv34iuvkZQQx4GsY3/Qixtf2XH5ms8j+/7OwYIDAFyefDmDEwdTWZmZmSQmJlZ6/lAUaXWy+oS+SKtTTdXn9NNPX6Kq/Sszb0g0CxVHVb8FuovICcA0EflYVXP8yrwAvADQsWtPpWEnUoe0K3LlVKHixld2XDRwEhfwWYZz8LTIs4g7TruDKKncAV1aWhqpqamVmjdURVqdrD6hL9LqFA71CWQT1lagjc9wijuu2DLuOY4kIMO3gKquBjKBHgGLtBIGNDibejH1ANhwYAPzt8wPckTGGFOzAplAFgOdRKSdiMQB4wD/vtBnA+Pd15cAX6qquvPEAIjI8UBXnCcihoy60Ylc0vkS7/DUlVODF4wxxgRBwBKIexJ8IvApsBqYrqorReQ+ESnsmXAKkCwi64DbcHr9BTgFWCYiS4H3cTpxPOaGxmC7stuVxLgXh32/83tW7FkR5IiMMabmBPQciKp+hNP1u++4u31e5wBjipnvNeC1QMZWHVoktGBEuxF8sOEDAKYsn8Jjpz8W5KiMMaZmhOxJ9HAxofsEbwL5/NfPWbN3DV0adwlyVCbc+F+4MXpIuyBFYkz5BfIcSK3QpXEXhrUZ5h3+z7L/BDEaY4ypOZZAqsGNfW70vv7i1y9YnbE6iNEYY0zNsARSDbo07sLw44d7h59d9mwQozHGmJphCaSa3ND7Bu/rtM1pdkWWMSbiWQKpJp0bdebstmd7hx/+/mFq0WPjjTG1kF2FVUW+V8+cUHABX8gXeNTDkp1L+HLzl5xx3BlBjM4YYwLHjkCqUZO41oztOtY7/NiSx8jLzwtiRMYYEziWQKrZDb1uoH5sfQA2HdzE9LX21EJjTGSyBFLNGsY35Lpe13mHn136LHtz9gYxImOMCQxLIAFw+QmXk5KYAsDB3IM8+v2jAVlP4WN2C/+MMaYmWQIJgLjoOP4y6C/e4VnrZ7Fk55IgRmSMMdXPEkiADE0ZypnHnekdfmDRA+QV2Al1U3V25GlChSWQALpj4B3UjakLwLr965i2cloZcxhjTPiwBBIAhXuG3y7N5rSkcd7xzy59ll/2/RLEyExtV7htHsjKtaMXU2V2I2GADW44ii0sZkXGCvIK8vjbgr/x+rmvExsVG+zQTIhRVTLytrMjdyNbln7E5kOb2Z+zn/1H9pOv+cRFxREXHUdeVgKNYpuTHNuK4+K7otoWEQl2+KYWsgQSYNESzQOnPMCl/7uU3IJcVmWsYsryKUX6zjK1V44nh3lb5vHezo9Yf3gpB/MznAk7yr+MV6cnkxLTgx6JQ+hYry+xUXH2PBFTIyyB1IAODTsw8cSJPLrEuZz3+WXPM6TVEHo27RnkyEywrNizgnfXvstn6Z+RmZdZpWVl5GSQwVcsy/yKOlKX3vVT6bn/Bto3bF9N0RpTPEsgNeSqblfx5a9fsnT3Ujzq4c/z/sz0kdNpENcg2KGZGlKgBczfMp9XVr5S4mXd8VEJpNTpzJB2vTi4pwGJ0Q2pF12faGLJJ49+JzTk42XL2Zu3g+1HNvJrzmpyCrK88x/RbL47+DGjZ33Mya1O5sY+N9K7ae+aqqKpZQKaQERkBPAEEA28pKoP+k2vA7wK9AMygLGqmi4iw4EHgTggF/izqn4ZyFgD7YNvfmVYvRv5OepWcgqy2Jq5letm/5lxLe5A3BOapTU72CNPw5eq8vXWr3n8h8dZu2/tMdPb1G9Dh5iT6ZLQj1Z1OhEt0Ywe0K7Yk9yDW7Vj18YW3uECLaDzCTk8u2AGKzK/Zm/e0bavhdsWsnDbQlJTUrmp7010atQpMBU0tVbAEoiIRAPPAMOBLcBiEZmtqqt8il0D7FPVjiIyDvgXMBbYA4xU1W0i0gP4FGgdqFhrSuPYFlzY7I+8tcPJoyuzFvLtgY84ic5BjswEysqMlTz6/aN8t+O7IuNjJIYR7UYwtstYejftzeyF6ZVafpRE0T25O2cl12N44yvZmL2CRQf+x8+Hv6NACwBI25LG/K3z+c0Jv+G4gnOpE1W3qtUyBgjsEchAYJ2qbgAQkbeB0YBvAhkNTHZfzwCeFhFR1R99yqwE6opIHVU9EsB4a0T3xJMZlHQu3x74CICP90whJekPpGB7h+HM/2ghJz+LdXGzeGfNOyhHnwtTN6Yul3a+lN90+w0tElr4L6ZKRIT29XrSvl5P+vSM4s45D7E8cx6Kkq/5TFs1jQYxHzKyyXWcQHK1rtvUThKohx6JyCXACFW91h2+EhikqhN9yqxwy2xxh9e7Zfb4LecGVT0TPyJyHXAdQNOmzfq9+MprJCXEcSAr95h4ihtflXFVmT9P85hy8Gm25G0BoL7U5/cNb6VNg6bHrKNQedcTKjIzM0lMTAx2GNWmrPoUfhaqyqrc5XyQ9T6HCg56p0cRxcmJJ3NOw3NoEH3sea9AbXM7PNv4MGsmG/PWF5neN64v5yVeTLP6kXMOrrZtc9Xl9NNPX6Kq/Sszb0ifRBeR7jjNWmcVN11VXwBeAOjYtafSsBOpQ4pvOy5ufFXGVWX+WOCFoS9w8axLyS7I5JAe4o3DbzLz3LeIj4kvrqrlXk+oSEtLIzU1NdhhVJuy6jNrwUay8g8wa9czrMpaVGTakNZDuGPAHbRLKv85rura5lrQiauTh7L0UBpzD07z9gz9Q+4PbDy4jScHPUSfZn1KjCuc1LZtLhQE8k70rUAbn+EUd1yxZUQkBkjCOZmOiKQA7wNXqep6IkybBm0Y1+IOotyPYOuRddy94G57DG6YWpO1mKd+/WOR5JEcn8xDQx/iP2f8p9TkEWgiwokNTmf2BbPplXiad/w+zw4mfDKBaSun2XZnKiWQCWQx0ElE2olIHDAOmO1XZjYw3n19CfClqqqINAQ+BCap6oIAxhhUHer15twmv/MOf5z+MU/9+FQQIzIVdTjvMPd/cz+vbb+fzPz93vH9G5zN7AtnM6LdiJC5SzypThKXtridMc1vp444R7r5ms/D3z/MHfPu4HDe4SBHaMJNwBKIqnqAiThXUK0GpqvqShG5T0RGucWmAMkisg64DZjkjp8IdATuFpGl7l+zQMUaTIOSzmVg/GDv8IvLX+SN1W8EMSJTXmv3rWXsB2OLPHUyMboRV7W8hwua/SFk7/HpXf80Jja8nZQ6R6/++zj9Y6746Ap+PfhrECMz4Sag50BU9SPgI79xd/u8zgHGFDPfA8ADgYwtVIgI5yVcyIGoPNYc/h6AB797kEZ1GnFu+3ODHJ0pycx1M/n7or+Tk5/jHdctYTCjm/2BhGJOkoeaRtGNuTbln6yMfpt3174LOD1GXzJrHFe0vJObzzw/yBGacGC98YaAaIlmbIs7itwx/Nev/8q8LfOCGJUpTo4nh7sX3M1dC+7yJo+6MXW5qNnNXNZiUlgkj0IxEsvdg+/mwmZ/JEaczj2zCw7xyta7+HDDh0GOzoQDSyAhIi6qDs+c8QwdkjoA4FEPt8y9ha82fxXkyEyhTQc3ccVHV/D+uve949onteet896ib4MzQuZcR0X1azCca1v/k8TohgDk42HS/Enc8r8Hmfn1BntwlSmRJZAQklQnieeGP0frROem+7yCPG5Ju4W5v84NcmTmx6wfGfvB2CJdkZzX/jzeOu8tOjTsEMTIqkdKfGeuT3mIZnFHL5z8Yu8bvL/rSfLVE8TITCgL6ftAaqMWCS145exXuPrTq9mSuQVPgYfbvrqNS5rdTo/EIWXOb31mVa+8/DweWfIIb+w5emFDbFQskwZOYkznMWUedRT3eYTqZ9Qotjm/a/0v3trxIBuyfwLgh0NfcDj/EGNb/DnI0ZlQZEcgIahlYkteGfEKbeo7e4OeAg/v7Pi3t/sTUzO2Z25nwicTilwVl5KYwuvnvs6lXS4N2yar0tSNTuSqVvcwusNo77ifD3/HtG33cij3UBAjM6HIEkiIapHQgpfPfpm2DdoCoCj/2/0cn2e8bjd91YCvt37NmA/G8NOen7zjhrUZxjsj36FbcrcgRhZ4MRLL/UPu59SGF3vHpees4JpPryEjOyOIkZlQYwkkhLVIaMG0c6bRI7mHd1zavum8t+txjuSHfb+SISm/IJ+nfnyKGz+/kQNHDgDOVXIXNrqQx09/PGTv7ahuIsLZTcZzdvJ477jVe1cz4ZMJbMvcFsTITCixBBLiGsc3ZsrZU+hcr5933NJDc/ntJ7/loMf2BqtTRnYG139+PS/89IK3B91mdZvxyohXGNZgWEQ2WZXl1EYXc0GziYj7U5F+MJ2rPr6KDfs3BDkyEwosgYSBerH1uKLlX+nXYLh33PI9y3l28238mv1zECOLHD/u+pFL/3cp327/1jtuUMtBTB85nRObnRjEyIKvf4OzGNfi/4iNcu4V2Xl4JxM+mcCqjFVlzGkinSWQMBEtMVzQdCLnNfmdtwPGzPx9TNl6J9/s/5+dF6mkAi1g2spp/PaT37IrexcAgnB9r+t5/sznSa5rz80A5zk2z575LHVjnIdR7Tuyj2s+vabER/Oa2sEu4w1BJV3mKSIMbjiSZnHH8d+Mhzlw5AD5ePhwz4usO7yU03IeqZb1VGbeis4fCvZk7+FvC/7Ggq1H++usG1WfMc1vo83hfkRHRQcxutBzUsuTeOmsl/j957/nYO5BMvMyuX7O9Tya+ihDU4YGOzwTBHYEEoY61OvN2+e9Tcs67b3j1hxezMWzL2b94WVBjCx8zNsyj4tnX1wkeaTU6cwf2jxO54R+pcxZu/Vq2otXRrxCk7pNADiSf4Sbv7yZTzZ+EuTITDDYEUiYSqmfwvUpD/HZnmksPOD0kr87ezevZN/FgAYjODt5PPHRCRVeblVvcvPOn5XLrAUbQ+7GuSP5R3hsyWPH9Hg8ofsE2uaM9PYJZUrWuVFnXh3xKr+b8zu2Zm7Fox7+b97/kZmXySWdLwl2eKYG2RFIGIuRWM5tei1XtrybhOgk7/jFBz/hyV8n8nPW4iBGF3p+2v0TY/83tkjyaFq3Kc8Pf57b+99uyaMC2jRow7QR02if5BwFK8q939zL1BVTgxuYqVF2BBIBuiT0Z2KbJ/gufxpzNzv9Zh3Mz+D17fezM20Rt/e/3du/VmUE4giiIsus6vpzPDk8s/QZXl31KgVa4B2fmpLKvUPupXF84wotL5SOqGqaf92njpjKuJlXs+3IOgAeWfIIB3MP8scT/1grL3uubewIJELUj2nME6c/wbgW/1fkaGTOpjmMen8UT/34VK184tySnUu45H+XMHXlVG/yqBtTl78N+htPDnuywsnDFNUovhFXt36AtvHdveNeXP4if//270WStYlMlkAiiIjQI/EUbj7uGU6sP8w7Prcglxd+eoGR749k+prp5OXnBTHKmrHr8C4mzZ/EhE8msOngJu/4QS0H8d9R/2Vs17G2h1xN4qPqMb7VZDrX6+8d986ad/jr138lryDyt7XazBJIBKoX3YCLm9/Cda3/Tffko3uGu7J3cf+i+xk5cyQz180kX/ODGGVg5OXn8cqKVxj5/sgiD0VKiE3gnsH38OLwF0mpnxLECCNTbFQdLm/5F3omnuod98GGD7gt7TbrdieC2TmQCHZc3a784Yw3mb1+Nk/88AR7svcAsDVzK3ctuItGMS0Y0nA0fRucQVxUfJCjrdq9JZ4CD/9b/z+eW/Yc27KK9tXUPeFkzmlyDbG7myKdJSLuYQlFMRLLmOa30bVVC+9jctM2p3Hj5zfy5LAnSYit+FWBJrRZAolwURLFBR0v4Kzjz+KdNe/w8oqX2X9kPwD7PDv4YM/zfLH3TQYlncNJWdcFN9hKyC/IZ86mOTyz9BnSD6YXmdYhqQNDEybQoV7v4mc21S5KornrpLtIjEvklRWvAPDdju/43We/4z9n/oekOkllLMGEk4AmEBEZATwBRAMvqeqDftPrAK8C/YAMYKyqpotIMjADGABMVdWJgYyzNqgXW4/f9vgtYzqP4fXVr/Pqqle9z3fILjhE2r7pzHtvBp3q9qN/0ll0rtefaAndO7Gnz1/FDwc/Z+H+2ezz7CwyrVGdRlzX6zrGdh3LR99sqdJ6iruvxZRORLit3200iGvAEz88ATh9t034ZALPD3+eZvWalbmM2nylWzgJWAIRkWjgGWA4sAVYLCKzVdW3B7ZrgH2q2lFExgH/AsYCOcBdQA/3z1STxLhEbuh9A1d1u4r7PpvCwv2zvD/ABVrAmsOLWXN4MYnRjeiReDKtd1xCgTYkKgSSiaqy7cg6Hlj0BrPSPyCnIKvI9MTYRMZ3H8+V3a605pIQcG3Pa0mMTeTv3/4dgHX713HVx1fx7BnP0r5h+zLmNuEgkEcgA4F1qroBQETeBkYDvglkNDDZfT0DeFpERFWzgK9FpGMA46vV6sXWY3DD8xmYdA6rs77h2wMfszF7uXd6Zv4+Fh34kEWffkj96MZ0TRhIx3p96FC3ZpuDVJUdR9JZnbWIFZkL2Jm76ZgydaMS+U33y2iamUq9zPp8/p3TKaLttQbfuK7jSIhN4K4Fd5Gv+WzN3MpvPvoNj57+KCe1PCnY4ZkqkkD14ioilwAjVPVad/hKYJBvc5SIrHDLbHGH17tl9rjDE4D+JTVhich1wHUATZs26/fiK6+RlBDHgazcY8oWN74q46p1mZ4ciIknKSEOoFrjLFxmcfzL5sYdIG3f1/yQs5hMLf7xpVFEcXyd42kddTxtYpy/Bu59JyXVqaKxH8jfz8a89aR7NrDR8wsZJTz3JDmqCSfXHcqJ8f1pmlg/sJ9lBetTkfUHe5sLxHr8rTi8glf2vEKuOmWjiGJc43EMrj/4mLJQ/HegLJmZmSQmJpZZLlzUVH1OP/30Jarav+ySxwrrk+iq+gLwAkDHrj2Vhp1ILabvJaDY8VUZV63L3P8LhbHDse2/gYi9uD6qxgxpR9yC/pyh+aRnr2Bl5gLW5X7H3py93jIFFLDxyEY2cnTexOiGNIlNoX/jrmRlNiAptgkJeZkk1uvBqSd1Z87i7UQTTbTEUEABffo3Y9aitRzOP8iB/D0cyNtDw3pZLNy1nJ256WTlHzgm3kKxUodz2p9N05yTOD6+G1ESVS3vR0U+oxrfPgKxzFLqUx3rOWZ5pDIsYxjXfvx7DuXvpYAC3tz7JvGt4rm5783ez7FQeZbpLy0tjdTU1DLLhYtwqE8gE8hWoI3PcIo7rrgyW0QkBkjCOZlugihaoulQrzcd6vXmvMH/5OkvP2bd4R/55fCPbD+y3vu0vkKZ+fvJzN9P+toVRRd0AJ749djlT15fzEr3lBxPHalL54T+nJAwiM4J/Rl7Svdif/RMaOuW3I0b2jzMa9vuZ0eu8/m9vOJlNh7YyD9O+QeJcZFz9FBbBDKBLAY6iUg7nEQxDrjcr8xsYDzwDXAJ8KXak5FCSkxUDO3q9qBd3R4MT76SrPwDND8+g/eWzmdzzhq2HVlHruZU6zpjpQ5t4rvSrm53rhhwJr+uS7KODsNMSUe9STFN+F3Kg0zf8TBrDjudfc7dPJfLPryMx09/nA4NO9R0qKYKApZAVNUjIhOBT3Eu431ZVVeKyH3A96o6G5gCvCYi64C9OEkGABFJBxoAcSJyAXCW3xVcJggSopM44/g+ZG5xrqIp0Hz2e3azJ3crzVsf5qu1KziUv4+sIzvIlBw8cpicvDwK8JCv+QhCYlwCUhBHfFQCSTFNaBCTzEntO7N3R32axx1Po9gW3iaNAS3asW29HW1EkjpRdbmi5Z18mjGVBftnAc6z1i/78DLuH3I/Z7c9O8gRmvIK6DkQVf0I+Mhv3N0+r3OAMSXM2zaQsZnqESXRNI5tQePYFozu3o6k/UXb2Et6Hsgx43q3Y1amJYraIkqiOafJNYzqeTKTv5lMtiebbE82f/rqTyzbvYwOeoEddYYB6wvLGBM057Y/l9fPfZ029Y+eLn1t1Ws8v/lP7M6t2k2gJvAsgRhjgqpzo868ff7bpKakesdtz93Is5tv4bsDn2CnRUNXWF/Ga4wJf4XNmWfUuZWEJp2Ys3cauQW55Gkus3c/y9qs7zn58D/L1QWKqVl2BGKMCQkiwuCGI3nr/LdoFnecd/zPh79j9MzRvLv2XXtIVYixBGKMCSmdG3Xm9ymPcFLSed5xmXmZ3PfNfVzz6TVsOLAhiNEZX5ZAjDEhJzaqDuc3vZ6rW/2d5NiW3vHf7/yei2ddzL+++xcHjpTcY4GpGXYOxBgTstrX68nENk+yud7HTFs5jXzNx6MeXl/9Oh9s+ICJfSZyUeeLiI0qesmvdQdfM+wIxBgT0mKj6nBrv1t5+/y36de8n3f8/iP7eeDbBxj5fuQ+ojnUWQIxxoSFro278srZr/DIaY/QKqGVd3zhI5rv3/IA93z8Enn5eUGMsnaxBGKMCRsiwlltz2LWBbO4pe8tRR6Rm1Gwh//ueoKz3zubtL3TOZx/MIiR1g6WQIwxYSc+Jp5rel7DJxd9whmNryA+6ugTKHdn7+bzva/zUPrVvLfzCdKzV9rNiAFiCcQYE7YS4xI5vfFYbj/+Rc6sdw71oxt7p+VpLj8e+oKXtv6FUTNH8dLyl/j1YDHPFzCVZldhGWPCQkldxAPUjU4ktd6ZnNLyWuJaruGp715ke+7R8ukH03nihyd44ocn6NyoM2cefybDjxtOh4YdEJEaq0OksQRijIkYMRLLyA4jyd/ena1HfuH7g3NYfmgeRzTbW2btvrWs3beWZ5c+S/N6zRncajCDWw5mUMtBJNdNDmL04ccSiDEm4ogIKfGdSYnvzLlNriW+1S98tukzFm5dSG7B0eet7zy8k5nrZjJz3UwA2jZoS0NtR5v4LrSJ70LzuLZES7TdR1ICSyDGmIgWF1WHkR1GMrLDSLLyspi3ZR5zNs3hm23fkJmXWaRs+sF0IJ2lh+YCzhFN09gUvinoRseGHenYsCMdGnagZUJLYqLs59PeAWNMrZEQm8A57c7hnHbn4Cnw8J8v57AueynrDy9lc84aCih6M6JH89ieu5EPNxQ9/xIt0bRIaEGrxFa0TmxN68TWtExoSXLdZJrUbUJyfDKN4htFfJKJ7NoZY0wJYqJiOK5uV46r25VhjceRV3CEjl1yePO7uWw+spbNOWs44Nld7Lz5ms/WzK1szdzKYhYXW0YQGsU3onF8YxrFN6J+bH3qxxX9S4xNpEFcAxLiEqgbU5f46Hjnf0w8hwsOk5efR0xUTMie6LcEYowxOF2m9GnWlU2Njt6cmJ2fyc7cX2nZJot1+9exbv86Nh7YyJ7sPWUuT1H25uxlb87eSsd0x+t3EC3RxMfEe5NLneg6xEXHERsVS0xUDLHRscRG+fxFxxIXFed97T+tcL4YceatCksgxphaoTIdLNaNTqRt3W6M7tKOWQs20j0RSIS8giP07RXH1kNb2Za5ja2ZW9l5eCcZ2Rls3LudTM9+DhdUz53w+ZpPVl4WWXlZ1bK86hTQBCIiI4AngGjgJVV90G96HeBVoB+QAYxV1XR32l+Aa4B84CZV/TSQsRpjTHnFRtWhfVI72ie1P2ZaYaLKVw9Z+Qfo3yOBj39YQ05BFtkFmRzJP0x2QRatmkdzKPcQh3IPkZmXSY4nh5z8HLI92eR4csg6kkUeeSHdSWTAEoiIRAPPAMOBLcBiEZmtqqt8il0D7FPVjiIyDvgXMFZEugHjgO5AK+BzEemsGsLvpDGm1intqCZaYmgQk8wJye1YWy/+mHlHD3KOaojH+fObPy0tjdNOOw1PgYfsfCepFCYZT4GH3Pxc8gryyCvIw1PgIS8/zzucV5BXZNi3bG5+Lp4CDx714CnwsIIVla5/II9ABgLrVHUDgIi8DYwGfBPIaGCy+3oG8LQ4Z4tGA2+r6hFgo4isc5f3TQDjNcaYkCIiznmL6FgaxDUIyDoe4IFKzxvIBNIa2OwzvAUYVFIZVfWIyAEg2R2/yG/e1v4rEJHrgOvcwcwLTmm/pnpCr3FNgLLPyoWXSKuT1Sf0RVqdaqo+x1d2xrA+ia6qLwAvBDuOqhKR71W1f7DjqE6RVierT+iLtDqFQ30C2RvvVqCNz3CKO67YMiISAyThnEwvz7zGGGOCKJAJZDHQSUTaiUgczknx2X5lZgPj3deXAF+q03H/bGCciNQRkXZAJ+C7AMZqjDGmggLWhOWe05gIfIpzGe/LqrpSRO4DvlfV2cAU4DX3JPlenCSDW246zgl3D/CHCL8CK+yb4YoRaXWy+oS+SKtTyNdH7EldxhhjKsOeSGiMMaZSLIEYY4ypFEsgNUxEXhaRXSKywmdcYxGZIyK/uP8bBTPGihCRNiIyV0RWichKEbnZHR/OdYoXke9EZJlbp3vd8e1E5FsRWSci77gXh4QNEYkWkR9F5AN3OGzrIyLpIrJcRJaKyPfuuHDe5hqKyAwR+VlEVovI4HCojyWQmjcVGOE3bhLwhap2Ar5wh8OFB7hdVbsBJwF/cLuiCec6HQGGqWpvoA8wQkROwulq5zFV7Qjsw+mKJ5zcDKz2GQ73+pyuqn187pUI523uCeATVe0K9Mb5nEK/PqpqfzX8B7QFVvgMrwFauq9bAmuCHWMV6jYLp/+ziKgTUA/4AacXhT1AjDt+MPBpsOOrQD1ScH6EhgEfABLm9UkHmviNC8ttDuf+t424FzWFU33sCCQ0NFfV7e7rHUDzYAZTWSLSFjgR+JYwr5Pb3LMU2AXMAdYD+1XV4xYptnudEPY48H9AgTucTHjXR4HPRGSJ26URhO821w7YDbziNjG+JCIJhEF9LIGEGHV2N8Lu2moRSQTeA25R1SIPQgjHOqlqvqr2wdlzHwh0DW5ElSci5wO7VHVJsGOpRqeoal/gHJxm06G+E8Nsm4sB+gL/UdUTgSz8mqtCtT6WQELDThFpCeD+3xXkeCpERGJxkscbqvpfd3RY16mQqu4H5uI08TR0u9yB8OpeZwgwSkTSgbdxmrGeIHzrg6pudf/vAt7HSfLhus1tAbao6rfu8AychBLy9bEEEhp8u3QZj3MeISy43e9PAVar6qM+k8K5Tk1FpKH7ui7OOZ3VOInkErdY2NRJVf+iqimq2hant4cvVfUKwrQ+IpIgIvULXwNnASsI021OVXcAm0WkizvqDJxeOEK+PnYneg0TkbeAVJyumncC9wAzgenAccAm4FJVrfyDlGuQiJwCzAeWc7R9/U6c8yDhWqdewDScLniigOmqep+ItMfZg28M/Aj8Rp1n1oQNEUkF/qSq54drfdy433cHY4A3VfXvIpJM+G5zfYCXgDhgA/Bb3G2PEK6PJRBjjDGVYk1YxhhjKsUSiDHGmEqxBGKMMaZSLIEYY4ypFEsgxhhjKsUSiIlIIpLv9tS60u1V93YRiXKn9ReRJwO8/gvcTiWrupwTRWRKNcV0vvtEUGOqhV3GayKSiGSqaqL7uhnwJrBAVe+pofVPBT5Q1RkVmCfGp2+qwnHvAg+o6rJqiElwOoYcoqqHq7o8Y+wIxEQ8t7uL64CJ4kj1eSbGQBH5xu3EbmHh3cAiMkFEZrrPYUgXkYkicptbbpGINHbLdRCRT9xO/eaLSFcRORkYBTzkHgV1KK6cO/9UEXlORL4F/u0bt3u3da/C5CEik8V5nkyaiGwQkZvc8W3d50hMFZG1IvKGiJwpIgvcZ0kMdN8HBdKA8wP+pptaIabsIsaEP1XdICLRQDO/ST8Dp6qqR0TOBP4BXOxO64HTu3A8sA64Q1VPFJHHgKtwerh9AbhBVX8RkUHAs6o6TERm43MEIiJf+JfD6ZMKnH6oTlbVfL/Y+uN00eGrK3A6UB9YIyL/ccd3BMYAVwOLgcuBU3AS2Z3ABW6574FTce5wNqZKLIGY2i4JmCYinXB6O431mTZXVQ8Bh0TkAPA/d/xyoJfbA/HJwLtO6xAAdfxXUI5y7xaTPMB5BsRuv3Efut2NHBGRXRzt4nujqi5317cS50FEKiLLcZ4/U2gX0KqYdRlTYZZATK3g9p+Uj/MDeoLPpPtxEsWF4jzPJM1nmm+/UAU+wwU4350onGdq9Clj9WWVyyphfDbO0Y8v35jyOfodLivWQvHuco2pMjsHYiKeiDQFngOe1mOvGkniaDfmEyqyXPe5JxtFZIy7HhGR3u7kQzjNTGWVK81qnKap6tSZY5vFjKkUSyAmUtUtvIwX+Bz4DLi3mHL/Bv4pIj9SuSPyK4BrRGQZsBIY7Y5/G/ize9K9QynlSqSqPwNJhV2XV5PTgQ+rcXmmFrPLeI0JYSJyK3BIVV+qhmU1x+n6/IyqR2aMHYEYE+r+Q9HzG1VxHHB7NS3LGDsCMcYYUzl2BGKMMaZSLIEYY4ypFEsgxhhjKsUSiDHGmEqxBGKMMaZS/h87GXhBO5ewxgAAAABJRU5ErkJggg==\n", 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" ] @@ -466,7 +466,7 @@ "outputs": [ { "data": { - "image/png": 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EbkVdUc+5g7qbAf/DGBI9C/zd1bptrqHZNuF8ec14y3s4ZzD+V79StPdwbNs3xEG9ec59Add3APn/by6dQ2cfMQvRaDSaUkdERmM87PVUSm30tDyaolOUc6gNjkajKRVEpDPGnMc2jB5hB4yXNeMx3vXQNyMv50bPobfP4Wg0mvJDCsZ7JlMxho3OYcx//VUbmzLDDZ1D3cPRaDQaTang7cuiNRqNRlNOKDdDavXq1VMBAQGeFqNYXLt2jWrVypcXhPKmk9bH+ylvOpWWPjExMReUUvXdXhHlyOAEBASwc6dH35crNtHR0fTu3dvTYpQo5U0nrY/3U950Ki19zH3pSgU9pKbRaDSaUkEbHI1Go9GUCtrgaDQajaZUKDdzOGUZESEhIYG0tGI5HvVKatasycGDBz0tRomh9fF+yptOJa1P5cqVadasGRUrViyxMouKNjheQLVq1ahRowYBAQGYPjPKPMnJydSoUcPTYpQYWh/vp7zpVJL6KKVISkri5MmTBAYGlkiZxUEPqXkBvr6+1K1bt9wYG41G412ICHXr1vX4KIo2OF6CNjYajcadeMM9RhscjUaj0ZQK2uBoNBqNplQoNwbncko6y39J8LQYGo1Go3FCuTE4mhsjMTGRsLC87tpnz57N3LlzC8z39ttvExwczPjxBbuVr169usN4V+pwNb2zOoqKiPDUU09Zw3PnzuXvf/97iZRdFGz1SU1NpVevXmRnZ5dY+b/99ht9+vQhJCSE0NBQ3nrrLadpV61aRVBQEK1ateLVV18tcn5boqOjmTBhwg3L//DDD9OgQYN8160jsrOzue222xg6dKg1zpFOrvCnP/2JFi1aFEvmotR9+fJlRo8eTdu2bQkODmbLli3WY2+99RZhYWGEhoby5ptvApCRkUHPnj3Jysq6IdnciTY4mhvivffeY82aNSxcuNDTopQYlSpV4ttvv+XCBYfu4wtFKUVOTuHu3YvCggULGDlyJL6+viVWZoUKFfj3v//NgQMH2Lp1K++++y4HDhzIly47O5upU6fyww8/cODAARYtWsSBAwdczm9PXFwct9122w3LP3HiRFatWuVS2rfeeovg4GBr2JlOhZGYmMj69evJyMggOTm5WHK7WvczzzzDwIEDOXToEHFxcVb59+3bx4cffsj27duJi4vj+++/58iRI/j5+XHHHXewZMmSYslVGrjV4IjIQBGJF5EjIjLTwfFKIrLEPL5NRALM+PEiEmvzyRGRCHfK6g0cbBvs1k9xSUxMJDg4mEcffZTQ0FD69+9Pamoqjz32GMeOHWPQoEG88cYbALz++uuEhYXRuXNn65OXPa+88gpt2rShe/fuxMfHW+O/+OILoqKiiIiI4A9/+IP1ad5ZemdYZAgLC8sjw0svvURQUBDdu3dn3LhxTntKFSpUYPLkyVadXCk/MTGRoKAgHnjgAcLCwti4cSNt27Zl4sSJtGnThvHjx7N27Vq6detG69at2b59u7W8u+++mw4dOhAaGsoHH3zgsM6FCxcyfPhwa3jp0qXcfvvttG/fnu7du3P+/PlC28Wexo0bExkZCUCNGjUIDg7m1KlT+dJt376dVq1a0bJlS/z8/Bg7dizLly93Ob89sbGxnDp1is6dO9OyZUuio6OLLDtAz549qVOnTqHpTp48yYoVK5g0aVKhOhXGrFmzeP755wkJCWH//v3FktuVuq9cucLmzZt55JFHAPDz86NWrVoAHDx4kM6dO1O1alUqVKhAr169+PbbbwHjWvLmhz+3GRwR8QXeBQYBIcA4EQmxS/YIcEkp1Qp4A/gngFJqoVIqQikVAUwAEpRSse6SVVM4hw8fZurUqezfv59atWrxzTffMH/+fJo0acL69euZMWMGMTExfPzxx2zbto2ffvqJDz/8kN27d+cpJyYmhsWLFxMbG8vKlSvZsWMHYPyJlixZwi+//EJsbCy+vr4sXLjQaXpn2MqwdetWqww7duzgm2++IS4ujh9++KHQncWnTp3KwoULuXLlikvlW9poypQp7N+/nxYtWnDkyBGeeuopDh06xKFDh/jyyy/ZtGlTviG6BQsWEBMTw86dO3n77bdJSkrKU2dGRgbHjh3D1v1Gnz592Lp1K3FxcfTr14+vvvoqT54ePXoQERGR77N27VqH+iYmJrJ79246d+6c79ipU6do3ry5NdysWbN8hqWg/PbExcVRo0YNtm3bxvz583nhhRduSPbCeOKJJ/jXv/6Fj0/u7c4VnezZv38/+/btY8yYMQQHB7Nv3758aVyR3ZW6ExISqFu3Lg899BC33XYbkyZN4tq1awDWB5qkpCSuX7/OypUr+e2336zHCvuPeBJ37jQQBRxRSh0DEJHFwHDAtu84HJht/l4KvCMiYueqdBywuNDakk5T6as3yAqZQ4XatUtA/JsLZ2v0LfGBgYFERBidzA4dOpCYmJgv7aZNmxgxYgTVqlUjJyeHkSNHsnHjxjzDJxs3bmTEiBFUrVoVgGHDhgHw008/ERMTQ6dOnQBjzqJBgwZcvHjRYXpn2MoAWGXIyclh+PDhVK5cmcqVK3PXXXcVWI6/vz8PPPAAb7/9NlWqVCm0/GHDhtGiRQtuv/12a9rAwEDatWsHQGhoKHfccQciQrt27fK039tvv81///tfwJgXOXz4MHXr1rUev3DhgvXp1sInn3zCkiVLSE9P5+zZs/nmmDZu3FigfrakpKQwatQo3nzzTfz9/V3OV5z8mZmZXLhwgWeffRaAiIiIfEOXRZG9ML7//nsaNGhAhw4dit2TsvD888/z4osvIiIEBwc77OGUlOxZWVnExcXx3nvv0blzZ6ZPn86rr77KSy+9RHBwMM888wz9+/enWrVqREREWIdafX198fPz89pdF9xpcJoCv9mETwL2jz/WNEqpLBG5AtQFbK/AMRiGKR8iMhmYDFA5oDIvhK4jZcoe6j3yPFQoO7v2+Pv7F3s8uCgUVIefnx8XL17Mk+bs2bM0atSIlJQUKlasaD2WlZXFtWvXSE5ORilFSkoKlSpVIi0tjfT0dJKTk8nOziY9PZ20tDRrvuTk5DxpwHh6T09PRynFuHHjmD17dh653n33XYfpneliX75FhpycHKflfPDBB3z66aeAMVRlkfWRRx6hZ8+ejB8/HqWUQ/kt5aekpFClShVrvH2bZWdnk5OTQ3JyMtevX7fOAWzcuJEff/yR1atXU7VqVQYPHpznPCQnJ5OVlUVqaqo17ssvv2Tz5s0sX76c6tWrM3DgQAICAvK0yYABA0hJScnXPi+//DJ9+vQhOzub5ORkMjMzueeeexg9ejT9+vVz2K61atUiISHBeuzo0aPUq1fP5fy27N+/n8DAQNLT00lPT2fTpk2EhIQUSXZbUlJSrO1q0cmW9evXs3z5clasWGG9FseMGcOjjz7qVCdH7Nixg1WrVrFr1y7AuM5CQ0PzpXdF9oLa00KtWrVo0qSJtW0GDx7M66+/bk1z7733cu+99wIwZ84cmjRpYj2WlpZGZmamQ13S0tJu2PDeEEopt3yA0cB/bMITgHfs0uwDmtmEjwL1bMKdgb2u1Fc5oLIK+yRMDZgbqpIWL1ZliV27dnlaBKWUUh06dFA//fSTUkqppKQk1bp1a3XkyBGVkJCgQkNDrelee+01NWvWLKWUUi1atFDnz59XSikVExOj2rVrp65du6bOnDmjQkNDrbpVq1YtT5rr16+rq1evqlatWqnXXntN7d+/X7Vq1Ur9/vvv1voTExOdpndEtWrV8siQkpJilWH79u3qtttuU6mpqSo5OVm1bt26wHIs/PnPf1bNmzdXM2fOzKejbfn2bWQffvDBB9XXX3+d79iyZcvU0KFDlVJKHTx4UFWqVEmtX78+nxzNmjVTqampSimlnn76afXmm28qpZRaunSp8vX1VSkpKQ51ccbVq1dVTk6OmjBhgpo+fXqBaTMzM1VgYKA6duyYSk9PV+Hh4Wrfvn0F5u/bt686efJkvvjPPvtMBQQEqLS0NJWcnKxuv/12tWXLliLJbottW169erXAtOvXr1dDhgwpUCdn8vft21etWbPGGj579qxq3LhxsWQurG4LXbp0UYcOHVJKKTVr1iz19NNPW49Z/ifHjx9XQUFB6tKlS0oppS5cuKCCgoKc1n3gwIF8ccBO5SY7YP9x56KBU0Bzm3AzM85hGhGpANQEbAewxwKLilRpPWHD+s+KLKwGPvvsM1566SUiIiLo27cvs2bN4tZbb3U5f2RkJBMnTiQqKoq+ffsyadKkfKuRIiMjGTNmDO3bt2fQoEHWIbSQkBBefvll+vfvT3h4OP369ePMmTNO07siQ+fOna0ydOrUiWHDhhEeHs6gQYNo164dNWvWLFSnp556Ks+Qj7Pyi8vAgQPJysoiODiYmTNn5hmSs6V///5s2rQJMFZnvffee0RFRbF7925atmxZLFfEv/zyC59//jnr1q2zzjWsXLkSgMGDB3P69GnAWETxzjvvMGDAAIKDg7n33nsJDQ11mj8nJ4cjR444nNCPi4tj5MiRdO3alaioKKZNm+ZU58IYN24cXbp0IT4+nmbNmvHZZ7n/e1v5HeFMJyCf/GvXriUjI4M777zTmr9hw4akpKRw8eLFIstdUN22cr/22muMHz+e8PBwYmNjrcOQAKNGjSIkJIS77rqLd9991zrkun79eoYMGVJkmUoNd1kyjOG6Y0Ag4AfEAaF2aaYC883fY4GvbI75YBiklq7UZ+nhhH0Spp6ZEqIyk5KcWnlvw1t6OCVJYU+bniA5OVkppdS1a9dUhw4dVExMjMt5Pa1PTEyMuv/++0usPHfqs3fvXjVjxgy3le+MktLJU/LbUxx9RowYoeLj450eL7c9HKVUFvA48CNw0DQm+0XkRRGxzPx+BNQVkSPAk4Dt0umewG/KXHRQFOIChWubtxSeUHNTMXnyZCIiIoiMjGTUqFHWJb1lgcjISOvci7cTFhbG66+/7mkxik1ZlT8jI4O7776bNm3aeFoUp4hh4Mo+NZtXUbfOvpXMCsaqqi+O3En7lxy/R+Ft7N69u0RehPMmvHWVTHHR+ng/5U0nd+hz8ODBPC/AAohIjFKqY4lW5IRys9OAXxa0/S3XeG49rXs4Go1G402UG4Pjmw1hx3MNzqEayWSePetBiTQajUZjS7kxOBVyhFu4xRo+0lhI3bPHgxJpNBqNxpZyY3B88aGxfxhizkmdaACX9+zysFQajUajsVCODE4FpEUYTc1XJnJ8hH2J2wvOpNFoNJpSo9wYHB/xJa1lG1qdyZ3H2Z96DFXC28RrNBqNpniUK4OTWa8RrS5XtsYl1Mkk88QJD0ql0Wg0GgvlxuCIjy+I0KZaoDXueAMh7dAhD0ql0Wg0GgvlyOAYu0O3bdLeGneqLlw9VDwnSTcb5cHFtCPX0Pa7T7sbd7uFTktLIyoqivbt2xMaGsqsWbPyHC/ILbGFgIAAbr/9diIiIujYMfd9P0dui0uL+Pj4PP5j/P39HcpQkKvrTp06FcnVNZSeu+jCzpu9C+yMjAzrPnvliXJjcJTpXKl2UDsaXjLmcbJ9hSMndheUTXODeJOL6RtxDa1U2XALXalSJdatW0dcXByxsbGsWrWKrVu3Wo9Pnz7doVtie1asWEFsbKzVEZ0zt8WlRVBQELGxscTGxhITE0PVqlUZMWJEnjSFubresWNHkVxdl6a76MLOm70LbD8/P3r16uXV7qKLQzkyOMafunJwWwJ+t3kB9OpRT4lUZAJmrnDrp7iUFRfTBbmGvlG30BERETfsFrp3794cMod4k5KS8vUoXUFErL2ozMxMMjMzrU7yrly5woYNGxy6JS6MgtwWF0RcXBw9e/YkJCQEHx8fRIS//e1vRdbLlp9++olbb701X8+jpF1dl5a7aCj4vDlygQ0wdOhQr3iQK0nKjcHB7OFUatmSFhdy1UqofJWsS5c8JVW5oay4mHbkGrok3EK/8sorN+wW+siRI9aNFffs2WP1BmrBVdfK2dnZRERE0KBBA/r162d165yQkED9+vUduiW2RUSsBtNiLAtyW+yMtLQ0xowZw9y5czlw4ADPPfccTz/9NHPmzCmyTrYsXryYcePG5YsvSVfXpeku2vEpIBYAACAASURBVIKz8+bIBTYYLju82V10cSg7bjELwzxZ4udHa9/GwBkAEhsI6fHxVCimz42bhfLiYtqRa+iScAsdEhJyQ26hjx8/TtOmTa03lT179hAeHp5HdlfdE/v6+hIbG8vly5cZMWIE+/btIywsjKysLHbt2sW8efPyuSW2ZdOmTfj7+5Oamkq/fv1o27YtPXv2dOq22Blr164lMjKSqKgoAMLDw1m1alWea6moLpczMjL47rvv+Mc//lGkfFA0V9el6S7agqPzlpiY6NQFtre7iy4O5cbgKJung7b1QrAYnOMNIPXgQappg1MgdevW5ZJdT/DixYsEBhqr/ipVqmSN9/X1JTU1tUTrV0rx4IMP5rvRFGfy+oknniAyMpKHHnqo0LT2jsts9fTx8bGGfXx8rBO40dHRrF27li1btlC1alV69+5NWlpannKqVKmSJy4uLi6PgYmJiWHMmDF58vTo0cPhXMLcuXPzOP+yUKtWLfr06cOqVasICwujWbNmNGvWzPrkPHr0aIeT2E2bNiU5OZkGDRowYsQItm/fTs+ePXnkkUesw3HPPvsszZo1c9Biuezbty9PL23Xrl35XD4UVacffviByMhIGjZs6FBu217XyZMnadq0KWAMU91///2MHz+ekSNHFij3tm3bWLVqFbt372bq1KmkpaXl6226KntBMjnD9rwlJSXx3XffsXLlStLS0rh69Sr3338/X3zxBWC4MK9cuXKB5ZUpSsvxjrs/rVoFq2WbjimllDr/8QLV+f9CrQ7Zdj33J6cOibwBb3HAVh5cTFuwuIaeNWtWibiF3rt37w25hZ4zZ47Vgdqvv/6q/P391fHjx107MTacO3fO6k74+vXrqnv37up///uf9Xj37t2duiVWSqmUlBR19epVdfXqVZWSkqK6dOmifvjhB6WUc7fFSjl2Gf3BBx+osWPHKqWUio+PV23atFEXLlwosk62jBkzRi1YsMDhscJcXf/xj390mM8b3EUXdt6UyusCWynjeizIXXRxKLcO2EobZdONr9I2hIBzNgsHLhz0hEhljvLgYtqCrWtob3ALHRcXR05ODu3bt+fFF18kJCSETz/9tMh1nzlzhj59+hAeHk6nTp3o16+fdSktwLx58xy6Jba4Lv7999/p3r271cXzkCFDGDhwIODcbbEzl9Hjxo0jJSWFsLAwJk+ezKJFi/IMKxaVa9eusWbNmnw9FIvshbm63rBhQz5X2d7iLrqw8+aIjRs3ere76OJQWpbN3Z9bg8KsPZysS5fUX6aEWHs4cx4NU9np6a48AHgEb+nhlCSedslc0hRHH1u30K1atfKqNimKLN7icrkwHOlUVmR3xF133VWgu+jioHs4bsC3Vi1aZtS0ho/XzSHjaNlZHq0pH1jcQl+5cgURKbMTv2XV5TKUXdkzMjIYMmSIV7uLLg7l0uAABNXIHQo63lBIK+D9DY3GXTz88MPUrFmTX3/91dOiaMoQfn5+3HfffZ4Wo8QptwanVfMIfHKMeZzfawuX4vOvs9doNBpN6eFWgyMiA0UkXkSOiMhMB8cricgS8/g2EQmwORYuIltEZL+I7BWRIq0N9G8bQlObd/HiT8cVXxGNRqPR3DBuMzgi4gu8CwwCQoBxIhJil+wR4JJSqhXwBvBPM28F4AvgMaVUKNAbyCxK/ZWC2tLCZqXa4ZQEjPkxjUaj0XgCd774GQUcUUodAxCRxcBwwHZnu+HAbPP3UuAdMV5T7g/sUUrFASil8u4b4gJ+LW4h4GIFNmFsyJhQPZUVK3eRXSt3aefwboHOsms0Go2mhHGnwWkK2G7GdBKw3+DImkYplSUiV4C6QBtAiciPQH1gsVLqX/YViMhkYDJA/foN4PJhoqOP5xaeVRswbNXxBkKlQ5u43jZ3R1bbtJ7E39+/2LvVeivZ2dnlSietj/dT3nRyhz5paWn5ttApTbx1a5sKQHegE3Ad+ElEYpRSP9kmUkp9AHwA0KptO0Wt1vS26bXsi+4ErAKMLW4qJqZBrdbW4729pIeze/fuMrtk1hnlaf8n0PqUBcqbTu7Qp3Llyjf00vON4s5FA6eA5jbhZmacwzTmvE1NjC7JSWCDUuqCUuo6sBKIpIg0vrU9/teMeZt0PyE5qXAfGTczy5YtQ0SsW+h7G7a7NbvKJ598wuOPP+4GaTQaTVFxp8HZAbQWkUAR8QPGAt/ZpfkOeND8PRpYZ775+iPQTkSqmoaoF3nnflyiSnDehQNn0xKLrMTNxKJFi+jevTuLFi0qkfJK2lthcQyORqPxHtxmcJRSWcDjGMbjIPCVUmq/iLwoIpY95j8C6orIEeBJYKaZ9xLwOobRigV2KaWK7EGsUps2tDiXGz7ll4RkZhRfqXJMSkoKmzZt4qOPPmLx4sWAsQ/VlClTaNu2Lf369WPw4MEsXboUgJUrV9K2bVs6dOjAtGnTrPtCzZ49mwkTJtCvXz8mTJjA+fPnGTVqFJ06daJTp0788ssvAJw/f55+/foRGhrKpEmTaNGihXXvM0fOzWbOnElqaioRERFWd9bOHLZ9/PHHtGnThqioKGt9Go3G87h1DkcptRJjOMw27m82v9OAe5zk/QJjaXSx8fX3N7e4MSbejtdX3H76BOktWt1IsW6l3af5t0kvKfY+uNfpseXLlzNw4EDatGlD3bp1iYmJISEhgcTERA4cOMC5c+cIDg7m4YcfJi0tjT/84Q9s2LCBwMDAfM6yDhw4wA8//ECDBg247777mDFjBt27d+fEiRMMGDCAgwcPMmfOHPr27ctf//pXVq1axUcffWTNv2DBAurUqUNqaiqdOnVi1KhRvPrqq7zzzjvExsYCeR22VaxYkSlTprBw4UL69evHrFmziImJoWbNmvTp08ejY9YajSYXb100UGK0qdUa2AXAifpCpd+OebXB8RSLFi1i+vTpAIwdO5ZFixaRlZXFPffcg4+PD40aNaJPnz4AHDp0iJYtW1p95YwbNy6Pm+Vhw4ZZnZ+tXbs2j4/3q1evWntTFgdmAwcOpHbt2tY0hTk3A+cO27Zt20bv3r2pX78+AGPGjNHbymg0XkK5NDjLf0mw/q7pE4hvdgzZvsK52kLOrsMYr/loLFy8eJF169axd+9eRITs7GxEhBEjRhSrPFunZjk5OWzdutVlJ1KuODcD5w7bli1bViyZNRqN+ymXBseW7Ka30uwCHDcdCJ5LiaeqZ0UqkIKGvdzF0qVLmTBhAu+//741rlevXtSpU4dvvvmGBx98kPPnzxMdHc19991HUFAQx44dIzExkYCAAJYsWeK07P79+zNv3jz+/Oc/AxAbG0tERATdunXjq6++4plnnmH16tVWb6NXrlyhdu3aVK1alUOHDrF161ZrWRUrViQzM5OKFStyxx13MHz4cGbMmGF1RZ2cnGx1rZyUlIS/vz9ff/017du3d1PLaTSaolBuN++0kN48kFvO565UO5NzCvQWN3lYtGhRvt7MqFGjOHv2LM2aNSMkJIT777+fyMhIatasSZUqVXjvvfcYOHAgHTp0oEaNGtSsWdNh2W+//TY7d+4kPDyckJAQ5s+fD8CsWbNYvXo1YWFhfP311zRq1IgaNWoU6Nxs8uTJhIeHM378eKcO2xo3bszs2bPp0qUL3bp1Izg42KFcGo2m9JHysr9Yq7bt1L8/+o7h3QLzDKmRk8PBj0eysJexxc2du3O4845PyKpTz2u2ttm9e7fXTmynpKRQvXp1kpKSrKu+GjVqZI1XSjF16lRat27NjBkzrPkKe2ktPT0dX19fKlSowJYtW/jjH/9oXRDgjeiXCr2f8qaTO/Q5ePBgvocw86X6jiVakRPK/ZAaPj40UY0Aw9Xr8QZCpZMJZNWp51m5yghDhw7l8uXLZGRk8MILL9CoUSMAPvzwQz799FMyMjK47bbb+MMf/lCkck+cOMG9995LTk4Ofn5+fPjhh+4QX6PReBHl3+AADau1xmJwTtSHCglHILyTZ4UqIzjbd2nGjBl5ejRFpXXr1uzevbvY+TUaTdmj3M/hAFRqGETNlNwtbq4keefWLRqNRlOeuSkMTnrzQAJstrj5PT2hgNQajUajcQc3hcHJaBZot8XNJSQj3XMCaTQazU3ITWFwcqpUpWVW7pvsxxso/E55hy8cjUajuVm4KRYNALSt1QZjL1BIaChUPn4EGOBRmZyRZ1l3CeDK8m8RYfz48XzxhbF9XVZWFo0bN6Zz5858//33JSpPSVK9enVSUlLyxF2+fJkvv/ySKVOmlEgds2fPpmLFijz33HNFluv06dNMmzbNuumpO4iOjsbPz4+uXbuWWJkTJ05k6NChjB49usTK7Nq1K5s3byYxMZHNmzdz3333lVjZmrLBTdHDAWh1a0cqZRjzOBf9hbTT+z0skXdRrVo19u3bR2pqKgBr1qyhadOmHpHlRt0aXL58mffee88tZReVJk2auNXYgGFwNm/eXKQ8pd0OgFXGxMREvvzyy1KvX+N5bhqDUy00nIDfc8NnrumVavYMHjyYFSsMLxCLFi3Kswv0tWvXePjhh4mKiuK2225j+fLlgHHz6NGjB5GRkURGRlpvKmfPnqVnz55EREQQFhbGxo0bAePJ38LSpUuZOHEiYDxRP/bYY3Tu3Jm//OUvHD161LqTQY8ePaxO4RISEujSpQvt2rXj+eefd6jHzJkzOXr0KBEREfz5z38mOjqaHj16MGzYMEJCQgDHLhAAVq1aRWRkJO3bt+eOO+7IV/aHH37IoEGDrIbZgjO5EhMTCQsLK7CtoqOj6dWrF8OHD6dly5bMnDmThQsXEhUVRbt27Th69CiAQ1cPiYmJzJ8/nzfeeIOIiAg2btzo1CWExXVEt27dePTRR/PIr5Ti8ccfJygoiDvvvJNz53InPWNiYujVqxcdOnRgwIABnDlzBoDevXvzzDPPEBUVRZs2bazneP/+/Va3EeHh4Rw+fDjPuZ85cyYbN24kIiKCN954g549e+Z56bd79+7ExcU5PLeass1NM6RWOSyUlksU8c0FgBMVz5OTno5PpUoelsx7GDt2LC+++CJDhw5lz549PPzww9abyCuvvELfvn1ZsGABly9fJioqijvvvJMGDRqwZs0aKleuzOHDhxk3bhw7d+7k66+/ZsCAATz33HNkZ2dz/fr1Qus/efIkmzdvxtfXlzvuuIP58+fTunVrtm3bxpQpU1i3bh3Tp0/nj3/8Iw888ADvvvuuw3JeffVV9u3bZ72JRUdHs2vXLvbt22fd4dqRC4ScnBweffRRq9uFixcv5in3nXfeYc2aNSxbtoxKdteNK3I5ayuAuLg4Dh48SJ06dWjZsiWTJk1i+/btvPXWW8ybN48333yT6dOnO3T18Nhjj1G9enWefvppAKcuIcBwHbFp06Z8PZz//ve/xMfHc+DAAX7//XdCQkJ4+OGHyczM5E9/+hPLly+nfv36LFmyhOeee44FCxYARk9p+/btrFy5kjlz5rB27Vrmz5/P9OnTGT9+PBkZGVY/RbbnZ+7cudah2jp16vDJJ5/w5ptv8uuvv5KWlqb3vyun3DQGp0Lt2rRIqQFcAyChYQ7pv/5KlXbu8z9T1ggPDycxMZFFixYxePDgPMdWr17Nd999x9y5cwFIS0vjxIkTNGnShMcff5zY2Fh8fX2trgAiIyN5/PHHyczM5O677yYiIqLQ+u+55x58fX1JSUlh8+bN3HNPrquk9HRjVeEvv/zCN998A8CECRN45plnXNItKirKamzAsQuE8+fP07NnT2u6OnXqWNMvWrSIFi1asGzZMipWrJivfFfkyszMdNhWAJ06daJx48YA3HrrrfTvb+xo3q5dO9avXw84d/VgT0HpLK4jkpOT8+TZsGED48aNw9fXlyZNmtC3b18A4uPj2bdvH/369QMgOzvbKifAyJEjAejQoQOJiYkAdOnShVdeeYWTJ08ycuRIWrdunU9GW+655x5eeuklXnvtNRYsWGDt9WrKHzeNwQFoWrElYOzGfKyRkLZ/vzY4dgwbNoynn36a6OhokpKSrPFKKb755huCgoLypJ89ezYNGzYkLi6OnJwcqxuCbt26sWHDBlasWMHEiRN58skneeCBBxARa157twMWtwY5OTnUqlXL6d5qtmW4iq3LBFddINgSEhLC/v37OXnyZB7DVRS53njjDYdtBeTpMfn4+FjDPj4+1t6Iq64eCkpn2w6uoJQiNDSULVu2ODxukdPX19cq53333Ufnzp1ZsWIFgwcP5v3337caMEdUrVqVfv36sXz5cr766itiYmKKJKOm7HDTzOEA1KofZl04cKmGcPLgDg9L5H08/PDDzJo1i3Z2hnjAgAHMmzcPy2avlm1prly5QuPGjfHx8eHzzz+3Dp+cOHGChg0b8uijjzJp0iR27TKc4DVs2JCDBw+Sk5Nj7WHY4+/vT2BgIF9//TVg3PQsY/rdunWzusBeuHChw/w1atTI9wRvizMXCLfffjsbNmwgIcFYJWg7pNa+fXvef/99hg0bxunTp/OV6YpcztrKVSyuHixYDLK9vs7SFUTPnj1ZsmQJ2dnZnDlzxtqrCgoK4vz581aDk5mZyf79BS+4OXbsGC1btmTatGkMHz6cPXv25Dnu6PxMmjSJadOm0alTpzzO+DTli5uqh5PZIojA3+FQcyO8/9xevLF/48ldrJs1a8a0adPyxb/wwgs88cQThIeHk5OTQ2BgIN9//z1Tpkxh1KhRfPbZZwwcOND6BL1x40bGjBlDxYoVqV69Op999hlgjN8PHTqU+vXr07FjR4dDQmDctP/4xz/y8ssvk5mZydixY2nfvj1vvfUW9913H//85z8ZPny4w7x169alW7duhIWFMWjQIIYMGZLn+MCBA5k/fz7BwcEEBQVZXSDUr1+fDz74gJEjR5KTk2Odc7HQvXt35s6dy5AhQ1izZg316uVuAOuKXM7aylXefvttpk6dSnh4OFlZWfTs2ZP58+dz1113MXr0aJYvX868efOcpiuIESNGsG7dOkJCQrjlllvo0qULAH5+fixdupRp06Zx5coVsrKyeOKJJwgNDXVa1ldffcXnn39OxYoVadSoEc8++2ye4+Hh4fj6+tK+fXsmTpzIjBkz6NChA/7+/jz00ENFahNN2cKt7glEZCDwFuAL/Ecp9ard8UrAZ0AHIAkYo5RKFJEA4CAQbybdqpR6rKC6nLonMBneLZD//RjHpu/uY2WU0bEb/Qu8MG+nxxcOeLN7guKit4r3brxNn9OnT9O7d28OHTqEj0/xBl68TacbpTy6J3DbkJqI+ALvAoOAEGCciITYJXsEuKSUagW8AfzT5thRpVSE+SnQ2LhKTnV/Wlzzt4aPNcwhPT6+gBwajcbdfPbZZ3Tu3JlXXnml2MZGUzZw59mNAo4opY4ppTKAxYD9WMNw4FPz91LgDinOjHARaFrxVuvvY42E63tL36WzRqPJ5YEHHuC3337LsypRUz5xp8FpCvxmEz5pxjlMo5TKAq4Adc1jgSKyW0R+FpEeJSVUzQZhVE43hhEvVxdO/eodK2LKi+dVjUbjnXjDPcZbFw2cAW5RSiWJSAdgmYiEKqWu2iYSkcnAZID69RvA5cNERx+Haxn5CrTEZ9arRuDvcPAWI37n8e1cdOJkrLSoXLkyJ0+epGbNmsVa8uuNZGdnF7hSrKyh9fF+yptOJamPUoorV65w7do1p04VSwN3GpxTQHObcDMzzlGakyJSAagJJCnDFKcDKKViROQo0AbYaZtZKfUB8AEYiwao1ZreThYNWOLTQhtx67L5HLzFuLEnVL7Mgx074Vu9aCuGSpKff/6ZrKwsTp2yb56yS1paWqHvi5QltD7eT3nTqaT1qVy5Mu3bt3f44nJp4U6DswNoLSKBGIZlLGC/Pex3wIPAFmA0sE4ppUSkPnBRKZUtIi2B1sCxkhAqp1oNAq/XAS4D8GsTSNu7h2rmMlBPoJRy+jJhWSU6OrpcrbzT+ng/5U2n8qYPuHEOx5yTeRz4EWOJ81dKqf0i8qKIDDOTfQTUFZEjwJPATDO+J7BHRGIxFhM8ppTKu7HVDXBLldzFckcbQ3Ksd8zjaDQaTXnGrXM4SqmVwEq7uL/Z/E4D8i1NUUp9A3zjLrkqN4+g3pVfuFBTSPcT9h/YTCMed1d1Go1Go+Em29rGQmqrYNqcyl2xsfdqPConx4MSaTQaTfnnpjQ4GY2b0+pc7sRZfN00MsydbjUajUbjHm5Kg4OPDy18WlqD8U2F1N2Fb3Co0Wg0muJzcxocoH699lTMNIbVztcSTu11vP26RqPRaEqGm9bgZLUM49azueHYM3qlmkaj0biTm9bgpLUMyrNwYL/v72SXo7eUNRqNxtu4aQ1OTtVqhOY0soZ/bSKkxu0pIIdGo9FoboSb1uAARDTuYP19rDFc2bXdg9JoNBpN+eamNjhNIrrS6KIxrJZZQYj9dYOHJdJoNJryy01tcKp16kTIidx5nN0ZR8lJT/egRBqNRlN+uakNTsWmTWmXXMsaPtAkm9TYOA9KpNFoNOWXm9rgAHRs1Mn6O76ZcGXHVg9Ko9FoNOWXm97gBNzWk4aXjGG1jIpCnJ7H0Wg0GrfgksERkW9FZIiIlDsDVbVzVN55nNRfycnI7zFUo9FoNDeGqwbkPQznaYdF5FURCXKjTKVKxaZNCbta0xre3zSbtD36fRyNRqMpaVwyOEqptUqp8UAkkAisFZHNIvKQiHjOX2kJICJ0atTRGo5vKlzZttmDEmk0Gk35xOUhMhGpC0wEJgG7gbcwDNAat0hWigTe1osG5jxOup+w6+A6D0uk0Wg05Q9X53D+C2wEqgJ3KaWGKaWWKKX+BFR3p4ClQbXbbyc8MXceZ3vmUbJTrnlQIo1Goyl/uNrD+VApFaKU+odS6gyAiFQCUEp1LDir91OxaVMir9Wzhve2UFzfrre50Wg0mpLEVYPzsoO4cuVApnNATyTH6OUcaQxntq73sEQajUZTvijQ4IhIIxHpAFQRkdtEJNL89MYYXisQERkoIvEickREZjo4XklElpjHt4lIgN3xW0QkRUSeLpJWxaBxl75W/zjKR9iWoN/H0Wg0mpKkQiHHB2AsFGgGvG4Tnww8W1BGEfEF3gX6ASeBHSLynVLqgE2yR4BLSqlWIjIW+Ccwxub468APLuhxw1SNiiJ8iXCkiRHeVe08Y0+fpmKTJqVRvUaj0ZR7CjQ4SqlPgU9FZJRS6psilh0FHFFKHQMQkcXAcMDW4AwHZpu/lwLviIgopZSI3A0kAG6dvV/+S4L1d1BGc+A3AOIChZRffqH2Pfe4s3qNRqO5aSjQ4IjI/UqpL4AAEXnS/rhS6nUH2Sw0xXL3NjgJdHaWRimVJSJXgLoikgY8g9E7cjqcJiKTgckA9es3gMuHiY4+Dtfy7xTgKN4+rknNICqnnyCtknC+lrDlxyVUrV+/ABVLhpSUFKKjo91eT2lS3nTS+ng/5U2n8qYPFD6kVs38Lu2lz7OBN5RSKSLiNJFS6gPgA4BWbdsparWmd7fAPL0WC47i7ePSO+QQdmg1O9sYdR7gKE917Yr4+d24RgUQHR1N79693VpHaVPedNL6eD/lTafypg8UPqT2vvk9pxhlnwKa24SbmXGO0pwUkQpATSAJoyc0WkT+BdQCckQkTSn1TjHkcJm0gNZ0Wl+NnW1SAYhpnsH1mBiqdenizmo1Go3mpsDVFz//JSL+IlJRRH4SkfMicn8h2XYArUUkUET8gLHAd3ZpvgMeNH+PBtYpgx5KqQClVADwJvB3dxsbAHx86NG0hzV4sLlw9ufVbq9Wo9FobgZcfQ+nv1LqKjAUYy+1VsCfC8qglMoCHgd+BA4CXyml9ovIiyIyzEz2EcaczRHgSSDf0unSpkWPAbQ8Y7yPk+0rbDryE0qpQnJpNBqNpjAKm8OxTzcE+FopdaWguRULSqmVwEq7uL/Z/E4DClwGppSa7aKMJUK1rt3ouFQ41tgIb6+VxNiERCq1DCxNMTQajabc4WoP53sROQR0AH4SkfpAmvvE8hy+1avRtUqYNbz7VuFKtN7MU6PRaG4UV90TzAS6Ah2VUpkY78YMd6dgnqR9h8HUTjaG0ZKrCjt2/c/DEmk0Gk3ZpygePNsCY0TkAYwJ/v7uEcnz+PftS4fDufM2GzhM5rlzHpRIo9Foyj6urlL7HJgLdAc6mZ8yv0u0M/yaNaVn2i3W8LYg4cpqvVpNo9FobgRXFw10BELUTbRcq0uH4dS4/g7JVYUkfyFm6zIG3F/YSnCNRqPROMPVIbV9QCN3CuJt1BkwiE6/5trXaHWIrAsXPCiRRqPRlG1cNTj1gAMi8qOIfGf5uFMwT+PXogU9rjezhrcGwdU1Zd6btkaj0XgMV4fUZrtTCG+l+23DqZb6HteqCBdqCjs3f0v/ceM8LZZGo9GUSVxdFv0zxg4DFc3fO4BdbpTLK6htN6z2c/ZBsi5e9KBEGo1GU3ZxdZXaoxj+at43o5oCy9wllLdQKTCQHim5Dtg2t4XLP5SKPziNRqMpd7g6hzMV6AZcBVBKHQYauEsob6JH5N1UTzV6ORdqCls2LfKwRBqNRlM2cdXgpCulrJ7KTFcCN8US6bpD76brgVxVV1dJIP1Yfn87Go1GoykYVw3OzyLyLFBFRPoBXwM3xX4vfs2aMiAn2Bre2lb4/buietvWaDQajasGZyZwHtgL/AFjB+jn3SWUt9Gp9ziaJBm9nLRKwuq936JycjwslUaj0ZQtXF2lloOxSGCKUmq0UurDm2nXAf+BA+h10Ncajm52hevbd3hQIo1Goyl7FGhwxGC2iFwA4oF409vn3wrKV97wrV6dQfV7IqaN3RMgHF2x2MNSaTQaTdmisB7ODIzVaZ2UUnWUUnWAzkA3EZnhdum8iNaDxxJ63DA4ykdY8ft6slNSPCyVRqPRlB0KMzgTgHFK4fPo6gAAIABJREFUKeuyLKXUMeB+4AF3CuZtVOtyO32P+1vDa0KzuLjsvx6USKPRaMoWhRmcikqpfDtWKqXOAxXdI5LnWf5LQp4PgPj6Mui2MdZ3cs7XEtb//Ak30VSWRqPR3BCFGZyMYh4rlzS8dxy99+aGVzQ8S2pMjOcE0mg0mjJEYQanvYhcdfBJBtoVVriIDBSReBE5IiIzHRyvJCJLzOPbRCTAjI8SkVjzEyciI4qjXEmy/JcEVh65Ttf09ta43a2Eg18v8KBUGo1GU3Yo0OAopXyVUv4OPjWUUgUOqYmIL/AuMAgIAcaJSIhdskeAS0qpVsAbwD/N+H1AR6VUBDAQeN/c3cDjVO48ivAE4x0cJcKyqxu1nxyNRqNxAVdf/CwOUcARpdQxc1ucxcBwuzTDgU/N30uBO0RElFLXlVJZZnxlvGgbnett29PnWG1reH07xbmlSzwokUaj0ZQNxF2T3iIyGhiolJpkhicAnZVSj9uk2WemOWmGj5ppLohIZ2AB0AKYoJTKtyRMRCYDkwHq12/Q4cOPP6dmNT+uXMs/veQovrhxNX7+iTnNV3DRXwCYvM6Pdve/ChWLt44iJSWF6tWrFyuvt1LedNL6eD/lTafS0qdPnz4xSqmObq8I1x2wlTpKqW1AqIgEA5+KyA9KqTS7NB8AHwC0attOUas1vbsFWleW2eIovrhx1/o1ZsCSVSzqYQytrQhPZ/zly9S5555i6RodHU3v3r2LlddbKW86aX28n/KmU3nTB9w7pHYKaG4TbmbGOUxjztHUBJJsEyilDgIpQJjbJC0iOVWrE1W9H5XTjd7hqXrC6lX/p/dX02g0mgJwp8HZAbQWkUAR8QPGAt/ZpfkOeND8PRpYp5RSZp4KACLSAmiL4XHUa0jvM5o79+SG/9viHCk//+w5gTQajcbLcZvBMSf9Hwd+BA4CXyml9ovIiyIyzEz2EVBXRI4AT2LsSg3QHYgTkVjgvxibhnrVUrCseg0ZU6M3vtlGL+dAC2Hr1+94WCqNRqPxXtw6h6OUWonhysA27m82v9OAfBMfSqnPgc/dKVtJ0HbCFLp+vJ6NYcbigcU1D9Ft1y6qRkZ6WDKNRqPxPrx20UBZoHJICPemhrGRAwBsb+vD9o//Re9IvZO0pmjYL1QZ3i3QQ5JoNO7DnXM4NwWdHniKTvG5iwU+r7GX6zt3elAijUaj8U60wblBqkVFMeFKqDW8PciHrR//y4MSaTQajXeiDU4J0Pmhv9D5kE0vp9Z+rm3f7kGJNBqNxvvQBqcEqNqxIw+k5O5lurOND78s+Id2XaDRaDQ2aINTQnR86Bm6HMjt5fyn6WGurl7tQYk0Go3Gu9AG5waxOGlbk1qLu86HWd/LOXiL8P1Xr6Aybjq3QRqNRuMQbXBKkAqDptB/d27407CLnFu00HMCaTQajRehDU4JktHkFh6pfxdV04xezpk6wsKN75B9+bKHJdNoNBrPow1OCXPr1KcZtSP3fdqvOqbz6zy9TFqj0Wi0wSlhKtSty/0dJ9PwktHLuVZFeO/yclL37i3xuizzR5aPRqPReDPa4LiBRg89wqNxda3h6HAffnr7GVR2tgel0mg0Gs+iDY4b8KlUiSGP/J0om5dB3ws6wfkv9QICzY2je7aasoo2OG6ievduPJ7dk0oZxtDab/WFjza9Tubp0x6WTKPRaDyDNjhuwPLkearnI4ze4muN/yoqiy1/f1LvQKDxGJZr88q1DN070pQ62j2BG8muXZdOgQ+x9fR/ONpEyKog/LvZPoIXL6L+uPs8LZ7Gy1BKkZR5hrMZCZyMXclvyb9xOe0yl9Mvk62y8fPxw8/Xj8xr1ahdsSF1KzbhlsptUSoAEfG0+BpNoWiD42ZSet/FU19uYXqD/WRWEI41Ft7/+V/8pUdP/Jo187R4Gg+TlpXGhpMb+Ob3lRy9HsvV7P9v77zjqyqyB/6d+3ry0gskJIEQCAhIL1JUUFFcC7oqYMdl1bWs/lZdRd1de1t3UVy7KGIvWEBUVFCkdxAIJYQkkIT0/lJend8f75FOTY/z/Xzeh3fPzJ175uVyz52ZM+cUegtyTryN9z4LI0Y/iEHW8fTxG45BM6p8OooOiTI4rY2mMebhOcx49CLeP9PrpbZwtIvRT9zB5JcXIgyGdlZQ0R7sKtjF58mf82P6j9ictma1VVhdSCG/8pvtV0zCwpCAiZxe8hd6B/duIW0VipZBGZw2wBjTgz+d+wAbU59iX4zArRM8O+AAff73PL3veai91VO0ER7pYVXmKuYnzWdL7pYm65g1f2JMiYyPH0xZQSBWXTB+ugB0GHDjZMRpwXz/206KnDlk29M4VL2Hak9Fzfl2WcXGsu+Zuuh7xkWP4/ahtzMkYkhbdVGhOCatanCEEFOAuYAOmCelfLZBuQl4DxgBFALTpZTpQojJwLOAEXAAf5dS/tyaurY2a2LH8KelA3ksPIlKsyA/WPD03g+Z9kZfqmKCWLQm7ZjTICoFcedFSsnqrNW8uPVFkouTG5XHBsSSoB9HP/8RRJv6ohM6po6Kb3JRf2x0PHlp3WuOPdJD4mnVvLpmIbtsqyly1s7FrT28lrWH1zIxZiJ3Db+LviF9W6eDCsUJ0moGRwihA14BJgOZwCYhxGIp5e461WYBxVLKPkKIGcBzwHSgALhESnlYCDEI+AHo0Vq6tglC4L76QW5+71bmXlAJwIb+Gqf9+iz9AmbjDm5n/RStQlJhEnM2z2FjTv2EfHqhZ0r8FKb3m86QiCEsXpt+Su1rQmNg2EDOD/Njcuj1pFXtYn3pN+yt3IhHeveBrchcwaqsVVx32nXEef6ASbM0t1sKxSnRmiOc0UCKlDIVQAjxCTAVqGtwpgKP+r4vBF4WQggpZZ2YyyQBFiGESUppb0V9Wx1PQBBxk//BBVse5IcRXq+iD8bbeWjJ65huea2dtVM0h4ajkWp3BSnGRXy671MktW7wFr2FaYnTuG7AdXT3796wmWYhhKC33+n09judoadrPPTT8+y0rUQicUs3C3YvIFD/LZeE38JphB2/QYWihRGttSdECHElMEVK+Wff8fXAGCnlnXXq7PLVyfQdH/DVKWjQzl+klOc1cY1bgFsAIiIiR7w1/32C/I2UVjTOQdOUvDmy5pwfsPx7Xuj2E+ndvUYnpFzy4PbBWK69GY7i3nqi1+ko2Gw2rFZre6vRYhyvP0f+FlJKdjt2sqTiK8o9ZTXlGhrjrOO4MPhCAnWBRz3/CE39fR1uib/FSEWVA70Gmu9eOdY9l+M6zLcVX5PmPFCvfLhxOBdZryAyoLEunZXf2z3XUkyaNGmLlHJkq1+IDu40IIQYiHea7fymyqWUbwJvAvTpf7okuC8Txzc9992UvDmy5pxffnlv/vFJPncHbafCIigOELzRZwevHUol6sZZTXX1hK/TUVixYgUTJ05sbzVajOP1Z9GaNCrcpSzKe4XdFevrlY3vMZ4HRj1AfNCJrdEVVjqw+/uxZF8mh8uqKahwUOFw4/RIwAWAJiDYbCDEYmBM3zCwu4gPsRDhb0QIUXN/dKcvfwo7i+3lK/ilbAFF1UUAbHVsJa3sMC+NeZ6hkUNP/YfpQPze7rnOSGsanCwgts5xjE/WVJ1MIYQeCMLrPIAQIgb4CrhBSnmAroSmY+TTr3DXLRfz3JRiPJrgQJTg0d0v8J9V/Qg4c0J7a6g4SfZVbOKrvP9hc9fmPgozhzF79Gwu6HXBcTdmZpVVsymjhKRcG3lNjKYb4pFQVOWkqMrJgQ2Haq/pZ2BIVCA940KQUiKEQAjBsMBJ/O2cK7h9ycPssP0KQLErh5lLZ/K3EX/jhgE3qM2jilanNUPbbAL6CiHihRBGYAawuEGdxcCNvu9XAj9LKaUQIhj4FpgtpVzTijq2G7qgIEKufJIbV9Ta/LUDBP/95A6qkpLaUTPFyVDprOSJdU/wfvYT9YzNyMALWHz5YqbETznqg9zucvPJxkNc/L9V/PvXVH5JLTohY3MsCiud/HygkMteWcPzK1NZe7AYu8vrPBBkCmJa93u5qtu9mIQZALd085/N/+GBlQ9Q6axs1rUViuPRagZHSukC7sTrYbYH+ExKmSSEeFwIcamv2ttAmBAiBbgHmO2T3wn0Af4lhNju+0S2lq7thSM6jtPPeJDJW2ujSn8x2sPrc2fiOHiwHTVTnAjJxclMXzKdz5I/q5FZdSHcEPUIl0XeQaCx6fWRSoeLN1ce4MznfmH2lzvZlVXWZL2G6ARYTXr02omNRLLK7Hy6I5vHlu9neUoBlQ7vdNyQgLO5M/heYkyJNXW/T/+ea7+7lkNlh47WnELRbFp1DUdK+R3wXQPZv+p8rwauauK8J4EnW1O3jkLl4NFcnHYxhSlL2NrHa//fGV9N8BPXcv0zX6GPiGhnDRVN8XXK1zy1/imq3dU1sgH+Y5kaeQf+TTgFAHg8kq+2ZfH8D/vIKatusg5412dG9QolxKARHWgmKsBEkNmAUSe4bEJvFq1Jw+HyUFzlJL/SgcVqYumObFKLKnF5GjsBVTjcLN6Tx9p//8LE+FDG9wwhRBfKn2OeIUn3CZ8nfw5ASkkKVy6awbVRD3H3eRc38xdSKBrToZ0Gfi+Un30uM5cJbJlLSI7xvr3OHVeC/8PX8MdnP0UfGtrOGiqOUO2q5ukNT/NVylc1MovewoWhtzAs4JyjTp9tPVTMo4uT2JFZ2mS5APpF+DM6NpiBkVamT+xzzGjORr1GtwAT3QJMTB0fT4K/kWqnm915NrZklbI7z0ZD21Ngc7BwZw7rD5VwVS8PvYIN/Gvsv3CVdOeb/NdxSSdVnnLmZ/2TPqmCi3pfdNK/j0JxLJTB6SCU/fFmnvrOwd/yfyQzwhv+5pkx2cjZ07ji2c+O34Ci1TlYdpB7VtxTL1pA76DezJk4h11JTc9OVznc/OfHfbyzJo2mdiBYDDquHh1HrFlPqF/z4uqZDTqG9whieI8gRgzoxqNf7GBVeu0azhEyS6t54TcYW3yYc0fGMiJwMt2MPfkg+0ls7hLcuJi9ajY/Je1kYsi0GiOqolsomovKh9NR0DT6Pf4cTx8cRWSx98nk0gueOSOHzx+chq686TdjRduwrWIb05dMr2dsLup9ER9f9DEJwQlNnrMxrYgpc1fy9urGxsao07j1rN6snX0O/7pkQLONTUNiQvy45LRuPHJuX87rE4ZR13jkte5QCVNeXElKYQUx5kRujXmeSGOtY+nyog/5Ku8l3NLVoropfr8og9OBEAYDQ55/jef2DaWbz+i4dYLnxuRw+NO70RcXHKcFlX64pXG6nTy78VneKXiHCqc3SKZBM/DPM/7JMxOewc/g1+gcj5R8vy+fGW+u42BhY8+voVEBPHB2bwYEmVm5veFOgZbF36jjktO68fCkPlw8OKpReWZxFS+vPcii3bkE6CK5ucdz9LYMrinfWr6cj7Ofxenp1EE+FB0EZXA6GJrZzPAX5jUyOi+fXci+r+/EkJPZzhr+fsi2ZTNz6Uw+3PNhjSzGGsMHf/iAaf2mNbleU1rt5NV1B1manN9oDSXUYuD9WaO5aWQs4W0cFSLYYuDla4Zzx9ieRDa4tgR+PlDI/9amU+0wcUP0I0xNmFpTvrdyIwsOP0a5o7xNdVZ0PZTB6YBoZjPDXpjHv/cOI6rQ+9SSQjD/zErW/3wXpgN721nDrs/qrNVcteQqdhTsqJGdE3sOn17yKQPCBjR5zr58G//+NZX9TYxqzuwVwgMTe3Nm3/b1OkwM9+fvZ/fm7OjG//XTi6t4/tdU9ufbeWL8E5wZfEVtWfUuZv0wi8KqwrZUV9HFUAang6KZzQx98S3mpI8l4XDtq/JXo118s+sB8r9f0o7adV3cHjf/2/Y/bl92O6V277qZTui4PORyXpz0YpN7a6SUrEgt5LX1h7A53PXKrEYdt42J48rTozDrdW3Sh+Nh1Gn8MUHHnWN7Eh1krldW4XTzxoZD/O/nFM4Pu4ELwm6sKdtTtIeZS2dy2Ha4rVVWdBGUwenAaGYzA+e8xpzKixl2oNbTaOVAyS3bZ6N9Ow88nmO0oDgZCqsKuXXZrby5482aCM+RlkjmT5nPOYFNuzzbXW7+vnAHXyXl0tAJbVxCGA+cnUD/yI4ZULJvuD/f3nUmAxroJ4E5PyWzYGsWYwIv57LIOxG+R0V6WTo3fH8DqSWp7aCxorOjDE4HR+j1xD/+DLMqruCc7bXGJSVa8O8ei6j4+GGE/eibCBUnxra8bUz7ZhobsjfUyMZEjeGzSz5jWOSwJs/JK6tmxpvrWbil/rqaAP7QL4L3Z40h0Nyxdx6E+Bu5eXQsF/WPoKE53Xa4jJfWpNPXOIkZ3e/HoHk96XIrc5m5dCa7C3c3blChOAbK4HQChBCU/PEmLou4g5nLJJpvNbrEKnh+xC72LLwZQ5YKhXMqeKSHBUkLuGnpTeRV5QEgENw6+FbeOO8NwixN543Zn1vOZa+sYduhknpys17j5tGxXJAYge4EQ9C0N5oQnN83gtvH9sTfUH/aL6O0mv+uSiPQNYxXz3sVi96bvK3YXsysH2YdNVW2QtEUHfv163fK0dJJl519Iad3j+HBRY8zd0o1NovApRd8MKaU4bv+ygDtAYga3+zrnMq5J3t+R6CgqoB/rPkHa7Jq48NatACu6nYPsZUj0GlNr7lsSi9i1rubKKuuvz8lwt/In0fF0j3A1Kp6txaJ4f7cc2Y8b23MIMdW6wZdWu3ipbXpvJ4wgnnnz+O2ZbdR5ijD5rRx60+3MmfiHM6KOasdNVd0FtQIp5NR1e90Am56mTkr4ojPqV012JoAN+Q8S9EX/0CrUlF/j8fKzJVcsfiKesYmxpTIHbEvkug/4qjnLd2VzbXzNjQyNqdFeB/WndXYHCHc38jfJvRiUr/63nQOt+Tm97awOy2Y+VPmE24JB8DutnP3z3ezNG1pe6ir6GQog9MJcYV3Y8zbn3P/3gn8YWPtuk5xgGDOkB0s++kG2L3+GC0cneZuHD1yXmmFo+b8jrQZ1e628+zGZ7lj+R01ycgAZg6cyZ9jniHYcHS35QVr07ntw604GoSKuXZMHDePjsPP0DG80JqL2aBj3o2jmNi7fgw/t0cy+8udLNkMC6YsoIe1BwAu6eL+lfezMHlhe6ir6EQog9NJ0fz9KZx1P1Ni7+KBLzUCK2pHOz8PcDCn+ilyljyCp6KiHbXsWOzI38H0b6bX28gZYYngjclvcO/Ie9GLpsPLSCn5fJ+DRxYnNQpRc9/5iTx52aBOs15zoug0weUDu3PV6d0bORO8tHw/L/9YzNvnz6d3UG8AJJLH1j3Gu7vebXNdFZ0HtYbTmRGCsjPPJ6x3P55a8CQLhmazOdH7DlEUKHg5cBtb/nM2942dTeL5V57yZZqz1tMSbTb3+tWual7Z/grv7X4Pj6wdnUyMmchj4x8j1Hz0aNwOl4fZX+zg2zRnPbkmYMaQaGJN+i6dKXNCr1ACTXre25rlS3Ht5bPNmew8VMK8P8/jT9/dwmF7CgD/3fJfyhxl/HXYX7v076I4NdQIpwvg6NGTsvte5pmA6/m/r9wE1RntrOtlZ0bGozz19EWUHepambpPhC25W7jymyt5N+ndGmNj0Vv4x5h/8NI5Lx3T2NjsLmYt2MSX2+rHOzPqBDePimVMbHCr6t5RGBwVyB1jexLcIMDonjwbt723j6vCH6WXeWCN/K2db/HUhqfqGXeFApTB6TJIo4nus2cTO/U5nv0qnLN31P5nd+oFn/Q4xMXfXMY7b/0Ve0XXj4mVV5nH7FWzmbl0JgfLal3Gx0SN4ctLv2R6/+nHfAMvq3Yx/Y11rNpfP2BqmL+RO8f1YkC3gFbTvSMSH+rHF7eNI9RS3+jsyCzl9bW5XBT8EIl+I2vkn+77lIdXP4zT42zYlOJ3jDI4XYyqxEEUPfga1zgu5Yn3PCRk1452iq3wgnEFF82fwEef/gu329F+irYSTreT+bvmc8lXl/Bt6rc1cn+DP4+MfYS3Jr9FTEDMMdvItdl5YXUaSYfrp37uFebHl7ePo2ewpVV07+gkRFj524R4YgLrh8MpqHTy8prDTDD/jdOtZ9bIl6Qu4Z4V92B3q0jTCi9qDacLIk1m8mfcgvnQucxZNI8ftuzgo4kaJVbvG31ugIdnqr8icsdiJpjOZ1C/mRh17f8Qbc7eHpfHxTcHvuH1317ncEX9WF8D/cdxYfgsDPkRiERxzOukF1fy5oYMKpz1Y6LFB2l8fts4wq0mtp9oh7oggWY9fx3fk/mbM9mbX+uQYnO4eW19JjcMv4X+id1r0lavyFjB7ctu56VzXsLf4N9eais6CGqE04WxxyUQ/9FHXD39cV752Mp1P7sJqKwd8eQFuPnS+D3/3Xs1v+55npyKnHbU9tRwe9wsTVvK5Ysu519r/1XP2CQEJXBT9BNcHTX7mO7OR9iZU87Law82MjaT+kUwe5SZcGvn3mPTUpj1Om4ZHceomKB6codb8s7mLPrpZnLToJtq5BtzNnLzjzfXBENV/H5pVYMjhJgihNgnhEgRQsxuotwkhPjUV75BCNHLJw8TQvwihLAJIV5uTR27OkLTCL7ySgYuWcrMATN5eZ5g2ko3/lW1hqfC5OEnwyou+HwyH+29lz229bil+xittj+frdrN7G9fYtLHF/D3lX8nvSy9pizEFMIDox7g80s/J8FvyAm19/76g7y9KaOeJxbAmNhgLukTTrXd2e57iDoSOk1w7dBobp9YP9upR8IDX+7EUHIJdw+7u0a+s2AnM5fOJK8y74Ta70h7txQtR6tNqQkhdMArwGQgE9gkhFgspawb8W8WUCyl7COEmAE8B0wHqoF/AoN8H0Uz0QUH0+2B+wm59hq6vTiXi19Zwi+DBd+O0sgL8U61eQTs1u9nd87TBLr9GBB8Nj1ypuGRwWii/Tc1Sik5bE/hyfUfsih9CdWe+nuMrAYrNw68kesHXH/C0zdSSpbszWNZSuM8L3ed25felq7t9twchBDcP6U/uQUVfLkrp1607P/+lMy1Y8bw4OiHeGbj0wCklKRww/c38Oq5r9I7uHf7KK1oV1pzDWc0kCKlTAUQQnwCTAXqGpypwKO+7wuBl4UQQkpZAawWQvRpRf1+lxhjYujxn+cJnTkT1+PPcf4bm9jYT/DjMEFSr9oBb5mukvXl37P+h+8J0ILpbz2DPn5DSbCc2IihpZBSkmNPZ0/FenbZ1pDraByk1KJZuW7g1UTYJuJnC2DZRu9b9PHWf1weycfbD7M5q/5UjwCmDY7insmJ6u36BDgrPpQgs3evjqvOCPHDDYeYXN6Xx854isc3/Au3dJNly+K6765jzqQ5nBF1RjtqrWgPhGy4dbqlGhbiSmCKlPLPvuPrgTFSyjvr1Nnlq5PpOz7gq1PgO54JjKx7ToNr3ALcAhARETnirfnvE+RvpLSisfdVU/LmyFq0TVc16M0E+VL/tqSeQcdIZVxa4cCUkUHYTz9gTdpJTgj8PFhjxWBR42DQEA2Nnqae9NB6Eqv3fgJ1Qcfs08nqXuouIc15gHRXKmmu/RS6ms4yGaaFM85yFsPMI4mwBpzUdapcknf2uEkuqX//GzW4sb+OQWFas/pzIv08WVmLtnmM/pxqmwdKPby1201V/TBz9AnWuGBACp+UvItDeutqaMwIncHYgLGNrg1N/x84HjabDau1Y+YeOhXaqj+TJk3aIqUcefyazadTe6lJKd8E3gTo0/90SXBfJo6Pb/KttCl5c2Qt2mbJfo7oDo29tVpD96k+uT24L4dPPwfToQMMWvcN3X76iekrPeyJE6zrL9jQT1DmX2t8PHhIs6eRRm2bVl0w4YYYRob2p8IWSJAhHH+nDavfIM48YyA/bcpGhw6d0OPBw9CRkSxan0ylu4xSdwGlzgKC/SpYm7eTXEc6Fe6jLy4bhIkLe19ARPUZ9DQPQBPaSf8eC5Yl88ZvhzhcVv/JaDV6F8N7hlgan1/nb9Tm90drtHmM/pxqmwnBcHdoNQu2HSa7tDZHU0qJB8/+0/nP5W/x8Nq/Ue4uwoOHj4o+whxt5u7hd9f8HY/Q1HWOx4oVK5g4ceJx63UWulp/oHUNThYQW+c4xidrqk6mEEIPBAEqaXo7YI9LIObquXz39VqCly1mwKofGXSwij/9CPti4Ld4jd96C9K6g2ywpmFzl2Bzl5CevKt+o6Uw91Djaz3aVMCDgiZkPkzCQqL/SE7zH0Oi/0imTxh4ylNdOzJL+O+qNMrs9Y1NrzA/rh8STfgJvEkrjk5UgJkvbx/HzHc2sS+3doNxan4F933o5PLBT/Br5X/IcXj/fu/seoe00jSenvA0VmPXGZ0omqY1Dc4moK8QIh6vYZkBXNOgzmLgRmAdcCXws2ytOT7FCeGMiCL/6lspnHodgat/pMea7xmQkcmADA9Xr4QyC+yNFeyP9n4ORIHd2LKL6gZhItbcn3jLQK4ddR6HUoKOGljzZNiaVcr93+/F3iDac89gC1/cNo7Vvx0+ypmKkyEqyMLMYdG8vSmDlMLaVBmFFQ7mr3dwxeAHSfV7i32VmwD4JeMXrv72al6c9CIJwQlHa1bRBWg1gyOldAkh7gR+AHTAO1LKJCHE48BmKeVi4G3gfSFEClCE1ygBIIRIBwIBoxDiMuD8Bh5uilbE4+dPyfmXc9Yj/8eyt74iaNVSrNvWE1jlYnSyZHSy973AIyA/CA6HCrLC4HCkiYLoYEoCNcr8BC6timqnEw8u3NKNQGA1+iM8RsyaP0H6cAL1YZzRO5GinAC6GXsSYuheM8Uyqns8hw80b+HeIyU/JOezNLnxMGpQNys3Do8hTO2xaVH8DDpuGxPHB9sPs61OxAa3hM9+K2JSwp8ZFxHN2tJFAKSXpXP1t1fzxPgnuKDXBe2ltqKVadU1HCnld8B3DWT/qvO9GrjqKOf2ak3dFCfrQDPFAAAar0lEQVSG0DQqBw2nctBwdGUlBK5dTo/NP+NI8xoBTUK3EuhWIhmWCl6Pdu8GUo/RROCZE0iJO52KIWNwB3idC6Y2sRYwdUg8i2wt7xFmd3n4aPthtmeXNSo7JyGMS06LRFNuz62CXqdxw/AeRPob+aFBTLpfDhQzoHwyj140huc2P0GVq4oqVxX3/Xofv+X/RoK8rEVGtYqORad2GlC0Le7AYIqnXMGZj9/LDx/+SOCGFQRsXIm+tKjJ+prDjm35crqzHCk0quP7UjlwOJXmi8AVCPrWvf1S8mzMWZVWL10ygE7AtMHRnBH3+4j23J5oQvCH/pF0DzDxyY7setOZu/NsvLokgKemvskLOx4iozwDgPd3v0+UcTXTuv+dCOOx494pOhfK4ChOGiEE9vhE8uMTyZ82C0vyLgLXryDkt3V4yhqPJACE9GBJ3YcldR8Hv/mYBLOFqv5DqBg4jMrThtLSA9pth8t46Id9VDjqR0wI9Tdy3ZBoEsL8WvR6imMzvEcQfxzbi+vnbajnsHEgv4K7FlTzz6lzWFf6CisyVwCQ7Ujj1Yz/48LwPzMqUE2xdRWUwVE0D01HVf8hVPUfwphR/2bZgiX4b1uPdesqDCUlRz1NV12Fdft6rNu9qbD3zwklqld/qhIHUZU4CHtsPGgnH93A5ZF8syeXFamNR11RASY+u20cW/fknnS7iuYzJDaYe8+MZ96mDDLquE1XOd08tPAAY+OmMyW2Dz+XvIfD48ApHSzOf5Xkis2Mq3yGSL/IdtRe0RIog6NoMYTRSOWAYVQOGEb+H87FVKYxomAvmd8sxZyResxz3UVFBBStJWDrWu+x2UJ1nwHkbx+Lny6S6vhEPNbAY7aRW27n/W1Z9R5mRxjRI4jpg6OIDfVj66l3UdFMgi0G7hrfi893ZLMxs/5+q3WHSulRMojnpr3NM5seJs/h9anfW7mRqV9P5Z6R93BF3ysa7dlRdB6UwVG0DkJg79mHiGsms3bExeiKC/Hbsx3/pK2E7N+Bu/DY26101VX479pCwa4tHJnFd0RGUd0rkcL9Z2AmHHtcAtJkRkrJB+sP8vzK1EbBN3UC/jioO+N7hqiYaB0Eo07jmqHR9A7z48ukXBx11nWyyqq5/d1spiQ+THzgYjaUeXMa2Zw2Hl/3ON+lfsc/x/6T3kEqFltnRBkcRZvgDgmjfNy5lI87l9Fje7L0s1/wT9qK357fMKfsRlddddw2jHnZGPOyydv4K3GA1DRyYxP532mXsNXcrVH96CAzM06PqokcoOg4CCEYGxfC9WcncOO8DRRU1mYGdbg8LN5dTGL4FKadNprlpa9T6MwGYHPuZq5YdAUz+s/gL0P+QpAp6GiXUHRAlMFRtDlC03DE9sYR25viKVeC2835oXY2LvwRS/IuLMm70Nuadj44ggR+iB3J2wMvxmZs7AAwpvwgTwTYyNoViKN7DI6oODzW31da6M7AwOgg7jurN5/uyK63XwcguaCCjHUW/tD/cXoMXMd7uxfglm5c0sUHez5gSeoS7hx6J39M/CMGrb4LdSO3+xNM5KdoXZTBUbQ/Oh2WQQMpKfWjZPJlICXG7AzMKbvpX5VDzrrNmLLSER7v1EumfzgvDbuKneGNd6VbnNXctvNrzju0GTfQvU6ZKyCI9H59iPSLwNE9BmdULI6oGJxhajG6PbEYdNw4vAeDugWwcGc2VXWm2KpcHr7YVcjwstE8c96ZfJr6MltytwBQYi/hyQ1PMj9pPn8Z8hcCpHqh6Ogog6PoeAiBIzoOR3QcUePj2bgmDWGvxpOeyk8HivjRFYyziYXj0wrTuW/Lx0RXNr0+pC8vpWrzFhruvvHo9RyIjaWHNQxHRBTOiO44I7pTHe5E2N1Ik7kVOqmoixCCkTFBJIT58WNaEWsP1P8bbj1Uwl/fFcwc93cuG3uI13a8WJPdNcuWxT/X/JMwLZyV36fxj/NvbI8uKE4AZXAUHR6PlKzPqeLbdB02d6g3YU0djHi4VZfJWVnL8HPZTrp9zeXCkZaGP2nUTduW9jL0BVyBIThDgnBGxZO3MZGgSj2ukAicoRG4QsNR4f9ajhCLgQ9mjeG+D7ewZG8eDnftb+vySOatTidkq4HbJ82FoNUs2P1uTerqQk8BX+bNZdUXHzHEcgGjg6bgpzu2Z6OibVEGR9Fh8UjJtzuyee7XVHLK7U3W6R/hz7TBUfxp8iUsWjMFPB4M+dmYMtIYLEpI27QTY3YmhpxMNJezyTaOh76sGH1ZMZaD6RSu/4WG7gn7/PzoGRSGKyQcV2gErpBwnKHh2DyDMGY5cAeF4rYGgqbceU8ETROc3TuM07sH8sWubHbl1n+JKK508tS3B+gd3oe7zpnPmqwvWFvydU0G2PyqfJZVfcCvxZ8xyHomIwLPQ8peykuxA6AMjqLD4ZGSHdnlLE3OJ/sohibIrOfS07oxokdg/QeJpuHs1gNntx5EjI9n7ZHFY48bQ2EeZ4U42bJ8M8acTIzZGRizM47roHA8ZGUlpspKTNkZ9eQZC6DXkTqahjsgmLQe3YnW+eMOCsEVFII7KJSy8n6Yc5y4g0JxBQQhzcqrDiDUz8CfR8WyI6ec75ILyCmrv78qtaCC+z9LJtJ/BOf0nYBdW8xGxwbK3d5Nv07pYFv5craVL2fZ128wtc9Uzu95PnGBce3RHQXK4Cg6EHaXhw0ZJfyaVkRBE1koAQya4LZJfYgx6jDpT2LEoOlwRkRhHR9Pib7+A0ertDG5h441P23BkJ+NIT8HQ34OweUFOLKyapwVmoPweNCXFlFdWkTDrC9ZH0FdjTx6PftDQ4kzWXFbA72fgCDc1kCK0uOx5jl9x16ZdPRotn4dFSEEQ6IC+fulg7j3wy0sSymoN80GkFfh4NPtDsLMZzOh9x8ZPyabedvmk+2o9VRLL0tn7ta5zN06l8SQRM7reR6T4yaTEJygRj5tiDI4inbncFk1TyzZzUfrD9bzUKqLAEbGBHFR/0hmnpd4ygnYmsLjZ8U8IB5bcf2Rxcjx8SxamYK+KB9D2maMVXoGWp0c+G0/+qICDEX56IsL0BxNj8JOFc3lwpWXh5m8RmW5iyG6gWwv0Mdkwe3nj8ffitvPSkZsN7pViZpjj7+V0oJe+GdVeY/dhbhlKJ7qqBbVvbWwGHVckBjBGXHBfL8vn/WHSmi4clZYDYt2F/JTioXh0Q8wLrqIg+5f2Vm+Erus3eeVXJxMcnEyr25/lW5+3RgbPZaxUWMZEzWGMEtY23bsd4YyOIp2wWZ3sS27jA2HSpoMRXMEIWB4dCAX9I2gW0A75KzR6XBFdMdl6EdVcN/603QAUnLRwBCWLd2CvqjAa5yK89EXFdBdVlJ86DD60mJ0lSfvzHAyaPYqNHsVFHvTANiSd9FwS+Thj6DhWGgf0EdvwOPnj8fsh8dswWPxIyM6nO6VEo/FJzP7UXQghsDsKl89PzwWP+yRLvRFxb46llOKf3cyBJkNzBgSzTkJYfy0v4Ath8twN4guUelwszq9hNXpGjGBFzIu5nLGjspjbc7PrM1ai8NTO3rOrczl65Sv+TrlawB6BfYiWMYTa+5HrLkf3Yy90Amd2sfTQiiDo2gziquc7Mgu4+OkHDakFjV6Q62LTngjDD8zbQhJ+4+Rf7q9EQJ9SAj2uATscfX3BY0ZH892n3ESTge60mLO6WlmzaokryNCSTG6smJidHYK0jLRlRajKy9FczY9ndhaaC4nWlkJlNUGW7Xt82Y/rEvu1/X3NQGkAnWDzHiMJpKt/sRrBjxGE9JkxmM04zGZyFwYRrcyVx2ZmcK9UQRlV+IxmZFGEx6TmUpjAab0Yq/MZMZjNOGprgaPp8bxItJq4tphPXj+6mHc/8l2NmeVNjI8AJll1WTurmbJHiOjel3DrP63EhCSwrailaw7vA6bs/6LQHpZOpDO9vJfANALAxGGGNZ5BtAnuA99gvuQEJxAlH8Uek09Pk8W9YspWo1ql5uf9+byVVIOyQUVHC47/tSTv1HHhJ4hjO8VQpDZQJ/IgI5tcE4QaTDiCu+GZWg8FRX1xx5jx8eztc6oSdirubBfIMtXJKErL0VnK/N+yktJ8JdkpGTWk+sryr0P4w6A5rDjLrLTVOq08h00GnXlQSOvv4NAzwayfUAi4NEbkAYj0mj0/qZBVmY7odgSyI+hiSwNG0SJvrHThUfChrQiNqQVAQb6WCYxKXQiLlcKdmsaaYY0DooMPNT/HV3SSbYjjW9T60/h6oSO7v7dibZG08Pagx7WHkT5RxFmCSPcEk6YOYwQc4gySg1Qv4aiRfBISXJuORsySjhUUsWhAheZFfto4qWzEQIY3yec+AATg6MCMOp+3+7D0mTG0KMH9l6NRzoTfBth63Lp2J4sWZ6EVmFDV1mBVlnOGbH+bNl6wHdsQ1dhI84fsg/meI/Li9HsDvRVFeA8NXfx9kBzOcHlhCqvC7SjIBczEAXcyDauEQtZE306P8WNYntkXzxHiSydUqWRkgXQDy2nLwklWYwvTSNY24/H/zCFYTZSoqEgqGmHArd0k2XLIsuWxSY2NVlHSAh0GQhxGQn0mLBKI1bMWDFh1cxYhQWrzo8AzYKfzoJFZ8GiM2HWWzDrzXhSMyisqsBgMKEZDKDTI/R6hMH7L3o9Qm+oORY6HdQ99n0wGDqMY4QyOIqTwun2kJJn47fsMvJsDnJtdu+n3IF9yZ6Tais60MTQqEBGxQRz0+SWdQT4PSE0DY+fFY+flSOpzQLHx1Nmrf97jh0fz+Yjv3HJfgjuy6XjevHNL3vRqirRqn2fqkrGxgeyaWsaWnWVT15Fn2A96Wm59eoFaW4qikq859urEe28CdYg3UzM2s7ErO0UmAP5JWY4v8QOJy2ooatFLR6hsT8klv0hscBZAJhcDnrtymF4dSZW3UE0Uy4O/xKKg6rJDpOUWI//AJcCSg1OSg1OoOL4ynt8nyP2PwLI+wTNIzE5wegEsxMMLjC4QV/zkeg9oKsjq18Oeo/AgIZeaujRoUdDL3QYaN01t4Yog6PAIyWVDjcH8m2kFlVS4XD7Pi62FlSwNbWI4monJVVObA43fLf3lK4jgJ4hFq4Z2xNdtYtwf2PLdkRx0gghkCYzbpMZN6E18oDx8ZSb6xusCePj2dDgpWD4+PjaFwWPB+Gw84chkfy4Ohlhr0Zz2L3/2u2M6hXA1p0ZXsPkK+sbZiI1PQ/NXl0jDzcLivNL0Bze84S9Gr3LgTzJkVh4dRlXpazgqpQVZPuFsj5qIOuiBpEUFn/Ukc8R7Hoj+0Lj2EccMK62oBKCi8qJdBQSKLMwa7no9UV4zGU4TFXYzQ6qzE5sFg+2Fkoq69EEVSaoMkFpkzVOdPQiAbfvU4c3m6PdydGqBkcIMQWYC+iAeVLKZxuUm4D3gBFAITBdSpnuK3sQmIX317lLSvnDsa7lcEsOFlex7VAx6cWVNfIjL1xbDhaRVlRZb6F6U3oRBworwSeVwIbUQlIKKmqOAdYdKGR/A5mUkjUpBezLt9WThyTnszevvixoXx578mw1IVAkELg3j6Tccm+FCg/SXo51Ty5Swq6c8np6WpJy2JFdhkd6jYPbI7FvzmDLwWLcHolbSjxSkulwsyu9qFbmkWzOr2BfZgl2tweHy4PDLbG7Pcxdd5BCmx2H20O10+O93o/Jx/qJT4neEf5E+xtJDPenT5g//kavx48azXRBNA1ptqAPD8cZUd6oOGh8PGXBjY3Y+gb3wsjx8fzWRLTnRasOIFxOhMOBcDrQnA7OHRTBLxtTEU4nWlEqwhTJ6IRgNu/MRHM6EA47wunk9O5+mFLzmOg8TEVpJntEAAf9I9joCSTDeHIpDkrMAZSYA6jd1uvD4fvU7CN24y8LMVOEQSvHQAWaVolOq0JoVQhdNVJXjUfvwK134tHceHQuPDoPbr0bl86DW+dGdqEZ5lYzOEIIHfAKMBnIBDYJIRZLKXfXqTYLKJZS9hFCzACeA6YLIQYAM4CBeLcdLBNCJEopG5jmWnJtduasTmPO6qYfZC+uSW8km9uE7H9rDzaSvbyusQzg1fWHGslea0L2+obGsjc3ZjSQZPBWI5mXeZuakG8/3Fi2u/G+DZpItdxahPgZ6O5vJC7YQpyhmLgeCVx/bl9lXBQtg6YhjSak0ese7wZMfeOx5/keYyVGCO5L4Ph4ygPq33MN3dl7Anf5XnzK7S4OFldxqLQKp6axKa2QcvtRHzUngY4KEUkFkbVvn00MMI6Nb1SiORGaE4QDoblAuEG4EMLt++5GCJe3rnDXkbtqy+rWE57aeuxqgb6eGK05whkNpEgpUwGEEJ8AU4G6Bmcq8Kjv+0LgZeFd3ZoKfCKltANpQogUX3vrWlFfxQkggO5BZgIMOrpZjURaTXSzGulmNXHDuX1ZvDbdW7GkFMxqxlbR8Qkw6RnUPYBB3QOYOj6er1enUlrtIsdmJ8/mIL/CgdRrJGWWUlzlPKY7f8sjAD149EiP1/uu5a+/oMVbPBqt+UToAdR9Nc8ExhytjpTSJYQoBcJ88vUNzm0Uv0MIcQtwi+/QdvC5i/e1jOptTjjQaXx/048in1n/sFP16QRQ/en4dLU+tVV/Gnqhtxqd+hVUSvkmbbrk1ToIITZLKUe2tx4tSVfrk+pPx6er9amr9QegNZejsoDYOscxPlmTdYQQerz7wgpP8FyFQqFQdCJa0+BsAvoKIeKFEEa8TgCLG9RZDBxJz3cl8LP0unItBmYIIUxCiHi8ebA2tqKuCoVCoWhlWm1KzbcmcyfwA1636HeklElCiMeBzVLKxcDbwPs+p4AivEYJX73P8DoYuIA7juWh1gXo9NOCTdDV+qT60/Hpan3qav1BqPS4CoVCoWgLutCWIoVCoVB0ZJTBUSgUCkWboAxOGyOEeEcIkSeE2FVHFiqE+EkIsd/3b0h76ngyCCFihRC/CCF2CyGShBB3++SduU9mIcRGIcRvvj495pPHCyE2CCFShBCf+pxhOg1CCJ0QYpsQYonvuNP2RwiRLoTYKYTYLoTY7JN15nsuWAixUAixVwixRwgxtjP352gog9P2vAtMaSCbDSyXUvYFlvuOOwsu4F4p5QDgDOAOX2iiztwnO3COlHIIMBSYIoQ4A2/opReklH2AYryhmToTdwN1Q3p39v5MklIOrbNXpTPfc3OBpVLK/sAQvH+nztyfppFSqk8bf/BG/dtV53gfEOX7HgXsa28dm9G3RXjj53WJPgF+wFa8UTIKAL1PPhb4ob31O4l+xOB9aJ0DLMEbM6Uz9ycdCG8g65T3HN79h2n4nLg6e3+O9VEjnI5BNylltu97Do2TIHYKhBC9gGHABjp5n3zTT9vxJqX8CTgAlEgpj6ScaTLcUgfmReB+qElpGUbn7o8EfhRCbPGFuILOe8/FA/nAfN+U5zwhhD+dtz9HRRmcDob0vs50Ol91IYQV+AL4PyllWd2yztgnKaVbSjkU78hgNNC/nVU6ZYQQFwN5Usot7a1LCzJBSjkcuBDvNO5ZdQs72T2nB4YDr0kph+HN1lZv+qyT9eeoKIPTMcgVQkQB+P5tIs9Ax0UIYcBrbD6UUn7pE3fqPh1BSlkC/IJ3yinYF4IJOle4pfHApUKIdOATvNNqc+m8/UFKmeX7Nw/4Cu9LQWe95zKBTCnlBt/xQrwGqLP256gog9MxqBvi50a86yCdAl86ibeBPVLKOXWKOnOfIoQQwb7vFrxrUnvwGp4rfdU6TZ+klA9KKWOklL3wRvP4WUp5LZ20P0IIfyFEwJHvwPl4k7p0yntOSpkDZAgh+vlE5+KNstIp+3MsVKSBNkYI8TEwEW/o8VzgEeBr4DMgDjgITJNStl3mtGYghJgArAJ2Urs+8BDedZzO2qfBeJOE6PC+lH0mpXxcCNEb7wghFNgGXCe9OZs6DUKIicB9UsqLO2t/fHp/5TvUAx9JKZ8SQoTRee+5ocA8wAikAjfhu/fohP05GsrgKBQKhaJNUFNqCoVCoWgTlMFRKBQKRZugDI5CoVAo2gRlcBQKhULRJiiDo1AoFIo2QRkcRZdECOH2RRJO8kV9vlcIofnKRgohXmrl61/mC2La3HaGCSHebiGdLvZl3FUo2gXlFq3okgghbFJKq+97JPARsEZK+UgbXf9dYImUcuFJnKOvE9vsiOxz4Ekp5W8toJPAG4h0vJSysrntKRQnixrhKLo8vvAntwB3Ci8T6+SEGS2EWOcLmrj2yG5vIcRMIcTXvjwk6UKIO4UQ9/jqrRdChPrqJQghlvqCSK4SQvQXQowDLgWe942yEpqq5zv/XSHE60KIDcC/6+rt200/+IixEUI8Krz5lFYIIVKFEHf55L18eVTeFUIkCyE+FEKcJ4RY48ulMtr3O0hgBXBxq//oCkUT6I9fRaHo/EgpU4UQOiCyQdFe4EwppUsIcR7wNHCFr2wQ3ujXZiAFeEBKOUwI8QJwA94IzG8Cf5FS7hdCjAFelVKeI4RYTJ0RjhBiecN6eGOagTeO2TgppbuBbiPxhmypS39gEhAA7BNCvOaT9wGuAv4EbAKuASbgNXwPAZf56m0GzsS7g12haFOUwVH83gkCFggh+uKNxmuoU/aLlLIcKBdClALf+OQ7gcG+CNnjgM+9s1UAmBpe4ATqfd6EsQFvDpT8BrJvfeFn7EKIPGpD1qdJKXf6rpeEN3GXFELsxJt/6Qh5QHQT11IoWh1lcBS/C3zxt9x4H7in1Sl6Aq9huVx48/msqFNWN66Yp86xB+//HQ1vTpmhx7n88epVHEVehXd0VZe6Ormp/T98PF2PYPa1q1C0OWoNR9HlEUJEAK8DL8vGXjJB1Ibln3ky7fry/qQJIa7yXUcIIYb4isvxTnsdr96x2IN3qqwlSaTxNJ1C0SYog6PoqliOuEUDy4AfgceaqPdv4BkhxDZObcR/LTBLCPEbkARM9ck/Af7uczJIOEa9oyKl3AsEHQnF30JMAr5twfYUihNGuUUrFB0YIcTfgHIp5bwWaKsb3lD+5zZfM4Xi5FEjHIWiY/Ma9ddnmkMccG8LtaVQnDRqhKNQKBSKNkGNcBQKhULRJiiDo1AoFIo2QRkchUKhULQJyuAoFAqFok1QBkehUCgUbcL/A9F26rjxEo5NAAAAAElFTkSuQmCC\n", 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\n", 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" ] @@ -523,7 +523,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -537,7 +537,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.9.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, @@ -560,4 +560,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} \ No newline at end of file +} diff --git a/local_optimization/Modelling/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb index 034348e..6c01075 100644 --- a/local_optimization/Modelling/handle_disable_ex.ipynb +++ b/local_optimization/Modelling/handle_disable_ex.ipynb @@ -42,12 +42,12 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 1, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -88,7 +88,7 @@ }, { "cell_type": "code", - "execution_count": 89, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -108,7 +108,7 @@ }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -124,7 +124,7 @@ " rdx[i*n+2] = 1.0\n", " rdx[i*n+3] = np.sin(x[4]*t[i])\n", " rdx[i*n+4] = x[3]*t[i]*np.cos(x[4]*t[i])\n", - " return rdx, inform" + " return inform" ] }, { @@ -136,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -172,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -212,12 +212,12 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -248,7 +248,7 @@ }, { "cell_type": "code", - "execution_count": 94, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -291,12 +291,12 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -319,7 +319,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -336,7 +336,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -350,7 +350,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.9.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, From d00f3a625a7cb9636d692b6e9cd6f0645d1795df Mon Sep 17 00:00:00 2001 From: Andrew Sajo Date: Fri, 4 Mar 2022 10:29:23 +0000 Subject: [PATCH 154/182] Update to new ifaces BXNL (rhs) --- local_optimization/BXNL/notebooks/orbit_ex.ipynb | 8 +++++--- local_optimization/BXNL/notebooks/simple_BXNL.ipynb | 6 +++--- 2 files changed, 8 insertions(+), 6 deletions(-) diff --git a/local_optimization/BXNL/notebooks/orbit_ex.ipynb b/local_optimization/BXNL/notebooks/orbit_ex.ipynb index c761eba..db7919a 100644 --- a/local_optimization/BXNL/notebooks/orbit_ex.ipynb +++ b/local_optimization/BXNL/notebooks/orbit_ex.ipynb @@ -23,7 +23,9 @@ { "cell_type": "code", "execution_count": 1, - "metadata": {}, + "metadata": { + "scrolled": false + }, "outputs": [], "source": [ "import numpy as np\n", @@ -119,7 +121,7 @@ " Simply return rdx[i] = 2r, i = 1, ..., nres.\n", " \"\"\"\n", " rdx[:] = 2.0*np.ones(nres)*x[:]\n", - " return inform" + " return rdx, inform" ] }, { @@ -373,7 +375,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.7.12" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb index 63839e7..2ad9a16 100644 --- a/local_optimization/BXNL/notebooks/simple_BXNL.ipynb +++ b/local_optimization/BXNL/notebooks/simple_BXNL.ipynb @@ -221,7 +221,7 @@ " rdx[i*n+4] = ((d[i] - mu)**2 - sigma**2)/sigma**3 * g\n", " # dg/dAg\n", " rdx[i*n+5] = gaussian(d[i], mu, sigma, 1.0)\n", - " return inform" + " return rdx, inform" ] }, { @@ -396,7 +396,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "4.4421102582032467e-08\n" + "4.4421102582032486e-08\n" ] } ], @@ -537,7 +537,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.7.12" }, "latex_envs": { "LaTeX_envs_menu_present": true, From 56f8fb0f5d5bd341fafef55ec5850e476789995a Mon Sep 17 00:00:00 2001 From: A Date: Thu, 17 Mar 2022 14:07:16 +0000 Subject: [PATCH 155/182] Update python-nag-opt-solvers-links.md --- .../python-nag-opt-solvers-links.md | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 922262b..34431a6 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -7,6 +7,10 @@ https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html + * SQP AS (FD) `e04sr (handle_solve_ssqp)` (Mark 28.3 / 28.4)
+ Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ssqp.html#naginterfaces.library.opt.handle_solve_ssqp
+ Example: https://www.nag.com/numeric/py/nagdoc_latest/_modules/naginterfaces/library/examples/opt/handle_solve_ssqp_ex.html#main
+ + * SQP AS (FD) `e04vh (nlp2_sparse_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp2_sparse_solve.html#naginterfaces.library.opt.nlp2_sparse_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp2_sparse_solve_ex.main
@@ -69,7 +77,7 @@ NOMS solvers are identified with "handle_solve" prefix. Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_ipopt.html#naginterfaces.library.opt.handle_solve_ipopt
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_ipopt_ex.main
- * CG AS (FD) (only bound constraints) `e04kf (handle_solve_bounds_foas)` (also works on dense)
+ * Conjugate Gradient AS (FD) (only bound constraints) `e04kf (handle_solve_bounds_foas)` (also works on dense)
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_bounds_foas.html#naginterfaces.library.opt.handle_solve_bounds_foas
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/FOAS
@@ -79,13 +87,13 @@ NOMS solvers are identified with "handle_solve" prefix. Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_dfno_ex.main
Demo: https://github.com/numericalalgorithmsgroup/NAGPythonExamples/tree/master/local_optimization/DFO
- * AS SQP `e04ug (nlp1_sparse_solve)` + * SQP AS `e04ug (nlp1_sparse_solve)` Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_sparse_solve.html#naginterfaces.library.opt.nlp1_sparse_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_sparse_solve_ex.main
### Dense - * AS SQP (FD) `e04uc (nlp1_solve)`
+ * SQP AS (FD) `e04uc (nlp1_solve)`
Doc: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.nlp1_solve.html#naginterfaces.library.opt.nlp1_solve
Example: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.nlp1_solve_ex.main
From 09bd32dcf514f1a5f2a5269c87f96b056d6a9af6 Mon Sep 17 00:00:00 2001 From: A Date: Thu, 17 Mar 2022 14:12:58 +0000 Subject: [PATCH 156/182] Update python-nag-opt-solvers-links.md --- .../python-nag-opt-solvers-links.md | 18 +++++++++++++++--- 1 file changed, 15 insertions(+), 3 deletions(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 34431a6..41f624b 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -7,9 +7,21 @@ https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/indexes/optimization.html Date: Thu, 17 Mar 2022 14:30:33 +0000 Subject: [PATCH 157/182] Update python-nag-opt-solvers-links.md --- local_optimization/python-nag-opt-solvers-links.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 41f624b..690065c 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -9,7 +9,7 @@ NOMS solvers are identified with "handle_solve" prefix. **Abbreviations used** -|Abb | Description | +|Abbreviation | Description | |--------|--------------| | (FD) | Indicates the solver does not require the user to provide 1st order derivativas and in which case it will use a Finite-Difference method to estimate them | | (no-FD)| Indicates that the solver requires the user to provide derivates| From 261cb3eb48aa4054fb62d11ffeb9412c01d6f42c Mon Sep 17 00:00:00 2001 From: A Date: Thu, 17 Mar 2022 14:41:04 +0000 Subject: [PATCH 158/182] Update python-nag-opt-solvers-links.md --- local_optimization/python-nag-opt-solvers-links.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/local_optimization/python-nag-opt-solvers-links.md b/local_optimization/python-nag-opt-solvers-links.md index 690065c..9175958 100644 --- a/local_optimization/python-nag-opt-solvers-links.md +++ b/local_optimization/python-nag-opt-solvers-links.md @@ -12,7 +12,7 @@ NOMS solvers are identified with "handle_solve" prefix. |Abbreviation | Description | |--------|--------------| | (FD) | Indicates the solver does not require the user to provide 1st order derivativas and in which case it will use a Finite-Difference method to estimate them | -| (no-FD)| Indicates that the solver requires the user to provide derivates| +| (no-FD)| Indicates that the solver requires the user to provide 1st or 2nd order derivatives| | AS | Active-Set Method | DFNO | Derivative-Free Nonlinear Programming | IPM | Interior-Point Method From e03050e58c9db61815bc58d4519a996216a48d9c Mon Sep 17 00:00:00 2001 From: Andrew Date: Mon, 28 Mar 2022 16:02:29 +0100 Subject: [PATCH 159/182] Update to Mark 28.3.0.1 --- .../quantile_linreg_easy.ipynb | 992 +++++---- .../dim2_spline_ts_sctr.ipynb | 1980 ++++++++++------- global_optimization/SQP_multistart.ipynb | 17 +- global_optimization/bnd_mcs_solve.ipynb | 34 +- .../BXNL/notebooks/orbit_ex.ipynb | 4 +- .../BXNL/notebooks/simple_BXNL.ipynb | 4 +- local_optimization/FOAS/rosenbrock2d.ipynb | 1022 ++++++++- multivariate_methods/k-means.ipynb | 8 +- operations_research/nag_rugby_tsm.ipynb | 4 +- roots/Anderson_Acceleration_Poisson.ipynb | 4 +- special_functions/mathieu_functions.ipynb | 10 +- time_series_analysis/cp_pelt.ipynb | 992 +++++---- time_series_analysis/inhom_iema.ipynb | 4 +- 13 files changed, 3408 insertions(+), 1667 deletions(-) diff --git a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb index 308dd71..0671543 100644 --- a/correlation_and_regression_analysis/quantile_linreg_easy.ipynb +++ b/correlation_and_regression_analysis/quantile_linreg_easy.ipynb @@ -188,36 +188,38 @@ "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", "window.mpl = {};\n", "\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", - " alert('Your browser does not have WebSocket support. ' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", "\n", " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", + " var warnings = document.getElementById('mpl-warnings');\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", " }\n", " }\n", "\n", @@ -232,11 +234,11 @@ "\n", " this.image_mode = 'full';\n", "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", "\n", - " $(parent_element).append(this.root);\n", + " parent_element.appendChild(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", @@ -246,285 +248,366 @@ "\n", " this.waiting = false;\n", "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " if (mpl.ratio != 1) {\n", - " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", - " }\n", - " fig.send_message(\"refresh\", {});\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_device_pixel_ratio', {\n", + " device_pixel_ratio: fig.ratio,\n", + " });\n", " }\n", + " fig.send_message('refresh', {});\n", + " };\n", "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", "\n", - " this.imageObj.onunload = function() {\n", + " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", - " }\n", + " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", + "};\n", "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", "\n", - "}\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", "\n", - "mpl.figure.prototype._init_canvas = function() {\n", + "mpl.figure.prototype._init_canvas = function () {\n", " var fig = this;\n", "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", " }\n", "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", + " this.context = canvas.getContext('2d');\n", "\n", - " var backingStore = this.context.backingStorePixelRatio ||\n", - "\tthis.context.webkitBackingStorePixelRatio ||\n", - "\tthis.context.mozBackingStorePixelRatio ||\n", - "\tthis.context.msBackingStorePixelRatio ||\n", - "\tthis.context.oBackingStorePixelRatio ||\n", - "\tthis.context.backingStorePixelRatio || 1;\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", "\n", - " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", "\n", - " var pass_mouse_events = true;\n", + " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", + " if (this.ResizeObserver === undefined) {\n", + " if (window.ResizeObserver !== undefined) {\n", + " this.ResizeObserver = window.ResizeObserver;\n", + " } else {\n", + " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", + " this.ResizeObserver = obs.ResizeObserver;\n", + " }\n", + " }\n", "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", + " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", " });\n", + " this.resizeObserverInstance.observe(canvas_div);\n", "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", " }\n", "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'dblclick',\n", + " on_mouse_event_closure('dblclick')\n", + " );\n", " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", + " canvas_div.addEventListener('wheel', function (event) {\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", - " mouse_event_fn(event);\n", + " on_mouse_event_closure('scroll')(event);\n", " });\n", "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width * mpl.ratio);\n", - " canvas.attr('height', height * mpl.ratio);\n", - " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", "\n", " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", " return false;\n", " });\n", "\n", - " function set_focus () {\n", + " function set_focus() {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", - "}\n", + "};\n", "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", + "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", - " var nav_element = $('
');\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", " }\n", "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", - " // put a spacer in here.\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", " continue;\n", " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", "\n", " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", " });\n", - "}\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", + " el.setAttribute('tabindex', 0);\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", + " } else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", + "};\n", "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", + " if (event.shiftKey && event.which === 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", - "}\n", + "};\n", "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " fig.ondownload(fig, null);\n", - "}\n", - "\n", + "};\n", "\n", - "mpl.find_output_cell = function(html_output) {\n", + "mpl.find_output_cell = function (html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", - " if (data['text/html'] == html_output) {\n", + " if (data['text/html'] === html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", - "}\n", + "};\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", "}\n" ], "text/plain": [ @@ -888,7 +1076,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1078,36 +1266,38 @@ "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", "window.mpl = {};\n", "\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", - " alert('Your browser does not have WebSocket support. ' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", "\n", " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", + " var warnings = document.getElementById('mpl-warnings');\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", " }\n", " }\n", "\n", @@ -1122,11 +1312,11 @@ "\n", " this.image_mode = 'full';\n", "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", "\n", - " $(parent_element).append(this.root);\n", + " parent_element.appendChild(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", @@ -1136,285 +1326,366 @@ "\n", " this.waiting = false;\n", "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " if (mpl.ratio != 1) {\n", - " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", - " }\n", - " fig.send_message(\"refresh\", {});\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_device_pixel_ratio', {\n", + " device_pixel_ratio: fig.ratio,\n", + " });\n", " }\n", + " fig.send_message('refresh', {});\n", + " };\n", "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", "\n", - " this.imageObj.onunload = function() {\n", + " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", - " }\n", + " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", + "};\n", "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", "\n", - "}\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", "\n", - "mpl.figure.prototype._init_canvas = function() {\n", + "mpl.figure.prototype._init_canvas = function () {\n", " var fig = this;\n", "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", " }\n", "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", + " this.context = canvas.getContext('2d');\n", "\n", - " var backingStore = this.context.backingStorePixelRatio ||\n", - "\tthis.context.webkitBackingStorePixelRatio ||\n", - "\tthis.context.mozBackingStorePixelRatio ||\n", - "\tthis.context.msBackingStorePixelRatio ||\n", - "\tthis.context.oBackingStorePixelRatio ||\n", - "\tthis.context.backingStorePixelRatio || 1;\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", "\n", - " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", "\n", - " var pass_mouse_events = true;\n", + " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", + " if (this.ResizeObserver === undefined) {\n", + " if (window.ResizeObserver !== undefined) {\n", + " this.ResizeObserver = window.ResizeObserver;\n", + " } else {\n", + " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", + " this.ResizeObserver = obs.ResizeObserver;\n", + " }\n", + " }\n", "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", + " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", " });\n", + " this.resizeObserverInstance.observe(canvas_div);\n", "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", " }\n", "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'dblclick',\n", + " on_mouse_event_closure('dblclick')\n", + " );\n", " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", + " canvas_div.addEventListener('wheel', function (event) {\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", - " mouse_event_fn(event);\n", + " on_mouse_event_closure('scroll')(event);\n", " });\n", "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width * mpl.ratio);\n", - " canvas.attr('height', height * mpl.ratio);\n", - " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", "\n", " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", " return false;\n", " });\n", "\n", - " function set_focus () {\n", + " function set_focus() {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", - "}\n", + "};\n", "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", + "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", - " var nav_element = $('
');\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", " }\n", "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", - " // put a spacer in here.\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", " continue;\n", " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", "\n", " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", " });\n", - "}\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " if (event.target !== this) {\n", + " // Ignore bubbled events from children.\n", + " return;\n", + " }\n", + " fig.close_ws(fig, {});\n", + "};\n", "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", + " el.setAttribute('tabindex', 0);\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", + " } else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", + "};\n", "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", + " if (event.shiftKey && event.which === 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", - "}\n", + "};\n", "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " fig.ondownload(fig, null);\n", - "}\n", - "\n", + "};\n", "\n", - "mpl.find_output_cell = function(html_output) {\n", + "mpl.find_output_cell = function (html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", - " if (data['text/html'] == html_output) {\n", + " if (data['text/html'] === html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", - "}\n", + "};\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", "}\n" ], "text/plain": [ @@ -936,7 +1124,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -974,7 +1162,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -988,7 +1176,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.8.10" } }, "nbformat": 4, diff --git a/time_series_analysis/inhom_iema.ipynb b/time_series_analysis/inhom_iema.ipynb index d81b735..824705a 100644 --- a/time_series_analysis/inhom_iema.ipynb +++ b/time_series_analysis/inhom_iema.ipynb @@ -1004,7 +1004,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -1018,7 +1018,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.8.10" } }, "nbformat": 4, From 5b57d369eb995e1e1978e6bf0478725ac4cc922c Mon Sep 17 00:00:00 2001 From: Andrew Date: Tue, 29 Mar 2022 18:08:03 +0100 Subject: [PATCH 160/182] Updates for Mk 28.3 --- .../dim2_spline_ts_sctr.ipynb | 2 +- local_optimization/DFO/DFO_noisy.ipynb | 4 +-- local_optimization/FOAS/rosenbrock2d.ipynb | 6 ++--- local_optimization/Modelling/LP_demo.ipynb | 4 +-- .../Modelling/handle_disable_ex.ipynb | 2 +- .../Modelling/production_planning.ipynb | 27 +++++++------------ 6 files changed, 19 insertions(+), 26 deletions(-) diff --git a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb index 669a34c..1defa4a 100644 --- a/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb +++ b/curve_and_surface_fitting/dim2_spline_ts_sctr.ipynb @@ -1076,7 +1076,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" diff --git a/local_optimization/DFO/DFO_noisy.ipynb b/local_optimization/DFO/DFO_noisy.ipynb index 289e7d6..83f36a2 100644 --- a/local_optimization/DFO/DFO_noisy.ipynb +++ b/local_optimization/DFO/DFO_noisy.ipynb @@ -1530,7 +1530,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -1544,7 +1544,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.8.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/FOAS/rosenbrock2d.ipynb b/local_optimization/FOAS/rosenbrock2d.ipynb index a79c808..ff28b88 100644 --- a/local_optimization/FOAS/rosenbrock2d.ipynb +++ b/local_optimization/FOAS/rosenbrock2d.ipynb @@ -28,7 +28,8 @@ "outputs": [], "source": [ "from naginterfaces.base import utils\n", - "from naginterfaces.library import opt" + "from naginterfaces.library import opt\n", + "import numpy as np" ] }, { @@ -308,7 +309,6 @@ } ], "source": [ - "import numpy as np\n", "from naginterfaces.base.opt import handle_set_get_real\n", "mult = np.empty(2*nvar)\n", "mult.fill(0.)\n", @@ -1355,7 +1355,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" diff --git a/local_optimization/Modelling/LP_demo.ipynb b/local_optimization/Modelling/LP_demo.ipynb index 4835a32..e0e6b4c 100644 --- a/local_optimization/Modelling/LP_demo.ipynb +++ b/local_optimization/Modelling/LP_demo.ipynb @@ -264,7 +264,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -278,7 +278,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.8.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/Modelling/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb index 6c01075..123446f 100644 --- a/local_optimization/Modelling/handle_disable_ex.ipynb +++ b/local_optimization/Modelling/handle_disable_ex.ipynb @@ -350,7 +350,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/Modelling/production_planning.ipynb b/local_optimization/Modelling/production_planning.ipynb index d8d3d63..00804a4 100644 --- a/local_optimization/Modelling/production_planning.ipynb +++ b/local_optimization/Modelling/production_planning.ipynb @@ -32,10 +32,10 @@ "- a unit of $A_1$ uses 6 square metres of packing material while a unit of $A_2$ uses 10 square metres; 6000 square metres of packing materials are available each day;\n", "- production of $A_2$ is limited to 100 units per day.\n", "\n", - "Note that since the chemicals are considered fluid, the quantities $x_1$ and $x_2$ are not limited to integer values.\\\\\n", + "Note that since the chemicals are considered fluid, the quantities $x_1$ and $x_2$ are not limited to integer values.\n", "\n", "The problem can be formulated as a linear program:\n", - "\\vspace{0.1cn}\n", + "\n", "\\begin{equation*}\n", "\\begin{array}{lll}\n", "\\underset{x\\in\\Re^n}{\\mbox{maximize}} & 2x_1+4.5x_2&\\\\[0.6ex]\n", @@ -43,14 +43,14 @@ " & 6x_1+10x_2 \\leq 6000, & \\text{ (packaging material constraint)} \\\\[0.6ex]\n", " & 40x_1+80x_2 \\leq 16000, & \\text{ (transport constraint)} \\\\[0.6ex]\n", " & 0 \\leq x_1, & \\text{ (capacity constraint)} \\\\[0.6ex]\n", - " & 0 \\leq x_1 \\leq 100 & \\text{ (capacity constraint)} \\\\[0.6ex]\n", + " & 0 \\leq x_2 \\leq 100 & \\text{ (capacity constraint)} \\\\[0.6ex]\n", "\\end{array}\n", "\\end{equation*}" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -131,7 +131,7 @@ "- production of $A_3$ is limited to 50 units per day.\n", "\n", "The problem becomes:\n", - "\\vspace{0.1cn}\n", + "\n", "\\begin{equation*}\n", "\\begin{array}{lll}\n", "\\underset{x\\in\\Re^n}{\\mbox{maximize}} & 2x_1+4.5x_2+7x_3&\\\\[0.6ex]\n", @@ -147,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -205,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -249,24 +249,17 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "opt.handle_free(handle)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -280,7 +273,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.8.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, From 8900d126cd3324a9b048afd32bbf720132fef13d Mon Sep 17 00:00:00 2001 From: shuanghuab Date: Thu, 18 Aug 2022 23:34:16 +0100 Subject: [PATCH 161/182] add notebook for nonlinear data fitting --- local_optimization/NLDF/Readme.md | 22 + .../NLDF/data_fitting_robustness.ipynb | 590 ++++++++++++++++++ local_optimization/NLDF/images/nldf_comp.png | Bin 0 -> 68254 bytes local_optimization/NLDF/images/nldf_lossf.png | Bin 0 -> 65515 bytes local_optimization/NLDF/nldf_contour.png | Bin 0 -> 136801 bytes 5 files changed, 612 insertions(+) create mode 100644 local_optimization/NLDF/Readme.md create mode 100644 local_optimization/NLDF/data_fitting_robustness.ipynb create mode 100644 local_optimization/NLDF/images/nldf_comp.png create mode 100644 local_optimization/NLDF/images/nldf_lossf.png create mode 100644 local_optimization/NLDF/nldf_contour.png diff --git a/local_optimization/NLDF/Readme.md b/local_optimization/NLDF/Readme.md new file mode 100644 index 0000000..3551ef4 --- /dev/null +++ b/local_optimization/NLDF/Readme.md @@ -0,0 +1,22 @@ +[![NAG Logo](../../nag_logo.png)](https://www.nag.com) + +# General Nonlinear Data-Fitting (NLDF) +[[`handle_solve_nldf`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_nldf.html) | [`e04gnf`](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04gnf.html) | [`e04gnc`](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/e04/e04gnc.html) ] + +Data fitting/calibration is widespread. Commonly used in by those needing to fit a mathematical model to an experimental data set. Application use is found, but not limited to, econometrics and finance, image processing, civil engineering, mechanical engineering, and astronomy. Widely used methods, such as the [least squares (LSQ) method](../BXNL/Readme.md), don’t always capture the underlying data distribution. When the assumptions are unrealistic or the data set contains various level of outliers, the need for robustness appears. + +Figure 1 shows the shapes of different loss functions and their performance in dealing with a data set that has outliers. Clearly in this case, the Cauchy loss function provides the best fit, and the model using infinity norm is heavily influenced by the outliers. + + + + +
Optimal orbit from data orbit measurements. + Weighted optimal orbit from data orbit measurements.
+ +**Figure 1.** Left: plot of various loss functions. Right: fitting results via various loss functions + +Within the [NAG® Library](https://www.nag.co.uk/content/nag-library) is a [nonlinear data fitting solver](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_nldf.html), which encapsulates a selection of calibration models (the loss function and regularization types), such as Least Absolute Value and Cauchy, making it a great starting point for the journey of exploring the nonlinear nature of your experimental data. In addition, the models can include general constraints such as bound, linear, quadratic, and nonlinear constraints. The switching between different types of models and regularizations is very easy. + +See the notebook below for the usage of [`handle_solve_nldf`](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_nldf.html) and a further discussion on the performance of loss functions regarding robustness. + +* [Loss functions and robustness in data-fitting](data_fitting_robustness.ipynb) diff --git a/local_optimization/NLDF/data_fitting_robustness.ipynb b/local_optimization/NLDF/data_fitting_robustness.ipynb new file mode 100644 index 0000000..1a47299 --- /dev/null +++ b/local_optimization/NLDF/data_fitting_robustness.ipynb @@ -0,0 +1,590 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c17c4002", + "metadata": {}, + "source": [ + "# Loss Function and Robustness in Data-Fitting" + ] + }, + { + "cell_type": "markdown", + "id": "a2ef8975", + "metadata": {}, + "source": [ + "## Technical Setup\n", + "\n", + "### NAG Library\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 28.5 or newer) and a license key. You can find the software and request key from our website here: https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux\n", + "\n", + "### Correct Rendering of this notebook\n", + "\n", + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter, it may be because you have not installed this extension. See at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html for further information." + ] + }, + { + "cell_type": "markdown", + "id": "d7c29645", + "metadata": {}, + "source": [ + "## Introduction\n", + "Fitting a non-linear model to data is typically modelled as a minimisation problem, where the objective function serves as a measurement of the quality of the model’s fit to data, depending on our parameters. A general model involves summing over our data points,\n", + "\n", + "$$\n", + "\\underset{x \\in \\mathbb{R}^{n_{\\text{var}}}}{\\text{minimize}} ~f(x) =\\sum_{i=1}^{n_{\\text{res}}} \\chi(r_i(x)),\n", + "$$\n", + "\n", + "where $x$ is a vector holding our model parameters, of which there are $n_\\text{var}$. We have $n_\\text{res}$ data points, and $r_i(x)= y_i - \\varphi(t_i;x), \\quad i = 1,...,n_\\text{res}$ is the $i^{th}$ residual, equal to the difference between the observed and predicted values of the independent variable at time $t_i$, denoted $y_i$ and $\\varphi(t_i;x)$ respectively. The loss function $\\chi$ has desirable properties such as being bounded from below, and increasing with $|r_i\\left(x\\right)|$. Summing over all data points then, the objective function will be small when the model fits the whole dataset well, which is what we want.\n", + "\n", + "There are plenty of choices for function $\\chi$, so how does our choice of loss function affect the fit we end up with? One important consideration is robustness. If some of the observed data points are far from the fitted model, how can we control the influence of those outliers? A robust loss function is one which doesn’t get thrown off easily by outliers in the data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "475d193d", + "metadata": {}, + "outputs": [], + "source": [ + "# import all packages necessary for notebook\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt" + ] + }, + { + "cell_type": "markdown", + "id": "edeb12b1", + "metadata": {}, + "source": [ + "## Single-outlier example\n", + "\n", + "To investigate the robustness aspect, here’s a toy dataset which is generated from $\\sin(t)$ and has an outlier at $t=1.5$, which is generated by $5\\sin(t)$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f4114a11", + "metadata": {}, + "outputs": [], + "source": [ + "# create data set\n", + "t = np.linspace(0.5, 2.5, num=21)\n", + "y = np.sin(t)\n", + "y[10] = 5*np.sin(t[10])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1f2e8656", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig1 = plt.plot(t,y,'*b')" + ] + }, + { + "cell_type": "markdown", + "id": "2fbc076c", + "metadata": {}, + "source": [ + "We will fit it with a model \n", + "\n", + "$$\n", + "\\label{model}\n", + "\\varphi(t;x)\\ =x_1\\sin(x_2t)\n", + "$$\n", + "\n", + "using a variety of loss functions provided by NAG’s data-fitting solver **handle_solve_nldf** (`e04gn`), which constructs the appropriate objective function for us." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "693292f1", + "metadata": {}, + "outputs": [], + "source": [ + "# create a handle for the model\n", + "nvar = 2\n", + "handle = opt.handle_init(nvar=nvar)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b7e8db17", + "metadata": {}, + "outputs": [], + "source": [ + "# register residuals structure\n", + "nres = 21\n", + "opt.handle_set_nlnls(handle, nres)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "685b0186", + "metadata": {}, + "outputs": [], + "source": [ + "# define the residual callback function and its gradient\n", + "def lsqfun(x, nres, inform, data):\n", + " rx = np.zeros(nres,dtype=float)\n", + " t = data[\"t\"]\n", + " y = data[\"y\"]\n", + " for i in range(nres):\n", + " rx[i] = (y[i] - x[0]*np.sin(x[1]*t[i]))\n", + " \n", + " return rx, inform\n", + "\n", + "def lsqgrd(x, nres, rdx, inform, data):\n", + " t = data[\"t\"]\n", + " nvar = len(x)\n", + " for i in range(nres):\n", + " rdx[i*nvar] = (-np.sin(x[1]*t[i]))\n", + " rdx[i*nvar + 1] = (-t[i]*x[0]*np.cos(x[1]*t[i]))\n", + "\n", + " return inform" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "296aeb8e", + "metadata": {}, + "outputs": [], + "source": [ + "# create the data structure to be passed to the solver\n", + "data = {}\n", + "data[\"t\"] = t\n", + "data[\"y\"] = y" + ] + }, + { + "cell_type": "markdown", + "id": "ab256fc3", + "metadata": {}, + "source": [ + "### Start with $l_2$-norm loss function - Example 1\n", + "Starting with one of the most common loss functions, the $l_2$-norm, we form the problem\n", + "\n", + "$$\n", + "\\underset{x \\in \\mathbb{R}^{2}}{\\text{minimize}}~f(x) =\\sum_{i=1}^{21} r_i(x)^2\n", + "$$\n", + "\n", + "which is just least squares regression. $l_2$-norm loss has low robustness against outliers, so we should expect that the solution will be affected heavily by this one outlier. Let’s solve from a starting point at\n", + "\n", + "$$\n", + "x\\ =\\ (2.1,1.4)\n", + "$$\n", + "\n", + "to see what this outlier does to the minimum." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "dca06b31", + "metadata": {}, + "outputs": [], + "source": [ + "# set loss function to l2-norm and printing options\n", + "for option in [\n", + " 'NLDF Loss Function Type = L2',\n", + " 'Print Level = 1',\n", + " 'Print Options = No',\n", + " 'Print solution = Yes'\n", + "]:\n", + " opt.handle_opt_set (handle, option)\n", + "\n", + "# use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "1dd02a32", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GN, Nonlinear Data-Fitting\n", + " Status: converged, an optimal solution found\n", + " Final objective value 1.470963E+01\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf 1.30111E+00 inf\n", + " 2 -inf 1.06956E+00 inf\n" + ] + } + ], + "source": [ + "# set initial guess and solve\n", + "x = [2.1, 1.4]\n", + "soln1 = opt.handle_solve_nldf(\n", + " handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "fbd3f796", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate fitted data using the optimal parameters\n", + "y_l2_fitted = soln1.x[0]*np.sin(soln1.x[1]*t)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "fbef37c2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the fitted curve\n", + "plt.title(\"Fitted with L2 Loss Function\")\n", + "plt.plot(t,y,'*b')\n", + "plt.plot(t,y_l2_fitted)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "32da7f42", + "metadata": {}, + "source": [ + "The single outlier was able to disrupt the fit, since $l_2$-norm loss makes outliers contribute heavily to the objective function and search direction." + ] + }, + { + "cell_type": "markdown", + "id": "6241b78c", + "metadata": {}, + "source": [ + "### Try $l_1$-norm loss function - Example 2\n", + "Using $l_1$-norm loss gives us the problem\n", + "\n", + "$$\n", + "\\underset{x \\in \\mathbb{R}^{2}}{\\text{minimize}}~f(x) =\\sum_{i=1}^{21} |r_i(x)|,\n", + "$$\n", + "\n", + "which is more robust against outliers. This means if some large portion of the data is well-fitted by some solution $x^\\ast$, there is likely to be a local minimum very close to $x^\\ast$ which is relatively undisturbed by the remaining data that is outlying to the solution $x^\\ast$. Here’s the solution, again starting at $x=(2.1,1.4)$, using $l_1$ loss." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "07e8bf50", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GN, Nonlinear Data-Fitting\n", + " Status: converged, an optimal solution found\n", + " Final objective value 3.989980E+00\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf 1.00000E+00 inf\n", + " 2 -inf 1.00000E+00 inf\n" + ] + } + ], + "source": [ + "# change loss function to l1-norm and solve\n", + "opt.handle_opt_set(handle, 'NLDF Loss Function Type = L1')\n", + "soln2 = opt.handle_solve_nldf(\n", + " handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "93472886", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate fitted data using the optimal parameters\n", + "y_l1_fitted = soln2.x[0]*np.sin(soln2.x[1]*t)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a1af726a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the fitted curve\n", + "plt.title(\"Fitted with L1 Loss Function\")\n", + "plt.plot(t,y,'*b')\n", + "plt.plot(t,y_l1_fitted)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5e02e4f9", + "metadata": {}, + "source": [ + "Clearly, this is a much better fit for most of the data, and the outlier hasn’t dragged the model off most of the data." + ] + }, + { + "cell_type": "markdown", + "id": "23ae855a", + "metadata": {}, + "source": [ + "## The trade-off of a loss function\n", + "\n", + "We can reuse the handle, the residual function (and gradient). Just changing the data and options, we can demonstrate more principles to consider regarding loss functions.\n", + "\n", + "There is a danger in choosing a very robust loss function. During an iterative optimization process, a loss function which is robust against outliers will usually prefer the data which is close to the current model. This means that if the algorithm finds local minima of the objective function, the search can fall into a local minimum when the model fits some subset of the data very well but fits the majority of the data very badly.\n", + "\n", + "To illustrate this, here’s a new dataset which we will try to fit with the same model, again starting at $x= (2.1,1.4)$. Most of the data was generated by $5\\sin(t)$, with the 3 data points at either end being generated by $\\sin(t)$." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "76ff9fcb", + "metadata": {}, + "outputs": [], + "source": [ + "# create the data set\n", + "y_new = y\n", + "for i in range(3,18):\n", + " y_new[i] = 5*np.sin(t[i])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "a7b7c87e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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6KUnPSbpu0eMXSbq4cvsxSTs6rGvLwt9PxT/vf5TbrlYbaKuucvmPqxjHvqir7VX+7p+T9Jll1um8jdWsq/M2VrOu1tpYY42xxi+6U8We0uclfbp8bJ+kj5a3/1zS0+Uv8Yikd1ee+5vlH+Y5Sb/RZV3l/T+V9BeLnnedpONlvccl3d5wXfdJOiXpf1SMad0uaY+kPZWGs7+s+7ikyY6210p13SPp+5KOlZfZ8vGrym31ZPl3/nTHdf1epX3NVP/Je7WBruoq17lN0v2Lntf29rpexXjuU5W/1c5ht7GadXXexmrW1Vob4xByAEiOIxMBIDmCGgCSI6gBIDmCGgCSI6gBIDmCGgCSI6gBILn/A4RgDmxmXGPFAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,y_new,'*b')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "9cc534b7", + "metadata": {}, + "outputs": [], + "source": [ + "# recreate the data structure to be passed to the solver\n", + "data_new = {}\n", + "data_new[\"t\"] = t\n", + "data_new[\"y\"] = y_new" + ] + }, + { + "cell_type": "markdown", + "id": "7e721f62", + "metadata": {}, + "source": [ + "We will fit this data set using 3 different loss functions with the same model $\\varphi(t;x)$ defined in (\\ref{model}) each time and discuss the results under the plots all at once below." + ] + }, + { + "cell_type": "markdown", + "id": "0caf334e", + "metadata": {}, + "source": [ + "### Fit model with the $l_2$-norm, $l_1$-norm and Arctan loss function" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "fa815c5c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "loss_functions = ['L2', 'L1', 'ATAN']\n", + "\n", + "# turn off printing of solver log\n", + "opt.handle_opt_set(handle, 'print file = -1')\n", + "\n", + "# solve using 3 different loss functions\n", + "for lfunc in loss_functions:\n", + " \n", + " # set option for loss function and solve\n", + " opt.handle_opt_set(handle, 'NLDF Loss Function Type =' + lfunc)\n", + " soln = opt.handle_solve_nldf(\n", + " handle, lsqfun, lsqgrd, x, nres, data=data_new, io_manager=iom)\n", + " # plot fitted curve\n", + " plt.plot(t, soln.x[0]*np.sin(soln.x[1]*t), label=lfunc)\n", + "\n", + "# plot data points \n", + "plt.plot(t,y_new,'*b')\n", + "plt.title(\"Fitted with Various Loss Functions\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "eed845f1", + "metadata": {}, + "source": [ + "### Fitted Models and Contour Plots" + ] + }, + { + "cell_type": "markdown", + "id": "49260d6b", + "metadata": {}, + "source": [ + "In the first row of plots, the data is fitted using $l_2$-norm loss, $l_1$-norm loss, and $\\arctan$ loss. Shown below each is the contour plot of the objective function value, where the black circles represent the parameters used to generate the data, the cyan circles represents the starting point for the solver, and the cyan wedges represent the optimized solution found by the solver.\n", + "\n", + "![Contour](nldf_contour.png)\n", + "\n", + "In the $l_2$-norm case in the left column, the outliers generated by $\\sin(t)$ have pulled the optimal solution away from $x = (5,1)$. The contour plot for $l_2$-norm loss indicates that we don’t have to worry too much about what starting point to use, since there are no local minima in the region displayed, other than global best solution.\n", + "\n", + "The behaviour of the solver is quite different when using an extremely robust loss function like $\\arctan$ loss, which looks like\n", + "\n", + "$$\n", + "\\underset{x \\in \\mathbb{R}^{2}}{\\text{minimize}} ~ f(x) =\\sum_{i=1}^{21} \\text{arctan}(r_i(x)^2)\n", + "$$\n", + "\n", + "The fitted model and corresponding contour plot for the $\\arctan$ case are in the middle. Here, there are eight local minima in the contour plot for $\\arctan$ loss, with seven of them being substantially worse solutions than the global minimum, and it is one of these we’ve converged to. Therefore, in this case the selection of initial estimation of the parameters is much more important.\n", + "\n", + "The model fitted with $l_1$-norm loss and the corresponding contour plot are in the right column. Looking at the contour plot, there are still a few local minima that do not correspond to the optimal solution, but the starting point of $x = (2.1,1.4)$ still converges to the global minimum, which lies at\n", + "$x = (5,1)$, meaning the part of the dataset generated from $\\sin(t)$ is effectively being ignoring. From the plots of the loss functions, we can see that $l_1$-norm loss is more robust than $l_2$-norm loss but less so than $\\arctan$ loss. \n", + "\n", + "So, what has happened in each case is: using $l_2$-norm loss, we move to the global minimum which is affected by the whole dataset. Using $l_1$-norm loss, we move to the global minimum which fits most of the data very well and ignores a small portion, treating them as outliers. Using $\\arctan$ loss we move to a local minimum which ignores a large portion of the data (treating them as outliers) and fits a small amount of data very well.\n", + "\n", + "## Conclusion\n", + "\n", + "The lesson here is that the same thing that makes a loss function robust – ignoring data that lies far from the current model to some degree – can populate the search space with local minima where the model predicts some of the data well and ignores most of it. In extreme cases like arctan loss, if the starting point fits some of the data very well, the model will likely just be optimized for that portion of the data, even if it is a small portion of the whole dataset. It is therefore important to try a variety of loss functions and stating points when setting up a data-fitting problem, since these will affect both the optimal solution, as well as how easily an optimal solution is found." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.9.13 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": 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zui#b{?iZfew;yylGL*~f_ysoe#Q4fff!2Q9vJcvTepKEp%?iJV!Ofrlz} z991V|mVUT6SeOlxLy1wGa?#~Hwrl2ONK?VciV7#e23ZouPw!Qww^7qL)q+!#-OxhI zW#wjv<-8<>IxpaHd%mK12}EmZ3>UIiH=_{euOf*d5>>v1D$jw>pn0a*)TzQ(hF!|r zF{rEDHa4oC%AoCAYMb!j?i;%>Rc>jICJc)#GJ`hFgeM{Ojp^y%ucn#`Pu)#;o^M;z zXP>9xG?21)-UP)t-sziB`+U9AcMGAqZgterddJ?0_o(nn rVNVr%2JuQ^FIViPO|KOG*E@(i>E->8Kj2StSv1 Date: Fri, 19 Aug 2022 21:59:28 +0100 Subject: [PATCH 162/182] change typo and fix equation ref --- local_optimization/NLDF/data_fitting_robustness.ipynb | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/local_optimization/NLDF/data_fitting_robustness.ipynb b/local_optimization/NLDF/data_fitting_robustness.ipynb index 1a47299..5176de2 100644 --- a/local_optimization/NLDF/data_fitting_robustness.ipynb +++ b/local_optimization/NLDF/data_fitting_robustness.ipynb @@ -16,7 +16,7 @@ "## Technical Setup\n", "\n", "### NAG Library\n", - "To run this notebook, you will need to install the NAG Library for Python (Mark 28.5 or newer) and a license key. You can find the software and request key from our website here: https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 28.5 or newer) and a license key. You can find the software and request a license key from our website here: https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux\n", "\n", "### Correct Rendering of this notebook\n", "\n", @@ -108,7 +108,6 @@ "We will fit it with a model \n", "\n", "$$\n", - "\\label{model}\n", "\\varphi(t;x)\\ =x_1\\sin(x_2t)\n", "$$\n", "\n", @@ -452,7 +451,7 @@ "id": "7e721f62", "metadata": {}, "source": [ - "We will fit this data set using 3 different loss functions with the same model $\\varphi(t;x)$ defined in (\\ref{model}) each time and discuss the results under the plots all at once below." + "We will fit this data set using 3 different loss functions with the same model $\\varphi(t;x)$ each time and discuss the results under the plots all at once below." ] }, { From 8b08e6d72676081f3c4350e1f25a617fba790692 Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Tue, 23 Aug 2022 15:50:48 -0500 Subject: [PATCH 163/182] Update data_fitting_robustness.ipynb edited subtitles and links --- .../NLDF/data_fitting_robustness.ipynb | 24 +++++++++++++------ 1 file changed, 17 insertions(+), 7 deletions(-) diff --git a/local_optimization/NLDF/data_fitting_robustness.ipynb b/local_optimization/NLDF/data_fitting_robustness.ipynb index 5176de2..6302b19 100644 --- a/local_optimization/NLDF/data_fitting_robustness.ipynb +++ b/local_optimization/NLDF/data_fitting_robustness.ipynb @@ -15,12 +15,12 @@ "source": [ "## Technical Setup\n", "\n", - "### NAG Library\n", - "To run this notebook, you will need to install the NAG Library for Python (Mark 28.5 or newer) and a license key. You can find the software and request a license key from our website here: https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux\n", + "### NAG Library install\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 28.5 or newer) and a license key. You can find the software and request a license key from our website here: [Getting Started with NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux)\n", "\n", - "### Correct Rendering of this notebook\n", + "### Correct rendering of this notebook\n", "\n", - "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter, it may be because you have not installed this extension. See at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html for further information." + "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter, it may be because you have not installed this extension. See at [nbextensions - LATEX for Jupyter notebooks](https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html) for further information." ] }, { @@ -538,13 +538,23 @@ "\n", "## Conclusion\n", "\n", - "The lesson here is that the same thing that makes a loss function robust – ignoring data that lies far from the current model to some degree – can populate the search space with local minima where the model predicts some of the data well and ignores most of it. In extreme cases like arctan loss, if the starting point fits some of the data very well, the model will likely just be optimized for that portion of the data, even if it is a small portion of the whole dataset. It is therefore important to try a variety of loss functions and stating points when setting up a data-fitting problem, since these will affect both the optimal solution, as well as how easily an optimal solution is found." + "The lesson here is that the same thing that makes a loss function robust – ignoring data that lies far from the current model to some degree – can populate the search space with local minima where the model predicts some of the data well and ignores most of it. In extreme cases like arctan loss, if the starting point fits some of the data very well, the model will likely just be optimized for that portion of the data, even if it is a small portion of the whole dataset. It is therefore important to try a variety of loss functions and stating points when setting up a data-fitting problem, since these will affect both the optimal solution, as well as how easily an optimal solution is found.\n", + "\n", + "[Learn more about the NAG Library](https://www.nag.com/content/nag-library)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d00b4ddf", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.13 64-bit", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -558,7 +568,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.13" + "version": "3.9.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, From 2214ce48d8264f835dd91bfcd7048a7b746c2b8d Mon Sep 17 00:00:00 2001 From: shuanghuab Date: Thu, 12 Jan 2023 23:21:42 +0000 Subject: [PATCH 164/182] code for dose response analysis blog --- local_optimization/NLDF/dose_resp.dat | 42 +++ local_optimization/NLDF/dose_resp.ipynb | 371 ++++++++++++++++++++++++ 2 files changed, 413 insertions(+) create mode 100644 local_optimization/NLDF/dose_resp.dat create mode 100644 local_optimization/NLDF/dose_resp.ipynb diff --git a/local_optimization/NLDF/dose_resp.dat b/local_optimization/NLDF/dose_resp.dat new file mode 100644 index 0000000..44658fc --- /dev/null +++ b/local_optimization/NLDF/dose_resp.dat @@ -0,0 +1,42 @@ +0.0005874,7.327 +0.0005874,-6.043 +0.0005874,-0.428 +0.002937,3.110 +0.002937,-2.340 +0.002937,3.103 +0.01468,-11.981 +0.01468,-4.885 +0.01468,-0.566 +0.03283,-4.475 +0.03283,-5.747 +0.03283,-1.660 +0.07341,-4.922 +0.07341,-4.183 +0.07341,-0.981 +0.1642,6.090 +0.1642,-10.287 +0.1642,-1.919 +0.3670,-11.767 +0.3670,-5.345 +0.3670,-7.134 +0.8207,-3.393 +0.8207,-2.099 +0.8207,-4.490 +1.835,-6.812 +1.835,-5.808 +1.835,-9.666 +4.103,-0.600 +4.103,-5.707 +4.103,-4.203 +9.175,4.313 +9.175,-8.110 +9.175,0.388 +20.52,-10.838 +20.52,-22.657 +20.52,3.820 +45.87,-34.218 +45.87,-30.895 +45.87,-23.929 +91.74,-30.911 +91.74,-44.233 +91.74,-36.776 \ No newline at end of file diff --git a/local_optimization/NLDF/dose_resp.ipynb b/local_optimization/NLDF/dose_resp.ipynb new file mode 100644 index 0000000..b57f9bf --- /dev/null +++ b/local_optimization/NLDF/dose_resp.ipynb @@ -0,0 +1,371 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bf21964c", + "metadata": {}, + "source": [ + "# Modelling dose–response relationships using data fitting\n", + "\n", + "The following is the Python code used to fit a nonlinear regression model to dose–response data of a chemical taken from the US National Toxicology Program library." + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "793e1544", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import warnings\n", + "from naginterfaces.library import opt\n", + "from naginterfaces.base import utils" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "bacb5e9b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# read in the data\n", + "df = pd.read_csv('dose_resp.dat', header=None) \n", + "data = df.values\n", + "t, y = data[:, 0], data[:, 1]\n", + "\n", + "# plot input vs output\n", + "plt.scatter(t, y, marker='*', color='b')\n", + "plt.xlabel(r\"Compound concentration ($\\mu M$)\")\n", + "plt.ylabel(\"Percent activity\")\n", + "plt.title(\"Dose–response data\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "82510304", + "metadata": {}, + "source": [ + "## Fit the model with the good starting point:" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "id": "061e8555", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " E04GN, Nonlinear Data-Fitting\n", + " Status: converged, an optimal solution found\n", + " Final objective value 1.219791E+03\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -inf -3.81844E+01 inf\n", + " 2 -inf -3.36193E+00 inf\n", + " 3 -inf 3.25418E+01 inf\n", + " 4 -inf -3.39512E+00 inf\n" + ] + } + ], + "source": [ + "# create a handle for the model\n", + "nvar = 4\n", + "handle = opt.handle_init(nvar=nvar)\n", + "\n", + "# register residual structure\n", + "nres = len(t)\n", + "opt.handle_set_nlnls(handle, nres)\n", + "\n", + "# define the residual callback function\n", + "def lsqfun(x, nres, inform, data):\n", + " rx = np.zeros(nres, dtype=float)\n", + " t = data[\"t\"]\n", + " y = data[\"y\"]\n", + " \n", + " # fit the hill function to the data\n", + " for i in range(nres):\n", + " rx[i] = (y[i] - (x[0] + ((x[1] - x[0]) / (1 + (x[2] / t[i])**x[3]))))\n", + " \n", + " return rx, inform\n", + "\n", + "# define the residual gradient\n", + "def lsqgrd(x, nres, rdx, inform, data):\n", + " t = data[\"t\"]\n", + " nvar = len(x)\n", + "\n", + " for i in range(nres):\n", + " rdx[i*nvar] = -1 + (1 / (1 + (x[2] / t[i])**x[3]))\n", + " rdx[i*nvar + 1] = -(1 / (1 + (x[2] / t[i])**x[3]))\n", + " rdx[i*nvar + 2] = (x[1] - x[0]) * ((x[3] * x[2]**(x[3] - 1)) / (t[i]**x[3] * (1 + (x[2]**x[3] / t[i]**x[3]))**2))\n", + " rdx[i*nvar + 3] = (x[1] - x[0]) * np.log((x[2] / t[i])) * (x[2] / t[i])**x[3] * (1 / (1 + (x[2] / t[i])**x[3])**2)\n", + " \n", + " return inform\n", + "\n", + "# create the data structure to be passed to the solver\n", + "data = {}\n", + "data[\"t\"] = t\n", + "data[\"y\"] = y\n", + "\n", + "# set loss function to l2-norm and printing options\n", + "for option in [\n", + " 'NLDF Loss Function Type = L2',\n", + " 'Print Level = 1',\n", + " 'Print Options = No',\n", + " 'Print solution = Yes',\n", + " ]:\n", + " opt.handle_opt_set (handle, option)\n", + "\n", + "# mute warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "# use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)\n", + "\n", + "# set initial guess and solve\n", + "x = [-40., -5., 30., -5.]\n", + "\n", + "sol = opt.handle_solve_nldf(handle, lsqfun, lsqgrd, x, nres,data=data, io_manager=iom)" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "92bc7d4d", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot result from NLS\n", + "plt.title(\"Dose–response curves\")\n", + "plt.plot(t, y, '*b')\n", + "dose = np.linspace(0.0005874, 91.74, 1000)\n", + "resp = sol.x[0] + ((sol.x[1] - sol.x[0]) / (1 + (sol.x[2] / dose)**sol.x[3]))\n", + "plt.plot(dose, resp, label='L2')\n", + "\n", + "# fit all loss functions and plot results\n", + "# loss function types\n", + "lossfuns = {'HUBER', 'L1', 'LINF', 'CAUCHY', 'ATAN', 'SMOOTHL1', 'QUANTILE'}\n", + "\n", + "# turn off log printing\n", + "opt.handle_opt_set (handle, 'Print File = -1')\n", + "\n", + "for lossfun in lossfuns:\n", + " \n", + " # set option for the loss function\n", + " opt.handle_opt_set(handle, 'NLDF Loss Function Type = ' + lossfun)\n", + " \n", + " # call the solver\n", + " sol = opt.handle_solve_nldf(handle, lsqfun, lsqgrd, x, nres, data=data, io_manager=iom)\n", + " \n", + " # calculate response using fitted parameters\n", + " resp = sol.x[0] + ((sol.x[1] - sol.x[0]) / (1 + (sol.x[2] / dose)**sol.x[3]))\n", + " \n", + " # plot curve\n", + " plt.plot(dose, resp, label=lossfun)\n", + "\n", + "# show the plot\n", + "plt.xlabel(r\"Compound concentration ($\\mu M$)\")\n", + "plt.ylabel(\"Percent activity\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "937d3904", + "metadata": {}, + "source": [ + "## Fit the model with the naive starting point and different regularisation functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "839d5752", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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Had0kES2K81tnDdLGREZtGuynNrHBfqogwSM0//WnNGhYWHJndCB3PdtAPcaEVl340RpNqvN+xmy1EsCqPSvJXV3IwX3OjXBxiQXkHo5n5YFPeXj1DGS1ICIIx07nPn4FKz/pw8CRX9D/rrcRBI84eda7jUc8JHgSSI1PJSUhxZnGp5CakMpxScfRNLUpTVOa0jCpIVJWXx7GxKjk5GR2795N48aN7W8jCFSV3bt3k5ycXKX9YjY5pKRAXt7pxywrOpIIFLJnyxG2/vQJxXg713Cms4cvprggqWT7FW/3ZcXbffEk5HPB1NNLtvc+CkTJRcmn/KwdD7QkgfYk0p5ETpAkukkyrUl0/jBK/jjcaaDzCSmQ2gTqNYGmHSGjF6S1rNJ7ZEwkZGZmkp2dTXW74jf+kpOTj7kCKhAxmxzKK2V5RFh/65NIcab7dev2vQRse+S3/OG13/D28r4cPpJMSmIel3f/jEev/g8tCr3XvmrJCUScaRHKYYrJBQ5TzB6K+VmK2SVF7KKYLVLERsnjMzlEgXuIxip0L47nvKJEzimKJw2PT9B6zMT3nF5ScAjJ/Rk5klOyrCijN0dO+x2FJ15Uds+Dplao+7+mhaatWle+mQEgIU5IivdvN62pmG2Q3rYNTjoJDhw4eo+DL4kros3Y9/2W7/7gFHJWtIG4YijyUL/bjzTuH6zrjYvwJP5MXOom4lI2EVdvPZ6EA6h6KDrUgYK9p1GYcxLOsNqBSSafTvITp3vWcFXcAo73bGN2UR9+XzCCPJIqP4AxJqqNPPd47hl4UrX2rahBOiZLDk6VkneudGJQzhqQy5Db99LguFMoLpU8//55ExoOPsh5gw4y/+0G7NvdlNsu9R/eunTKLSsH+2+jpeaL2ZG/jnWHPue7+Pkcqv8i9eOa0LPhYE5J60+8JFT2Ul3dgMuYX3wXe356nkvWT6Jr80Q+OvVvqCcmPwK1Vh34LWeCrEtmzW+8K0tMfjNs2ACjRsGbb/qvExFObVePWwbW818J3LDAKXVce20ar77qvZO6XQijPQEYQGFxIQs2L+DFNS+yYMe/+e7wLEZ1G8WgEwaVNIYH5iFYkkWbOWP5P887cPadoQrcGFOLxeSlrC1bQvPmZa9Thaefrvhy1ZoOE1od8Z54+rXtx3P9n+PfF/6b5vWa85fP/sJN79/E+n3rq3aw026GTpfCgkdh74+hCdgYU6vFZHIAZyyGsng8sGVL2QkgWMOE1oSI0KdlH6YPnM74M8azfv96rpx9JS+seqFq1zIPeASKi+Czp0IXrDGm1orZ5JCdDR06+C8XcUoWZSWAaBomVEQY3GEwsy6fxTkZ5zBx6URu//h29ufvD+wA6ZnQ9RpY/iLk7gltsMaYWicmk0NKCrRqBWvX+q+78EInAXhLA75deEfjMKGNkhvx5PlPcs9p97Bo6yJ+/d6vyT4YYAddp42AwjxY/VZIYzTG1D4xmRy8JQDvcKzJyU4pYuBAmDPH+cL39qt0+PCxCcA7TOjixc40GrrQEBGGdhrK1AumsvvwbobOGcqqnwO4vLbFqdDkRPjmjdAHaYypVWL2PodbbnHaHRITnTEcWrSAr76Cdu18L3M9qrZ0xLdx/0ZumXsL+/P3868L/kXXpl0r3mH+I85j7A9Qv1l4gjTGRAXreK8MviWAzp2dq5PGj4+udoXqaJfejmkDpnFc8nGM+GgEK3auqHiHDhcAChsXhiM8Y0wtEbPJYeZMePZZ6NYNvAMqTZnitEW8+mp0tStUVYt6LXiu/3M0Tm7MqHmjKr7UtWU3SE6HDf8LW3zGmOgXs8kByi8lXHhh6NsVQt3td/N6zXn6gqdJjEtk5NyR7Di0o+wNPXHQ7hzYsCA0gRhjaqWYTg7lXX00Zw5MmgRduzrTmTODf+5w3EiX2SCTyf0mcyD/ALfOu5XcgtyyN2x7JuzfDAe2hS4YY0ytEtPJAcJ/9VG4b6Tr1LgTT5z3BOv2rePPn/657BvlWrlDG279KjRBGGNqnZhPDjNnhr6U4CsSDd5nZJzBHT3u4MMfP2Taqmn+G7Q4FSQOtlhyMMY4Yj45hFukbqS78eQbuaDtBTz51ZN8se2LY1cmpkKzzrBlWWiDMMbUGpYcIiASN9KJCA+e+SBt09ryx0/+yL68fcdu0KobbFtpfUIbY4AAkoOINA5HINEmlFcThbsqyys1IZVHz36UPfl7eODzB45tf2jWGQ7vgUM2NKMxJrCSw2IRmSEiF0ndH5+wRCS65Q6HTo07cXv325n701zeWvfW0RXN3JGkdn0XkbiMMdElkORwIjAV+DWwVkQeFpETa3JSEblKRFaJSLGI9Cq17l4RWSci34tI/5qcpzqioVvuUBt28jBOa3Eaf13yVzYf2OwsbNrJme605GCMCSA5qOMjVb0OuBkYBiwRkQUi0rea5/0WuAI4ps8GEekMXAucDAwAJotI8EfO9lG6+qi2d58RCI94eOish4iTuKPVSw1aQFI67FoT6fCMMVEgoDYHERktIkuBscBtQBPgLuC/1Tmpqq5R1e/LWDUIeEVV81V1I7AOOK065whU6eqjaOyWOxRa1GvBmJ5j+GL7F7y57k2neNTsJCs5GGOAwKqVPgfSgMtV9WJVnamqhaq6FPhXkOPJADb7zGe7y/yIyHARWSoiS3ftqnojakXVR9HYLXcoXHnilfRs3pPHvnyMXbm72CY9OffBB+rs6zXGBC6Q5PAnVZ2gqiUjyIjIVQCq+mh5O4nIXBH5tozHoCDEjapOVdVeqtqradOmVd6/ouqjSF1NFG4e8XB/3/vJL8rn4S8eZsLbV7NoU0/GjyuIdGjGmAiLD2Cbe4DXSi27F5hR0U6q+stqxLMFaO0zn+kuC7pYqT6qTFZ6Ft/89gu+OnL0ozBlahxTptaeMSyMMcFXbslBRAaKyFNAhoj8w+cxDSgMUTyzgGtFJElE2gEdgCUhOldJ9dHs2dC8OWzaFKozRbd165VWZ8/Hk+iMcpSaXFjnGuGNMVVTUbXSVmApkAcs83nMAmp0iamIDBaRbKAv8K6IfACgqqtwSimrgfeBUapaVJNzVWTSJPj2W5g+3UkUWVmhOlN0a5OZwGltO1JckEhCfB55+XExWYoyxhxV6TChIhKvqqEqKQRFdYYJBYiPh6IyUk8sVqdccQWsL15EYfcn6P3F7RxIPrfOtrUYYxzVGiZURLztDMtF5OvSj5BEGibeK5XKSgyxWp0ycya8N709qW1/oNE191hiMCbGVVStNNqdXgJcWsaj1ip9pRJAXJyTMGK5OqVV/Vb8NqElH5HD4m2LIx2OMSaCyk0OquodFuxXQIGq/uj7CE94oeF7pZLHfQeuuAJuuaXu3tMQqBub9iajsJDHvpxIUXHImnuMMVEukPscGgAficgnIvI7EWke6qDCwXul0ldfwa23QmFh3b6nIVBJx7Xjjj37+H7vD8xaPyvS4RhjIqTSBumSDUW6ANfglCSyq3kfQ0hUt0HalOH799GXr+H6ruezreAA7wx+h9SE1Mr3M8bUOtVqkC7DTmA7sBtoFozATBRKz0CA37f6BbsO7yp7WFFjTJ0XSMd7t4rIfGAe0Bi4WVW7hDowEyFpTldW3YrjuLDthUxbNY0dh3ZEOChjTLgFUnJoDdyhqier6v2qujrUQZkISjkOElJhfzZ39LyDwuJCnlr+VKSjMsaEWUX3OaS5TycCP4lII99HeMIzYSfilB72Z9O6QWuGdhrKrPWz+G6PdeVtTCypqOTgHathGU43Gr5daFjrb12WngEHnP4Ob+5yM+lJ6Tz25WMEevGCMab2q+g+h0vcaTtVbe9OvY/24QvRhF1aJux3kkNaYhoju47ki+1f8MmWTyIcmDEmXAJpkJ4XyDJTh6RnQM4OKDwCwNUnXk3btLb8benfKCyO6m62jDFBUlGbQ7LbttBERI7zaW/IopzR2UwdkZYBKBx0bpJPiEtgTI8xbNi/gZlrY/wuQWNiREUlhxE47QsncWx7w9vAP0MfmomYdDf3Hzg6ztIv2vyCHs16MGnFJA4VHIpQYMaYcKmozeHvqtoOGFuqzaGrqlpyqMvSMp3p/qPJQUS4q9dd7Mnbw7PfPhuhwIwx4RLIfQ7FItLQO+NWMd0aupBMxJWUHLKPWdylaRcGZg3khVUvsP1QjPdQaEwdF0hyuFlV93lnVHUvcHPIIjKRl9QAktOPKTl4je45miIt4p/LrfBoTF0WSHKIExHxzohIHJAYupBMVEjLKGmQ9pVRP4PrO11vN8YZU8cFkhzeB14VkX4i0g942V1m6rK0Vsc0SPv6bZffkpaUxmNL7cY4Y+qqQJLDH4D/Abe4j3nA3aEMykSBtFZwYGvZqxLTuKXrLXyx7QsWbVkU5sCMMeFQaXJQ1WJVnaKqV7qPp1XVhgir6xq0gpydJTfClXb1iVfTpkEbuzHOmDoqkDukO4jI6yKyWkQ2eB/hCM5EUForQCGn7KuSEuISGNNzDOv3r+fNdW+GNzZjTMgFUq30HDAFKATOB14ApocyKBMF0ryXs5ZdtQTQr00/ujfrzqTldmOcMXVNIMkhRVXn4Qwp+qOq3g9cHNqwTMSltXKm5TRKg3Nj3NheY9mdt5vnvn0uTIEZY8IhkOSQLyIeYK2I/E5EBgP1QxyXibSS5FB+yQGcG+MGZA3g+VXP24hxxtQhgSSH0UAqcDvQE7geGBbKoEwUSE6HhHpwwP9eh9JG93BvjFthN8YZU1cEcrXSl6qao6rZqnqTqv5KVReHIzgTQSIV3uvgK7NBJkNOGsLb6962G+OMqSMCKTmYWFXBvQ6l3dzlZhomNeThLx62G+OMqQMsOZjypWUEnBzSk9IZ03MMy3cuZ/aG2SEOzBgTaoHc53BmIMuqQkQmish3IvK1iLxZqtfXe0VknYh8LyL9a3IeU0NprZz+lYoDu+dx0AmD6NKkC39b+jcOHDkQ4uCMMaEUSMnhqQCXVcVHwCmq2gX4AbgXQEQ6A9cCJwMDgMluR38mEtJaghY5d0oHwCMe7utzH3vz9jJp+aQQB2eMCaX48laISF/gDKCpiNzpsyoNqNEXtqp+6DO7GLjSfT4IeEVV84GNIrIOOA34vCbnM9XkeyNcWsuAduncuDNXd7yaV75/hSs6XEHHRh1DGKAxJlQqKjkk4tzPEA808Hkc4OiXeTD8BnjPfZ4BbPZZl00541WLyHARWSoiS3ft2hXEcEyJAG6EK8tt3W8jPTGdBxc/SLEWhyAwY0yolVtyUNUFwAIRmaaqP1b1wCIyF2hRxqr7VPVtd5v7cLrleKmqx1fVqcBUgF69etnlMaEQQBcaZUlPSufOXnfy50//zIzvZ3DNSdeEIDhjTCiVmxx8JInIVCDLd3tV/UVFO6nqLytaLyI3ApcA/fTotY9bgNY+m2W6y0wkpDaGuEQ4WLXkADDo+EHM2TCHx5c9zjmZ59CyfmDVUsaY6BBIg/QMYDnwJ+D3Po9qE5EBOGNCXKaquT6rZgHXikiSiLQDOgBLanIuUwMlN8JVPTmICOPOGIeijF883u59MKaWCSQ5FLrjOSxR1WXeRw3P+0+c9ouPRGSFiPwLQFVXAa8Bq3FGmxtlY0dEWBXudSgto34Go3uMZtGWRbyz4Z0gB2aMCaVAqpVmi8itwJtAvnehqu6p7klV9YQK1j0EPFTdY5sgS2sF2V9We/drO17Lexvf49EvH6Vvq740SWkSxOCMMaESSMlhGE410mfAMvexNJRBmSjirVaqZrVQnCeO8WeM53DBYe7/7H6rXjKmlgik4712ZTzahyM4E17btsG558J238Hf0jKg6Ajk7q72cds3bM+YnmNYkL2AGT/MqHmgxpiQC6T7jFQR+ZN7xZJ32NBLQh+aCbcJE2DRIhg/3mdhA/cqoyre61DakE5DOKPVGUz8ciIb9tsos8ZEu0CHCT2Cc7c0OJeWPhiyiEzYpaQ4FyZNmQLFxc5UxFle3XsdSvOIhwfPfJDk+GTuWXgPBUUFNQ/cGBMygSSH41X1/wEFAO6lpxLSqExYbdgAQ4ZAaqozn5oKQ4fCxo1U+y7psjRNbcr9Z9zPmj1reHzZ4zU+njEmdAJJDkdEJAVQABE5Hp+rlkzt17IlpKVBXh4kJzvTtDRo0QKo3wwkLqAR4QLRr00/hnYayvQ103lv43uV72CMiYhAksM4nHsOWovIS8A8nBvYTB2yYweMHAmLFzvTkkZpT5zT7lDDaiVfd/W8i25NuzHus3Gs37c+aMeNRmU28htTC0gglxaKSGOgD0510mJV/TnUgVVFr169dOlSu7o2ZP5zASSkwLBZQTvkztydXD37ahokNuDli1+mfmL9oB07mtx6Kzz9NIwYAZMnRzoaY44lIstUtVdZ6wK5Wmkwzl3S76rqO0ChiFwe5BhNNAtwLOmqaJbajInnTmTzwc3cvfBuCosLg3r8SKuwkd+YWiCgaiVV3e+dUdV9OFVNJlakZ8L+bOdbLoh6t+jNH0//I59s+YRHljxSp26Qq7CR35haIJDuM8pKIIHsZ+qKRu2gMA9yth+9eilIru54NdkHs3lu1XO0btCaYScPC+rxI6XCRn5jaoFASg5LReRxETnefTyO04WGiRXHtXOme0Lzs/eOnndwQdsL+NvSv/HBpg9Cco5IKLeR35haIJASwG3An4FXcS5n/QgYFcqgTJRp5CaHvRsh68ygH94jHh4+62F+Pvwz9yy8h5T4FM7JPCfo5wm3mTOPPp9kQ2qbWqbCkoOIxAHvqOo9qtpLVXur6h9V9VCY4jPRIL21c69DiEoOAMnxyUzqN4mOjToy5n9j+HyrDRtuTCRVmBzcsRSKRSQ9TPGYaBSX4DRK7w1ta2qDxAY8fcHTZKVncfvHt1uCMCaCAmlzyAG+EZFnROQf3keoAzNRplE72Lsp5KdJT0pn6gVTaZ3WmlHzRjH3x7khP6cxxl8gyWEmTpvDQo6O52AN0rHmuHYhrVby1TilMc/1f47OjTtz14K7eHPtm2E5rzHmqEobpFX1ebdvpTaq+n0YYjLR6LgsOLwHDu+DlIYhP523BDFm/hj+8tlf2H5oOyO6jsAjgfyeMcbUVCB3SF8KrMDpXwkR6SYiwetHwdQOTTo4093rwnbK1IRUnvrFU1x2/GVMXjmZsQvGkluQG7bzGxPLAvkZdj9wGrAPQFVXADYSXKxpepIz3bk6rKdNjEvkwTMfZGyvscz7aR7D3h9G9sHssMZgTCwKJDkU+Haf4QpuPwom+h2XBfEpsPO7sJ9aRBh28jD++Yt/suXgFq6afZV1921MiAWSHFaJyBAgzh0i9CngsxDHZaKNJw6angi71kQshLMzz2bGZTM4vuHx3L3wbv786Z85VGC33BgTCoEkh9uAk3EG+PkvsB+4I4QxmWjVtFNESg6+MupnMG3ANIZ3Gc7b697m8rcvZ2H2wojGZExdVG5yEJFkEbkD+H/AT0Bf9w7pP6lqXrgCNFGkWSc4uNW5YimC4j3x3Nb9Nl4Y+AL1E+ozat4o7l5wN7tyd0U0LmPqkopKDs8DvYBvgIHAY2GJyESvZp2c6a7Ilh68ujXrxmuXvMaobqOY+9NcLn7zYqasmGJXNBkTBBUlh86qer2qPg1cCdT+ntBMzTQ/2Zlu+zqycfhIiEtgZNeRvD3obc7KOIvJKydzyZuXMOOHGRQUFUQ6PGNqrYqSQ8lflqrWrWG6TPWkZUD95rAl+oZkbZ3WmsfPe5wXB75Iy/otGf/5eAbOHMhLa14ir9BqQY2pqnLHkBaRIsB7KYgAKUCu+1xVNS0sEQbAxpAOo5eHONVKt38V6UjKpap8tvUzpn49la92fkWj5Eb8qsOvuOrEq2hZv2WkwzMmalQ0hnS53WeoalzoQjK1VmZP+P5dyN0DqY0iHU2ZRIQzM87kzIwzWbZjGdNWTeOZb5/hmW+f4ZzMc7jqxKvo26ovCZ6ESIdqTNSKyHCfIjIBGIRzM91O4EZV3SoiAvwduAinlHKjqkbvT9RYlNnbmW5eAh0HRDaWAPRs3pOezXuyNWcrr//wOm+sfYP5m+fTMKkh/bP6c1G7i+jWrJv12WRMKeVWK4X0pCJpqnrAfX47TuP3SBG5COe+iouA04G/q+rplR3PqpXCqCAPHm0LvX4DA/4a6WiqrKCogE+3fsq7G95l/ub55BXl0TSlKedknsPZmWfTt2VfUhNSIx2mMWFRrWqlUPImBlc9nOFHwSlNvKBOxlosIg1FpKWqbgt7kKZsCcnQpi+s/1+kI6mWhLgEzmt9Hue1Po9DBYf4+KeP+d/m//HBpg94Y+0bJHgS6Nm8J71b9KZX816c0uQUEuMSIx22MWEXkeQAICIPATfg3HF9vrs4A9jss1m2u8wvOYjIcGA4QJs2bUIaqyml/Xkwdxwc2ApprSIdTbXVS6jHpcdfyqXHX0pBUQHLdy5nQfYCPtv6GU8tfwqApLgkujTtQpcmXejcuDOdG3cmo34GTg2oMXVXyKqVRGQu0KKMVfep6ts+290LJKvqOBF5B3hEVRe56+YBf1DVCuuMrFopzHZ+B5NPh4H/D04fEeloQmJf3j6W7VzGsh3LWLp9KWv3rqXQvaI7PSmdTo060fG4jrRv2J526e1on96e9CT/0XS3bYNrr4VXX4UWZf01GFMDNf18VVStFJE2h2MCEGkDzFHVU0TkaWC+qr7srvseOK+yaiVLDhEwuS8kp8Nv3o90JGGRX5TP2r1rWb17dclj/b71HCk+UrJNo+RGtEtvR5sGbWhZvyUZ9TN4YUIfZr7YlOHDlX9NsUZvE1y33gpPPw0jRsDkyVXfP+qSg4h0UNW17vPbgHNV9UoRuRj4HUcbpP+hqqdVdjxLDhGwcCJ8/CDcvhwaxebwHkXFRWw9tJWN+zeyYd8GNh5wpltytjD/+vfQgiS/fTwJR7jtg7tpktKEximNaZzcmCYpTWiS0oRGyY1IT0qnXkI9u3rKVCglBfLKuLczORkOHw78ONGYHN4AOuJcyvojMFJVt7iXsv4TGIBzKetNlVUpgSWHiDiwDZ48BU4bXiuvWgq1Tdn5jB5TwAfvppB/OI6E5AI6nP0tXX/zIodTNrL78G725u8tc1+PeEhLTCMtMY30pHTneVJaybLUhFRS41NJTUilXkK9kuep8c4jJSGFegn1SI5LtraROmrbNhg7Ft56C3JzITUVBg+Gxx6rWvVSNF6t9KtyliswKszhmOpIawknD4avXoSz74J6TSIdUVTJykyiVZMkCvKdX3NHjiRw7gndmXxt95JtCooL2HN4Dz/n/czuw7vZfXg3B44cYH/+fg4cOcCB/APO9MgBNh/cXPK8WAMba0sQkuKSSIxL9Jses8yT5Lc+wZNAvCeeeE88cRJX8jzeE0+8HH0e53HWJUhCyfPS23jEQ5zEISJ48ODxePBwdFnJOvGUPI5ZhxDnicOD55jtY1nLlpCW5pQekpOdaVpacNu1Ina1kqkDzh4L386E+X+Fi/8W6Wiizo4dMHIkDB8OU6c6v/Z8JXgSaF6vOc3rNQ/4mKrKkeIjHCo4RG5BLrmFuc7U+7zw6PNDBYcoKCogvyif/KJ8jhQdOWaaX5TP/oL9HCk+csyy/KJ8CosLKSwupEiLgvyuBI9vAvGIB0FKps7/gohQ8p+bUEovD3hbdwqUvW2pZeVte8w5S53LV+nlvglREOZ9fSsnXrSf/7u5iI0fXOD3+aqpiDdIB4NVK0XQnN/Dkn/DDW9D+3MjHY0JMlWlUAuPJoviomPmSx7qrCsoLihJKr4JRlUpprjkeVnTYi0+ugylqNidll7ns32xFlPMsesU9Zt6X0vJf+73XqDbKorzfwXb+uxT1rbHLPdd5gRSEs8xUz123neZ18XtL+bqjldX69836qqVTB3yy/thw3yYcSMMmw0tTolwQCaYRIQESbB+qGKQXRJhaiaxHlz3CsQnw/OXwHfvRjoiY0wQWHIwNdf4eLjpXUhvDa8MgRcGwZrZUFCFa+qMMVHFqpVMcDRqD7+dB0uehk//Aa9eD3FJTjVTs86Qnul0tZGUBon1Iak+JKSCJx48cSBx4PE4U/G4yzxAJVelBHTVSgDbBOs4xoRbQrJTgg8ySw4meOIT4Yzb4PRbYNMnsH4ebFkOP3wAh3ZGOjpj6qYz74ALHgj6YS05mOCLi4fjz3ceXoVHIGc75OfAEe8jF4oLQYuguNidFvlMK7ueP4Ar7YJ1NV4duKrP1FEtu4bksJYcTHjEJ0LD2Os91zreM7WVNUgbE0ITJsCiRTB+fKQjMaZqLDkYEwIpKU4b95QpTo3ZlCnOfEpKpCMzJjCWHIwJgQ0bYMgQp0M0cKZDh8LGjZGNy5hAWXIwJgTC0TGaMaFkycGYEPF2vLd4sTPdvj3SERkTOLtayZgQmTnz6PNJkyIXhzHVYSUHY4wxfiw5GGOM8WPJwRhjaqlt2+Dcc0PTnmXJwRhjaqlQ3mRpycEYY2qZcNxkacnBGGNqmXDcZGnJwRhjaplw3GRpycEYY2qhUN9kaTfBGWNMLRTqmyyt5GCMMcaPJQdjjDF+LDkYY4zxY8nBGGOMH0sOxhhj/FhyMMYY4yeiyUFE7hIRFZEm7ryIyD9EZJ2IfC0iPSIZnzHGxKqIJQcRaQ1cCPzks3gg0MF9DAemRCA0Y4yJeZEsOTwB3A2oz7JBwAvqWAw0FJGWEYnOGGNiWESSg4gMArao6spSqzKAzT7z2e6yso4xXESWisjSXbt2hShSY4yJTSHrPkNE5gJldQN1H/BHnCqlalPVqcBUgF69emklmxtjjKmCkCUHVf1lWctF5FSgHbBSRAAyga9E5DRgC9DaZ/NMd5kxxpgwCnu1kqp+o6rNVDVLVbNwqo56qOp2YBZwg3vVUh9gv6puC3eMxhgT66KtV9Y5wEXAOiAXuCmy4RhjTGyKeHJwSw/e5wqMilw0xhhjwO6QNsYYUwZLDsYYY/xYcjDGGOPHkoMxxhg/lhyMMcb4seRgjDHGjyUHY4wxfiw5GGNMLbVtG5x7LmzfHvxjW3IwxphaasIEWLQIxo8P/rEtORhjTC2TkgIiMGUKFBc7UxFnebBYcjDGmFpmwwYYMgRSU5351FQYOhQ2bgzeOSw5GGNMLdOyJaSlQV4eJCc707Q0aFHWCDrVZMnBGGNqoR07YORIWLzYmQa7UTrivbIaY4ypupkzjz6fNCn4x7eSgzHGGD+WHIwxxvix5GCMMcaPJQdjjDF+LDkYY4zxY8nBGGOMH1HVSMdQYyKyC/ixmrs3AX4OYji1mb0XDnsfHPY+HFVX34u2qtq0rBV1IjnUhIgsVdVekY4jGth74bD3wWHvw1Gx+F5YtZIxxhg/lhyMMcb4seQAUyMdQBSx98Jh74PD3oejYu69iPk2B2OMMf6s5GCMMcaPJQdjjDF+Yjo5iMgAEfleRNaJyD2RjidcRKS1iPxPRFaLyCoRGe0ubyQiH4nIWnd6XKRjDQcRiROR5SLyjjvfTkS+cD8Xr4pIYqRjDAcRaSgir4vIdyKyRkT6xuJnQkTGuH8X34rIyyKSHIufiZhNDiISB0wCBgKdgetEpHNkowqbQuAuVe0M9AFGua/9HmCeqnYA5rnzsWA0sMZn/lHgCVU9AdgL/F9Eogq/vwPvq+pJQFec9ySmPhMikgHcDvRS1VOAOOBaYvAzEbPJATgNWKeqG1T1CPAKMCjCMYWFqm5T1a/c5wdxvgQycF7/8+5mzwOXRyTAMBKRTOBi4D/uvAC/AF53N4mV9yEdOAd4BkBVj6jqPmLwM4EzCFqKiMQDqcA2YvAzEcvJIQPY7DOf7S6LKSKSBXQHvgCaq+o2d9V2oHmk4gqjJ4G7gWJ3vjGwT1UL3flY+Vy0A3YBz7lVbP8RkXrE2GdCVbcAjwE/4SSF/cAyYvAzEcvJIeaJSH3gDeAOVT3gu06da5zr9HXOInIJsFNVl0U6ligQD/QApqhqd+AQpaqQYuQzcRxOaakd0AqoBwyIaFAREsvJYQvQ2mc+010WE0QkAScxvKSq3tFod4hIS3d9S2BnpOILkzOBy0RkE0614i9w6t0bulUKEDufi2wgW1W/cOdfx0kWsfaZ+CWwUVV3qWoBMBPncxJzn4lYTg5fAh3cqxAScRqdZkU4prBw69WfAdao6uM+q2YBw9znw4C3wx1bOKnqvaqaqapZOP/+H6vqUOB/wJXuZnX+fQBQ1e3AZhHp6C7qB6wmxj4TONVJfUQk1f078b4PMfeZiOk7pEXkIpw65zjgWVV9KLIRhYeInAV8AnzD0br2P+K0O7wGtMHpAv1qVd0TkSDDTETOA8aq6iUi0h6nJNEIWA5cr6r5EQwvLESkG07DfCKwAbgJ5wdkTH0mROQB4Bqcq/qWA7/FaWOIqc9ETCcHY4wxZYvlaiVjjDHlsORgjDHGjyUHY4wxfiw5GGOM8WPJwRhjjB9LDsYYY/xYcjDGGOPHkoOpFhFpISKviMh6EVkmInNE5MRIx1VVInK/iIyNdByVccdauDUY+4nIZ0GKKUVEFrjd31e27QgRUfdmQ++yUe6y/iKy0Kd7ChMFLDmYKnO7FXgTmK+qx6tqT+Be6niPnRHWECgzOYijvL9lv/1U9YwgxfQbYKaqFgWw7anASuAkABFJxbnzeBewAmesiGuCFJcJAksOpjrOBwpU9V/eBaq6UlU/EZE73RG0vhWRO7zrRSTLHWFsmoj8ICIvicgvReRTd5Sx03y2eckdiex190vEewy/Y7v7fOuzzVi3NJDlHuPf7qheH4pIirvNfW4MiwBvX0J+ROQGEflaRFaKyIsBxFHe+fyOIyLXi8gSEVkhIk97f31XcJxHgOPd7Se6230vIi8A3wKtReQttxS3SkSGu+Ees597jpzqvpZShuLTx5CIzBcR75d/Y99/F6ALTvcTJ7nztwMzgGJV3QG85R7PRAtVtYc9qvTA+cN+oozlPXH6a6oH1AdWAd3ddVk4fdWcivOjZBnwLCA4XSS/5W6jwJnuPs/i9HdU7rHdfb71iWEscL/P+bq5y18Drvc5TiqQBqzznqPUazkZ+AFo4s43CiCOss7ndxygEzAbSHCXTQZuKPU+lT5O6deZhdMvVh+fZd4YU3ASRuPS+7nrc6rzWkodIxHYXmpZNuBxn58PvOyzbhfQHngfpzSzHDgPmOuujwN2RfqzbY+jDys5mGA6C3hTVQ+pag5Od8dn+6zfqKrfqGoxzhfRPHW+Gb7B+UIC2Kyqn7rPp7vHDOTYZdmoqivc58vcc5ztHidXnTEsyuuJ9xfADFX9GUCPdjZXURxlna+s4/TD+WL+UkRWuPPtK4m7LD+q6mKf+dtFZCWwGKc7+g7l7OdV1dfiqwmwzzsjIm2BLe6/LTglha/dda2B3aq6AWgG/B54CjgR598edaqmjohIg0piNmFiDUCmOlZxtPviqvDtxbLYZ76Yo5/F0j1BVtYzZCHHVo8ml3O+Ipxf1KEU6PkEeF5V763hcQ6VHNBp6P0l0FdVc0VkPse+F1VVWQyHSx2/K24ycPUEXnWfn4qbBICDOIPnnIbTI/JXPvskAXk1iNkEkZUcTHV8DCT51GsjIl1wGhYvF6cv/HrAYJyuwauijYj0dZ8PARa5zz8p59g7gGZuHXcScEklx1/oHifF/ZV6aQWv8SoRaey+vkaVxFGeso4zD7hSRJp5l7m/vCtyEKjoV3U6sNdNDCcBfQLYr6qvpYSq7gXiRMSbILrhJgsR6YBTVehNCF18nk8EfueWFEqShvv+/KzOADsmClhyMFXmVgUNBn4pzqWsq4C/AluBacASnLEh/qOqy6t4+O+BUSKyBjgOmOKe86uyju1+mYx3l38EfFdJ7F/h/KJdCbyHM+hTWdutAh4CFrhVNY9XFEcF5/M7jqquBv4EfCgiX7txt6wk7t3Ap27D8cQyNnkfiHfft0dwqpYq3K+qr6UMH3K02q8r4HFf419wBsjxDhJ0Kk4bCKr6jqp+7i7vjFMKBaeN4t0qnNuEmI3nYKKGiGQB76jqKZGOxVRORHoAY1T11yKyFuihqgereayZwD2q+kNQgzTVZiUHY0y1uCWP/4lIujNb7cSQCLxliSG6WMnBGGOMHys5GGOM8WPJwRhjjB9LDsYYY/xYcjDGGOPHkoMxxhg/lhyMMcb4seRgjDHGz/8HndP3QUt3JaAAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# set loss function to huber\n", + "opt.handle_opt_set (handle, 'NLDF Loss Function Type = HUBER')\n", + "\n", + "# set initial guess and solve\n", + "x = [30., 30., 30., 30.]\n", + "\n", + "# regularisation types\n", + "regs = {'OFF', 'L1', 'L2'}\n", + "\n", + "# solve huber loss function with various regularisations\n", + "for reg in regs:\n", + " # set reg type\n", + " opt.handle_opt_set(handle, 'Reg Term Type =' + reg)\n", + " # call the solver\n", + " sol = opt.handle_solve_nldf(handle, lsqfun, lsqgrd, x, nres,data=data, io_manager=iom)\n", + " # calculate response\n", + " resp = sol.x[0] + ((sol.x[1] - sol.x[0]) / (1 + (sol.x[2] / dose)**sol.x[3]))\n", + " # plot curve\n", + " plt.plot(dose, resp, label='reg = '+reg)\n", + "\n", + "# show huber curves\n", + "plt.title(\"Huber loss function\")\n", + "plt.plot(t, y, '*b')\n", + "plt.xlabel(r\"Compound concentration ($\\mu M$)\")\n", + "plt.ylabel(\"Percent activity\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "f86a8a83", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# set loss function to NLS\n", + "opt.handle_opt_set (handle, 'NLDF Loss Function Type = L2')\n", + "\n", + "# solve huber loss function with various regularisations\n", + "for reg in regs:\n", + " # set reg type\n", + " opt.handle_opt_set(handle, 'Reg Term Type =' + reg)\n", + " # call the solver\n", + " sol = opt.handle_solve_nldf(handle, lsqfun, lsqgrd, x, nres,data=data, io_manager=iom)\n", + " # calculate response\n", + " resp = sol.x[0] + ((sol.x[1] - sol.x[0]) / (1 + (sol.x[2] / dose)**sol.x[3]))\n", + " # plot curve\n", + " plt.plot(dose, resp, label='reg = '+reg)\n", + "\n", + "# show NLS curves\n", + "plt.title(r\"$l_2$-norm loss function\")\n", + "plt.plot(t, y, '*b')\n", + "plt.xlabel(r\"Compound concentration ($\\mu M$)\")\n", + "plt.ylabel(\"Percent activity\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "d8984282", + "metadata": {}, + "outputs": [], + "source": [ + "# destroy the handle\n", + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1258bec0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From c8350e1d765ed63e0b602b531243303b44a67f43 Mon Sep 17 00:00:00 2001 From: shuanghuab Date: Mon, 16 Jan 2023 15:07:51 +0000 Subject: [PATCH 165/182] fixing typos --- local_optimization/NLDF/dose_resp.ipynb | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/local_optimization/NLDF/dose_resp.ipynb b/local_optimization/NLDF/dose_resp.ipynb index b57f9bf..6bc07cb 100644 --- a/local_optimization/NLDF/dose_resp.ipynb +++ b/local_optimization/NLDF/dose_resp.ipynb @@ -12,7 +12,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 1, "id": "793e1544", "metadata": {}, "outputs": [], @@ -27,7 +27,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 2, "id": "bacb5e9b", "metadata": {}, "outputs": [ @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 3, "id": "061e8555", "metadata": { "scrolled": true @@ -152,7 +152,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 4, "id": "92bc7d4d", "metadata": { "scrolled": true @@ -160,7 +160,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -184,7 +184,7 @@ "lossfuns = {'HUBER', 'L1', 'LINF', 'CAUCHY', 'ATAN', 'SMOOTHL1', 'QUANTILE'}\n", "\n", "# turn off log printing\n", - "opt.handle_opt_set (handle, 'Print File = -1')\n", + "opt.handle_opt_set(handle, 'Print File = -1')\n", "\n", "for lossfun in lossfuns:\n", " \n", @@ -217,7 +217,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 5, "id": "839d5752", "metadata": { "scrolled": true @@ -225,7 +225,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -268,13 +268,13 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 6, "id": "f86a8a83", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -289,7 +289,7 @@ "# set loss function to NLS\n", "opt.handle_opt_set (handle, 'NLDF Loss Function Type = L2')\n", "\n", - "# solve huber loss function with various regularisations\n", + "# solve NLS loss function with various regularisations\n", "for reg in regs:\n", " # set reg type\n", " opt.handle_opt_set(handle, 'Reg Term Type =' + reg)\n", @@ -311,7 +311,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 7, "id": "d8984282", "metadata": {}, "outputs": [], From d726a6beaca1f5f3c267924fcc320cef60bbed55 Mon Sep 17 00:00:00 2001 From: Charlotte Silvester Date: Wed, 8 Feb 2023 12:41:05 +0000 Subject: [PATCH 166/182] Updating terms --- .../Modelling/handle_disable_ex.ipynb | 16 ++++++++-------- .../Modelling/production_planning.ipynb | 13 ++++++++++--- 2 files changed, 18 insertions(+), 11 deletions(-) diff --git a/local_optimization/Modelling/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb index 123446f..332e987 100644 --- a/local_optimization/Modelling/handle_disable_ex.ipynb +++ b/local_optimization/Modelling/handle_disable_ex.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Installing the NAG library and running this notebook\n", + "# Installing the NAG Library and running this notebook\n", "\n", - "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "This notebook depends on the NAG Library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the NAG Library.\n", "\n", "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] @@ -15,7 +15,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Removing outliers from a calibration problem with the NAG optimisation suite\n", + "# Removing outliers from a calibration problem with the NAG Optimization Modelling Suite\n", "\n", "## Correct Rendering of this notebook\n", "\n", @@ -327,11 +327,11 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "The solver featured in this notebook is accessed via the Optimization Modelling Suite (delivered with the NAG Library). Learn more about the [Optimization Modelling Suite](https://www.nag.com/content/nag-optimization-modelling-suite) or complete the [form](https://www.nag.com/form/optimization-solutions-enquiry) and we’ll get back to you as soon as we can." + ] } ], "metadata": { @@ -350,7 +350,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.10.8" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/local_optimization/Modelling/production_planning.ipynb b/local_optimization/Modelling/production_planning.ipynb index 00804a4..f545e18 100644 --- a/local_optimization/Modelling/production_planning.ipynb +++ b/local_optimization/Modelling/production_planning.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Installing the NAG library and running this notebook\n", + "# Installing the NAG Library and running this notebook\n", "\n", - "This notebook depends on the NAG library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the library.\n", + "This notebook depends on the NAG Library for Python to run. Please read the instructions in the [Readme.md](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#install) file to download, install and obtain a licence for the NAG Library.\n", "\n", "Instruction on how to run the notebook can be found [here](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/Readme.md#jupyter)." ] @@ -255,6 +255,13 @@ "source": [ "opt.handle_free(handle)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The solver featured in this notebook is accessed via the Optimization Modelling Suite (delivered with the NAG Library). Learn more about the [Optimization Modelling Suite](https://www.nag.com/content/nag-optimization-modelling-suite) or complete the [form](https://www.nag.com/form/optimization-solutions-enquiry) and we’ll get back to you as soon as we can." + ] } ], "metadata": { @@ -273,7 +280,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.10.8" }, "latex_envs": { "LaTeX_envs_menu_present": true, From 5852e39fdba772b082dd9e6fac5690160cf53b35 Mon Sep 17 00:00:00 2001 From: Charlotte Silvester Date: Thu, 9 Feb 2023 17:17:12 +0000 Subject: [PATCH 167/182] remove reference to pdf version --- local_optimization/Modelling/handle_disable_ex.ipynb | 2 -- local_optimization/Modelling/production_planning.ipynb | 2 -- 2 files changed, 4 deletions(-) diff --git a/local_optimization/Modelling/handle_disable_ex.ipynb b/local_optimization/Modelling/handle_disable_ex.ipynb index 332e987..eab610d 100644 --- a/local_optimization/Modelling/handle_disable_ex.ipynb +++ b/local_optimization/Modelling/handle_disable_ex.ipynb @@ -21,8 +21,6 @@ "\n", "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", "\n", - "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", - "\n", "## Calibration problem\n", "\n", "Consider a simple calibration problem where we want to fit the 5 parameters of a model $f$ to some given data points. The model is of the form:\n", diff --git a/local_optimization/Modelling/production_planning.ipynb b/local_optimization/Modelling/production_planning.ipynb index f545e18..5ead7d4 100644 --- a/local_optimization/Modelling/production_planning.ipynb +++ b/local_optimization/Modelling/production_planning.ipynb @@ -21,8 +21,6 @@ "\n", "This notebook makes use of the `latex_envs` Jupyter extension for equations and references. If the LaTeX is not rendering properly in your local installation of Jupyter , it may be because you have not installed this extension. Details at https://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/latex_envs/README.html\n", "\n", - "The notebook is also not rendered well by GitHub so if you are reading it from there, you may prefer the [pdf version instead](./static/portfolio_optimization_qcqp.pdf).\n", - "\n", "## Problem description\n", "We consider a situation where a factory can manufacture two different chemicals $A_1$ and $A_2$. The goal for the factory is to determine the quantities $x_1$ and $x_2$ of each chemical to maximize profit under the following circumstances:\n", "- a unit of $A_1$ weighs 40kg and a unit of $A_2$ weighs 80kg;\n", From 81cb11b033f9af87de819e574afc6852a993de8e Mon Sep 17 00:00:00 2001 From: shuanghuab Date: Thu, 28 Sep 2023 11:58:39 +0100 Subject: [PATCH 168/182] dynamic pricing using the NAG Library - Python Notebook --- .../Modelling/dynamic_pricing_lp.ipynb | 401 ++++++++++++++++++ 1 file changed, 401 insertions(+) create mode 100644 local_optimization/Modelling/dynamic_pricing_lp.ipynb diff --git a/local_optimization/Modelling/dynamic_pricing_lp.ipynb b/local_optimization/Modelling/dynamic_pricing_lp.ipynb new file mode 100644 index 0000000..61aa817 --- /dev/null +++ b/local_optimization/Modelling/dynamic_pricing_lp.ipynb @@ -0,0 +1,401 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Installing the NAG Library and running this notebook\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 26.1 or newer) and a license key. You can find the software and have a license key (trials are available) from our website here: [Getting Started with NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Dynamic pricing in revenue management using the NAG Library" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Disciplined pricing tactics are the key in revenue management in order to sell the right product to the right customer at the right time. Commonly implemented pricing strategies include cost-based pricing, market-based pricing, dynamic pricing, price skimming, etc. It depends on various factors such as the nature of the business and the target market to decide the most suitable strategy. During the pricing process, optimization plays an important role in demand forecasting and revenue maximization. In this notebook, we show how to use the NAG Optimization Modelling Suite (delivered with the NAG Library) by implementing a dynamic pricing strategy which achieves increased revenue over random pricing and price matching strategy. \n", + "\n", + "The models considered here do not assume that the demand as a function of price is known in advance, but rather assume parametric family of demand functions that are learned over time. During the learning process, the Linear Programming (LP) solver [handle_solve_lp_ipm](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_solve_lp_ipm.html) in the NAG Library is used to build and solve the models. Included in the NAG Optimization Modelling Suite, the LP solver is well suited for this task, due to the great flexibility provided on building and modifying the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Import the optimization module from the NAG Library for Python, and necessary packages\n", + "from naginterfaces.library import opt\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "We focus on a market with two companies competing for a single product in a dynamic environment, in which each company not only estimates its own demand, but also needs to predicts its competitor's demand and pricing strategy. For simplicity, we assume an uncapacitated setting, i.e., there is no limitation on the capacity that each company needs to allocate.\n", + "\n", + "Linear function is one of the most commonly used demand functions in theory and practice. Assuming the true demand parameters are time dependent, the demand function of company $k=1,2$ can be defined as\n", + "$$d_{k,t} = \\beta_{k,t}^0 + \\beta_{k,t}^1p_{1,t} + \\beta_{k,t}^2p_{2,t} + \\epsilon_{k,t},$$\n", + "where $p_{1,t}$ and $p_{2,t}$ are the prices of company 1 and 2 at time t, respectively. This model assumes that demand for each company $k = 1, 2$ depends on its own as well as its competitors current period prices $p_{1,t}$ and $p_{2,t}$. $\\beta_{k,t}^i$, $i = 0, 1, 2$ are unknown parameters and $\\epsilon_{k,t} \\sim N(0, \\sigma_{k,t}^2)$ is a random noise.\n", + "\n", + "In the beginning of each period t, company 1 knows the realizations of its own demand $d_{1,s}$, its own prices $p_{1,s}$ , as well as its competitor's prices $p_{2,s}$, for $s = 1, \\ldots, t-1$. It does not directly observe its competitor's demand. The objectives are to estimate its own demand, its competitor's reaction and finally, set its own prices dynamically to maximize the total expected revenue.\n", + "\n", + "In this exercise we define the true models of demand are as follows.\n", + "$$\n", + "d_{1,t} = 50 -0.05p_{1,t} + 0.03p_{2,t} + \\epsilon_{1,t},\n", + "$$\n", + "$$\n", + "d_{2,t} = 50 +0.02p_{1,t} - 0.06p_{2,t} + \\epsilon_{2,t},\n", + "$$\n", + "where the $\\epsilon_{1,t},~\\epsilon_{2,t}\\sim N(0, 16)$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def demand_true(company, p1, p2):\n", + " if company == 1:\n", + " return 50 - 0.05*p1 + 0.03*p2 + np.random.normal(scale=4.0)\n", + " elif company == 2:\n", + " return 50 + 0.02*p1 - 0.06*p2 + np.random.normal(scale=4.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Demand estimation\n", + "The following optimization problem is solved in order to estimate the demand of company 1.\n", + "$$\n", + "\\min_{\\hat{\\beta}_1}~~\\sum_{\\tau=1}^{t-1} |d_{1,\\tau} - (\\hat{\\beta}_{1,\\tau}^0+\\hat{\\beta}_{1,\\tau}^1p_{1,\\tau}+\\hat{\\beta}_{1,\\tau}^2p_{2,\\tau})|,\n", + "$$\n", + "$$\n", + "s.t. ~~ |\\hat{\\beta}_{1,\\tau}^i - \\hat{\\beta}_{1,\\tau+1}^i| \\leq \\delta_1(i), ~ i = 0, 1, 2, ~\\tau = 1,2,\\ldots, t-2,\n", + "$$\n", + "$$\n", + "~~ \\hat{\\beta}_{1,\\tau}^0\\geq0,~\\hat{\\beta}_{1,\\tau}^1 \\leq0,~\\hat{\\beta}_{1,\\tau}^2\\geq0,~\\tau = 1,2,\\ldots, t-1,\n", + "$$\n", + "where $\\hat{\\beta}_1$ is defined as an array of all the variables. Note the first set of constraints is to control the changes on the parameters.\n", + "\n", + "Once the optimal solution $(\\hat{\\beta}_{1, \\tau}^i)^*$, $i = 0, 1, 2$, $\\tau = 1, \\ldots, t-1$ is obtained, the new estimate is given by an average of the estimates of the N previous periods\n", + "$$\n", + "\\hat{\\beta}_{1, t}^i = \\frac{1}{N}\\sum_{l=t-N}^{t-1}(\\hat{\\beta}_{1, l}^i)^*,~ i = 0, 1, 2.\n", + "$$\n", + "\n", + "By introducing auxiliary variables $y_\\tau$, $\\tau = 1, \\ldots, t-1$, the above optimization problem can be reformulated as the following linear programming problem.\n", + "$$\n", + "\\min_{({\\hat{\\beta}_1}, y)}~~\\sum_{\\tau=1}^{t-1} y_{\\tau},\n", + "$$\n", + "$$\n", + "s.t. ~~-y_\\tau \\leq d_{1,\\tau} - (\\hat{\\beta}_{1,\\tau}^0+\\hat{\\beta}_{1,\\tau}^1p_{1,\\tau}+\\hat{\\beta}_{1,\\tau}^2p_{2,\\tau}) \\leq y_\\tau,~\\tau = 1,2,\\ldots, t-1,\n", + "$$\n", + "$$\n", + "~~ -\\delta_1(i)\\leq\\hat{\\beta}_{1,\\tau}^i - \\hat{\\beta}_{1,\\tau+1}^i \\leq \\delta_1(i), ~ i = 0, 1, 2, ~\\tau = 1,2,\\ldots, t-2,\n", + "$$\n", + "$$\n", + "~~ \\hat{\\beta}_{1,\\tau}^0\\geq0,~\\hat{\\beta}_{1,\\tau}^1 \\leq0,~\\hat{\\beta}_{1,\\tau}^2\\geq0,~\\tau = 1,2,\\ldots, t-1.\n", + "$$\n", + "Here we assume the prices for both companies range in the interval $[100, 900]$, the time horizon is $T = 150$. And the initial prices are $p_{1,1} = p_{2,1} = 500$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Fix the random seed\n", + "np.random.seed(5)\n", + "\n", + "# Big bound to inform the solver on infinity\n", + "bigbnd = 1.e20\n", + "\n", + "# Optimization model parameters\n", + "delta = np.array([30, 0.05, 0.05])\n", + "T = 150\n", + "\n", + "# Initial prices\n", + "p1 = [500]\n", + "p2 = [500]\n", + "\n", + "# Array to store realised true demand of company 1\n", + "# For final revenue calculation\n", + "demand_1_true = []" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can go ahead and initialize an empty model. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Initialize an empty problem\n", + "nvar = 0\n", + "handle = opt.handle_init(nvar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Observe that for $t = 2, \\ldots, T$, the model is getting bigger with more variables and constraints added. At each time period t, a new set of 4 new variables $[\\hat{\\beta}_{1,t-1}^0, \\hat{\\beta}_{1,t-1}^1, \\hat{\\beta}_{1,t-1}^2, y_{t-1}]$ is added, as well as the contraints involving them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pricing optimization\n", + "Company 1 can set its prices by maximizing its current period t revenues. That is to solve the following unconstrained quadratic programming problem\n", + "$$\n", + "\\max_{p_1,t}~~ p_{1,t} (\\hat{\\beta}_{1,t}^0+\\hat{\\beta}_{1,t}^1p_{1,t}+\\hat{\\beta}_{1,t}^2\\hat{p}_{2,t}),\n", + "$$\n", + "which has the optimal solution of the form\n", + "$$\n", + "p_{1,t}^* = \\frac{\\hat{\\beta}_{1,t}^0+\\hat{\\beta}_{1,t}^2\\hat{p}_{2,t}}{-2\\hat{\\beta}_{1,t}^1}.\n", + "$$\n", + "Note we've still got to estimate the price of company 2 at time t in order to use the pricing strategy above. For simplicity, we use an average of the prices company 2 sets in the N previous periods,\n", + "$$\n", + "\\hat{p}_{2,t} = \\frac{1}{N}\\sum_{l=t-N}^{t-1} p_{2, l}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Pricing of company 2, estimated by company 1\n", + "p2_est = lambda p2 : sum(p2)/len(p2)\n", + "\n", + "# Optimal pricing for company 1\n", + "def optimize_p1(t, p1, beta_t, p2_est):\n", + " \n", + " # When t = 2, the data is insufficient\n", + " # the linear programming problem has multiple optimal solutions\n", + " # Heuristic to make sure price 1 is well-defined\n", + " if (beta_t[1] == 0):\n", + " p1_opt = p1[t-2]\n", + " else:\n", + " p1_opt = (beta_t[0] + beta_t[2]*p2_est)/(-2.0*beta_t[1])\n", + "\n", + " # Project price if outside of interval\n", + " p1_opt = max(100, min(900, p1_opt))\n", + "\n", + " return p1_opt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With pricing functions prepared and empty model initialized, we are finally ready to build up the models and solve along the line for different time periods. With the NAG Optimization Modelling Suite, adding variables and constraints is very straight forward, which makes it very easy to learn the demand function coefficients with new data coming in after each time period, as demonstrated with the following code." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "for t in range(2, T+1):\n", + " \n", + " # In each demand estimation, 4 new variables will be added to the model\n", + " # [beta_0, beta_1, beta_2, y]\n", + " opt.handle_add_vars(handle, 4)\n", + " \n", + " # Only the auxiliary variable y will oppear in the objective\n", + " # Set y coefficient in the linear objective\n", + " opt.handle_set_linobj_coeff(handle, nvar+4, 1.0)\n", + "\n", + " # Set bound constraints for beta\n", + " # Beta_0\n", + " opt.handle_set_bound(handle, 'X', nvar+1, 0.0, bigbnd)\n", + " # Beta_1\n", + " opt.handle_set_bound(handle, 'X', nvar+2, -bigbnd, 0.0)\n", + " # Beta_2\n", + " opt.handle_set_bound(handle, 'X', nvar+3, 0.0, bigbnd)\n", + "\n", + " # Get realised demand for the previous period for company 1\n", + " d1_true = demand_true(1, p1[t-2], p2[t-2])\n", + " # Save true demand for previous period\n", + " demand_1_true.append(d1_true)\n", + "\n", + " # Add first set of contraints\n", + " opt.handle_set_linconstr(handle, -bigbnd, d1_true, [1, 1, 1, 1], \n", + " [nvar+1, nvar+2, nvar+3, nvar+4], [1, p1[t-2], p2[t-2], -1.0])\n", + " opt.handle_set_linconstr(handle, d1_true, bigbnd, [1, 1, 1, 1], \n", + " [nvar+1, nvar+2, nvar+3, nvar+4], [1, p1[t-2], p2[t-2], 1.0])\n", + "\n", + " # Add second set of constraints to control beta to vary slowly\n", + " if (t >= 3):\n", + " opt.handle_set_linconstr(handle, -delta, delta, [1, 1, 2, 2, 3, 3],\n", + " [nvar+1, nvar+1-4, nvar+2, nvar+2-4, nvar+3, nvar+3-4],\n", + " [1.0, -1.0, 1.0, -1.0, 1.0, -1.0])\n", + "\n", + " # Call the linear programming solver\n", + " # Choose the algorithm that will be used\n", + " opt.handle_opt_set(handle, 'LPIPM Algorithm = SD')\n", + " # Turn off printing of the log\n", + " opt.handle_opt_set(handle, 'Print File = -1')\n", + " sol = opt.handle_solve_lp_ipm(handle)\n", + "\n", + " # Calculate beta for period t based on the estimates for previous periods\n", + " beta_t = [0.0, 0.0, 0.0]\n", + " for i in range(0, nvar+4, 4):\n", + " beta_t+=sol.x[i:i+3]\n", + " beta_t /= t-1\n", + "\n", + " # Get optimal pricing for company 1 at time t\n", + " p1_opt = optimize_p1(t, p1, beta_t, p2_est(p2))\n", + "\n", + " # Save optimal pricing at time t\n", + " p1.append(p1_opt)\n", + "\n", + " # Assuming company 2 is implementing price match\n", + " p2.append(p1[t-2])\n", + "\n", + " # Update number of total variables in the model\n", + " nvar += 4\n", + "\n", + "# Solving process finished, deallocate problem model\n", + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Results\n", + "After the pricing stage, we are ready to calculate the actual revenue for each strategy. For comparison, we implemented two other strategies: random and price matching. The random prices are generated under the uniform distribution from the price range. The price matching policy sets the price for the current period the company 1 set in the previous period." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Calculate revenue based on the pricing strategies\n", + "revenue_opt = 0.0\n", + "revenue_price_match= 0.0\n", + "revenue_random = 0.0\n", + "\n", + "# Get the true demand for period T for company 1\n", + "# since it was not used/generated during the pricing stage\n", + "demand_1_true.append(demand_true(1, p1[T-1], p2[T-1]))\n", + "\n", + "# Generate prices based on uniform distribution for comparison\n", + "p3 = np.random.uniform(100, 900, T)\n", + "\n", + "# Calculate revenues for each strategy\n", + "# revenue = price * demand\n", + "for i in range(T):\n", + " revenue_opt += p1[i]*demand_1_true[i]\n", + " revenue_price_match += p2[i]*demand_true(2, p1[i], p2[i])\n", + " revenue_random += p3[i]*demand_true(2, p1[i], p3[i])\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "fig = plt.figure(figsize=plt.figaspect(0.3))\n", + "ax = fig.add_subplot(1, 2, 1)\n", + "\n", + "ax.plot(np.arange(1, T+1), p1, 'b', label='Company 1')\n", + "ax.plot(np.arange(1, T+1), p2, 'g', label='Company 2')\n", + "ax.set_xlabel('Time period')\n", + "ax.set_ylabel('Price')\n", + "ax.legend()\n", + "\n", + "ax = fig.add_subplot(1, 2, 2)\n", + "strategies = ['Opt', 'Price matching', 'Random']\n", + "ax.set_xlabel('Strategy')\n", + "ax.set_ylabel('Revenue')\n", + "ax.bar(strategies, [revenue_opt, revenue_price_match, revenue_random])\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By the plot above on the price history over time, we can see the price of company 1, by employing the optimization learning approach, converges to a stable status as time goes. Company 2 is always one period behind as it uses price matching. From the figure on the right, for this single simulation, we can see using the optimization approach achieves much higher renenue than price matching. And random pricing is the worst in this scenario. \n", + "\n", + "In this notebook, we have shown how to use the NAG Optimization Modelling Suite for pricing strategies under complex market conditions and demand. The flexibility provided makes it very efficient to conduct simulations in search for the most suitable pricing strategies.\n", + "\n", + "Learn more about the [NAG Library](https://www.nag.com/content/nag-library) and the [NAG Optimization Modelling Suite](https://www.nag.com/mathematical-optimization/)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.17" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 638fd2ea058e1918085a54b2274c9fcfe70e623d Mon Sep 17 00:00:00 2001 From: Charlotte Silvester Date: Wed, 1 Nov 2023 11:37:43 +0000 Subject: [PATCH 169/182] portfolio optimization using cvxpy notebook --- .../portfolio_optimization_using_cvxpy.ipynb | 121 ++++++++++++++++++ 1 file changed, 121 insertions(+) create mode 100644 local_optimization/SOCP/portfolio_optimization_using_cvxpy.ipynb diff --git a/local_optimization/SOCP/portfolio_optimization_using_cvxpy.ipynb b/local_optimization/SOCP/portfolio_optimization_using_cvxpy.ipynb new file mode 100644 index 0000000..350540b --- /dev/null +++ b/local_optimization/SOCP/portfolio_optimization_using_cvxpy.ipynb @@ -0,0 +1,121 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9a8d9072", + "metadata": {}, + "source": [ + "# Installing the NAG Library and running this notebook\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 29.3 or newer) and a license key. You can find the software and have a license key (trials are available) from our website here: [Getting Started with the NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux)\n", + "\n", + "We are solving a classic portfolio optimization problem using the NAG Library integration in CVXPY. It can be formulated in the following way:\n", + "\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " &\\min_{x \\in \\mathbb{R}^n} &&\\frac{1}{2} x^T Q_0 x + r^T_0 x\n", + " \\\\\n", + " &\\textrm{subject to } &&\\frac{1}{2} x^T Q_1 x + r^T_1 x \\leq 0,\n", + " \\\\\n", + " & &&e^Tx = 1,\n", + " \\\\\n", + " & && x \\geq 0,\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "where $e$ refers to the vector of all ones." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "dcbfd044", + "metadata": {}, + "outputs": [], + "source": [ + "# Import modules\n", + "from cvxpy import Minimize, Problem, Variable, quad_form, sum, atoms, OPTIMAL, NAG\n", + "import numpy as np\n", + "import naginterfaces" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4d4bec67-2af9-4d14-932c-ac616f223be8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.17415932352686342" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Define number of assets\n", + "n = 500 \n", + "\n", + "# Generate random data\n", + "np.random.seed(2)\n", + "r0 = np.matrix(np.random.randn(n, 1))\n", + "r1 = np.matrix(np.random.randn(n, 1))\n", + "q0 = np.matrix(np.random.randn(n, n))\n", + "q0 = q0.T * q0\n", + "q1 = np.matrix(np.random.randn(n, n))\n", + "q1 = q1.T * q1\n", + "\n", + "# Skip psd check due to issues with ARPACK\n", + "q0 = atoms.affine.wraps.psd_wrap(q0)\n", + "q1 = atoms.affine.wraps.psd_wrap(q1)\n", + "\n", + "# Create the cvxpy problem:\n", + "# Define the variables\n", + "x = Variable(len(r1))\n", + "\n", + "# Define the constraints\n", + "constraints = [\n", + " 0 <= x, \n", + " sum(x) == 1,\n", + " 0.5*quad_form(x, q1) + (r1.T @ x) <= 0]\n", + "\n", + "# Define the objective function\n", + "objective = Minimize(0.5*quad_form(x, q0) + r0.T @ x)\n", + "\n", + "# Set up dictionary for option setting\n", + "nag_params = {'SOCP System Formulation':'AS',\n", + " 'SOCP Factorization Method':'MA86'\n", + " }\n", + "\n", + "# Define the problem\n", + "prob = Problem(objective, constraints)\n", + "\n", + "# Solve the problem using NAG\n", + "prob.solve(solver=NAG, nag_params=nag_params)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 2ad7a0ed736985d39ebe45dc79ac0ae7a70fd621 Mon Sep 17 00:00:00 2001 From: Caleb Hamilton Date: Sat, 18 Nov 2023 18:53:55 -0700 Subject: [PATCH 170/182] Update nag_logo.png --- nag_logo.png | Bin 10702 -> 1928742 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/nag_logo.png b/nag_logo.png index 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z?Fn4tB$A*W$8hqYHWWu-TJ-_tS5V89A^o5#FcrkOV>^F0r-d z!@6JJI`{TJJw9;sNLHqpkkJBW10rqw+DGz>1|dXZ{6{_e#Q{ddE4FI{z48LDNTN|8 z4=|9WA; zq7}_8xl~nEILulXh!{fn*iMSzcLMmDrbwLnh8@u;9eTiC-#Gi213xpVDwXJE>ga!m zv@_G^ms8N@tqrTzY+kyi;dj5fchlOs#HbNQ#0e=C{DKwf$^drOUJ6KHEYG8KM~mCM z{fAe4J+rnzw30)26L$ z>5e>vv@zNX3I|Kc9A;8VDa9h*fST}_;Z=J~8u|V2oKcmEN5VFj0%!ILnYiiYnH@kKt3kVhUXP-cOWVi8u03+Z`N9zBrm;e9(07*qoM6N<$f*7>F A{Qv*} From 25676fbdd6027c8048462c697eccad176a270ce1 Mon Sep 17 00:00:00 2001 From: Charlotte Silvester Date: Tue, 5 Mar 2024 10:48:08 +0000 Subject: [PATCH 171/182] adding milp finance notebook --- .../portfolio_optimization_using_milp.ipynb | 580 ++++++++++++++++++ 1 file changed, 580 insertions(+) create mode 100644 local_optimization/MILP/portfolio_optimization_using_milp.ipynb diff --git a/local_optimization/MILP/portfolio_optimization_using_milp.ipynb b/local_optimization/MILP/portfolio_optimization_using_milp.ipynb new file mode 100644 index 0000000..b2e596c --- /dev/null +++ b/local_optimization/MILP/portfolio_optimization_using_milp.ipynb @@ -0,0 +1,580 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cac8a62f-1a60-440e-a4db-616c55986648", + "metadata": {}, + "source": [ + "## Installing the NAG Library and running this notebook\n", + "To run this notebook, you will need to install the NAG Library for Python (Mark 29.3 or newer) and a license key. You can find the software and obtain a license key (trials are available) from [Getting Started with the NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linuxto).\n" + ] + }, + { + "cell_type": "markdown", + "id": "f120907d-0410-4d07-aec3-b0163e539031", + "metadata": {}, + "source": [ + "# Portfolio optimization with MILP using the NAG Library\n", + "\n", + "A mixed integer linear programming (MILP) model is an extension to a linear programming model where some or all of the variables are constrained to be integer. The ability to handle integer variables makes this an extremely powerful tool with applications in a huge number of industries. Here, we will consider a MILP model of an optimal mean/Value-at-Risk (VaR) portfolio optimization problem by [Benati and Rizzi (2007)](#References). This is an extension to a classic Markowitz model in which the aim is to maximize returns while minimizing risk. However, in this instance, the variance risk measure has been replaced by VaR.\n", + "\n", + "VaR is a widely used risk measure in portfolio management: it quantifies the maximum potential loss within a specified confidence level over a defined time frame. Specifically, VaR is simply the $\\alpha$-quantile of the return distribution function. Unlike other risk measures such as standard deviation or expected shortfall, VaR provides a clear and intuitive assessment of downside risk, making it a preferred choice for investors concerned with the probability of experiencing significant losses. While the mathematical properties of VaR are slightly unappealing (it is a piece-wise linear function and not convex), simplicity in its interpretation makes VaR a popular tool nonetheless.\n", + "\n", + "In this instance, VaR is calculated using a non-parametric method - this means that no assumptions are made about the distribution of portfolio returns. Instead of fitting a parametric model (e.g. normal or student-t distribution) to historical data, which can be restrictive, we use historical simulation. This method reorganizes historical return data, putting it in order of worst to best. The $\\alpha$-quantile is then estimated by the position of the observation that has the $\\alpha$-percent of data on the left.\n", + "\n", + "In this notebook, we solve the \"Min Risk/Fixed Return\" implementation of this problem. This problem contains VaR constraints, cardinality constraints, semicontinuous constraints, a minimum return constraint, a budget (full investment) constraint, and long-only constraints." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "6290f139-6198-4657-8407-0c134b3e7ff1", + "metadata": {}, + "outputs": [], + "source": [ + "# Import modules\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt, mip\n", + "import numpy as np\n", + "import time" + ] + }, + { + "cell_type": "markdown", + "id": "946f315c-92cb-4d53-a187-2123f45509b4", + "metadata": {}, + "source": [ + "For this model, we need to set some parameters. \n", + "\n", + "We have past observations $i \\in I=\\{1,\\dots,T\\}$ and assets $j \\in J=\\{1,\\dots,K\\}$.\n", + "\n", + "We set $r^*$ to be the minimum expected return that will be accepted and $r^{\\textrm{Min}}$ is the minimum return that can be observed in the market. We also choose $r^{\\textrm{VaR}}$: a parameter set by the decision maker to control risk. They will only accept portfolios for which the probability of a return less than $r^{\\textrm{VaR}}$ is less than or equal to $\\alpha^{\\textrm{VaR}}$. Further, we have probabilities $p_i$ associated with each observation $x_i$. These probabilities represent the occurrence of past realization $i$. For illustrative purposes, we set each observation to have equal probability and we synthetically generate returns data." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4dc120e8-9e78-45a6-846c-12a90658f69c", + "metadata": {}, + "outputs": [], + "source": [ + "# Set parameters\n", + "n_assets = 300 # K\n", + "n_periods = 20 # T\n", + "r_star = 0.05\n", + "r_min = -1\n", + "r_var = 0.05\n", + "prob = 1/n_periods\n", + "\n", + "# Synthetic data generation of expected returns for each asset\n", + "np.random.seed(0)\n", + "expected_returns = 0.25 * np.random.randn(n_periods, n_assets) " + ] + }, + { + "cell_type": "markdown", + "id": "26a04836-73b7-4150-b510-3f6a1753afcc", + "metadata": {}, + "source": [ + "Next, we define the variables used in the model:\n", + "* Variables $\\lambda_j$ are the percentage of wealth that is allocated to asset $j$.\n", + "* Variables $x_i$ represent the portfolio observed return in time $i$.\n", + "* Variables $y_i$ are binary (associated with $x_i$) and used for modelling the VaR constraints.\n", + "* Variables $z_j$ are binary (associated with $\\lambda_j$) and used for modelling the cardinality and semicontinuous constraints.\n", + "* $\\alpha^{\\textrm{VaR}}$ is the probability associated with VaR." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4b81e7b1-aac9-49a0-8c06-bef34f503409", + "metadata": {}, + "outputs": [], + "source": [ + "# There are asset_weights[n_assets] + binary_y[n_periods] + observed_return[n_periods] + binary_z[n_assets] + aVaR[1]\n", + "n_vars = n_assets + n_periods + n_periods + n_assets + 1\n", + "\n", + "# Create index sets for each set of variables:\n", + "idx_asset_w = np.arange(1, n_assets+1, dtype=int)\n", + "idx_bin_y = np.arange(n_assets+1, n_assets+n_periods+1, dtype=int)\n", + "idx_obs_ret = np.arange(n_assets+n_periods+1, n_assets+2*n_periods+1, dtype=int)\n", + "idx_bin_z = np.arange(n_assets+2*n_periods+1, 2*n_assets+2*n_periods+1, dtype=int)\n", + "idx_avar = [n_vars]\n", + "\n", + "# Initialize the problem handle:\n", + "handle = opt.handle_init(nvar=n_vars)\n", + "\n", + "# Set binary variables:\n", + "opt.handle_set_property(handle=handle, ptype='Bin', idx=idx_bin_y)\n", + "opt.handle_set_property(handle=handle, ptype='Bin', idx=idx_bin_z)" + ] + }, + { + "cell_type": "markdown", + "id": "10f71de2-da9b-4bf5-817d-576956196ead", + "metadata": {}, + "source": [ + "## Constraints:\n", + "Since this is a MILP model, we set all linear constraints using [***handle_set_linconstr()***](https://support.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_set_linconstr.html).\n", + "\n", + "The first constraint that we implement enforces that the optimal portfolio should be greater than the **minimum acceptable portfolio expected return**:\n", + "$$\\sum_{i=1}^{T} p_i x_i \\geq r^*.$$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0cc5b36d-0ed7-4925-acff-a07cda854dcf", + "metadata": {}, + "outputs": [], + "source": [ + "ones_periods = np.ones(n_periods, dtype=int)\n", + "opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=r_star,\n", + " bu=1.e20,\n", + " irowb=ones_periods,\n", + " icolb=idx_obs_ret,\n", + " b=[prob]*n_periods\n", + ");" + ] + }, + { + "cell_type": "markdown", + "id": "3ea59af3-a465-4dae-a732-1878d401e892", + "metadata": {}, + "source": [ + "Next, we need to enforce that $x_i$ is the **result of the percentage of wealth allocated to each asset and the expected return of that asset** for each time period:\n", + "\n", + "$$\\sum_{j=1}^{K} \\lambda_j r_{ij} = x_i \\quad \\forall \\, i=1,\\dots,T.$$" + ] + }, + { + "cell_type": "markdown", + "id": "d2a523e8-9a71-4e24-979d-dd07243a1fbf", + "metadata": {}, + "source": [ + "This requires slight rearrangement to be input into the model - we stack the variables $\\lambda$ and $x$ and express the rearrangement in matrix notation:\n", + "\n", + "\\begin{equation*}\n", + "\\begin{bmatrix}\n", + "r_{i1} &\n", + "\\dots &\n", + "r_{iK} &\n", + "-1\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "\\lambda_1 \\\\\n", + "\\vdots \\\\\n", + "\\lambda_K \\\\\n", + "x_i\n", + "\\end{bmatrix}\n", + "= 0 \\quad \\forall \\, i = 1,\\dots,T.\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8dbfe45d-cd8d-4ac5-a923-2c62c4b0d296", + "metadata": {}, + "outputs": [], + "source": [ + "ones_assets_1 = np.ones(n_assets+1, dtype=int)\n", + "for i in range(n_periods):\n", + " i_obs_ret = n_assets + n_periods + 1 + i\n", + " returns = expected_returns[i, :]\n", + " returns_x = np.append(returns, -1.)\n", + " idx_col = np.append(idx_asset_w, i_obs_ret)\n", + " opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=0.,\n", + " bu=0.,\n", + " irowb=ones_assets_1,\n", + " icolb=idx_col,\n", + " b=returns_x\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "09ef6f86-37f9-4c81-a4e9-9114d9560cee", + "metadata": {}, + "source": [ + "Next, we want to add constraints that **prevent the selection of portfolios with VaR below the threshold**. To do this, we introduce binary variables $y_i$ associated with each $x_i$. Then the VaR constraint can be modelled in the following way:\n", + "\n", + "$$r^{\\textrm{Min}} + (r^{\\textrm{VaR}} - r^{\\textrm{Min}})y_i \\leq x_i \\quad \\forall \\, i=1,\\dots,T,$$\n", + "$$\\sum_{i=1}^{T} p_i(1-y_i) \\leq \\alpha^{\\textrm{VaR}}.$$\n", + "\n", + "The first constraint enforces that $y_i$ is equal to $0$ for $x_i$ less than $r^{\\textrm{VaR}}$. In the second constraint, this corresponds to $1 - y_i = 1 - 0 = 1$, leading to the summation of probabilities of time periods $i$ with returns less than the VaR threshold. If this probability is greater than $\\alpha^{\\textrm{VaR}}$, it results in an infeasible portfolio.\n", + "\n", + "Rearranged into matrix notation, the first constraint becomes:\n", + "\n", + "\\begin{equation*}\n", + "\\begin{bmatrix}\n", + "(r^{\\textrm{Min}}-r^{\\textrm{VaR}}) &\n", + "1\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "y_i \\\\\n", + "x_i\n", + "\\end{bmatrix}\n", + "\\geq r^{\\textrm{Min}} \\quad \\forall \\, i = 1,\\dots,T,\n", + "\\end{equation*}\n", + "\n", + "and the second constraint becomes:\n", + "\n", + "\\begin{equation*}\n", + "\\begin{bmatrix}\n", + "p_{1} &\n", + "\\dots &\n", + "p_{T} &\n", + "1\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "y_1 \\\\\n", + "\\vdots \\\\\n", + "y_T \\\\\n", + "\\alpha^{\\textrm{VaR}}\n", + "\\end{bmatrix}\n", + "\\geq 1.\n", + "\\end{equation*}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "132124cd-faec-4f3a-9efa-3b8ec5e04b29", + "metadata": {}, + "outputs": [], + "source": [ + "y_coef = r_min - r_var\n", + "for i in range(n_periods):\n", + " y_i = n_assets + 1 + i\n", + " x_i = n_assets + n_periods + 1 + i \n", + " opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=r_min,\n", + " bu=1.e20,\n", + " irowb=[1, 1],\n", + " icolb=[y_i, x_i],\n", + " b=[y_coef, 1.]\n", + " )\n", + "\n", + "ones_periods_1 = np.ones(n_periods+1, dtype=int)\n", + "idx_bin_avar = np.append(idx_bin_y, idx_avar)\n", + "opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=1.0,\n", + " bu=1.e20,\n", + " irowb=ones_periods_1,\n", + " icolb=idx_bin_avar,\n", + " b=np.append([prob]*n_periods, 1.)\n", + ");" + ] + }, + { + "cell_type": "markdown", + "id": "e1a63193-f373-4d39-a32d-d371b832b27b", + "metadata": {}, + "source": [ + "**Full investment** constraint:\n", + "\n", + "$$\\sum_{j=1}^{K} \\lambda_j = 1.$$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0efec5b9-1b3a-4d83-9791-65942f7fa985", + "metadata": {}, + "outputs": [], + "source": [ + "ones_assets_float = np.ones(n_assets, dtype=float)\n", + "ones_assets = np.ones(n_assets, dtype=int)\n", + "opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=1.0,\n", + " bu=1.0,\n", + " irowb=ones_assets,\n", + " icolb=idx_asset_w,\n", + " b=ones_assets_float\n", + ");" + ] + }, + { + "cell_type": "markdown", + "id": "a3577eb0-3492-4921-9c93-de327fb41b62", + "metadata": {}, + "source": [ + "Next, we want to add **semicontinuous constraints** to confine the optimal allocation of the assets to be between $5\\%$ and $70\\%$:\n", + "$$\\lambda_j \\in 0 \\cup [0.05, 0.7] \\quad \\forall \\, j = 1,\\dots, K.$$\n", + "\n", + "Using binary variables $z_j$, the semicontinuous constraint can be expressed as follows:\n", + "\n", + "$$0.05 \\cdot z_j \\leq \\lambda_j \\leq 0.7 \\cdot z_j \\quad \\forall \\, j=1,\\dots, K.$$\n", + "\n", + "These constraints enforce that if $z_j$ is equal to $1$, then $\\lambda_j$ can take any value in the interval between $0.05$ and $0.7$. When $z_j$ equals $0$, then $\\lambda_j$ must also equal $0$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "cc09f5a8-b2da-443c-8026-2a88ad2c4ea8", + "metadata": {}, + "outputs": [], + "source": [ + "for j in range(n_assets):\n", + " lambda_j = 1 + j\n", + " z_j = n_assets + 2*n_periods + 1 + j\n", + " opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=-1.e20,\n", + " bu=0.0,\n", + " irowb=[1, 1],\n", + " icolb=[lambda_j, z_j],\n", + " b=[1., -0.7]\n", + " )\n", + " \n", + " opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=0.0,\n", + " bu=1.e20,\n", + " irowb=[1, 1],\n", + " icolb=[lambda_j, z_j],\n", + " b=[1., -0.05]\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "934646d5-57e8-43f2-adb6-828f17473105", + "metadata": {}, + "source": [ + "Next, we want $10\\%$ of the assets to be included in the optimal portfolio, so we add a **cardinality constraint**:\n", + "$$||\\lambda||_0 \\leq 0.1 \\cdot K.$$\n", + "\n", + "This can be modelled by adding a binary variable $z_j$ for each $\\lambda_j$. When $z_j$ is equal to $0$, this indicates that asset $\\lambda_j$ is not allocated; when $z_j$ is equal to $1$, asset $\\lambda_j$ has been allocated. Then the cardinality constraint can be modelled by summing the binary variables:\n", + "\n", + "$$\\sum_{j=1}^K z_j \\leq 0.1 \\cdot K.$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "bea9b819-077e-4075-a954-2fcf3357a197", + "metadata": {}, + "outputs": [], + "source": [ + "opt.handle_set_linconstr(\n", + " handle=handle,\n", + " bl=-1.e20,\n", + " bu=0.1*n_assets,\n", + " irowb=ones_assets,\n", + " icolb=idx_bin_z,\n", + " b=ones_assets_float\n", + ");" + ] + }, + { + "cell_type": "markdown", + "id": "810bba10-a1aa-4cd4-95d5-9b0d968495be", + "metadata": {}, + "source": [ + "Bound constraints to **prevent short-selling**:\n", + "\n", + "$$\\lambda_j \\geq 0 \\quad \\forall \\, j=1,\\dots,K.$$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "afb2b374-e6c6-4f1d-af3e-b69ace80ae57", + "metadata": {}, + "outputs": [], + "source": [ + "# Set bound constraints:\n", + "zeros_asset_w = np.zeros(n_assets)\n", + "neg_lrg_bnd = np.full((n_periods + n_periods + n_assets + 1), -1.e20, dtype=float).ravel()\n", + "bl = np.hstack([zeros_asset_w, neg_lrg_bnd])\n", + "opt.handle_set_simplebounds(\n", + " handle,\n", + " bl=bl,\n", + " bu=[1.e20]*n_vars,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "70f84e9d-b236-4342-9999-d3bf1b226488", + "metadata": {}, + "source": [ + "## Objective function:\n", + "We want to minimize risk:\n", + "\n", + "\\begin{equation*}\n", + "\\min_{\\alpha^{\\textrm{VaR}},\\lambda,x,y} \\alpha^{\\textrm{VaR}}\n", + "\\end{equation*}\n", + "\n", + "\n", + "Even though the objective function is linear, we use [***handle_set_quadobj()***](https://support.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.handle_set_quadobj.html) because it is sparse." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "07fa779f-a9f6-4aa0-a187-3d088cad238b", + "metadata": {}, + "outputs": [], + "source": [ + "# Set the objective function:\n", + "opt.handle_set_quadobj(\n", + " handle,\n", + " idxc=idx_avar,\n", + " c=[1.0],\n", + " )" + ] + }, + { + "cell_type": "markdown", + "id": "3bfe7a7c-ad79-491f-918d-3d23a30172d5", + "metadata": {}, + "source": [ + "## Optimal mean/Value-at-Risk model\n", + "We can now specify the full model and solve it using the [**MILP solver**](https://support.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.mip.handle_solve_milp.html).\n", + "\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " &\\min_{\\alpha^{\\textrm{VaR}},\\lambda,x,y,z} &&\\alpha^{\\textrm{VaR}}\n", + " \\\\\n", + " &\\textrm{subject to } &&\\sum_{i=1}^{T} p_i x_i \\geq r^*,\n", + " \\\\\n", + " & &&\\sum_{j=1}^{K} \\lambda_j r_{ij} = x_i \\quad \\forall \\, i=1,\\dots,T,\n", + " \\\\\n", + " & &&r^{\\textrm{Min}} + (r^{\\textrm{VaR}} - r^{\\textrm{Min}})y_i \\leq x_i \\quad \\forall \\, i=1,\\dots,T,\n", + " \\\\\n", + " & &&\\sum_{i=1}^{T} p_i(1-y_i) \\leq \\alpha^{\\textrm{VaR}},\n", + " \\\\\n", + " & &&\\sum_{j=1}^{K} \\lambda_j = 1,\n", + " \\\\\n", + " & &&\\sum_{j=1}^K z_j \\leq 0.1 \\cdot K,\n", + " \\\\\n", + " & && 0.05 \\cdot z_j \\leq \\lambda_j \\leq 0.7 \\cdot z_j \\quad \\forall \\, j = 1,\\dots, K,\n", + " \\\\\n", + " & &&y_i \\in \\{0,1\\} \\quad \\forall \\, i=1,\\dots,T,\n", + " \\\\\n", + " & &&z_j \\in \\{0,1\\} \\quad \\forall \\, j=1,\\dots,K,\n", + " \\\\\n", + " & &&\\lambda_j \\geq 0 \\quad \\forall \\, j=1,\\dots,K.\n", + " \\end{aligned}\n", + "\\end{equation*}" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "2cbeef24-1946-4718-8d37-20c0adbecd51", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " H02BK, Solver for MILP problems\n", + " Begin of Options\n", + " Print File = 9 * d\n", + " Print Level = 1 * U\n", + " Print Options = Yes * d\n", + " Print Solution = No * d\n", + " Monitoring File = -1 * d\n", + " Monitoring Level = 4 * d\n", + "\n", + " Infinite Bound Size = 1.00000E+20 * d\n", + " Task = Minimize * d\n", + " Time Limit = 1.00000E+06 * d\n", + "\n", + " Milp Presolve = Yes * d\n", + " Milp Random Seed = 0 * d\n", + " Milp Feasibility Tol = 1.00000E-06 * d\n", + " Milp Rel Gap = 1.00000E-04 * d\n", + " Milp Abs Gap = 1.00000E-06 * d\n", + " Milp Small Matrix Value = 1.00000E-09 * d\n", + " Milp Detect Symmetry = Yes * d\n", + " Milp Max Nodes = 2147483647 * d\n", + " End of Options\n", + "\n", + " Status: converged, an optimal solution found\n", + " Final primal objective value -5.551115E-17\n", + " Final dual objective bound 0.000000E+00\n", + "\n", + " Computation time: 0.405 seconds\n" + ] + } + ], + "source": [ + "# Set some algorithmic options:\n", + "for option in [\n", + " 'Print Level = 1',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)\n", + "\n", + "# Start timer:\n", + "start_solve = time.time()\n", + "\n", + "# Call the MILP solver:\n", + "mip.handle_solve_milp(handle, io_manager=iom)\n", + "\n", + "# Print computation time:\n", + "end = time.time()\n", + "print(f\"\\n Computation time: {end-start_solve:.3f} seconds\")\n", + "\n", + "# Destroy the handle:\n", + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "markdown", + "id": "93760299-5a24-44e0-8c4c-3472b207c25e", + "metadata": {}, + "source": [ + "In this instance, we solved a model with $641$ variables ($320$ of which were binary) and $644$ constraints. This was efficiently solved in $0.41$ seconds.\n", + "\n", + "Using MILP allows the modelling of complex constraints, adding flexibility and sophistication to your problem. The MILP solver used in this portfolio optimization example is available in the NAG Library Optimization Modelling Suite. Learn more about it [here](https://nag.com/mixed-integer-linear-programming/). " + ] + }, + { + "cell_type": "markdown", + "id": "def14a4d-181f-4b62-a7c9-81a82f0dbc17", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "Benati, S., & Rizzi, R. (2007). A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem. *European Journal of Operational Research*, *176*(1), 423-434." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 8387db41b51e29d8acd3b13c8554156cc1454a59 Mon Sep 17 00:00:00 2001 From: shuanghuab Date: Fri, 22 Mar 2024 13:23:15 +0000 Subject: [PATCH 172/182] python notebook on energy modelling using MILP --- local_optimization/MILP/BESS_MILP.ipynb | 668 ++++++++++++++++++++++++ local_optimization/MILP/Grid_Model.png | Bin 0 -> 42269 bytes 2 files changed, 668 insertions(+) create mode 100644 local_optimization/MILP/BESS_MILP.ipynb create mode 100644 local_optimization/MILP/Grid_Model.png diff --git a/local_optimization/MILP/BESS_MILP.ipynb b/local_optimization/MILP/BESS_MILP.ipynb new file mode 100644 index 0000000..ee528d4 --- /dev/null +++ b/local_optimization/MILP/BESS_MILP.ipynb @@ -0,0 +1,668 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing the NAG Library and running this notebook\n", + "The model in this notebook is solved by the NAG MILP solver featured in the NAG Optimization Modelling Suite. To run this notebook, you will need to install the NAG Library for Python (Mark 29.3 or newer) and a license key. You can find the software and obtain a license key (trials are available) from [Getting Started with the NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linuxto).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## **Battery sizing problem in a Grid-connected Microgrid using MILP in the NAG Library**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Energy storage systems (ESS) are increasingly recognized as vital components of traditional power grids combined with renewable energy sources for several reasons. Firstly, the stability and reliability of the power grids can be enhanced by ESS, which provides fast-response ancillary services such as frequency regulation, voltage control, and grid balancing. These services help mitigate the impact of sudden fluctuations in electricity demand or supply, reducing the risk of blackouts and ensuring a more resilient grid infrastructure. Secondly, ESS allows utilities to shift electricity generation from times of low demand to times of peak demand, helping to manage load profiles more effectively. Moreover, ESS plays an important role in helping smooth out the variability and intermittency associated with renewable resources such as solar and wind power. This enables greater penetration of renewable energy into the grid without compromising reliability or stability.\n", + "\n", + "At Mark 29.3 the NAG Library features a new Mixed Integer Linear Programming (MILP) solver, which is a powerful tool for the design and operation of energy storage systems, including optimal sizing and configuration, energy management and dispatch, and risk management. In order to illustrate the usage of the MILP solver, we build the model and solve an optimal battery sizing problem for a microgrid that is connected to an external grid and consists of a battery energy storage system (BESS), several generators and loads. The model also provides optimal operation of the system, including generator scheduling and power dispatch, battery charging and discharging schedule and optimal grid power import. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **Microgrid Modelling**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The microgrid of interest in this notebook is depicted in Figure 1. Loads demand can be fulfilled by generators, batteries and the external grid. Generators are assumed to be owned by a utility, therefore the energy management system will find an optimal schedule for all components to minimize the operation cost of generators and the battery. The planning horizon $N$ is set to 24 hours.\n", + "\n", + "\"GRID\"\n", + "\n", + "Figure 1: Grid-connected microgrid model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### **Decision variables**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The decision variables controlling various components in the microgrid are listed below.\n", + "- Generators\n", + " - $p_{ij}^g$: dispatched power from the $i$-th generator at the $j$-th hour.\n", + " - $s_{ij}$: binary switch that is equal to 1 if the $i$-th generator is online and 0 otherwise at the $j$-th hour.\n", + "- BESS\n", + " - $p^b_j$: power discharged or charged to the battery energy storage system at the $j$-th hour.\n", + " - $c^b$: power rate of the battery energy system.\n", + " - $e^b$: energy rate of the battery energy system.\n", + "- External grid\n", + " - $p_j^{im}$: imported power at the $j$-th hour." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### **Model parameters and coefficients**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model parameters are defined directly in the code cell below for building the model later. See the comments for the description of each parameter. Fuel cost of the generators are usually calculated using a quadratic function. Based on the property of the quadratic function, in practice it is reasonable to linearize it using piecewise functions and then make use of the powerful MILP solver. In this notebook, we'll simply adopt a linear approximation to the quadratic function for illustration purposes." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " a b pl pu ut dt\n", + "Gen1 0.010694 142.7348 30.0 70.0 8.0 6.0\n", + "Gen2 0.018761 168.9075 50.0 100.0 8.0 6.0\n", + "Gen3 0.007612 313.9102 30.0 120.0 8.0 6.0\n" + ] + } + ], + "source": [ + "# Import necessary libraries\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Generator parameters\n", + "# Number of generators\n", + "n_gen = 3\n", + "# Data frame for the specifications of the generators\n", + "df = pd.DataFrame(\n", + " {\n", + " 'Gen1':[0.010694, 142.7348, 30, 70, 8, 6],\n", + " 'Gen2':[0.018761, 168.9075, 50, 100, 8, 6],\n", + " 'Gen3':[0.0076121, 313.9102, 30, 120, 8, 6],\n", + " }\n", + ")\n", + "df.index=['a','b','pl','pu','ut','dt']\n", + "print(df.T.to_string())\n", + "spec_gen = df.T.to_numpy() " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above DataFrame contains all the specification of the generators. The fuel cost is defined as the linear function\n", + "$$\n", + "cost_i(p_{ij}^g) = a_i * p_{ij}^g + b_i\n", + "$$\n", + "for generator $i$ at the $j$-th hour. $pl$ and $pu$ are the minimum and maximum power output of the $i$-th generator respectively. The rest of the parameters are\n", + "- $ut$: minimum up time of the generator\n", + "- $dt$: minimum down time of the generator" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Battery parameters\n", + "cost_bat_power = 0.2\n", + "cost_bat_energy = 0.25\n", + "# External grid import price\n", + "cost_imp_energy = np.array([\n", + " 0.09, 0.08, 0.08, 0.08, 0.08, 0.08, 0.09, # 12:00 AM - 6:00 AM\n", + " 0.11, 0.13, 0.12, 0.11, 0.10, 0.10, 0.10, # 7:00 AM - 1:00 PM\n", + " 0.11, 0.12, 0.13, 0.14, 0.13, 0.12, 0.11, # 2:00 PM - 7:00 PM\n", + " 0.10, 0.09, 0.09 # 8:00 PM - 11:00 PM\n", + "])\n", + "\n", + "# Number of hours in the planning horizon\n", + "n_hours = 24\n", + "\n", + "# Plot import energy cost\n", + "plt.figure(figsize=(7.5, 2.5))\n", + "plt.plot(np.arange(n_hours), cost_imp_energy, marker='o')\n", + "plt.title('Hourly Electricity Prices')\n", + "plt.xlabel('Time (Hour)')\n", + "plt.ylabel('Electricity Price (USD/kWh)')\n", + "plt.xticks(np.arange(0, 24, step=1))\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Load demand to be fulfilled by the energy management system\n", + "load_demand = np.array([\n", + " 200, 180, 170, 160, 150, 150, 170, 250, 320, 300, 280, 260, 270, 280, 290, \n", + " 300, 320, 350, 340, 330, 320, 280, 240, 220\n", + "])\n", + "\n", + "# Plot load demand\n", + "plt.figure(figsize=(7.5, 2.5))\n", + "plt.plot(np.arange(n_hours), load_demand, marker='o')\n", + "plt.title('Load Demand')\n", + "plt.xlabel('Time (Hour)')\n", + "plt.ylabel('Load Demand (kW)')\n", + "plt.xticks(np.arange(0, 24, step=1))\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **Mixed Integer Linear Programming using the NAG Library**" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [], + "source": [ + "# Import the NAG Library for Python\n", + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt, mip\n", + "\n", + "# Total number of variables in the model\n", + "# generators: 3 * 24 * 2\n", + "# battery: 24 + 2\n", + "# power import: 24\n", + "# pg + pim + cb + eb + pb + s \n", + "nvar = 3*24 + 24 + 1 + 1 + 24 + 3*24 \n", + "\n", + "# Create a problem handle to hold model data\n", + "handle = opt.handle_init(nvar=nvar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The objective function which is the total operation cost of the utility is defined as\n", + "$$\n", + "\\min \\sum_{j=1}^{n\\_hours} (\\sum_{i=1}^{n\\_gen} cost_i(p_{ij}^g) + cost\\_imp\\_energy_j*p_{j}^{im}) + cost\\_bat\\_power * c^b + cost\\_bat\\_energy * e^b\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "# Set objective coefficient\n", + "idxc = list(range(1, 3*24 + 24 + 1 + 1 + 1))\n", + "c = np.tile(spec_gen[:,0], 24)\n", + "c = np.concatenate((c, cost_imp_energy, [cost_bat_power, cost_bat_energy]))\n", + "\n", + "# Set model objective\n", + "opt.handle_set_quadobj(handle=handle, idxc=idxc, c=c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The load balance of every hour needs to be met, therefore we have the following power balance for $j$-th hour:\n", + "$$\n", + "\\sum_{i=1}^{n\\_gen} p^g_{ij} + p^b_j + p^{im}_j = load\\_demand_j.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [], + "source": [ + "# Add power balance constraint for each hour\n", + "for hour in range(n_hours):\n", + "\tirowa = np.full(5, 1, dtype=int)\n", + "\ticola = np.array([3*hour+1, 3*hour+2, 3*hour+3, 3*24+hour+1, 3*24+24+1+1+hour+1], dtype=int)\n", + "\ta = np.full(5, 1.0, dtype=float)\n", + "\tbl = np.full(1, load_demand[hour], dtype=float)\n", + "\tbu = np.full(1, load_demand[hour], dtype=float)\n", + "\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The generators' power output should be within the limits given as $pl$ and $pu$ in the generators specification, when they are online. Therefore the generators limits constraint for the $i$-th generator at the $j$-th hour is defined as\n", + "$$\n", + "pl_i*s_{ij} \\leq p^g_{ij} \\leq pu_i*s_{ij}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [], + "source": [ + "# Add generator limits constraint\n", + "for generator in range(n_gen):\n", + "\tfor hour in range(n_hours):\n", + "\t\tirowa = [1, 1, 2, 2]\n", + "\t\ticola = np.tile([3*24+24+1+1+24+hour*3+generator+1, hour*3+generator+1],2)\n", + "\t\ta = np.array([spec_gen[generator, 2], -1.0, spec_gen[generator, 3], -1.0], dtype=float)\n", + "\t\tbl = np.array([-1.e20, 0.])\n", + "\t\tbu = np.array([0., 1.e20])\n", + "\t\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Each generator has a minimum up and down time constraint:\n", + "$$\n", + "\\sum_{t=j}^{j+ut-1} s_{it} \\geq ut*(s_{ij}-s_{ij-1}),\n", + "$$\n", + "$$\n", + "\\sum_{t=j}^{j+dt-1} (1 - s_{it}) \\geq dt*(s_{ij-1}-s_{ij}).\n", + "$$\n", + "Note we assume all generators have the same minimum up time and minimum down time for simplicity." + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [], + "source": [ + "# Add minimum up and down time constraints\n", + "ut = 8.0\n", + "dt = 6.0\n", + "s_start = 3*24 + 24 + 1 + 1 + 24\n", + "# minimum up time constraints\n", + "for generator in range(n_gen):\n", + "\tfor hour in range(1, n_hours):\n", + "\t\tirowa = np.array([],dtype=int)\n", + "\t\ticola = np.array([],dtype=int)\n", + "\t\ta = np.array([],dtype=float)\n", + "\t\tfor i in range(hour-1, min(hour+ 8, n_hours)):\n", + "\t\t\ticola = np.append(icola, s_start+i*3+generator+1)\n", + "\t\t\tirowa = np.append(irowa, 1)\n", + "\t\t\ta = np.append(a, 1.0)\n", + "\t\ta[0] = ut \n", + "\t\ta[1] = 1 - ut\n", + "\t\tbl = 0.0\n", + "\t\tbu = 1.e20\n", + "\t\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)\n", + "# minimum down time constraints\n", + "for generator in range(n_gen):\n", + "\tfor hour in range(1, n_hours):\n", + "\t\tirowa = np.array([],dtype=int)\n", + "\t\ticola = np.array([],dtype=int)\n", + "\t\ta = np.array([],dtype=float)\n", + "\t\tbu = -1.0\n", + "\t\tfor i in range(hour-1, min(hour+ 6, n_hours)):\n", + "\t\t\ticola = np.append(icola, s_start+i*3+generator+1)\n", + "\t\t\tirowa = np.append(irowa, 1)\n", + "\t\t\ta = np.append(a, 1.0)\n", + "\t\t\tbu += 1.0\n", + "\t\ta[0] = dt \n", + "\t\ta[1] = 1 - dt\n", + "\t\tbl = -1.e20\n", + "\t\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Battery power at any time cannot be off the limits. Therefore we define the following power rating limits constraint.\n", + "$$\n", + "-c^b \\leq p^b_j \\leq c^b.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [], + "source": [ + "# Add battery power limits constraints\n", + "for hour in range(n_hours):\n", + "\tirowa = [1, 1, 2, 2]\n", + "\ticola = [3*24+24+1+1+hour+1, 3*24+24+1, 3*24+24+1+1+hour+1, 3*24+24+1]\n", + "\ta = [1.0, -1.0, 1.0, 1.0]\n", + "\tbl = [-1.e20, 0.]\n", + "\tbu = [0., 1.e20]\n", + "\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Energy rating of the battery storage system follows\n", + "$$\n", + "-e^b \\leq \\sum_{j=1}^t p^b_j \\leq 0, for ~t = 1, \\ldots, n\\_hours.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [], + "source": [ + "# Add battery energy limits constraints\n", + "for hour in range(n_hours):\n", + "\t# rhs\n", + "\tirowa = np.array([],dtype=int)\n", + "\ticola = np.array([],dtype=int)\n", + "\ta = np.array([],dtype=float)\n", + "\tfor i in range(hour+1):\n", + "\t\ticola = np.append(icola, 3*24+24+1+1+i+1)\n", + "\t\tirowa = np.append(irowa, 1)\n", + "\t\ta = np.append(a, 1.0)\n", + "\tbl = -1.e20\n", + "\tbu = 0.\n", + "\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)\n", + "\t# lhs\n", + "\tirowa = np.array([1],dtype=int)\n", + "\ticola = np.array([3*24+24+1+1],dtype=int)\n", + "\ta = np.array([1.],dtype=float)\n", + "\tfor i in range(hour+1):\n", + "\t\ticola = np.append(icola, 3*24+24+1+1+i+1)\n", + "\t\tirowa = np.append(irowa, 1)\n", + "\t\ta = np.append(a, 1.0)\n", + "\tbl = 0.\n", + "\tbu = 1.e20\n", + "\topt.handle_set_linconstr(handle, bl, bu, irowa, icola, a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The imported power is limited to $15$ kW maximum.\n", + "$$\n", + "0 \\leq p^{im}_j \\leq 15.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [], + "source": [ + "# Add limits to the imported power\n", + "for i in range(n_hours):\n", + "\topt.handle_set_bound(handle=handle, comp='Var', idx=3*24+i+1, bli=0., bui=15.)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [], + "source": [ + "# Switches for the generators are binary\n", + "switches = np.arange(3*24+24+1+1+24+1, nvar+1)\n", + "opt.handle_set_property(handle=handle, ptype='Bin', idx=switches)" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " H02BK, Solver for MILP problems\n", + " Status: converged, an optimal solution found\n", + " Final primal objective value 1.218345E+02\n", + " Final dual objective bound 1.218345E+02\n" + ] + } + ], + "source": [ + "# Set options\n", + "for option in [\n", + " 'Print Options = NO',\n", + " 'Print Level = 1',\n", + "]:\n", + " opt.handle_opt_set(handle, option)\n", + "\n", + "# Use an explicit I/O manager for abbreviated iteration output:\n", + "iom = utils.FileObjManager(locus_in_output=False)\n", + "\n", + "# Solve the problem.\n", + "x, _, _ = mip.handle_solve_milp(handle, io_manager=iom)\n", + "\n", + "# Destroy the handle:\n", + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can extract the optimal configuration from the solution." + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Power Rate Energy Rate\n", + "Battery 45.0 135.0\n" + ] + } + ], + "source": [ + "# Generator schedule for 24 hours\n", + "switch1 = np.array([x for i, x in enumerate(x[-3*24:]) if i % 3 ==0])\n", + "switch2 = np.array([x for i, x in enumerate(x[-3*24:]) if i % 3 ==1])\n", + "switch3 = np.array([x for i, x in enumerate(x[-3*24:]) if i % 3 ==2])\n", + "# Generator energy for 24 hours\n", + "generator1 = np.array([x for i, x in enumerate(x[:3*24]) if i % 3 ==0])\n", + "generator2 = np.array([x for i, x in enumerate(x[:3*24]) if i % 3 ==1])\n", + "generator3 = np.array([x for i, x in enumerate(x[:3*24]) if i % 3 ==2])\n", + "# Power import\n", + "power_import = x[3*24 : 3*24+24]\n", + "battery_power_rate = x[3*24+24]\n", + "battery_energy_rate = x[3*24+24+1]\n", + "battery_power = x[3*24+24+1+1 : 3*24+24+1+1+24]\n", + "\n", + "df = pd.DataFrame(\n", + "\t{\n", + "\t'Battery':[battery_power_rate, battery_energy_rate],\n", + "\t}\n", + ")\n", + "df.index=['Power Rate','Energy Rate']\n", + "print(df.T.to_string())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model gives the optimal battery power rate as $45$ kW and optimal energy rate as $135$ kWh. We can plot the battery discharging schedule and energy import schedule as below. It's shown that the battery charges itself during off-peak time and dispatches during peak hours to mitigate the need of importing external energy. The imported energy is kept well under $15$ kW and only happens during the second peak." + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot dispatching from battery energy storage system\n", + "plt.figure(figsize=(7.5, 2.5))\n", + "plt.plot(np.arange(1, n_hours+1), battery_power, marker='o', linestyle='-')\n", + "plt.title('Battery Dispatching Power for 24 Hours')\n", + "plt.xlabel('Time (hours)')\n", + "plt.ylabel('Power (kW)')\n", + "plt.xticks(np.arange(0, 25, step=1))\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot power import from external grid\n", + "plt.figure(figsize=(7.5, 2.5))\n", + "plt.plot(np.arange(1, n_hours+1), power_import, marker='o', linestyle='-')\n", + "plt.title('Import Power for 24 Hours')\n", + "plt.xlabel('Time (hours)')\n", + "plt.ylabel('Power (kW)')\n", + "plt.xticks(np.arange(0, 25, step=1))\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **Conclusion**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook, we illustrated how to use the MILP solver featured in the NAG Optimization Modelling Suite from the NAG Library to model a microgrid and design it's battery energy storage system capacity. The model is also able to give operational schedules for various components in the microgrid. The model can be easily extended with additional components, such as additional power source from solar panels or wind farms and more switchable loads. The [NAG MILP solver](https://support.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.mip.handle_solve_milp.html) serves as a powerful tool for modelling and managing energy systems. Learn more about it [here](https://nag.com/mixed-integer-linear-programming/). " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.17" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/local_optimization/MILP/Grid_Model.png b/local_optimization/MILP/Grid_Model.png new file mode 100644 index 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b/local_optimization/Modelling/Readme.md @@ -42,7 +42,7 @@ width="100" height="80px" alt="Data fitting Plot"/> # Useful Links * [Background to Optimization Methods](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#algorithms) -* [Nag Blog](https://www.nag.com/content/nag-blog) +* [NAG Insights](https://nag.com/insights/)

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It produces a plot showing the steps taken by the solver to find the solution point." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from naginterfaces.base import utils\n", + "from naginterfaces.library import opt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Add objective function, gradient and monitoring callback" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "objfun = lambda x, inform: ((1. - x[0])**2 + 100.*(x[1] - x[0]**2)**2, inform)\n", + "\n", + "def objgrd(x, fdx, inform):\n", + " \"\"\"The objective's gradient.\"\"\"\n", + " fdx[:] = [\n", + " 2.*x[0] - 400.*x[0]*(x[1]-x[0]**2) - 2.,\n", + " 200.*(x[1]-x[0]**2),\n", + " ]\n", + " return inform\n", + "\n", + "\n", + "steps = []\n", + "def monit(x, rinfo, _stats, _data=None):\n", + " \"\"\"The monitor function.\"\"\"\n", + " steps.append([x[0], x[1], rinfo[0]])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Specify initial guess" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "x = [-1., -1.5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the nonlinear objective (add to handle)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "nvar = len(x)\n", + "handle = opt.handle_init(nvar)\n", + "opt.handle_set_nlnobj(handle, idxfd=list(range(1, nvar+1)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Add the box bounds on the variable x to the handle" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "bl = [-1., -2.]\n", + "bu = [0.8, 2.]\n", + "opt.handle_set_simplebounds(\n", + " handle,\n", + " bl=bl,\n", + " bu=bu,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Set some algorithmic options" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "for option in [\n", + " 'FOAS Print Frequency = 1',\n", + " 'Print Solution = yes',\n", + " 'FOAS Monitor Frequency = 1',\n", + " 'Print Level = 2',\n", + " 'Monitoring Level = 1',\n", + "]:\n", + " opt.handle_opt_set(handle, option)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use an explicit I/O manager for abbreviated iteration output" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "iom = utils.FileObjManager(locus_in_output=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve the problem" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " ----------------------------------------------------------\n", + " E04KF, First order method for bound-constrained problems\n", + " ----------------------------------------------------------\n", + "\n", + " Begin of Options\n", + " Print File = 9 * d\n", + " Print Level = 2 * U\n", + " Print Options = Yes * d\n", + " Print Solution = All * U\n", + " Monitoring File = -1 * d\n", + " Monitoring Level = 1 * U\n", + " Foas Monitor Frequency = 1 * U\n", + " Foas Print Frequency = 1 * U\n", + "\n", + " Infinite Bound Size = 1.00000E+20 * d\n", + " Task = Minimize * d\n", + " Stats Time = No * d\n", + " Time Limit = 1.00000E+06 * d\n", + " Verify Derivatives = No * d\n", + "\n", + " Foas Estimate Derivatives = No * d\n", + " Foas Finite Diff Interval = 1.05367E-08 * d\n", + " Foas Iteration Limit = 10000000 * d\n", + " Foas Memory = 11 * d\n", + " Foas Progress Tolerance = 1.08158E-12 * d\n", + " Foas Rel Stop Tolerance = 1.08158E-12 * d\n", + " Foas Restart Factor = 6.00000E+00 * d\n", + " Foas Slow Tolerance = 1.01316E-02 * d\n", + " Foas Stop Tolerance = 1.00000E-06 * d\n", + " Foas Tolerance Norm = Infinity * d\n", + " End of Options\n", + "\n", + " Problem Statistics\n", + " No of variables 2\n", + " free (unconstrained) 0\n", + " bounded 2\n", + " Objective function Nonlinear\n", + "\n", + "\n", + " -------------------------------------------------------------------------------\n", + " iters | objective | optim | dir\n", + " -------------------------------------------------------------------------------\n", + " 0 6.29000E+02 5.00E+02 3.50E+00\n", + " 1 6.29000E+02 5.00E+02 3.50E+00\n", + " 2 4.00000E+00 0.00E+00 1.80E+00\n", + " 3 4.00000E+00 0.00E+00 1.80E+00\n", + " 4 3.99156E+00 2.80E+00 2.80E+00\n", + " 5 3.99156E+00 2.80E+00 2.80E+00\n", + " 6 3.98433E+00 1.44E+00 1.44E+00\n", + " 7 3.97076E+00 5.76E+00 1.79E+00\n", + " 8 3.41157E+00 1.66E+01 1.60E+00\n", + " 9 3.15876E+00 2.07E+01 1.65E+00\n", + " 10 2.34744E+00 2.55E+00 2.29E+00\n", + " 11 2.06122E+00 5.09E+00 1.83E+00\n", + " 12 1.97065E+00 6.49E+00 1.88E+00\n", + " 13 1.77751E+00 9.58E+00 1.99E+00\n", + " 14 1.19453E+00 2.20E+00 8.93E-01\n", + " 15 1.12429E+00 2.33E+00 2.01E+00\n", + " 16 1.01998E+00 5.04E+00 2.02E+00\n", + " 17 8.94996E-01 8.97E+00 2.02E+00\n", + " 18 7.06184E-01 1.32E+00 1.10E+00\n", + " 19 5.06340E-01 5.11E+00 1.91E+00\n", + " -------------------------------------------------------------------------------\n", + " iters | objective | optim | dir\n", + " -------------------------------------------------------------------------------\n", + " 20 3.21115E-01 1.03E+00 3.67E-01\n", + " 21 2.99551E-01 9.31E-01 9.31E-01\n", + " 22 2.51003E-01 2.68E+00 1.75E+00\n", + " 23 2.14196E-01 4.82E+00 1.66E+00\n", + " 24 1.15236E-01 1.17E+00 3.70E-01\n", + " 25 8.06733E-02 1.98E+00 1.73E+00\n", + " 26 6.60815E-02 4.33E+00 1.79E+00\n", + " 27 5.37636E-02 3.33E+00 1.80E+00\n", + " 28 4.02960E-02 3.44E-01 3.44E-01\n", + " 29 4.02960E-02 3.44E-01 3.44E-01\n", + " 30 4.00937E-02 1.94E-01 1.94E-01\n", + " 31 4.00937E-02 1.94E-01 1.94E-01\n", + " 32 4.00000E-02 0.00E+00 0.00E+00\n", + " -------------------------------------------------------------------------------\n", + " Status: converged, an optimal solution was found\n", + " -------------------------------------------------------------------------------\n", + " Value of the objective 4.00000E-02\n", + " Norm of inactive gradient 0.00000E+00\n", + " Norm of projected direction 0.00000E+00\n", + " Iterations 32\n", + " Function evaluations 75\n", + " FD func. evaluations 0\n", + " Gradient evaluations 36\n", + " NPG function calls 18\n", + " NPG gradient calls 3\n", + " CG function calls 9\n", + " CG gradient calls 5\n", + " LCG function calls 48\n", + " LCG gradient calls 28\n", + " -------------------------------------------------------------------------------\n", + "\n", + " Primal variables:\n", + " idx Lower bound Value Upper bound\n", + " 1 -1.00000E+00 8.00000E-01 8.00000E-01\n", + " 2 -2.00000E+00 6.40000E-01 2.00000E+00\n", + "\n", + " Box bounds dual variables:\n", + " idx Lower bound Value Upper bound Value\n", + " 1 -1.00000E+00 0.00000E+00 8.00000E-01 4.00000E-01\n", + " 2 -2.00000E+00 0.00000E+00 2.00000E+00 0.00000E+00\n" + ] + } + ], + "source": [ + "ret = opt.handle_solve_bounds_foas(handle, x, objfun=objfun, objgrd=objgrd, monit=monit, io_manager=iom)\n", + "steps.append([ret.x[0], ret.x[1], ret.rinfo[0]]) # Add last step" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Retrieve Lagrange multipliers" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lagrange multipliers: [-0.4 0. ]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from naginterfaces.base.opt import handle_set_get_real\n", + "mult = np.empty(2*nvar)\n", + "mult.fill(0.)\n", + "ret = handle_set_get_real(handle, \"Dual Variables\", 1, 2*nvar, mult)\n", + "print(\"Lagrange multipliers: \", mult[0:-1:2]-mult[1:ret+1:2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Destroy the handle" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "opt.handle_free(handle)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Evaluate the funtion over the domain" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "x_m = np.linspace(bl[0]-0.5, bu[0]+0.5, 101)\n", + "y_m = np.linspace(bl[1]-0.5, bu[1]+0.5, 101)\n", + "z_m = np.empty((101, 101))\n", + "j = y_m[0]\n", + "for i in range(0, 101):\n", + " for j in range(0, 101):\n", + " z_m[i, j], _inform = objfun([x_m[i], y_m[j]], 1)\n", + "nb = 25\n", + "x_box = np.linspace(bl[0], bu[0], nb)\n", + "y_box = np.linspace(bl[1], bu[1], nb)\n", + "box = np.array([np.concatenate([x_box, bu[0]*np.ones(nb), x_box[::-1], bl[0]*np.ones(nb)]),\n", + " np.concatenate([bl[1]*np.ones(nb), y_box, bu[1]*np.ones(nb), y_box[::-1]])])\n", + "z_box = np.empty(box[0].shape)\n", + "for i in range(0, (box[0].size)):\n", + " z_box[i], _inform = objfun([box[0][i], box[1][i]], 1)\n", + "\n", + "X, Y = np.meshgrid(x_m, y_m, indexing='ij')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot function and steps taken" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Jupyter magic for displaying figures inline:\n", + "%matplotlib inline\n", + "steps = np.column_stack(steps)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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OvV4/o7HgvCzLCCEwODhImqZn/PraML6AJEmSJEmSJEmSJEmSFjEW3KGMAbWVrGUsOH/9GCP9/f2USqU1uYfWnS8oSZIkSZIkSZIkSZKkRdamvNGGOxMxoMuyaqdIkoQ8z6lUKsQYKZVKxrCSJEmSJEmSJEmSJEnaVowFt6hTxYDdZow0BpQ6S5KEEALVapU8z+nt7TUYlCRJkiRJkiRJkiRJ0rZhLLhJPdQYMIRg6KRt4xTLpZ8xIQTSNKVer5PnOf39/T5HkiRJkiRJkiRJkiRJ2haMBTeIMaC0Oc0Hg81mkxgj/f39zsIpSZIkSZIkSZIkSZKkLS+cYsau9ZnOaxvqFgPOh4CrWSbYGFCalWUZjUaDQmH9+ub55zVJEgYGBkjTdN3urTPCF6gkSZIkSZIkSZIkSdIixoIPkjGgtH7a7TbNZnNdY8F5WZYRQmBgYGBD7q8HzResJEmSJEmSJEmSJEnSIpYvp7A4/judGNBlgqXtIU1T8jynXC7T399PqVTa6CFJkiRJkiRJkiRJkiRJp81Y8CRijDSbzSVhoDGgtDE28nlLkoQ8z6lUKsQYKZVKPv+SJEmSJEmSJEmSJEnaUowFT8IwUNo8TrFk+ppLkoQQAtVqlTzP6e3t9b0gSZIkSZIkSZIkSZKkLSPZ6AFI0qlsdCg4L4RAmqY0Gg2q1eqmGZckSZIkSZIkSZIkSZJ0KsaCkja9zRTlhRBIkoRWq0WlUiHP840ekiRJkiRJkiRJkiRJknRKxoKn4DKj0uawmZ7F+WCw3W5TLpfJsmyjhyRJkiRJkiRJkiRJkiSdlLHgKWymQEnS5jG/JHGe55TLZVqt1kYPSZIkSZIkSZIkSZIkSerKWPAUQgibaglUSZtLmqYAVCoVms3mBo9GkiRJkiRJkiRJkiRJ6sxYUNKmt9mD3SRJSJKEarVKvV7f9OOVJEmSJEmSJEmSJEnSzmMseAouQyxpNUIIJElCvV6nVqsZDEqSJEmSJEmSJEmSJGlTMRY8BWNBSas1Hww2m00qlYrBoCRJkiRJkiRJkiRJkjYNY0FJG2/6gVMeslXC3flgsN1uUy6XyfN8o4ckSZIkSZIkSZIkSZIkGQueylYJlKStKhz8Nsndt530mK02Q998MJhlGeVymSzLNnpIkiRJkiRJkiRJkiRJ2uGMBSVtnPIxkjs/Qigf2+iRnHEhBNI0JcZIuVym1Wpt9JAkSZIkSZIkSZIkSZK0gxkLnoIzC0prpN0kueM/oN2E2gRk7Y0e0ZpIktnXbKVSodlsbvBoJEmSJEmSJEmSJEmStFMZC0pafzGS3PlRwsyR2e0QoHb0JIdvrWWIl0uShCRJqFar1Ov1Lf99JEmSJEmSJEmSJEmStPUYC66ScY905oT93yAc/N+F7Tg2QGgdP/k5W3yWzxACSZJQq9Wo1Wq+UyRJkiRJkiRJkiRJkrSujAVPIYSw5SMlaVOZPEDy3Y8vbMaRYUJhBurbd2bBeSEE0jSl0WhQqVS2zfeSJEmSJEmSJEmSJEnS5mcsKGn9NKukd/wH5BkAsa+f0DMFQKgf28iRrZv5YLDdblMul8nzfKOHJEmSJEmSJEmSJEmSpB3AWHAVnFlQOgNiTnLvrVCbjQMpFAhDLZh/vE4ys+B2Mx8MZlnGzMwMWZZt9JAkSZIkSZIkSZIkSZK0zRkLSloX4fBtULt3YTuO9UBondjfGIe81enUbbtcb5qmAMzMzNBqdf7ukiRJkiRJkiRJkiRJ0plgLLgKIYRtGytJ6yFM3UVy+AuE0AACcfcwIaksPShG6LAU8XZ/9pIkIYRApVKh2Wxu9HAkSZIkSZIkSZIkSZK0TRkLroLLEEsPQf0Yyf6bZ38OkTg2TChMdjw01I50vcx2fg6TJCFJEiqVCvV6fdsHkpIkSZIkSZIkSZIkSVp/xoKS1k7WINn375A1AIilXsJwBt3Cv3r3WHC7CyGQpim1Wo1arWYwKEmSJEmSJEmSJEmSpDPKWHAVtvOMZtKaiZFk/4cI9aOz20lKGI3Enu7PU+gSC+6UZ3A+GGw0GlQqFYNBSZIkSZIkSZIkSZIknTHGgquwU0Il6UwKR75AmPrewnYc64O0AcXuAVynZYh3WjA3Hwy2223K5TJ5nm/0kCRJkiRJkiRJkiRJkrQNGAtKOvPKd5Mcvm1hM44MEUplAEKh2f28Vnn2vx1uPhjMsoyZmRmyLNvoIUmSJEmSJEmSJEmSJGmLMxZchRCCswtKq5UdI6l9BOZmBIwDuwh9Uyf2pw1IOr964vAQ8MA6DHJrSNMUgJmZGVqt1gaPRpIkSZIkSZIkSZIkSVuZseAq7bSlUKUHJa+TzNxECNOQJMSePsJQGZbFtrHUs+LU2NdP2D1DiEfXa7RbQpIkhBAol8s0Go2NHo4kSZIkSZIkSZIkSZK2KGPBVXBWQWkVYk5S/k9CdhxCIPb2E0YzCB1C21Jx6XahSDinBSESssNLL2uoS5IkpGlKtVqlXq/7O5EkSZIkSZIkSZIkSdJpMxaUdEaE6qcJrXsAiATy3UVImp2PLS4KcENCPK8A6dwyu7nLEHcSQiBNU2q1GrVazWBQkiRJkiRJkiRJkiRJp8VY8DQY50idhcb/kNS/vLDd3jVM7O9+fCy0T/x8zgChVDtxrfwYxNaajHOrmw8GG40GlUqFPM83ekiSJEmSJEmSJEmSJEnaIowFVyGE4FLEUjet/STl/1rYbPeN0O6rkBeyrqeEdDYOjGNDhIGZpTtjhPzwok0j3cXmg8F2u025XDYYlCRJkiRJkiRJkiRJ0qoYC0p60GI+RVr+d2A2DMyLu2gPlud+bnQ/McmJoyOEkamOu0N26EwPdVuZDwbzPGdmZoYs6x5mSpIkSZIkSZIkSZIkSWAsuGrOLCgtFWnSSv8/Yj4bB8a0l+Zwgzj3rMQkJ6aljufmhX6ys3Lo8lyF7IGl2z5/HaVpCsDMzAzNZnODRyNJkiRJkiRJkiRJkqTNzFhQ0mmL5LSTDxOTI8S0lxgKNEYSYrJ0yeBY6Fl5blKkPFoiK3YOCQHIl84s6FLE3SVJQgiBSqVCo9HwdyVJkiRJkiRJkiRJkqSOjAVXKYRghCPNycJt5OEeAPJCidZwPzFtrTguLxSWbMeQUBnZRZZmtAvdn6eQH4U4ez2fu1NLkoQ0TalWqwaDkiRJkiRJkiRJkiRJ6shYcJVcBlWalYU7yJKvABCB+uAAWanW8di8mC/Zrg2N0SrNRoCtDnHhwj2SPtocPTMD3iFCCKRpSq1Wo1qtGgxKkiRJkiRJkiRJkiRpCWNBSauW8wPayScXtpvxbCpJsfvxxebCz42BPTT6GgvbMYnkSadliktMDvbRTo7NbsdorLtK88Fgs9mkUqmQ5/mpT5IkSZIkSZIkSZIkSdKOYCy4SsZK2ulyjtJKbwZmA7R2HGU65DRDzuwcgyvFpEVMCrR6R6kO1ldeM+1benxImBoYIUty2uHwmf4KO8J8MNhutymXy2RZttFDkiRJkiRJkiRJkiRJ0iZgLLhKxoLaydpUaKX/AczODJjFXUyGAhDIiURWzhAIQAi0+kaoDLegwzOUpYWFn2OAcv8emoX23D2PnOmvsWPMB4N5nlMul2m32xs9JEmSJEmSJEmSJEmSJG0wY0FJJ5XTYjz5NHlszW33Mhn6lswlmNHf+dzYz9TgILFLbNsunLhKtfdsaqUTUVsWJsmpEWPnWQt1ammaAlAul2k2m6c4WpIkSZIkSZIkSZIkSduZseAqObOgdqJIznhyG81wjIxeIkWmGCZftuxwFksdzi1yNOymQbHr9VvpbIBY79lDpXfl7Hft4OyCD1WSJIQQqFQqNBoN40tJkiRJkiRJkiRJkqQdylhQUkeRyFRyO/XwQwBalJiJu2mTrzi2RWHZJwnH4rk0gWZYefzCPZJIvedsZvqyjvvbPPBgh69FkiQhTVOq1Sr1et1gUJIkSZIkSZIkSZIkaQcyFlwlZxbUTlMO36YcvruwPR1HaITOUV9jWRA4GS+gPvfItMmJK2LCWXkcZKLvJMsUh9lY0OfvoQshkKYp9XqdarVqMChJkiRJkiRJkiRJkrTDGAtKWqEavs9U8lUAItBkD1NJoFtelpERKQKRGS5gZknbF8gZWHFOpJejYYh26L5McTscJo+dA0WdvvlgsNVqUalUyPPusz5KkiRJkiRJkiRJkiRpezEWPE3OxqXtrs5BJpIvLGxncYxpmFt8uKfLWYGMAarxPCY7vFayWFqyHSlwnDEyoBG7v4YiGS0mT/cr6CRCCCRJQrvdplwuk2XGmJIkSZIkSZIkSZIkSTuBseAqhRBcClXbXpUpjiX/TWQ2IMvjMBOL/u5j7O167kw+yvHQebnh5pJXTcJEPIfm/L6QAZ2frZl4DpXUWPBMm59hMM9zyuUyrVZro4ckSZIkSZIkSZIkSZKkNWYsKAmABhW+n95OmxSAyC7GQ4GwKORr0zkGzBniaBihW/TXDDnMLWI8Fc+lHk7M0BkJxDi47IxINZ5LJURq4fiD/k46uTSd/beuVCo0m81THC1JkiRJkiRJkiRJkqStzFjwNDizoLarFo25ULBBi5QYBxinh+XxX2suJFwsjwMcZpBGgPkgcLkMiLGfcjyfSofHqL1seeN6PIfpueNqyXi3BlFnQJIkJElCpVKh0Wi41LokSZIkSZIkSZIkSdI2ZSx4GowFtR1ltPh+cjsNKgDUKTEZ+jpmf42QLdmOsY+jYZgIZERYFv0tNhXPXQgAl2suihCbcQ+Ti561FjVaVFf7dfQgzC9LXKvVqNVqBoOSJEmSJEmSJEmSJEnbkLHgaQghGNFoW8nJuDf5GrUwBUCgyPEwQNbl1ZATiLEPgEiJY2GUxflgjL0dz2vHMSbDQNdxNOaWKW7HUcZDyvKpBGuJSxGvtRACSZLQbDapVqu+6yRJkiRJkiRJkiRJkrYZY0Fph4rk/CD5BuVwbO6TlJk4REYg6RL9AeT0ECkwHvfQWravHYorjs/iMEdDkcZJXjcZ0IxncTyU6LTmcDU5tuIznXnzwWCr1aJcLpPn+UYPSZIkSZIkSZIkSZIkSWeIsaC0A0Ui+8J3mQoPzH2SUI3DNMPsbHIZpa7nNikyEc+m0WFJ4WZc+mHOEEdCL4EwN3tguvIkgNjPccaIHUJBiNSMBdfNfDCYZRnlcpksy059kiRJkiRJkiRJkiRJkjY9Y8HTkCT+urT1RSJ3hX0cnVt6GAL1OEJ9UafX6vpqCIxz1pJjF6uHnPmZAWMc4Ah9hLnt2f/3dRhQL8fDIC1WzkoIs/FiK1RpUjnVV9vRYp7TLJfPyLVCCKRpSp7nfPvb3+aOO+44I9eVJEmSJEmSJEmSJEnSxrF+k3aYe8P9/DA5RIMABBpxlOqy+K8WYD7UW6wSz+J4SOn+6ggQ+yH2cTQMsnxJ4SyWlh1dYjwMkcHcGFbeEyDGIcaT6VN+t53s4Fe+QlrqPiPkg5GmKV/84hf5/Oc/f0avK0mSJEmSJEmSJEmSpPVnLCjtIPvCQe5N7gdmg8BGHKXSYZbANoGwbKa/WjyLqTC7jHCIvV3v0aCfo2GYvMOSwo1Fr5xAkQlGaM9tZ0CIPSsvmA9yPJSYSqZW7hMAMwcOML1v3xmPBQEmJyfZs2fPGb+uJEmSJEmSJEmSJEmS1pex4GkIocvaq9IWcH94gLuSfXNbkTwOU6dDnLegd+HYRjyLiVBY2JPROUoLlDjGbrIuV6wtLFOcMhlHaS7bn7MsQowDHE96CcBUmCJ2mXlwJ2s3Gtx9yy0MP/zha3L98fFxxsbG1uTakiRJkiRJkiRJkiRJWj/GgtIOcDAc4bvJfXNbERhmKiTkXaI/gCwWgUiTszi+KBQEaHV8dRQ5zijTIT1J0hcgDjIdd9Po0N42F81mGGIfxxfFg63QpBIqXa+8U9338Y9Tn5xk7LLL1uT64+Pj7N69e02uLUmSJEmSJEmSJEmSpPVjLHganFlQW9FBJvhO8v25rQhxmAlmlxNuUuh6Xo1AK+7h2LLliAGqISwJAgMFJhmjSSAH0k7LCc8dOcFu6l0epVqYHWOIvUyE/hXR4WQy2XW8O9HRb3+bo9/+Nv179tA7Orom95icnDQWlCRJkiRJkiQ6wIqVAAAgAElEQVRJkiRJ2gaMBR+EGF0KVVvD/jDD15Ijc9FdJMRhJkK6sL8WQtelfasMcyx0jv4yIFkIAlMm427qnCgAO89YGKjHMconWfo4A4hDTISBjksZT4aJrufuNPWJCe77+McBGF2jWQXBZYglSZIkSZIkSZIkSZK2C2PB0+DMgtpK7g9lvpQ8QCUABEIcYnxRKAjQIpB2mDkwxmEOhz7S2H2Z4kgPkDIV91Bb9my0OsxY2IhjzISEaghA52cpUGSCsY6hIMB0Mk3Wde/OkWcZd91yC+1GA2DNliAGmJ6eZnh4eM2uL0mSJEmSJEmSJEmSpPVhLHiaDAa1FRwIZb6UHCISCQTyfJTx0GXJ4eVBYBzmgdBLIBA7zhA4q0GR6Q6hIEA1JEtmLGzE3UyH2ddNBJLYu+KcQJEpdlFbdM/lcx5GIuNhpuuYdor9t91G+eBBAEqDgwxecMGa3s/3niRJkiRJkiRJkiRJ0tZnLChtMwdCmS8mh8jnUrtC7Gcm9Hc9PguLZhaMQxyaCwUBmqQdzwkkHGc3lS4RWRtI55YpbsaxhVBw3vJligMFphiiSZi7ZqfrBlpxhENJtet32Qmm7ruPg7ffvrA9dtllxnySJEmSJEmSJEmSJEk6JWPB02SUo82sUyh4NBRpdlgWeF49zgWBcYhDoW8hFAQoh5WviEBCJY4xGQqkJ7luTg/NOMZUWBkc1ha9egIFZhimuXAeJPStuGs7jjATAkeS8pJZC3eSvFzm0Gc+Q4wnvv/oj/7omt2vVqvR27tyFkhJkiRJkiRJkiRJkiRtPcaCp8lYUJvVfdT5QnKQnEgkLoSCgUA5pF3zumoI5B1CQZgN99J4YubB+VCwPBcAhuVLGM+JwHSXUHD2nhBICRSYjsPUl+1vz888GGezwHYcZnru2auFFtOhcZLfxPYUY2TqQx9iZnx84bNSXx/DF1+8ZvecmJhg9+7da3Z9SZIkSZIkSZIkSZIkrR9jwdMUQlgyq5e0GXw/NPhEOkMaUyKRYhzkWCgtxH85UFwU/S2WxEEmGFkRCp4wu5zw8lAQoMXKa0YgjyMcTrrPSBcIhNjPdBym0eG2VWbjxghkcXjFMsaHk5mu196ual/+MtUjR2i1WsDsu+jSKx5JknYOMs+E8fFxxsbG1uz6kiRJkiRJkiRJkiRJWj/GgtIWd0+o86lkem5p3sJcKLgy4gsdwr4k7uJg6CfvsG9ei8JcKLh7SSgIUAnJshkLA1kcYTwUyQgUusw8mJAyzmjHUBCgDiSxRBZHmElWxnAPJNNdx7sdte6/n8ptt1Epnvh3umBkiJGHX7Km9x0fH3dmQUmSJEmSJEmSJEmSpG3CWFDawv5vqPPpZGZu4WFoxl0dQ0GAJoWFnyMQ4i4Ozi09XF+0b7kqCeU4RjmsfF20CBQWZiwMtOMIE4vun7MyFkxImYlDTIbOIeG8WhxjOiR0mshzKtSp0jzp+dtFXqsxffPNxDyn3Jz9zsODAzysWYM1jgVdhliSJEmSJEmSJEmSJGn7MBY8TUnir0ybw52hxmfnZxSMUGj3c7Td3/X4cjixtG+IQzwQ+heWHi6HpOMyxAkpk+ymObcUcWclToSCS6PD+rIZC+dDwXpIloWGS8U4zGQYmBttJ4EDSf0kY9o+Zj7yEbLpadqlEvVajVKpyI/mTcKPXAaF7pHnmeAyxJIkSZIkSZIkSZIkSduH5Zu0Bd1Bhf+TzMxuREjaAxzPSlRjIImdH+sWgQIFYJjDoW/Jvtgh3EtImY4jlEOh4xLG8+oUaHYIBQFmFkWICSnTDFNfNENhXBEhBmIcYjKks+d2/C6BZhzm3mT7zyxY/cpXaNx1FwC1vj5CCPxoX4medov4iB9b8/uPj4+zZ8+eNb+PJEmSJEmSJEmSJEmS1p6x4GkKYeXsa9J6iTFyW5bzzdCa+wBoDzKez8Z8gUAxdpltLgZq2RhH6O24O18UBM7OKDhKZS4AbHRdpjgwFUeZ6hAKzkvpJaXANMM0ls1eWFty3UAeh5hcdK0k9rD0kZsNBasBjiQNKmRd77vVtQ4epPLZzy5sl9tt9o4MMVKrEHt613wJYoDJyUmXIZYkSZIkSZIkSZIkSdomjAWlLSLGyCeynC9mOVlWIMRAbA8ymS8N9bK8Q7gXA7Gxi5nWQNfr1+fCvZQCE4xSI13YN90hBgwktPIhJkKRUpflhAGasYdJhlaEggCVkJCQMh8KToV0yf4GpUX3CzTmQsF5P0xqXe+7lcV6jembbyZmszFkVixSTAIXVqZmD7jsckjTk1zhofviF7/Ivn37XIZYkiRJkiRJkiRJkiRpmzAWlLaALEY+lOV8PY8A1LICrfYgUx3CwFq+NCILMZA1hjjW6mWmXSR2ucdMSCjEEscYpc7Sa2QEinHxzIMJ9XxoISKMXWYeLMYCD+SjHUPBhWvFHrI4vCIUBGY/i4FAQi0OU1t2mR+k2zMWzD73SbLJyYXt9uAgP9quL7yw4yPXfgnigYEBPvOZz3DgwIE1v5ckSZIkSZIkSZIkSZLWnrHgaXIZYq23Zoz8e5Zz51woWIxQn+qlmnUO9CoxJcTZv9MQExq1EcZbPQA0YkIx7/zYl7Ii49luml1fC7OxYEJCJQ5RXhT3VTvEgsVY5Fi+iwoFSt2WRiZhOo4yHTrfMyeQxn5qcYh6h0fvWGgyQ7vLtbem5Fu309j3w4XtkCScE5uUstnvGQd3wcMuXvNxXHnllVx66aW8/vWv52Mf+9ia30+SJEmSJEmSJEmSJElry1jwQYqx2/xs0plTi5F/bed8fy4U7ImBfKpEvZXS2yX6AyjFIklMqNVGmMqWLhFcyFcuGdzTLnBsahha3ZcTrlIgJWUmDlNdNvNgmYRk0eukGIsczQfI5mYUjLHEcrPLGO/iSOghdJl5MIkJk3GkYygIEIH7kkbXMW814YH7Kdz+Oerl+sJnQxcM01OrLmzHH78C1ilajjHy8Y9/3NkFJUmSJEmSJEmSJEmStgFjwdMUQnB2Qa2LqQz+vQoH5sLUvjzQnCzSzOZmDWx1/ztstUpMV0eZ6TD7YLO99LPeVonDU8PkMVBrdpsBEJp5kalsiHqH10ZYtExxKZY4kg+SLzquGovLjk+px11UQiDCkiWO5yUUqDLIsaQHOsSEESjEfv43jcSuiytvIbUqhU/eTDMpkTWaAPSdNUR/mhHm4+Q9uwj/zxXrNqQYI2eddRYvfelL1+2ekiRJkiRJkiRJkiRJWhvGgtImdLgF1x9LOVybfUQH2wnVySLt/EQ012x2fnx7s4TyeD+1PO24f6ZdWEjrepq9HJrexXyMV26nFOLKMK+3nTI9sYu03dN1zM1YpBR7eCAfIC6L+2ZISOdmI0xIqcZd1BYd02LpzINpLFChn2aAGALFZTMTzoeCkyFlKuQcDlnXcW0JMVL4zIcI5Wlqc9+1MNDL6K4KsTL73eJAD8klg8Thc9ZpSNsgwJQkSZIkSZIkSZIkSdICY0Fpk7mvATccS5nOoNYMDDUTpqYL5MsivmozIVn2WX8rpXKkRLmeUOjSerViQilPKdX6eWBmYMkSwIFAadnMg32tAuOTA7RjIGt1DhABGo1eDmX9dJoFMBBIYpE0FpmJu1i+cPAkhYXzCrHIdOinSWC+V2usiAkHmAwnxvK9pNV1XFtB+vUvkvzwXgBqlQYhTdl9ToSQEqeqxDQl3RvI9/7Yuo1pZmaGoaGhVR27f/9+fv7nf54f+7Ef44orruCtb30rAOPj41x99dVcdtllXH311UxMTACzIeIrXvEKLr30Uh71qEfxjW98Y+FaN9xwA5dddhmXXXYZN9xww5n/YpIkSZIkSZIkSZIkSTuUseCD4DLEWiv/Ww3863hKIwIRhtrQmi5Ch9n+iIG+7MQjPNhImTpaJI+BQKCvy2R7AYhTgxyp9i8JBee1Fy1F3N8scmyynzh3/3KjsGIsEeir9nB0uo/+7CQxYauXKQbolPVFoBSLFGKJidBHe9m4pkKBZP51FQeYCktfXfekbVpbdCnisP9e0q/9HwBahV7a1Tqje/sp0iBmfQQi6cP7SQot8gt+fN3GNT4+zu7du1d1bKFQ4M1vfjPf+c53+PKXv8zf/d3f8Z3vfIe/+Iu/4IlPfCJ33303T3ziE/mLv/gLAG699Vbuvvtu7r77bt75znfyW7/1Wwv3fMMb3sDtt9/OV77yFd7whjcsBIaSJEmSJEmSJEmSJEl6aIwFHwRjQZ1pMcLnZwI3TyZkcTboG2pFpsuBQrt7BBdas7PvDVYLjB8vsnhWv9Ba+XeaROifCtRmCiv2zZtpFCFCX73Ekam+Jdds5Qm9+aLXRgz0lns5Xu6ZDQ+bxY7X7G0WODo9uBAddtJq9zEResk7BIyRQJr3kMdBZsLK11aTyD1bcXbB8jTFT32I+SkUq6GHgfOG6E9mAIjTLcKFwySlGfKzL4NS/7oNbWJigrGxsVUde9555/HoRz8agF27dvHIRz6SAwcOcMstt/DCF74QgBe+8IXcfPPNANxyyy1ce+21hBD46Z/+aSYnJzl06BAf//jHufrqqxkbG2N0dJSrr76aj33sY2vzBSVJkiRJkiRJkiRJknYYY8EHIYRAjFtzFjNtPlkOHz0cuG1m9nEsAH21yHR1NpprLF+zd5FqPWGgXGRisrhilsBaPbB4sr1ihJ6JQKWWUGmErg9/Owb6pvs4NtPXcebB0JydPTDEQGG6l4nqiSWCK410xfx+/Y0iU+UespjQ0+ocKfbVSxyc2QVx+ahmr5bEwHRjiEq3UDcG7sy32Osszyjc9l9Qr574KAmM9M6GgnnohZ6EZNc0ANne/3ddh3c6Mwsu9oMf/IBvfvObPPaxj+Xw4cOcd955AJx77rkcPnwYgAMHDrB3796Fcy688EIOHDjQ9XNJkiRJkiRJkiRJkiQ9dFusrpG2l1obPrAv4etHE0oReoC0HKk2TkRx1WagU2KXAul4QrXLLIGtLNA3V+715sDxhFrzxCM/kK88J4kwOBNplTvPEAhQaxRJYyBO9THdWHpcM0sWlkaOEfpqJcYrPcS56LDZWDrWGKG31svxai8xJvS2V36XQh5oV/s42i5R7BAEhhiIrT7ui4HDWyjiTe/8NMmB/QvbWU8vu/orhDD7HWLoIz27TgiR2DdM3HPJuo7vwcSC5XKZZz3rWbzlLW9haGhoyb4QgrOySpIkSZIkSZIkSZIkbSBjwQfB4EVnwrEGvPvelH2VQAgw0I60p6HRXvr3FQL0L4vgeoDiRKRaC/Tl3QO5YhsG29A8ltBaft3W0vOKEXqmI+VaoFHrPu6sGYjH+6k2O0eKSTOdDQWrvUzUSkv2TTcKpHNLEccY6K32Mb7omEZ9aXyYthPq1X5qeTI7y2Fr6fWSPNBu9VGdu+Y3VsxruDklB+4kue//QpbNfZAQzumjQOvE9q46IbQByB72E7N/COvodJYhBmi1WjzrWc/iec97Hr/6q78KwDnnnMOhQ4cAOHToEGeffTYAF1xwAfv3nwgl77//fi644IKun0uSJEmSJEmSJEmSJOmhMxZ8EIwF9VDdW4b33Jsy3pzdHiKSTc4uSdxR68SP/THSPgr15lx01+pyDpDOQPlYQp6v/JtdvExxbx5hAmpzMxrWWoGeDt1dfzvSnkhImt1fHdVqgZ5yH5OLZhH84Q9/yPe+9z0g0NMsQAyUyn1MLJuZcLpZoDAX/pXaKZVqH814YuwTzRJzE++R5gmNVj/1Rfu/C1Q2+eyCYfoIhW99FOonxp1ftIukdaLQzM8fJYmz23F4iPyi9V2CGGZjwT179qzq2BgjL33pS3nkIx/J7/3e7y18/vSnP50bbrgBgBtuuIFnPOMZC5+/973vJcbIl7/8ZYaHhznvvPN40pOexCc+8QkmJiaYmJjgE5/4BE960pPO/JeTJEmSJEmSJEmSJEnagTpPDSZpTcQIXzke+NThhPkJAYczmJwOlArAENChRa3VA5RgKIvMHAtL5s+r1sLsVIPLDDdgfDIl3Q2dGsRWBn1E0ixQnQjkiw4KQE870iieGMxQMzIzPXvvVh0YXHnNQoQwk9DaxUKK/PWvf52PfexjJEnCK1/5SuppkVAvMZWlHUYVKDaKFNLIRL1Em/aSorlNSikrkScZM61esmVnZ0T+h8DPdLjyptCqU/jaf0C7TZiqAhDPGyIMNGGyPrc9TAizBWjs6yO/5CIoDKz7UCcmJla9DPEXv/hF3ve+9/HjP/7jXHnllQD8+Z//OX/0R3/Es5/9bP75n/+Ziy66iJtuugmApzzlKXz0ox/l0ksvpb+/n/e85z0AjI2N8frXv56f+qmfAuCP//iPT2t2Q0mSJEmSJEmSJEmSJHUX4sln4drcU3RtkDzPaTQaJIkTM2r12jncenfCXW2oxkAK9DYjleqJIK93d1wyU96CCCN9kYnp0KklpG8sUpvbk0borUYqldntXaMw0+mkCGOlnPFa57/j/t5IdTAQIww3ItMzYSFkjBF6xqC56Lq9eSSfCTQzGN4VmSzCpz79Kb5y++1ccOGFHLj/fn75F67mp654LGEIGl0m6BzJMqb6IpFAq9UiCWHJEryjsU21J+8YQMYIe5pFru3JKWy2CUBjpPDVfyc5fDeRQcL9ZeLwAGFvlVgfIhyfIo4MEs6rw6EckoT4sJT2xdcQe89f9+H+xm/8Bq973eu44oor1v3eZ8hm+wuQJEmSJEmSJEmSJEnaUNZu0jqYacB7v5Vwx+FAIYPeEClUWBIKApSWT5UHpMBAJRKnu9dPpfbs/3uAwtSJUBAgtFY2vyHCUCtSH+/eU1XrgVIOQ5XIdDksuXkI0JuduO5AFmlNzYaCABOTTT74wZv4yu2385jHPpYXXvtCzh7YxTe/9L80M+jpMKYYZ2cvnCyn9Gdh9oNlMfNQC8anS5SyDq+uGOhvlHigVeB/25vv1Zbe9QWSw3fPbtQTYk8RLmgBEaar0NdLOLdGbPUDEC/shcGzNiQUBBgfH1/1zIKSJEmSJEmSJEmSJEna/DZfUbMFhOCEVVq9H07BP30z5cDc9H5JLdKcCjRaK4/NGku3e4kUJqAyE2jXu9+j2YDBPNI+Bo3m0r/Pam3pdgHoq0ampwOVeqDU5ZrFyP/P3p0FWXZX957/rj2cecrMGlWlkRICScZiEsKYoduiMYPl7nbbF2MDtsJ0tMPuBw8PlwgTAU92dAd+6LBvB9cgMA7TYC5gMVlgMAJJIAYNCEtXlCQkUM2VefKcvc+wx//qh52VQ2UWYA1oYH0CRdae195nn8PLL9aiPXLEyc7ve75WTy+H2Vg4kx2Mo5gbPvgPPHDX3fzq61/Pa1/7WnoOfuH5V3P02AmGK0OSuWzpWyoKvVSJkiqU6KVbk4mq0EuFaOYjCF6ydYSxqFBLakRFtf72zF8f8/x0ICcfwD98a7WgAnECF9UQL0NdG1FFz1fwSohydF8HqU0oB1c/ZTWvrq7aCGBjjDHGGGOMMcYYY4wxxhhjjDHGmGcRCwsa8yRRhW8dFf7hHp9JBij0RFk96eGdI8g2m8v6l7LrIDsppGuhvOm0Gl28/UIQTCFdFsodZvMWJbTWknkNVbzxRoBQBJo7jCJvOoUxZNNzB2PnqTCYKVG0kfs7ceIEN3zwBobDIb//5rfzohe9mF6mxLFwxRVXggj3fO8eshLaa9cNFJpzJd4UcpzMhWDt36JKLxGiZOPnajz3CVy1f+AEb15juqnb4KoT7nu6dBecrhDe9RnOPCWljR5oIuG02p746AUNJEjRsg2dEOlEaLiAa1/2lJVdFAW12rmipMYYY4wxxhhjjDHGGGOMMcYYY4wx5pnmaZKmeWbSHUJWxgBkBXzufuELD3k4hUCqUb3RWBAPmrLzu6NAm2ocb3QC3Fnhv9ZZ+3tAN1PiodDk3O9jWEBXlXQoZGd1NMzP6mbYLZV0JORlNSY5YDtPoZMqbsb6eOL777+fD3/4w4gIv/f23+P8859HP1GiWdUtsNvtcskll3DPPfegTvFSaDjFm8Ks2BpKVBVamVRBwplHnJ31U6VCPfWplx7FvE7itv+UfePp0F2wzAi+/y8bbRgBbdfwWuO1JR+6gjQm1TapIwtxdejgZVWa0xhjjDHGGGOMMcYYY4wxxhhjjDHGmCeAhQUfAxGxUcTmnJZjuOEWjweOV+9Iy1dkWgXvzpBi52MDgWCoRCuyY05Mio30Wx2oRUo8rnZ06fb9gSqBOILodDXO92zTuRCu7dfLlHgkW0J27bMOqqsSTpVJImQJqFNuvvlmPvHf/ht79uzh+t+/ngN79lCbKZw1OvmFL3whcRTx4EMPUk5Bp0K2QzdEgDwGf+ozO0eHwDz2SeY1ct3+oEJVJjO4N3kKf+JUCX74GWS0srGq28FrjDeW2z2kUy1r2MBrRyCK6+7F9V7wMy/5jLIs8Tz7vwdjjDHGGGOMMcYYY4wxxhhjjDHGmGcTS4MY8wT63hHhA1/zOR0Ls6nQ95TZqpCfFQ6cTYWzGwG2RJEhTIbnDqJOJ9VxXSBfgSTZ2HenMcU+0J4p46HQ8ndusycCzVLpzJUo3n7tTU3x6DiliIR0rRPgOMr4xD/+A7fdeiu/eNVVvPV338ruThuZwTwXivnWcz330ufS6nS452u3MJsIjWLnmlqqZBOP8Bzbu6rMEo9Wvn1bXRVJYO6EW6Y+5VPUXdA/+XVk9QfIdAaA1uvoHh9cWS132tBaS3j6AdpvghRos0O5+0qQnXo6/myMRiMGg8FTdn1jjDHGGGOMMcYYY4wxxhhjjDHGGPPEs7DgY2SdBc1meQGfvdvjn+/0yMqqQ2DLKeVk5/ekKNkI7yn0VJmdFPIM8hya5wj2lSUsZo7o5HrmbF01wnjjuKYq/qjqHAgQnrX/+n6shRTnO9c6nQo1hX6pTCJZD9+trKxwwwdv4PA99/Krr389b3rjmxh4HmksZGvXms6F+qZzeZ7H1Zdcxv2HjxONI5IdQpM9p8ynQqFQJttr6pVKPBcUmM9g80TntlOKRMjWug2OSuHO+c/+Z07GD+Af/xrkTUDB8+EiQdKqjaLWaugekGwG4qH7akg6QcMmbp+Pyot+5jVvNhwOWVpaekprMMYYY4wxxhhjjDHGGGOMMcYYY4wxTywLCxrzOJ0aV2OH7/rR2tjhQJEZTGLBP0dADyBwEACdVIlObQ3NhTuM5g2B1lwpI2/HEcUAmoMq9EpIhkK2qaNhOtshmKdKuiqMIqF2jl8DX6A9dYw3dR188MEHueGGG0iShLe97f/gJS96cRXii4XNpYtAfa07YAC0UuWKq14OwF1330VaQGe9eOgVSjSV9TLnqdBaG4PsKXQKJcoE1krJS6G7dv5e6Zglsq2T4K2TgPk5Rh0/GSRZIfzhpwGFWQkIelELCQpkOgXfhws8JKv6QOreDqohAG5/ifNeChL+7ArewerqqoUFjTHGGGOMMcYYY4wxxhhjjDHGGGOeZSws+BiJCKpP0XxT87SgCnccFj54UzV2GIWer8yGQr42Hnc2YVtA7ww3BVmFyXh78i87a3xvG0VHMJvJjz3nbCL0EyVarerbLM2g6VUrRaGXK9FQcFqF+ho7vM8NUWozZTaq7k9VueWWW/jYxz7GwsIC119/PRedfzGD1BHNNkJ8W2qaCk1VvCnMMmEwGPCc5zyHO++8k6Io0ETxgU6uRMmmc6yV4yUQotRyZZJvv8BsCr3MESXe9seiEJbKreOzBzQ/SYqE4AcfhzJFtYZMZ+iBHtKK0bQFKHqwiQQ5Mp2ii32kHSGzHLc/gLCJ8uKfTa0/xnA4ZHFx8akuwxhjjDHGGGOMMcYYY4wxxhhjjDHGPIEsLPgY2Rjin2+zBD7+VY/Pf8sjy6EXKi2nRKtb34s8h2ZwVoRNoa9KfEzwztF5cD4X6r5WAcRSmS4LRfljzkkV7AsniqbnrrtWQh1ozJQo3hruy2Zb9+2iZGMhyYU0EzSZ8tGPfpSvffWrXHnllbz97W9nX7+HN4EsPvf3oVUoYcz6aGKAl139MmbTKffeey/lHJozZZLtfI5yDrU5JOX27Z5CIwOS7UFFX6uxxFEh3DHxOXWO8z9h1BE88ikkHVbLWRNd6iIL42p5UqD7e0hrgks7aKeNLIzRtIsuelBPKHg1yM8o2Phj2BhiY4wxxhhjjDHGGGOMMcYYY4wxxphnn+CpLsCYZ5qHjsGnv+4zSarlbqAwhlmxcxgtVDjTKLAmEMyU8UyqEb2eku4QghOBZgn+XInm24NwNbdxTlUYeEq81iUwqCmcK282haKE0m2/ZpIJzbaSOKFbbg0THnn0CJ+68YNMayGvf8MbeOFVL2IgSjSqRgZnuVBrQHb2mONSiSZCs6XQ3Fh/8cUXs3vPHr79lX/jhYdeQE2o5iyfpYcynXt0PK1SjpufK4qfw6QQ/Bz8AZx5lDUUrxSma/fpgC+MfH53d3HOEc6Pl3/8K3jxwxsrnIfsq4KCWjahEyD9alkKD9k9qnar+0hrROI9j0CveHKK+w9aXV3lwIEDT3UZxhhjjDHGGGOMMcYYY4wxxhhjjDHmCWSdBR8j6yz48yfP4aZvCR/5tyoo6EsVZotXhNnaGOIdj1vr2NcVpRxWo4TXtyU7H9P1lfwUzOY7v2fzaXU9D+gVynilCgoCTCeCf9ZhAvRUGZ8SGnLu8dm1HBpJFfBDAIVv3v5NPvwPH8aTAb//9rfz4he+iL5TxmPZuGWBRrlx3hBopWvnYW0U8VnXfc1VV3HyxJSHfvAIcSzbsoJ9VaJpdY1oIjQ2PeAWis6FZC2gWSq0C13f5nIhcVvP92ji8d34yfnJ8+b34C/fsb6sXh32TECqIlSayO64+rd2kKUYUPJwCWmNmHt7gVcgO81xfgqsrq7aGGJjjDHGGGOMMcYYY4wxxhhjjDHGmGcZ6yz4GFlY8OfLkRPw6S975Ppfc7EAACAASURBVLVquR0oeSxEa6Nt8wyaPWWeb38v0kToe8o42r5tNhXqCxsjej2BTqlEwyok11iEdIdRxVkG/bZjHnnEZ11TFdp+NX4XoC6KN4MorQKAfsG2ToUAHVHmJ4W8XS0nScJnP/tZvn///Tz3ssv4tV/7NfbvqzOf6/p9b7mXWJB+FdbLJsJsU8dEEQgyIKyaHjYLuOS5L6Ld+Trf+MY3uPjii2mWSu4LgUKtUEbpRp0iECRAowo9xnPZls2MYmEwcIwLb9s2H2io8qWVgIuaGYMduhg+VpIfwR9+DcqiWuH56K4WXrYKgAubSH0MKOqFuIaHrwVpbQkvTEllibl3Kb1y7xNX1ONkY4iNMcYYY4wxxhhjjDHGGGOMMcYYY559rLOgMT9GUcCXvi586JM+KyNBU+iJMl0RsmzrvuEODfvavhJMQM/RQVAEGt5aRzxPCWKIxlWoT6QK+m2jVQ068sjyc9Q9r0KDPVHykTBPN4J7k3hr58EzXQcnQyHLoeMrR48c5QMf+ACHDx/mV669lt/8336TPa062XI1rngneQGLhTIdC/kOAcc4Eroo/hwmKQRBwMte9jIe/sEPOHb0GJNYaKNICrO1AOTmTnuTqbCQO6IdgoJnnkkeCXrWxjqKXyjTQsgcfO50sN6F8XErxwTjT2zMhEbQA03ETauy/BrFUhOREhWPeX8Bj5g8GJDWQxwBq36PTnn1E1TQE2M0GllY0BhjjDHGGGOMMcYYY4wxxhhjjDHmWcbCgo+RiFh3wWe5R4/D+z/u8Y27vKpbX13JhxCPd/7c08nGKGIP6KNMT1WhwjOjiHeSzatxxrMV2Rb+y2ZsGW9c95RmrkSrwizesUEgAMlUGJTVfmcH45yD9lpAsSFKfa7rAUV1ypf/5d/4+w//Pc453vrWt/Lya66hR3WuyURo+duTdr5A18FsuHM9qtALFG+y0UUR4MUvejGNZpNbbruVDuBPICsV1Y3/AEKUVqlkO4x79oE2SpQK06QKJJ7RFqXIhMxtPKkfzj2+ufoE/PRpRjj+OOJmyLT6gHVfD+qKFBnqeWQHagRZioowHywSuoLSa7PaDghdwXLYpF2+DI/G46/nCZJlGcPh0MYQG2OMMcYYY4wxxhhjjDHGGGOMMcY8y9gY4sdBVS0w+CyUZXDrt4Wvf7cKCXoCnUCJVqpAXWcJJjt0CkxTaHUVcZCPhXEm62m+2VR2HCnc9BW3Amlz5/coSYRmW5llQt+HyabwX1FAJ4TJWQHDdlCF6vTHjNrNZtBrwGS0cb7xeMyNN97Ioz/6EVe+/Lm87o3XsdCqo7O1scNrtxOcNca45SnFVJgUAEKrpVtHEAM9X4liqcYJDyBfu2gYhlz9kpfwtc99jvtf+Mvs278HGSilVscrSkMdZbY21jiDTkOZrBXQEMXlMN0UBkxi8LrVWOUo3f5cO55yy3LAwUbO+a3H2GJQlSD6NFKcQrMu4mJ0sYcsjtFRDxUh39cFv8TLp8x7uylqBfXJnNVOl9DVWA0Ucc+nqZc8thqeJO95z3v4/ve/z2AweKpLMcYYY4wxxhhjjDHGGGOMMcYYY4wxTyDrLPgYWUjw2enBh4T3fcDnrrurcbaduuKnEI02gn/eOWbYegKNZKOb4GYiUN/UkU/WxubOTwnpXLZsO1u9hE6pREO2dQmUfNM5gb5XjUjOc0h26MIHEAj4EyGLdf189913H3/3d3/HiRMn+LXrruOtv/Gb7G3WSUaybexwHAmBUI3+9ZTZWMiKTc9h7d5VlZo4wtwxipSyLCnyklqeURYlZVESaME1L3gRtfZubrn1FlCPrnr4vo/n+Qw8YTbRLR0X80l1r11Pyc7qGghQ5MIgcVXAcZMzY5knqVAofOp4QFzwmPjTr+Clh6uFuaCdDrIvBvWR+YRi14CyOyOY+qSdJZJOQi0NWO30KTyfuQeZnMegfOFjK+BJ9O53v5vZbMZf/MVfrHd2NMYYY4wxxhhjjDHGGGOMMcYYY4wxz3wWFjQGiGP45I0e/9/HPUZjyGZCP1Qmwyp4t9lkXHXIO0MVOqHiT2GyfO6vVDYBtOomWJ8r0fLGSdK1bZupQj9U5idgOtk5nDqJhMBbO2eqjDeFGrMMOrWtJ+0EClOYTqGuQpqmfObTn+FTn/wkS0tLvOMP3sGLf/EF6Kgat7xTVEwVOmtjgccj1scFO+coy5LRqsNzOS1y5lHJLHE4dev3N4t9Ql8Y1Dxc4hOEHV5+zct58IEHOHr0KJNIqInSxTFNAsTzqmusJRvTTFgsHPF8+4jlmigNVVZWPdqbgm7eWrAxyjeez6QQ/vlYQObO+ZHtyJt/F392+9rD8KEskINzQNF5m6Lfp1icIEWIw2fWyxAXMK35lD7k2ieRJfrFSwio/ccu/jMQhiEXXngh8/mcv/7rv36qyzHGGGOMMcYYY4wxxhhjjDHGGGOMMU8Q+Qmdo6yt1DmoKkmSICLWZfAZzDn4zp3CzV/zSDNAod9R4kjoDJRouvNn290F8RxCHxoFxOONba1dymyH8beeQL+nrC7vfM7mLmWeV9tqHoSFMo2r5c4umKTbjxGFxQXHymjnkGK3r8Qq1ShldEuHxEd++BCf+cpnieIJr/ilV/CqV72KfkOYR0JRQm+pCtet/0Zo9d63A0eWKFm96r64pR4RPJSFNgwLb8fvhoiy2FGWU299mnGWZ/yX//JfWFpa4g/e9js0ajDelGUuXYk6JfShjpAUgr+g5Lpx/ranpCkUa50GQ1/RgSCiBA7m5dZa2r6SFMIlbcdvHCzwfpqvcflDasOPglbzpLXoQ2+OhFU7xXK+SL47RgVkvkDSmKMiFG4J502Zur2A0nAvYJe76Ke44M9elmW84Q1v4PbbbydNUxqNxlNd0mNlP8zGGGOMMcYYY4wxxhhjjDHGGGOMMZsET3UBz1QWEnzme/RR+OIXPY4vV6G3VlNxOVV3PiBPzn2sS5VBDaIVIS63bgt3yCh1akoWCc4/9zsTqjBf6yYYr24dryuFcnb2qRkoOoPpaam+yTucOh4L3SUljWS9q16WZnzpy1/irjvvZNd5Nd7+9rdz/sEDtFHGK4A6FGUWOYpg46SeB21R4nEVAux1Ic63fg9agSOfe6wOob4I2eZnUy5T94Gsw+rpOkFfKdfCfrWwxi+/4pV88Z8/xr3fe4hDzzlEY0lJ1gJ+vufTCEqSuWPqBPGglUIeVonmvq/E862dEPOyGkcchx7zTRtUoR8ocV7t/8DE43PHA960v+DHf6VX8NMvbgQFxUf7Di+ogoKFdCl2VUHBUtsUzRQFZm4/vjck0j34+Hj6nKdtUBBgdXWVpaUlROSZHBQ0xhhjjDHGGGOMMcYYY4wxxhhjjDFnsTHE5udOHMONN3p86EM+x44JvbbSaymzSEjmG2mx2VSo17Y312zVFTdzxCuCK7dtZjLayO2FPnQFJqeFLIVpxDkDaflUaRXKeEVwZ43GjUdC4Ff/FqDnK/OhkCRVza369jo9qtG7EkOWV10BH374Yd73X9/HXXfdxdVXv4z//fr/k+cc3AuTgtGqw7lyfWRwmnh064LneXQaQr3wmM0CfM/DE498Khv5RFV6gTKJh6TFENWU+qYZwaqwkHwCPfL/4k6+F2/lvfRX34sf/SNSHMcT5VUv+UUWd1/Cl770ZcrS4SWKrh3bCxxJ4uHUXx9JPJkIXZSeKNFZQUFV6IXKKPJoFxtbhCooGOVb939kKnz2uL9trPGGGXgfx0vi6vwizPtLSDgBoPTazJsN1AOnTWa6gOKY6H6QnKnuodQWTi/gvPK557rI08JwOGRxcfEn7nf99dezZ88errzyyvV17373uzlw4ABXXXUVV111FZ///OfXt/3lX/4lhw4d4rLLLuMLX/jC+vqbbrqJyy67jEOHDvFXf/VXT+zNGGOMMcYYY4wxxhhjjDHGGGOMMcaYddZZ8HEQ2TSi1Tzt5Tl885vCbbd5ZFk1DrfbzcAJ0bi2bX8RqIdU44mpxto2QyUaAwi9vhLF25N/ZQG9hkIJk6EQbwr+FTl0+xDPNtZ5XtV5MBoKvd3nfp9ageI8yGIhyrZe118LLaoqKLRrSjpWVjMIQsfMy7n5Kzdz1113srC4yO/+zu9ywfkH6ADlXChLwd+h66FmjkEdxmMBBEXJZESgTZK0Tq+rZCV4OUSRkAdfw8kPAUgmPvXFOs71aGqdU975eIODSKl4rmQ0S6h3I/AdZQGzPODaa6/lnz72Mb797W9zzTXX0Ft0OIRo5q09q6pG5xx1cZSRR9bcWrMn1YjhKKn2jUZCe0nJBEKoOiyeuT+Ffk2JMuF7Y5+kFH79QEFtS4y6AO8TSJ4gRdVuMuntwgsdkilO6pxuLtD3TqFaY5nd9GSVue4jIcAjZEabUPdwQXkF8jSfjjscDllaWvqJ+/3e7/0ef/zHf8zb3va2Lev/5E/+hD//8z/fsu6+++7jox/9KPfeey/Hjh3j2muv5fDhwwD80R/9Ef/6r//KwYMHeelLX8p1113H5Zdf/sTdkDHGGGOMMcYYY4wxxhhjjDHGGGOMASwsaH4OqCr33uv4+tcDTp70UFV6vYI0zYgiRUTw/ZCy3B7iSqaCh9JpKZOxEs029slzB/jbjmm3HV6qjEbbtwFoXo0UVoVeS0ljIZpU5y3OMfo49EGmEE8F0LX/6XpYdXRa8QfV+hYQndwYD3z/fT/gX2/9BOO58tKrr+Y1r34Ng1ZANoFJLrR7umWUcE6Oj087BDcW0g6c6ZWoFBwNvrD2XD0GWU6S78Z3LQK/ha/n4+t+PEp8Mtr5KaaFIy5W0WAKwUYrRlWo9VcZZzeB9gnllRx6ziEOXXopt9x6Cy+96vnkqz2y1tZn4Xke3ZojmkIKdAOYrP2S1X1FSiHeHKYUkBhqHZjqprHKQCvU9fHMAA9PPT5+JOCN+wsGYXXHyOcQOYKX9ABIu0vMOymDaYpKyOnmbhpSvQvL7KUGpAxYlYC6C4mljl/u5SL39A8KwsYY4p/kVa96FY888shPdc4bb7yRN7/5zdTrdS6++GIOHTrEt771LQAOHTrEJZdcAsCb3/xmbrzxRgsLGmOMMcYYY4wxxhhjjDHGGGOMMcY8CSws+DiICM65LUEr8/Ty8MMl//ZvBceOOfp9aLU8ICPe1O5PVWm3S6Jo69dBVanXCuoC0aoPZwW9ZlOh2VKStFpfrym1sCSOqzBgraZk2fZ3YzIW2osOyYV4Zev2aSQ0F5R5ulaDU7oNx3QsrBRKe0GZzjfCbbIe4hMGgTIee8xKD9+HKI744he/yOHvf589+9q89a2/wUUXHKQlVRfDM6/tZCw0dinpWse9fw++S1EfUo661LVOH3B+l5rWqBHSLF9E3c+oM2d62tHevUqcRczlJEq+VpejWZ9z7FSb1mINx24C1yKgjq8edb+k5SWMTjraS0NmZcqZqejX/sq1/Nf/5//m05/+Mv/L//y/0msq0drz8URpB0o8DxBxOOeIY6G/qGgA01S2jBJWhX5diTMhjJWwo+QIdU8RhEmx8fwbnuIEfjj3uOGRGq/bW3B57yt43n2oE7z5jKy5wLSXUy/qCFOW6/vJfKWrY1Z0f9W90AnLXojnOowF5m43L3ZX4D1Dpr7/tGOIz+Vv/uZv+PCHP8xLXvIS3vve97KwsMDRo0e55ppr1vc5ePAgR48eBeD888/fsv6b3/zmYy/eGGOMMcYYY4wxxhhjjDHGGGOMMcack4UFHwcLCT59HT/u+MpXCh56qOpk12goqjFJUse57fvnec7mr0OrVQAJcezodkN26iAoAvW6kuXQaTviSEmTM0k1pdncHhb0PKXbLdACxlEAa90Bz3QIVFWkdJSlR7NWjTKOhmdG8Hp4qniebHn3GjXFKyE+7eMCcOq44zt3cPNXb8Y5x6tf8xqufuk17D5POD0u+BRHaIQBTfVpEtDUgEUEpMZi6HEgPY/5dBc5OamkjMYpbukESaGoQqORkI3rqBN8CehMF/DCNg3XINSAbq3ES5RyqtQkoZavEktJKiOmMqVRnzKa1XClDz40UlB/icB7gKZ3hKXd+3jlq9/EV796M1dccZhLDz2X9q4qyKclxPON5wGgrqSMwbW8LUFBD2jXdX1kc1YI9anS6ypTFcpN+3ZDZVpuBA0Lhe9O7kGC27m4JbTyNmUoTBYdCNTyjNX6Puaho60+I/YyE6i5FkOvwLlFliVlyh7+x/IX8J8hQUGowoKXXnrpYzr2D//wD3nXu96FiPCud72LP/uzP+OGG254gis0xhhjjDHGGGOMMcYYY4wxxhhjjDGPhYUFzbPK6dMFt9+ec/fd1XKt5mg0cqKoIEmg260Rx9tDnrNZSbPpACUMU+K4WN82meQEQY2iOPs4h7oMX0Ki8fZaptMSXRt7q+rodgtms5KVFSUIlLIE2Br88zyPPIF+E+JRgAh4m3Jm00io96qAoucpnTpEq9V5HMrn6kMevfcRJvEyu1/xMn7pBb/IBQsdOk4oIqEohPP8NnMK5lIwJCX1SpiUBEsF+WodAQJPaGmNFm2aGrBUQEhIyynZafDIySQjIyWdpbA74lQeEdQn/GjcqIr1wcOjFrUY7PLx8wMs+DXy1RpNcfgUlMwoplNqS8vk3lGGs4KyCLnmmmu477/fx0033cT577iAwbzGJBBKt/UzaIQCpUc8U2qlEnSFQtfGEXPWOGKFOpCNwesqJQIKvZoSFRvdGhu+0qs/xPntmxjmQhQLnaTB0u6CjpQEZcA0aDIJq2RhSp2JONAOsZezrANOeBl13cfr82dWUBBgNBr9VGOId7J37971f7/jHe/gTW96EwAHDhzg0UcfXd925MgRDhw4AHDO9cYYY4wxxhhjjDHGGGOMMcYYY4wx5ollYcHHwToLPn0sLxfceuucf//3FN8XarUmzWZOFOVk2cZ+zmVUkbGt6nVHqxUzHApJsnWbatVpMIrCtWWl18vIspTxuKDbbZFlAaps6RBYFEq7XbUxLMuSaG2WrucJzgn9PkwmGx0LRapA4WTi8DRg8+t1LBM8UToedHylHsB8AtGs2mk6nfLlr9/GQ//D5cjll1L7xeczFuWmpkNXE1ChqdAfQCvt01VhUYWOE/a0FI0djbBgpXTMKZhJwWzt76ok/KhIUBFcGkIAotAkoK0N2nRZmuzmIr+OPwkIKFFyUklIJSUhIc9GDIk5OmfLr05N67S8GoPJ+fhej45rUtMG4gtvfOMb+dAN7+crN93IG970n+gOlHjT59KtKdMEnPPxPEeWOtqBo9mRLV0CAQKpAoTR2sjoMFZaXUVqEJUbQcFOqJT+Chd0voDgCD2YaYNh3XFkDu3CIygHNBop9RIK3U3ux8xch1XqrPohmcJ5bi+/+gwMCsLjG0N8/Phx9u/fD8CnPvUprrzySgCuu+463vKWt/Cnf/qnHDt2jAceeICrr74aVeWBBx7g4Ycf5sCBA3z0ox/lIx/5yBN2L8YYY4wxxhhjjDHGGGOMMcYYY4wxZoOFBR8HCws+9U6eLLjttjn33ZeiCrWa0myWODdlPN7++UwmBY1GnTStlsPQ0WzmxHHGaCR4XhN3Vvc6VSVJMsrSo9vNKYo5o1G5HgxM0xll2QFYD/h5ntBsOur1lPE4BGRLh0AAtzYPuQofliRJSRRV50ySgmqQbnXCfxn7nMwFag7GStcFdBU6njJfPsGxB+6njOc8/5sn+JXXLDFo1FmdK6sxTFEmokxQEilYFcdRUbJQQRSN18b6jqHX9+kWIT0VeupxSQCDQghPCp1BzunSMaVgJjlTKZhKxrAx5pGxEOwuKIIqUBkgdDSkQ4PdtTb+qYNcuMvD5QEqGYkkzEnQRkQ8zziaxEj/OKlfX7tjoX/I41XXvpKvfeHrXHTJfTz/+ZfT3e2YlUI7VKKZdybjh+d5iCheUeJmHi7cCAA2A6UoYJpvfK6+gptC0D3zGUO/rsyYcFH/X2nKKnUfpq7GMvvph8t4PhzJ9hEGCWEpnM730g4S5rTIpE0QpqQ0uNgt8br88mdkUBCqsOBP01nwt3/7t7n55ptZXl7m4MGDvOc97+Hmm2/m7rvvRkS46KKLeN/73gfAFVdcwW/91m9x+eWXEwQBf/u3f4vvV0HZv/mbv+F1r3sdZVly/fXXc8UVVzyp92eMMcYYY4wxxhhjjDHGGGOMMcYY8/NKzgSezuHHbvx5V5YlWZbhnZ0CM0+6Rx9N+cY3Yh54AJyDRkOp1UriOF/rBBgwm4U7Htvv15nPPRqNKiS4uSNgr9dgPBaqRV3b5uh0HEEA47Guh0Q3wqJCq9VhPq/eg3q9JAwz4jgHoNlskSTbg4vfOuZxLA/p+CVNHN1a1S2vW4NuXVnqh+udB5dRZkHJyZFj4oSkGXDkRM7KLMU1OhDWqpOGCnWHTDy6PvR9pbf2d+ArvUDZs6jsrcPqWIkVYlEiccQoya6S5UyIpGTWdOjIg7VRyr7C4qLSTQMGKuytQS/xaCceTSANcqbdnEgLJpKTNhLGSUGUl9UpfId0IXABPQ3YVfOpjVv0qNHTkAaCv3vGcj5HGjHL05zn5If4yD98hJWVFf7gD/6A/bu7SBum2dbvXD1QUJininOO3qISi0+/ocSJbPkh69aUSVGtU4V+T3FtmGnKhUufoaNj9gYnmKvPUbmIgR8T+HNG5S4SadOtLzN0uxG/Bt6UedAlEEchAYfy/fxP5aUIz9wg8Rvf+EY++9nP0uv1nupSHq9n7odgjDHGGGOMMcYYY4wxxhhjjDHGGPMksLDg4+CcI01TCwv+jKgqhw8nfOMbMY8+mqKqLC3VyXO3FsyTLftWIb2tx9frSq2WM516FAWcCQSeedUbjYAkqSMiqCqdDkDCfO5otwOm050DiN1ujfm8RrOZrocEN7aFxHFty7pGw3HL0YLvngqI4jpJsf2c9YbQ9QIW+iVtLemFjl4d3GyV733nqzx6+AEWF5f4lWuv5aJDl5A1HMdHMC6EeT1gZeIRlTAuhbisgnG0qFJ/M6Hnw8BXBgEs+MpCoAw85aL9Dk2EeQaRKBHKWBxjUSbdkmVR4lpJPvbXH3mgMEDYvaj0Cp/9odAcBywi+MCMglgyioWEUZgzynJW84JEyvX79VVYaAiDZp3WvEVfa/SpkwwjPvCBD7B3UOctb/tDOp2AtA6qVaizCgRWy3CmY2PJwoKyqsF6jUIVwoyyja6DdV9RH7yg4PzzP09QP8WSGwMZx7gQP/Dp+ieZlAuMgi5db8JMOyS1BoGmZGED5wWICoeKC3hdecEzOigI8OpXv5o77rjj2dA59Rl/A8YYY4wxxhhjjDHGGGOMMcYYY4wxTyQLCz4OFhb82UjTknvumfKtb00ZDgtA6XaFosjXRgRXY35ho0MgKJ1OjSjyAKXZdHhezmRShQp7vQZxvLVD4Jm/rVYTEUU1ZTbbCLNVYcMWWba1vjBU6vWc/+sjTdJc6Lag21S6LaXXhE4LFnot2jVYGji67arr4Jnr1WotpnMhzoQ4gzgTogzSoGA0DxiOPaJUmJ8dKKwHdFXYNXB0xNEPlUFDGTTgwILgFf76WOSwpkxFOR7BqITYD1hJhFEBq6Uwc1INJfeBAJq5shgoiwEsBspSoCz6yoU9JQiVaCZMUEaijFBWxTHEEXdKVmsOl/rrZfZUWFJhCY/z6rAr8GhlPgFCRkksOWNS8vack5OSaW9GJBuRu7qvNGcF3/vw13j+rvN5wxveQKerzDxohTA5q2tjq+ZIcyXNld6CMhGfWqD4HszLjX27dWVaCk6VA3u/xEL3EXw8dgXHeYSLoOERlAWCIwoHODwCKZiEdZz6+CGk0kRUuLy8gNeW5/1U7/PT3ate9Sruuuuup7qMJ4KFBY0xxhhjjDHGGGOMMcYYY4wxxhhjNgme6gKeyZ4Fnbee1paXM+64Y8R3vxvRaIRMp0Kvp8xmGVHkqLoCKq1WwHRabukQCEIUzel0ajhXMpuViIDvVyG2PC/xvNq2a3a7DpF4LWS4lYjQaJRkWXWOWq0KCcZxTp7D1VeGnFr2mcyEeC4cHwqzM0E231V/y5x6CL12SK+l9NvK7l2OhoT028piR7niQE6WZWRZdW+nThXcdttt3Pnd7+E1Bjz3BS/lwHMuxzUDluMawwk8klZhw/V8lELQ8FkIlF0DR9cJi01YaCgXN+G8XTmTaXUfnihhCx4dCsNCWC1h3BeWp8LDqfC9mQch4ICjymJLWWooSwHsDpRdgfILTaUTwGRZqHUdxwWG4hhKFSQcNQvuTgq+M/WQuiJ16KvHbvU4L/TYU7bZO+pxGQJDqC8VPJrnZO0ZJ5OCVT/jF664ku984Wb27t3LK3/phXQbME42f05Kr6lEiYB6eJ4jWnUsLhRM8Mk2BQV7DSXKq+U9S7ex1HuETCFIc45mF0BbIPdoSMFyuEDqQd0pk7CB0xBEmJctct/jxeV5XFvu+w+/309HPyE8bowxxhhjjDHGGGOMMcYYY4wxxhhjnsEsLGieVorC8f3vT7njjlUeeWSOqqPZFPI8oyiE4VDZHAisZEBI1eBR8H2h03EkSUYYwngseN7WYGeWlXQ6MJmACHS7JfN5xk03wZ13CoNBi3Zb6XSUbg96XaXbhV4vY8+eGvV6SRznW7oMXn1ohlzaptxoRogfONKi4MRyQTxrM5oI0QyimTCeCkeXheSBEqQOngPN8Snpt316rZJZdJTlkz/AJVOed/nLefUrXsAFB5s4lzGfp/QucURRNRq5cDBOhVECoxTmQcaJlRqnh8LhFEq3EazzBZb6wr6eMvBgoabsaiqHmkrgQatTMm16eJ5Sq8Ejy8JKIaz41d+hLzw0EZwKNIDjyqJfhQf3xB4X7nfsdh7PC5VWqETDOrrWiXC5dEyaBUcLWG7nHI7XQo4htIE96rEvFi5a8FmIFzm49jm7Fx5g0ve8KQAAIABJREFU9NARvvC5f6LX6XHo0KX0l5SoEAJfqQcQzTfdoy/02sLK2KPdUqRVfdZByHpQcPfgDvYt/ndSBZxHLiFJK6BwEKQBpxqLpBmIaxLVFZfUSP0WfgiZV+OVxR5e6fY8vpf+aWQ2m9Fut5/qMowxxhhjjDHGGGOMMcYYY4wxxhhjzJPAxhA/DtUI3AQRsS6Dj4Fzbr2T2YkTM+6+e5UHH5wwHILvK+22R5blpGmVvuv1msRxtf/m562qNJutKggWFEwmKWdea98XVBs4t/363a6PiDCZZOvb779fOHzYYzavM1r1iSeQZ8LGVyEHfFpt6PeUfh96PaXXg35fOe9Ag8D3WFhQguDM2GPW6m8QRf5ZVShh3RHPhSPHfUZTYXlU8MiRMcPIgd+HWg/KWtWdUDPa9YLFjrLQhV0DWOx0WOjAQlcJfKXbLUmSnDxX2u0m06mPajXeeJjAcC6M1bGSKSeX64zTTR0JURYasKtZcv5+ZaDCUl1ZbIC/qYmf5yuNgXJiKhyNPU4XwulcOFUIqwXgCSxAPVX2eMq+UNlXU/aH1Wjjdt1R78Jo5pGinBbHaXGcxDHsFCxPQQNFO0K39NinHucHwu7U8fkPfZSVk6f4nbf8Duedd4Cl3Y5xIZRu452oh4p4kOSCU4crHd2W4nc9Iq326w0e5PxdX+HMdOey6JPVC6pXoUYmNQrfIdJm6nkEAQxlkU49JfEavL7Yw4vdrh//kj/DPProo7zzne/kxhtvfKpLeSLYj7IxxhhjjDHGGGOMMcYYY4wxxhhjzCYWFnyckiQBbCTxuZwJBKoqbi2Rd+ZvFGXcf3/Mv/97xKlTCSLQavnUagGjUc7ZjzQIPMqytmVUqghkWUE1ktijVtv+OVQhvY31nQ6oFkwmGZ1Ok+l0p9dcqdVaFIXi+8rycsbKiiOKIY6EOG4xHlddC6MIiuJMoFCAgFotZzCAwUDX/oPFJWVxoUW3W4Uhu11HmmZkmUME5nPHrbd+kzvvvIuiyHne857HL/3SK9h73h6mqc8PjyqjqbAaC8MYhvHamOOgBbkPoWOxnbHQduzqK0s95cBuj16zTj2s7r9ed4RhThxX12y3m4xjn5U5rMyF5ZkwLB2npo7lKVVIEcETZXcL9rSU/X3HhUvK/q5SZNuft4TKci6cBB6MHScyZVVqlHggUKsrezPlQEs5uKjs85WeD4GvNAKYTIUc5ZQ4hp2SI6HjVKdkdQog+Cju+GnyL9/CO177GnqLB6sOg7mHKvRbSpyBroUCEaVTd6xOFc8Tul2o7T5Ca/Ad2uEyKOSyxAwI/ARPagzdLmrBCM9vc5ou/XDKcX+Rb3/1i+y/5Pn82YWv4AXa/clfgGeYe+65h/e///188IMffKpLeSLYj7IxxhhjjDHGGGOMMcYYY4wxxhhjzCY2htg8bucKBJ4J9Z0JUooIs1nB4cNj7r9/zNGjOUWhtFoeg0HAdJozn+d4HtuCglCNKO52IY6h3RZESqbTjBtvHHH4cALUqdWEXs+n2/Xodqu/g0HCYNBizx6hXi+ZTFivRzVH1d8W9qzVhE4nYTx25HnVQbDfP7NV6fVyomij1Z7nKadPF5w+XZIkTU6eFEZjYTgUHvqBUBZnzi8gMOjnLCyULCxAq5Vy/MS9PPLwNyhLx5VXXs7LX/5yLrxwCZGCyWTOnn5AOwi31TlPldTlnBrVOX4ahhEsR8IjJzzKM90UfZ9eE/btKlhsFuweKHsXYKkLRZESeE32toULFkvCsFgPEhYOEt/x8KmQU1Ph1Ez4QSJ8bzmABwGFpV2ORSnoElNPTxFMf8Dy8QkrwyGrq6vk3jIEPfA8Xvsb19E6eCVHZsJxhG+NPW7PBTzotR0HS+WADwdrjr2hcACfS1KPXw6U0chjhnLCKzkmjmMHFzntw/s/9E/89pt/G/Q8+ktKGUCUbjyjMFACHyaZj+87nCsJGqeQ9p30ZIInMJMBJ12XBf80gR/yqNtDz4+RoMUR6bM7mHNcFrnlS19mNc74zn/+z/z97Xf/B78lzwzD4ZClpaWnugxjjDHGGGOMMcYYY4wxxhhjjDHGGPMksM6Cj1Oapqjqs7qz4JkA4E8bCATwvI0g3WRS8MADY+6/f8SPfjTBOUerFdJo+ERRSVFsnRGsqrTbDWaz8qx1PmFYdeDLso1jjh3LWVkpyTKflRUljkuiyBFFJdNpCTiqJmNVTfV6FSjs930GA59du5q0WtXywYM+9XrJdJojItTrddJ0+zPxPKjVGtRqynSaUZabux0KntegLM/UDkmizOdw/HjOcNhkeQVOnswZrQrO1c7cJSItdu9Wdu3KGQwKdu1Wdi0pS0uwsNBgMpH159HpgHMl83lJt1snjjeyv87BaCoMJzCelxw5WefUqsdKBM6d+YyU3X04uD/gvCVh0CjZu+CobYoQiwi+H1IUE06cWOXUqTEnVqecnMAwbzALu2hvH3QWIAMKh5cOaRerLIUzDvYKLrqwxjduu5WHfnCKX7/u17niiisAKBWGAidr8EDkcyQX4rKqreYpF/UdB0rlwho8d19JXHh4onRbEE1hNB7zj//4j0ynU97yn67j4ksuo9mFmKqrYKehzHJwax0Gw0AJO8vU9t1KoI499WWmrs/pcMCClxGGM46xDw9o1hJOyAJdUSZeyL985VvEK6c48pd/z/Hb76DZbG5/KZ4FPvnJT3Ls2DHe+c53PtWlPBGevT/KxhhjjDHGGGOMMcYYY4wxxhhj/n/27jRKrqu+9/537zPV3JPUrZZkyZItD5I8G9tgg23gYkiMIZCATYIdnIHhhrCem4SHteDJk5gkDDf35sklCWEMg2cCAQwOYBJsM1m25QlbtgZrllpSTzXXGfd+XpxWq1utYByLODH/z1q9pK46tWufU6f61W/9/kKIfwcJCz5HcRxjjPkvHxb8WQOBc89zbiBw7v+NsRw40GHbtjrbttXpdAytVka57KAUdLsJWZZfM8/ziOOFt1mx6NLpmJmAoCIME+I4T9/VagHNZrbgNdZCsVjAcfIgXKcTkySWdjuj3bY0mw71ekajkYcJG438//n7ayADLEGg6O/Pg4TDwwXKZY+BAZfBQYdaTVOpKJQyaK3mjTeeq1Yr0GhAqQSOY2i3YwCyLGPXri3cc89jjI3tx/cD1q+/kBNXnQNUmBjXjB3QTE4opqfnj9IdHHRYNOSybBkMDyf092cMDFjyS68IgtJssNFxLOVyRquVYq2dGcXskhmYbMKhumK8rhjvWPYdNPSi0uy3vRKEFJ1pdHKArPskzYkniKMjI3eV0vT19TE4OMjwcInhkRr4K0kKwzRMhbGOZn9bEaUKAij5lqXljImnH6K+61Fe/4qLWLf2VKoVS6upMEZRXWxoh5pGCgcV7Iw0O9qayZlGxkBZThrNWF2AExzLgJPvpd1p8aVbPsPYRI//9spXcv7551MuW7wq1CM921BZKVoit0ll+fdBh/TbhFQZDupFeErR704zlo2ADwWbMq0r4LkkSvPtH2ygdXCMg3/+WXbd/xC1Wu2Yn/kLwWc+8xmKxSJvf/vbn++tHA//tf8oCyGEEEIIIYQQQgghhBBCCCGEEEIcZxIWfI6SJCFN03lhuf+snmtD4E87x3o9ZNeuJtu3N9mxo0mvl1AsOnieJk0NSQJJsvB2qlQC2u0jLYFKQamkcRyLUppGI1nwGq0VSrnz2vxKJY3r5ufUanHM8GYemMtf47p5kC+OE6anY5LEY2wspV7PqNcN9XrG9HRGvZ7ONP8pwOA4GQMDmsFBh8FBh+HhMn19DkNDLqWSnj2HalVhrabVykON7XabRx99jI0bN9JuNxkaGuH881/C2WevZ2DAp9vNRzLnDYolul1IU5iagokJxcSEol5XHDjgMjHJ7DfT9WB4sWVkxLJihceiRQ6rVqX0eilzv9t5MLNEvd6jXp+i2x1j//4ppqbqTE1NM9XsENuTwF8KwVIoLAGvDGmGUob+asJwWXHiqMMpK4sM9kGhYGavZ7Xq0G7n528tVKqWfXXYOanZ09TsszDVPnz/9FhaiFk7UuHEPsPiEjjaUhjIz6fZhsM5r1YGu2PFPkexeVLR6tNgYNC1nFLNOCWwDCYR3/j619i2dStnrFvNlb/yK2gvoNJnaaeKagVapkvfintwvR6eA24ScUAN4vvgJpa2LqIKijR2SXyH2PPJrMvXv3cPnf2HmPrg37F148MMDw//m9+BF4K//Mu/5Mwzz+SNb3zj872V40HCgkIIIYQQQgghhBBCCCGEEEIIIYQQc0hY8Dn6zxYWPFYg8PD/nykQ+LOeg7WWiYkee/e22LOnxe7dTRqNkFLJm12j10vmhfnyMbkL2wCNsfT3F2b33unEs/v0PIcs0xiz4GVUqz7WglKWbjcmy44cVKmUaLcXvpfnKYpFjzQ1dLvxUc9p0tQ90uRHPmq4WFS0Wgm7duUhwsnJlOnpjKmpPExojAbyub2lkmJ4WDM4CENDDiecUGBiYoynnnqYrVu3Yq3hxBNXccEFL+Lcc0/DWod2O+Hor2Cx6NLrebN7qFQs3W5KmuZthllW4MBBxaFDikMHFQdnfqLIAg5KQ39/TLXSxPcnMGYP3e4upqb2EscJUAAcQNHX18fAwAADA4OMji6mr2+E0dEarjtAJ3LYN6HYP6nYN6kZmypjMgWuYaiUccKwYcViy8oR6K9alHJxnDyI2enMz2lZC1QsWyZT7vzBLnrBMBSHACj7llOGDSf3G1aPWpw5Qc9iwZAZRRwrrIWpDPYVFJutYntDk6HwteXkwOAdeIxHv/XPVIsFXvPq17B+3Um4BYspR/jL7iUotLEaTFig7bm4PvQShbU+qqToJgW0r+gpj8j4fOue79LYso/mRz7Onq3b6OvrW3gjvsC8//3v5w1veAOXXXbZ872V40HCgkIIIYQQQgghhBBCCCGEEEIIIYQQc0hY8Dl6PsKCcwOBSWroRRaLpeBalDo+gcDDrLU0mzEHDrQ5cKDD/v0txsbagEJrheMosswQhilZZqlUfFqtZEGzX96YV6TbTfE8TaGgUcoShikASQLHuhfzNsAMay1B4BAECmMM3W5CoeDS6x0rFOiQZS7G5AHBQkGRZRndbkyl4tNuH/u2rtUKtFqWclkBdl5wsVrNn5vLGEurldLrafbvTxkbC5mczBgfT2eCewA+EFOtpqxcWeGUUyqMjGgqFUt/f5lO59jXvb8/wBhmxwjP32fAwYMx09PTtFqHqNcPMjZWZ2IiZXo6IElOAJYBS8mDgaBUSrk8ychIwpJRh5NPChgZqeG6edDRdS2lkqLT8cmyhRkrpSyVquapHQG7Dir2HFLsHVdESX7sUJ/h1BMtozWHlSNQ8Oe/tlq1dLsKXYBmM+Lmm2/mUDPmRVe8kW5xhK0HNGGqwLesGLGsGTScs8zgZYq5t1IxMBir8Et5cHBHpHk6U2xONd1I4WCofu8m6tsf4uR15/Gyl1/MiefvZmhkP8aBblYgUgWcwBBnDlFaRRc6RFkR61VIdMqu6R4P3vcA0z/ZgfrMF9i9Ywe+7/OL4J3vfCfvfe97OfPMM5/vrRwPEhYUQgghhBBCCCGEEEIIIYQQQgghhJhDwoLPUZZlxHF83MOCcwOBh9sB09Sybwx2jSkmGprxtiayoHxwfMBV9NcswwOKNYsNq/rhGNN4j8laS7udMDXVY2Kiy/h4j/HxLu12TKcT43nOTDDQEkUprqsJw3RBKx4cbhHMxwcrBYWCg+tqlIIosoThwjBhrRbQbM4fOey6imLRQWuHXi8ljucHAwsFlzBcWDtYKjkUiy6djqHXS+ZdA2uhUinQ6RxZS+v8NUoZkkQdc03X1RjjYUwefiuXNZA3Ifq+w/R0zObNW9i06Ql27doFFFmyZC1LlpyCUiNMTORhwjQ9HOaExYt9hofLjI56LFniMjLiMjioMSYjijLCEMbHp5menmZqaoqpqSmmp6eZnJwiiqbIGw0DQFGr1RgYGGBwcJDR0UFKpaUsWtRPoTDIjp2KvXtg7z7NwYMabAGwLF4MJ55oWLPGMDycUirZmc/Bm3tnUK1aosgQx3YmvJkHDI2BQ3U40FRs3gm7DykS66GMZvkiy6pRy1mnZAxVII7zDyEoWBKg0+lxy82fYHw85M1vuoYVK09kf1uxdUqxPVEcjPNxw4tLltOGDGsXGVYttvNGFBdKhqAPmrEis4rdkWJ3pnjlQMT3vn8/D2z8MWuuaHPGyYZlK5ZS6x8l8pZQKNZBOzTsYgKvRZz5TKkS3cl9/HD7OJ16k/p9D3OdE/C//vIvF97gL2BvfvOb+dSnPsWyZcue760cDxIWFEIIIYQQQgghhBBCCCGEEEIIIYSYQ8KCz9FzCQseHQg8eoRwmlrGx2H/fsWuXR6T05okBdcD5WpQEGfgBooE8IoWo0EXFDqw9Ncs65Yb1g5bsjSl00nodGJarYR2O6bRiGg0IprNiDTN6PXSmVBfHgpMkowkMfi+JgwXNvjVaj7N5pFxvlorgsDF9xVKqZnA2/xA4dwg4VxKQbmcjzG21hBFKVGUopSaGct77GtYrfrEsZ1pHLT0evHs+ONCITjmvj3PATTFojMz+jiZbe8rl33abbMgzKhU3vaXJJZuN8EYSxRFbNmyhU2bNrF9+1NYW2FwcJB169Zx3nlnsmTJIFGUEgQuzWaGMZZ6PePgwZSDB1MOHEg4eFDR6WggAzKCoIPjTJEk+0mSHYDh8NewWq2weHGRgYEhhoaGqNWWMTAwyMBA/2xDIEAQQKkUUK+bBWHOOIZ63WfbNo+9e2HXLkMy83EsWmxZudKy9vQCIyMwOAhJks1pScw/Y88rEUVQrUIYWpIkfz7LYO+EZs+Uz5Y9DgemNWRQK1tOWWY4ZbllxbBlcCgjTDRTUz1uvOlG6vU6V199NSeddAK+l48w7jmWx1uaJ8c1e3sKjGK4YFm32LB+sWFRxeL4EKZQ6re0Yk21ZOmlkBkFKoPVG9l34AnCxlM0mykH6WdRtczggE/bWYzSHmRN9toSrbF9dKt9dLsp7W9+i1veeh1XXHHFsW+6F7BXvepV/Ou//ivFYvH53srxIGFBIYQQQgghhBBCCCGEEEIIIYQQQog5JCz4HD1TWPBYDYFzf+DIqGBjIAwzwjBj9+6EsbGUeh0mJzOazZRGQ5EkGms1SrmAS2Y0yrFkZFhXYR1LpixGGzInI9OG1M/oK4ec4jQIdN7YF4YxaWpJU4Mxh8NoPq1WxNEZG8/TWJsHxxxH4/sOrntkDHHeOpeRJNnsuRQKDnGcYY4q6bPWUq0GpKnF8/K2wTTNxxi7rp63n7nyRrt0dm3fVzOBvQTHcY4ZCsybB5m9xsWixnUVcZzi+w7N5sLX5NehQKuVoTWUyw7WWrrdGGMsaZrwxBNb2bp1G08//TRZllKr1Vi3bi1nnXUWK1cuI8ssnc6RRsMkianXm4yPTzM1Nc309BTT05NMTe2n220Dg+QjgxfhOKMYM4S1ebuf6/osWaJZs6bA0qUuo6N5GDO/JkWazSPXtVzWaG1ptRJKJY9ez1twbkEAnmcBl3ZbkWVw4IBi1y7Fzp2aPXsgyzRKB5xwguGkkwwnn2RZtMiiVP4+AwMOYRjMXtu5XBdKJUuvFzDV0Dy9X7F1n2b7AUVmFKWS5ZQlhvPWGxZXodtrc+ONX6Td2sc117ydZctOmF2rWDb4fbB3UvPUlObxccVYS0PRsrpqOXvYsGbQ4rmWar+hpzVxlgcFC6c/Ti+oU0tCPC9icyNgfKKO6u5mZysgdHz8zji9xStxDCSlAmMH6gTf+Ge+8YH3s379+mPeGy9kjz76KO9+97t5+OGHn++tHC8SFhRCCCGEEEIIIYQQQgghhBBCCCGEmEPCgs+RMYZerzfTiPfMgUCl1OwP8KwaCa211Osxe/bE7NoVc+hQyqFDhsnJjFYLGg1DZhXWOqDAKoVbVEQmw1ShvjhghDbr/EkW1zTtdojrarRWgEIp8H2HNLUoZWfOj9nwXpqmxPHCEb3lskenM78t0Np8pG2aGlxXoZTGmLytME0NnnfstsJKJQ8sKqWw1s40FTpordBa02yGC8KEhYJLFM1v0cvHH7sUiy5RlNHtphx9rxeLBXq9dN6ei0UH39dYq2i1EqyFgwcPsm3bNrZu3crY2G4goFLp49RTT+XMM9eyZs0KoihkfHySffsa1Ov12ZHBU1NTdLsdIALKQI9qtczAwAgDA0MMDg6yZMkgpdIwg4ODeJ6HtZZGI2NiImPnzpAdOwzj49nseY2OuqxY4bNqlc9JJ/VRqeQtjlE0/7PJA5ZqJkioZoKEKUqB42ggIJvzEVSr0O0atm2z7Nkb8NSTARMT+X3a129Ytw5OPy1j8WJDf79Hs+nPvlZrqFSg1co/h2JRE4YB1iqUsvhFeHSz5sndmm37FEmqqPRZzlidsWZJmzu+/AU6nQ5vueYtjI4updZn6fZAO+BUIIwVhYJlMoIH9jn8ZFzTihTlsuXcxYazhw21wFIZyohPepKoNIXKYLHfYK9ZQqw1gzZhyinTcx2qVjHpuvheke0Hx/jBPY+w7K5v8c3//T8ZHh5GKTWvrfEXwYc//GE+/vGPc/DgQTxvYdD0vyAJCwohhBBCCCGEEEIIIYQQQgghhBBCzCFhwedoenqa17/+9dx6662USqUFoUB4doHA5yKOM/bti9mypcfevZaxsYxDhxTNliVKINYZ+5aXyRQsth3OqkyzKOgRhum8dUollzhOSdMj4TNrLYWCC+RhMMfRMwE+Zv5Vs62AaWqIYzMTGPRpNKIFY33ztsJ81DLYmbZCjePo2SBhGKbzgoGepzEGsmx+KC5vuyuQZcw2FfZ6yWx4sFj054UCD/N9B3AIAg1YwjAhSQz1ep2DB/fw1FN72bVrJ+12C4AlS0YZHV3K6GgfaWoYH59kfLzO9PQ0nU57ZtUEqFAu5yOJBwYGGBnpY3h4kKGhRfj+AL6/MIiVB/sMpZKD41ja7SOjkWu1AocOGfbuTdizJ2b37oT9+2OsBaUsy5eXWb06YPVqnyVL3Dn3naVSKRDHHDOYWS57dLsulQpEUUYc26P2VGTPHs2ePZonn1Jsf9qSZXk74KmnGs4/v8DwsKJatXQ6dl7wMF/fQSmXXk+TZUc+/ySFHYfgid2ap/ZpbKZY3J/S3n8PprWB37r+GvoHls8erx1L/7BlqpeHWgGUtuztKX6w0+Hp6TzoetbKjIsveZy+kXH8AEpYxnWZSGuKrqKdeaSBA7ZA5Bq0LvHklp08+INHOPvBe/jaJ/6Ovr4+siwjmZnN/AIJzf1MjDGsXbuWF73oRdx6660UCoXne0vPlYQFhRBCCCGEEEIIIYQQQgghhBBCCCHmkLDgcfDxj3+ce++9l0996lP/YcHAZ2t8POHJJ2O2bI+4u+Wzr+nQaUE17mH2bmSx3sP6tesIgsMBIUuppGfGEucNg4cb6YIAut143vpKQbns0m7HHK2vzycMUxwnDwPmYTaLtZCm+djlo2/DY7UVHn48ywye56AUZJklDPNgY7UaHPP9PS8PqxljKBTypkJr83BgEDjs2TPBnj172LVrN7t27aQ5M9s3H6k7hOtqoqhFp9MCXMABUsrlwdlA4MDAAIODgwwNDTIyMkqpFOA4lm43mQlEguMolHJnf4c86FgquXgepKmm2z32aORSqUivZ6hWHZIko9GI2bs3YceOmN27FWNjeYCyWNSsWeOzfn3ACSc4lEoOcewvuL6OoyiXQSmXRuNY72ipVjVKBTSbeeYqiuDppxVPPaXZuk2RpYpqLWDdWjjjDMPixXb2nKpVRRwbgsCn2fSOCjAyMz5Z0Q1h24RiwybNeEdDGuH0fsKvvHI5p5w4RKlsSDNFFClqiwytRFEpQxhDOhNA7BjL/ZOKqUXbGD5hjKGK5YSKxnMDTKDQribOSlDKiLMS1lF0M59Ht27nqXt/yGv2PMXn//ZjBEEwe/a/iIHBer3Otddey1ve8hYGBgb41V/91ed7S8+VhAWFEEIIIYQQQgghhBBCCCGEEEIIIeaQsOBxYK3l+uuv54wzzuAd73jH872dZ5QYuGmfQ6tpeOqpNp/7+9thyoPpMZjaCckYZ555DpdccglLl47g+8y2DB4uCHRdS5Kk5HkcCyiMsfi+otuNsDYP8mWZQSlFrebRaIQLGgZLJXemQfDwIxbX1QSBOzMqN78Fs8wSxxlxnNHXFxyzrVApRRAcGW8cBPlI4bzlERqNiGazxZ49e9i5cyf7948xPT1FmnaA4pyV0pkfQ7ncR3//UgYH8zDg4ODATFvgYhzHm92352mKRQdj8tHTnY7lWFmlctmj1coolz08TxGG+Tkdvhbd7sLPq1x2cBx1zPa+w7LMZ/v2hM2be2zZ0iMMLVrDypU+Z59dZcWKEuWyplBQeJ6l3U5nmgkhCIqE4eFraKlUHOI4I4rsTJtjcfZ98+cVzaZh0ybFpk0u27aVsFaxZNRw0YWGM84wZNmRPx21Wh4YrNUsnY6a1zJoLfT1WdCWTbs1P348Y+t+D1CsPqHHy9YHLB3K1/J8S6FsyXxFN8rvu2rN0oqgvXIfQf8ODsWWbZMBh9qDrF7e4oSaJmWQSrVNM6xCwSOylh89sYV9d3yDd9UcPvRnNxwz5PuLFhjcvn07H/zgB/nHf/zH53srx4uEBYUQQgghhBBCCCGEEEIIIYQQQggh5pCw4HEShiEvf/nL+dM//VMuvvji53s7z6idwpfGHOot2L9zD/d+/4c8/oMHIPSgaWB6CnoJmAitNWvXnsqSJQMsWrSYkZHFLFq0iCDwMCYfl5v/5OGvPLAXzhnFnI8rdl1NmqYcyfgprLUzDYGGOM5IkiMjhh1HzbT6LUzI1WoBzWYeGCwUnJnWwjywqP7q/6N3aJrEcdlfrfGI67C116Mwvy5GAAAgAElEQVTXq2PM0aEvi+cphob6Wbp0KQMDi6lU+meCgYP09ZWJIhY08yml6O/3ybJ8hG8Yzj2vw2OF5++7VHJwXVDKodFYOBb58Hk1GinlsovnKTqdI+Ogq1WfVmv+RnxfUSxq4tgQRQ7G5C2Q+/YlbNkSsXlzRL2eAh6rVweceqrP6acXKBSOhOOCwMEYn2JR0+tlJMn898jHFXtUq4pu15AetfUsc3jsJwUefMBhfByCwHLGmYYXnW/o789bBh3Hp9Hwj7oeBmsVvV5+4So1SzeGycYUn/7HHSSFc0AVWDVq+KWXZAxULcYorIX+IYMtQCNUtE/cT2FgnEKhThz7jNlhmmGHnU3FAbOI0wZClvV7xOUSaa/Hvfc/xtTNN/LRV13Iu971rmN+DkfO7RcnMLhx40ZuueUWPvGJTzzfWzleJCwohBBCCCGEEEIIIYQQQgghhBBCCDGHhAWPo127dvHa176Wf/qnf2J0dPT53s4zGgvhpr0uhcTSihQlx+L0oNeI+NG9P+Q7X/4mtAx0k3wGrc2ACEgAQ7VapVbrY3CwQqVSob+/n2q1RqlUoVotUi4XAGdea1up5BJFMVlm5u2lWHSJ44Qss7Pjjh1H43l5u+DhFsEkSeh0OrTbXdrtBtu3jzExMUG9Pk2r1ebN7RanENPDw85khSzwFPC051Cu+qwqltGnnEJw6lrK5T6CIMD3HdLUYMzCW75WC+h2LYWCg9aQJBm9Xoq1llqtQKu1cFwyQLns4zgaYwzdbjK7dt6AGBCGc9/LUizmYUJjNJ2OWbCetVCtFuh2MyqVfL+dzpGQYrUa0GodOd7386bFHTt6PPFExKZNhunpDK0Vp5zic+aZRU4/PaBY1BijaLWcBW2NjgPlsgJcmk13wZ6KRYXWBnDodAL27FFs3Kh58kmwVrN2reXCCzOWLLH09QU0mx6eZwkCS6ul5wUsSyWD0pAoxf4Dk3zxxtvJKuvRiy4jjBxOW2G4/OyMlcsMra7CWEt65n6i0WlKUQurYMofxjEWV3WZcIbYPKUYazmk1QIn+j2e+uH3SW77B25+37t49atffczP7Wi/KIHBu+66iwceeIAPfehDP/W466+/nm984xsMDw/z+OOPAzA1NcWb3/xmdu7cyYknnsjtt9/OwMAA1lre8573cOedd1Iqlfjc5z7HueeeC8DnP/95/uzP/gyAD3zgA1x33XXH+5QkLCiEEEIIIYQQQgghhBBCCCGEEEIIMYeEBY+zu+66ixtuuIGvf/3rBEHwnNb69KcnOXAgZdUqn5NO8lm9OmDx4oWBrufi4Ybie+OapKMouZZWrOgzlqgFjlL0pht8/64f8YN/uZd0OmTtSadzxtq1TBw6QL1+iEbjAPV6nXp9emacL4ADHA4IdvD9AsVikWKxgOd5OI7GdQ1ae7iui9YOAMakZFlCmlqyLMMYQ5Kk9Hoter02cWxYeL9GwJHrfAMJBSwBCSkaiyJDE+GSodFYfFJ6KiB75StgZAS1Zy925QpKp66i04lxHE0QOLiuxhhLGGYUi94xQ4F58M8lDDMcJx9FrDVEUUqW5U14xwog+r5LljkUiw5KWbrdZDZA6fsOSeLNO1etFeVyHpyMY0UULVzT2rzREDRZdjhIeOReKRYdtm+3PPZYjyefjGZCh4qzzy5yzjlFli2r0Gwe3h8UCopWK51pjLTUamVaLY21diZAaOl0zJywYj5uuFTStNtw7/cVDz2kiULFqtWGyy8znH66S73uY+2Rffm+xfeh1crHRSttKfdZDk0d5BOfvhXHK3HahW/j0d0lMuCi0w0vWZfBGfvoDNdxe5ay36IeDBP7mv60y1TQT6g1hUyz1wTc/7RHJyrjfPc7fPu6JVxw9toF1++n+UUIDN52223U63X+8A//8Kced++991KpVLj22mtnw4Lvfe97GRwc5H3vex8f/vCHmZ6e5iMf+Qh33nknH/vYx7jzzjvZsGED73nPe9iwYQNTU1Ocf/75PPjggyilOO+889i4cSMDAwPH85QkLCiEEEIIIYQQQgghhBBCCCGEEEIIMYeEBX8OPvrRj7Jt2zb+6q/+6jkF+665Zhd33NGcNwK3WtWsXu2zZk3AyScHnHyyz6mnBqxZE1CtOs/6PayFr4w5jHWg1VEooOyC7UHWA63AJpbOwSbf+Ma3eOzHP2ZRbTnX//pbGaotgtSATYCYbrfO1NQk7fY0zWaLXq9Dt9sjDNvEcZ1OpzMTBszIspQsi0iSFGMy0jQPpRmTkWUxxhjSNA8PzuwUMLiuT6VSoa+vn6GhIUZGlrBy5TLK5UF8P8D93OdRY/sBqBHSoIDSGnPWWeidO2F6Go8MNXNrexgcDEproiteg3P+udRTF71vH2rXbuzKFdjly1EKikWPbjeb3U+h4OL7GqUUUZS3DR79eZfLHp1ONnOtLaWSh+dpsgy0hmYzOeY9UqkEdLt5QNBaQ6eTzN4HxaJLGOp590Wp5OI4lm43w3X9Y4YJPU9RrXq0WhCGhq1bIx55pMf27TFKwSmnBLziFYMsXx7Qbi8c/ayUnRnLrOj1FjYflkqaQsFlctKbPacogoceUtx3n0evZzn1VMNVV7kzIVGoVqHVYjY8aC309Vk6HSjVYMf+A3z+i1+kWMp4/a/9dx54eoAndipOee0ezrlskr4SDGQJ40GNEE3VWJp+QKI17lRI3Kuzc8LyyP33MtQdZWLlr3PKoOWW10WcOvTs/ry90AODf//3f8+iRYt429ve9ozH7ty5kyuvvHI2LHjqqady9913Mzo6ytjYGJdddhmbN2/m7W9/O5dddhnXXHPNvOMO/xweeXz0cceJhAWFEEIIIYQQQgghhBBCCCGEEEIIIeaQsODPgTGGq6++mpe//OVce+21z2mtKDLs3p2wfXvM9u0RTz8ds21bxLZtMbt2xZg5ma3RUZdTTw04/fTC7L+nnx4wNLRwfOxcnRQ+udPFTS2k0E4V1kJ/Yml3ZwKEjqUxqdjz9JPcfuuXyOoRV//qW1h32lpUD7IEtEqBGMiADGsTkiTEWgNkNBoTTE2NcfDgOJOTk4yPTzI1dYB6vQEc2WMQBCxaVKJWW8zQ0CCDgwMMDAwyNDTIokVl2u1owTlUqy6tVoy1Fu9zn8Mb24dTDAjOOJ343HNRJ66CXbtwPvVpktSggKRQIgvjeetYoFbxaLbT/DfHxfzGWwhOXkkQuFhrSRI7O4b4sErFp91OmJ9PygOFpZJHHEOvly4Yv1yrBTSbeQDN2vz4IHBI0wzXdWg2F4b28vfzMMbFdRXdbkqaHlk3byZ0sRaUgnLZwVpLp5Pvua+vSLN5ZO/1esZjj4U88ECXKLKsXFnmJS8pc+KJft70p6BadQhDQ5qC5xVnw4h5y6CDUtBu5y2DtVqBRiNvWKxUNL1eHv67/37NffflQcnLL3e54AKNUkdGVBeLBlD0ekeCg7UBw/7JfXzyc7dSLJX5nd+9hn0rujyZNAgTWDHoMLzMxTiawPFoWgc3UHTGDKWf3EurW+Hih79HY+px3vulL3H/eJlr7wiIM7jpdREvX7kw9PjTGGOI4/yeeaEFBj/0oQ9x0UUXcdVVVz3jsUeHBfv7+6nX60B+TwwMDFCv17nyyit53/vexyWXXALAK17xCj7ykY9w9913E4YhH/jABwD44Ac/SLFYfMZWw2dJwoJCCCGEEEIIIYQQQgghhBBCCCGEEHP89BSZ+HfRWvPZz36Wyy+/nPXr13Puuef+u9cKAs2aNXlzIFTnPRdFhu3bY7Zujdi8OWLLlvzfL35xmnb7SAhqyRKXdesKrFtXYP36/Oe00wKCIA9qlV149XDGNw84ZCkoCxXP0tEKFULgWHqZotAPa9eezjve/fvcesstfOH2z3PVL/8aL77wRbipIWpopie7TIwfYHLyIBMT40xOHmR8fD/1+iR5iDAPFPp+wKJFi1m6dC3r1w+wdGmVUqmfxYuHqFZLKKXwPLA2wRhmR91aC/39DnGckmeBLMbkTXl5CC4ifdtvkc6cexuo1XwajR5qYAnqLb852xhYCDTqs1/AZBYUeIsH8afHUe0WQ2TEuMRZSvT1OwgvuYSwUqE4Pka4bCV22bJ5n0W7HVOr+WQZOI4iyyxhmBCGCb1eTLVaXBAUBOh2Y2o1D1CEYUoUJUTR4TbFhFKpMKfNMG8QPBwQLBad2aDh/Psipb/fxRhNt5vNhBhzSilarZBSqYC1Cs/TaA0ve1mZiy4q8vDDIfff3+WWW2KWL/f5pV+qMjLizQstZlmI5wX4fj6SuNs1M2vnzzebIYsWBTSbHq2WnbmP4ZJLMi6+GO78Z4d/+RfLQw8ZrrpKceKJUChYmk09u0ZQsLg+tNqaanAC177xzXz+9r/j1p1f4xUvOZMLih5P7CjyyN4yIzbm9OUePVOgUE2Y2GPp23Q/4VSB37zrC7xxw1dJ/+RPSItFLl1h+MFbQ974lYA3fDngC6+NuWrNsQOZx6K1xvd94jgmSZIXVGBwamqKoaGh57yOUuq4jkoXQgghhBBCCCGEEEIIIYQQQgghhBDHh4QFf04qlQo33ngjb3rTm7jjjjtYtGjRcX+PINAz7YGFeY9ba9m3L2HTpohNm0I2bQp54omQT35ykjCcGb/rKU47LeCss4qcfXaBs84qsmSkSr2k6LQVzUijlaXaB60pRWYUFd9iiyntruHll7+Mb8c9vv7Pt/OjH92LMZap8Tq0IzA+2AzPdRgaGGbFinWcd16Nvr4qQ0ODjIwMUK2WSNOIbjdG6zwY6PsWpbKZxj6LtRbHcTAmIk0txuQ/vZ6lUvFoNruAwlqLUopGw1Ct+rRaMY6j0VqhNaSpYXCwRJKk6LWrUetOwto8ZOj9znVEW3YQL19Bunw5PWNQmzbhfeMOCiYiwkVNT+PecQeWvDexphM6111PsOYktAZjLFGU0WhEM02B85sPlVJ0uxFB4JGmUCzmrXtJko8u7nYtoOe1Ax6WZQnVqo+1aubYdPa5djukWAzo9bKZEccunpcf12j0qNUKZNn8clCt89HGWRaRpv68ccK+r7nggiIvfWmZRx4J+e53Qz75ySlOPtnnla+sMjiYNwiWSpo0jYnjgCQ5sv7hBsJeDyYnU6pVNdNwaKlUNMZoej248pczzlhv+OadLp//vOXSSzUXXaRwHFDaUq1BswNRN2+4rPVbnOJyXv3nv8VjO+7m8Uce4OxzL2bZyn4qwy02bi6zu13l8mW7aTw4Tnn/AZxOwv/91f/DRTs3QqGAednLZvd5Qs3ynatDfuXLAW+9w+f210dcsfpnbxh8oQYGp6en/91hwZGREcbGxmbHEA8PDwOwbNky9uzZM3vc3r17WbZsGcuWLePuu++e9/hll132XLYvhBBCCCGEEEIIIYQQQgghhBBCCCGegYwh/jn72te+xsc+9jG+8pWv4LrPbzYzTS1PPx3xk5+EPPZYyKOP9njkkR4TE3mzmqo4LL5mGcv7NUN9CW6xRcI0nbF9TOyZYKLept7qYRsTEGpwqygFtlFnycgaTj75FEYXV+nzh+mvDjE0UMZRlrCr8F2LMQbHiUnTBMcxGGPROqHXC/E8heuCUhZrY9I0I44taZqhlKJSgVZrfgivXHbodnscfQ/PNgke1W5Wq3k0Gt0Fj5fLHt1uwuFlrLW4Y/so7tuNWroE3Wjg3H03tl4nRRPiUg0U9aWrsatXodIMu3IFdvlylIJi0aXbTWf+7+E4GrBkmSGK7IIAH+THhWEGKIpFB9d1SBJDr5fMPGex9ui2Nku16qG1Q6+XEcfzA2/WWqrVEp2OmRkVbGm3j5xnELjEsT87rrha1USRIYry+8H3Xe6+O+aHP+ySZZZLL63w4heXZtcPAocsCzAmH0UchpAcVXTY3+8SxwHd7txHFbWaol7XfOtbLo88olm5Et56rUF7ijTNzzMoWJwAOiGMnT5NOtwla+xkw32b6Q0t5bKzTyejxN56xuPbS0Suz0v2/4iVE9tY8Z2/5er/8Q5OqtcxL3sZ5sILF1zzRgSvua3AtmnF994Ssm7xs/tz90IbSfyGN7yBm266aTbo99McPYb4j/7ojxgaGuJ973sfH/7wh5mamuKjH/0o3/zmN/mbv/kb7rzzTjZs2MDv//7vc//99zM1NcV5553HQw89BMC5557Lxo0bGRwcPJ6nJPWGQgghhBBCCCGEEEIIIYQQQgghhBBzSFjw58xayx//8R/T7Xa54YYb/tON57TW8u1vP8SnP/0DtmzR7CmfRnzi6dAr5gmysAfBJGXTYGBQsXI0ZXhkgMXlIUqlRSzqK/DFG29n88OP8qY3/Abnnn0G3R6UrIVUkSSQJlDyLFmi6PUgCDI8LyTLDL1ehutaisUYYzKsNSSJIQgszWaEteC6eZAwCCzGxMy9hEodHlVsZ0OD1oLvK8IwQevDByuUAs+DLEtnflfz1kmSjDTN3//wWp6Xj2pOd+zGuelmyNKZ1aCPkDoFwOJr0Ndfhz75JKw1WMu88b+HlUreTBNg/rvWUCjko4WVUjSbKcf6SlYqAa1WhtZ6JvgH3W5Clpl/I0xoKZU8HEdhjKbTWThq11pLf38BY1za7WxB6BKgry+gXtfccUeTxx8PGRpyuOqqGqOj+dqVikMYFoii+euWy/lI4U7HUig4ZFmBOM4DiXGsieMje92yxeGrX/UoV+C3fzelVIbyTLug0XBw/STxSITfTlAYtqeGRx94hJUoRgcX4e6vM1kaYkN2IepgyMWPv4Mbv/i/f6bg2VhbcfEXC/QHlh+8NaT0LDN/L6TA4OWXX8599933jKHma665hrvvvpuJiQlGRkb40z/9U17/+tfzpje9id27d7Ny5Upuv/12BgcHsdbye7/3e3zrW9+iVCrxD//wD5x//vkAfPazn+Uv/uIvAHj/+9/P2972tuN9Sv+5/tgKIYQQQgghhBBCCCGEEEIIIYQQQjzPJCz4HyDLMq666iquueYa3vCGNzyntcbH4Q/+wOessw3nnmM45xxDf/9z299v//Zvc8stt7B8+XLOu+BC2mdfgx+M0gxHabVLHDpkObAjhC7guQwPu6xa7rBmic/wkgKOa7jtps+wZ/MOrv2N/87y5cupFCx0od3IRwwXA0vSg25LUSzmI4ezLKLdzvD9PAiodUQcx4Rh3jpYLCo8Lw9i5Y2D4DiWbrdHkmQYY1BK4TgK34deb344r1x26PVCzFETZqtVj1YrH2E8V6Xi0W7Pby+EI4FBb/8+3J070PUpnAcewGJxMdQpYlFYx8WuXYtZezp+KcDs3E16Qt44mLMUCi7Fok+WZTPNgem896rVCjSb8x8rlVxcV+M4munp+JifYaUS0OlkswHBTiedbTDMg4geSZJfCN/XFAoOYZi3EeZBRDsbnsybHB2yzNLpZPT1BTQaiu3bE+68s0m7bXjNa2qcc05hJpjpAEWiKB83bC0zo5Vnztpa+vo8lCrQaBwJogUBeJ5Dq6UZG1PcequD68J1v5lwwipopoaJc6eplyNIFH0kHCpVSQ9MUnj0cVqFEuXxDq1qHwfqMU/8+Ic4hRs4+2SH73wkJvgZs3v/ukvz2i8V+B8XJHzwZQsDns/khRIYvPTSS2eb/l4gJCwohBBCCCGEEEIIIYQQQgghhBBCCDGHhAX/g+zYsYMrrriC6667jjAM+bVf+zVOPvnkZ73Oo48prrkmYNcuPfvYyScbzjvPcMGLDBdcYDjjDMOzySyNjY3x0pe+FN/3ueeeexj3hvmnXQ6VNA+QtTKIE6jvjti+KWHHzojdhwxZJ4MOLFvisuxEzaZN38VM7+A9v/cOypUavVBRthZlwBjodhUVz0IGoOj1LKVSRprm7YJZZnHdhEajh+/nAUDHsVgbEccZcZxhDDMjixPCMMPz8rCg1uD7hizLR/nmLFqDtXlr3uFbXSlwHEjTdKal8EimSGtIknxUb5YZssySpoYgcGcCiha1dy/OzTdDmqEwlIlpE8x5V/BJKRNjtE/yu79DsuwEwvBIa2CtFtBsLgwm5uOAiwBkmaXXy1sT4fBY4SLt9pEwoeNoSiUXay1aa5pNs2BNOBw4dElT6HRSji64rNUCokgTBHkL4dGjkmu1gDR1CUPL7bdPs2VLzNq1AVdeWcN1FX19Htb6NJtHFrbWUqk4WKtnxhArajWfXs+lWHRnjlUz+zMcOqT59GdctILf+r2Q1kunCQdilAY3dplq1tE7dhLsrNMYrlKcyngsTNnRiND3/B2f+X/fgbf0an79QwH/1xsT/uxtP3vw73f/2edLTzk89lshJ9Se/Z+9F0JgUMKCQgghhBBCCCGEEEIIIYQQQgghhBAvbBIW/Dl73etex+7du+nr62NwcJANGzZwww03cMUVV/xMY1L/LZOT8PAjmocf0jy4UfPAAw4HD+bZmGLRcv55hhe/2PDil2RcdKGhVvvp623cuJFXvepVnH/++Xz963dwy+4i9UjRrisCz1LwLa1EUQgtvZ7GUYZDBxKe3hyyeVPG3r0JNs4gjfFVk8suPYn16wJGFmnCaUUUKhzHUipYiKDTVBgDhYIlCAxJktHrgTGWSiXDcSLAkKaGXs9QrRoajQjfVzMBQdA6wZiULMuDfWlqKJUUzWZv3ojhINAYk8426x1Wqbi0270F1yJvGFzYPFgsukRRHhj0DuzH370TXSnh9rqwZhWJW8A8+jjJhgehm69bIaJx5gWYK3953lp58M8jSSy+r1FKzZxrOvNeHt3uwtHBjqMolQKU0iSJods9EvyzNm8mbLXy13memhkBnB+Xj0BW88Yc52FDhzQ1uK5LqzX//bRWlMsOUWQIgiNhwB//uMPdd3dYtarA1Vf3o1Qe2CwWC7TbHBUSPLwWVCqaOHbQuki36+B5liCwtFr52OKJCfj8P2mGrm5w0etaFAJD9GSLuL6XQm+azkQVZ0STDJ7K7ihm073fgW9/kLPWrOCuu+6iXC7zrv/jc+N3HX741yFnrPrZ/oTtbSrWf7rA75yd8j9f/uzbBeG/dmAwTVNe9apX8cADDzzfWzmeJCwohBBCCCGEEEIIIYQQQgghhBBCCDGHhAV/zqIoIgiC2d9vuukmbrvtNm666SYcxzlu72Mt7N2r2LBBs+F+zX33aR59VJNlCq0tZ59teOlLDZdemnHxSwyVysI1brvtNq6//nquv/56/uDPP8ZXdjnoRNHp5Zkb17GUPUtzUmFt/pijLVVrma5btm1PeeDBMXZu6kKvH7RiZKnP2lN81q8OWLrEpRcqsgyKyqJNvrdeT1EsGlqtjGIRXNeitaHV6pLN5OV8H4rFFGtjjIEkMTMjdC2tVjjvPPr6NGEYzTQOKpTKxxgrZbD2cGBQcbh5MMvmNgxaQKF1Hj48fG2ttaSpxfMU3W7M0V8bx1F4niYMs7x58KabIMtQQI0erbMuxL3yCtxqBcjbCqMoIwhcut2F4TTHyccOJ4mhWPTwPE2aZnS7KVprHMcljueHH621lEouhYJPGBq63WReaBKgUvHpdPJApLV2XkuhtdDXV6DRMDNNhIp2O29lPKxWK9DraYpFlw0bunz1qw1GRz3e8pZ+fD8PFnpegelpZzbEmLclatptZkdCa63o6wvodj2iSAOWWr9lylruGYrZvqPNiaN1luzZiRu3cGsp0+FyKqeOMF1bzqaHHmH8npt57eIDXPmaV/POd76TSy65hC9/+cuEWYkzf6fIS9Zl3P7/HHts87Fcd4fPv+5y2P7OHt6/86v5XzUwODExwTve8Q6+/e1vP99bOZ4kLCiEEEIIIYQQQgghhBBCCCGEEEIIMYfzJ3/yJz/t+Z/6pHhmruvO+/2MM87g/vvv56GHHuKSSy45bu+jFPT1wdq1llf9N8P1b8t497tTLrs044QTYGxM8bWvOdx8s8df/7XL977nsH+/oliEJUssSsH69euJ45i//du/5aSlQyw6+QI6KbjGkpg8IBilij7fEpDH6lKjMBpIFCcsdTj/7H4m2xs5sO8uzjprPXHo8uijPe5/sMMjGxNaLcuiIU3foCYJFZ22JjMKhaJcUdiZccW9nsbzPAoFQ7GocF1FHGu01rTbCVmmAI21mr4+D8+DQsHB9x3SVFEouLTbEXFsiWNDFFmyTGGtodNJiaKMKDKEocHzXDqdmCg6/HhGGOajh9vtiCQxJEk+kjhJDOWyT5LMbf3LRwAHgYvvawrDg/gnr8Lvr6L+f/buPFyrut7///Oz5nveG9hMAirihAokKuQ8FDnnVA45lnosNbNOnV/HOunpVHbU6pRmYeacZipiKuKUE8okCoqKqMg8Cnvf8xo/3z/W3hu2qICaVr/347ru64I1ftbivvnrdb3erS00V66luGIhtVlzaWby+IVWogWLYM7LxBrctlaiSKO1xvMsslkL103Ddlqr7jV1NSNqrUlzpgaGocjnbVzX7AyqxQRBhGUZROtzgBgG5HJpeM3zDMrliDDsmXi0bQPbhkzGpFpNeoQRtdad56eByWpV0aePRd++FtOnN1izJmbkyCzNJjSbEYWCQmuTfN4kigyazTSMqJSiWLQJQ4t6PW2E7NULnIxieQyvDW8woDmfsFHhpcXb05tVZHorKgP2QO20E+/EFs9Pfozyg1dwxal7cfnPfsrIkSPZbrvt+M1vfsPMmTP5yknHEcY2f3zI5qQDI3oVNu83ZCi4da7FQVvHDCl9uJx02rBoEMcxSZJ8rIHgv6clS5bwwgsvcMIJJ3zaS/k4XfZpL0AIIYQQQgghhBBCCCGEEEIIIYQQ4h+JNAt+CsIwZNy4cVx00UWMGzfuE7tvvQ5Tpxk88YTJ448bvPBCGmTq00czblzMYYfGHHJIyDnnnMRDDz3EH+9+iHktB1DQmjgAw4ZKqLAMja5AEkE+AwkaK1GU13UWeSUB43/3K5rr4JxzLySKHOa/7vP6S2M86ksAACAASURBVFXeejUCZdC/v8OokS677+RSLJiEoabeUJSKCeVyQjYLlgVKJVSrDeI4/SoqBfl8gtZNlFIkSRoG9Lxko/HD+bxBo9HobOmjs2VQY1kJSVfFXXeToCaOYzb8yiuVhuySJALShsIk6QrrKZrNkDjW3Q2EAI5jEseaON6g9W/NGswHHqRl6RuU8Uj69sVatQKPCMsyic45m3jw1tTrIUnS8yeXjj5OejTyZbMWhpGOE67Vou59GzJNA8exsW2TJNHUalGPNsRi0aWjI8E0Fbmc3X0MrG8YLJd15xhiuztw2SWbTQN/2azFU0/VeOCBCnvvneXAA/OdAUaTZlNh2x61GoCiWDRpNEzCziJF11XYtkWlYlDLBiwa8CbxsrfpVVnJmqCNh7OH0qqbfOaAHFZT8eZbC3jt4Un0e/MW/vyHq9hzzz17PPOtt97Keeedx7hx47jq6jvY7d9KXHJKyPdPjtgc7zRgyDVZfrx/wLf32rxz3s8/W8Pg1KlTmThxIldfffWnvZSPkzQLCiGEEEIIIYQQQgghhBBCCCGEEEJsQMKCn5KVK1fy+c9/nttvv51tt932U1nD6tXw2OMmkyebPPqoydq1CsfR7LtvwKuv/IR6/U98/87HaWb6E5QBFK6lcR0gZn04EHBtjRMl1OoGiVYsX7GcG8dfzYjtRnDSSV+m1oREQ1yOeX66z9y5NZYvTcfk7jgky+6fybLddjbZnEaRUK/r7mY8100wzQaWlTbtBUGCbachwi5KQbGoiSIf0zRQCqIoDQZ2jTPuChKmI4Mjms2egbBczqRe93n3b6JYtOnoqG800rdQcDYKKAJ4noXvR9i2iWUZmKZCoVHPTcV94H4qsUGI2T30ODngAOyD9ycMk3eFBbuaBm2CIG01bDajHvfL5ZzukB+kIT7LUt1NiFqbGzUIpi2DDpZlsm5dzLt1tQh6nsvatQnvzlx5noHjmJ3hQRffhwceKDN7dpOvf72N3r3tHgHG1lYX3/eo1zvHWVtp4LFcNiAIqa+axYKt19LQJrm1VcKW3nRstyur1vRh3lKLz+7Y5M03X2DV03czrs88rh//O3r16rXRugFuuOEGLrjgAo444ghWbnUvlqV47Ar/PY99L9v8NsNRwyJ+M27j0dBb6p8pMDhp0iTmzp3LZZf9S5XxSVhQCCGEEEIIIYQQQgghhBBCCCGEEGIDEhb8FE2dOpULL7yQBx98kFwu95Gu9cZSxdTXDL6wR0xbacvPjyKYOtXg/gdM7rvPZOFCA4jw2mby+e+OZPddTcJ4ffbGMjTZSFMLFHGSbs9amsZaKOQgTDSTHnmaZyc/wIkn/Bvbbz+UXDYdd1xdo0hixapVEbPn1HlpVo1mu6Z3H4c9RmcZOcojn4vRGjwP4hggoV5vdIfp0nBg2jAIiijSNBqaQoGNgn25nKJeb2JZ6Thjw1AYBhhG1BkM1J0jctMgXRwHnS18XdfQOA7dY4ANg+6WPsNQRFEIpC2HUZQQRQmeZ9Jo9GzzA7D+9jjZ556igdPZaQjJ0KEkJ59Eseh0H58+T9QdXEyDiWGP59Jak8nYZLMWQaCp16ONmgld1yKKDLROxxB3tRF23SdtGEwDiI5j4HkWzabuHkFcLDp0dNDZFmgRx1Crxd3rSIOHGXzf5Kqr3iGTMfja13qhFBQKFkGg8P30/ELBBjzKZQvdDLCen0Gj4wVeOnQYiWmQxaSyzQjCvm0UGtARGTzzoIFqzkPPvJAfn30g3/rWtzAM4wO/y+PHj+fiiy9m6BfuY4U6klV3NVCbGRv7zB89dmtLuPmoYPNO2IR/lsDgbbfdhu/7XHTRRZ/2Uj5OEhYUQgghhBBCCCGEEEIIIYQQQgghhNiAeemll37Q/g/cKT6aQYMGobXm2muv5aijjtqooW5L3Piwxbd/5/Lrey2eeNGkvaYY2EtT2swMomHAkCGaz30u4RvfiDjiyIhqdSmzZ+R4fVlfnplp0L4S7IympQU0CtuEoAIFV2MamkZkUPCgUlFEkWLYtlvxymtzeHXuPEaO3IM4tvEDRS4HngnFkmLIEJc99sozoL/J0sUxs1+s88ILNaJY0buXSRQpggB8Px1t6zgxrmsAmmo1bfErl0PCMA3PJYmipcXCcTSua2DbBkmSHler+cSxIgw1QaCJY4MkSajXo84xuwnNZoLjWFSrPkEQd34S6vUEz7OoVAJ8P+n+NJsxnmdTqfgbtPmlwcJ83iYIYkB1ji42cLIu3pwXyCQ+rkqwTIVau5Z42UqCle9g2wYVI9MdTOwSBDGFgo1pmmSzdudzpW2DjUaE51k0GutbB7VOWwld18K2DaIIms2kOwTYJY4TWlocwOgMCerukc8pTbFoEQTp/jDUKJU+Tz5vY9sW5XJEPm9h2yazZjXYZhuHtjaPRkMRx3SPJa7VDPz2KqWZf6Nw920syGnePGAIqn8Be+D21NtGYfTPYbxjYBoJb748n/aX6xhTE566ay+OO+64zfqNjB49mlKpxF/un01YOoxzDm+Sy3xwwLDLtbMsBuQ0x+64cePih6GUwjAM4jgmSRJM0/xYrvtxe/LJJxk4cCAjRoz4tJfycfqXqkkUQgghhBBCCCGEEEIIIYQQQgghhPioJCz4KRs9ejSTJk1i0aJF7Lnnnh/6OmN2SjhiTETfFpj9lsHtj1tcPdHmkecNqk3FkH4J+czmXUsp6N8fjvlinv797mTSPT+hbdQ+LHu7hRdnmMx9URFqyLdC0dXUGgZhoMjaGtvWNBsAikSb9O03hBlTn8CMY3YZvj1BBEGscCyoVQwsA0oFGDjYYsTwDFsP8SiX4fmZTWbMqKFUzNCh6Wjdet0gk1FUKhFxDKZpYBgGuZyBbWsMIx2/W6+D6xpUKiFBoIkiTRDQ2dwX43kmrmviOAa2beG64DgmjmNi2wZaK/J5B62T7nuYpiKONdmshVJgWUbnOenx2ayF4xi4rtV9fVBkMjZaa7ROA3ZRrkBz6+2IevfFP+hz1HfeDf3KqxjvvINauJDoxZfJDx9GkM2TzVpkMhaua2IYino9JJOxqVQCgiDp0Vro+zGlkovj2Liu1TmuWeP7CUEQ43kGcZwG5mxbkcvZWJbRGXiMyGZNfD8Nt6WtjWkwsdFIA5SZjCJJFGB0NgRaPcKDQZAwdKjJzJkRa9Yohg/3Oq9jEUUWjXea8PQUWu69g/CNJczea1dWHzgUY/8dsHrvSCPqhd0L1DsKv6PCtKens+rRG9klKrJmyd5ceUUblrX5v4e99tqLVxYZvLZmBxY88+8ce9TBm2wk1Bp+PMVmzMCELwxNPvDYLfHPEBicPHkyu+yyC8OGDfu0l/JxkrCgEEIIIYQQQgghhBBCCCGEEEIIIcQGJCz4KVNK8YUvfIHvf//7bLvttmy99dYf8jowoBfsPyLhnMMjTjwgYkBvzUsLTG57zOLqiRbTXjUxDdhuoMbazLzS7rt/hrXLn+PJFx/msBMGMXyHfqztUMx+3mTmswbryopiTpPPQxQrmoGi5IELKANy+RIdtYCZ055l6LYjKBayFLKgDU3sQxwr/EARBIpMVtPWy2D33T2GDXMpVxQzZ1aZNi0dNTxkiIVlGWSzAAlhCGEIzWYaFmw0EsDA80wMwySbVTiOwjQhSaDRSNv+qtWwu0nQ9xO0NgiCCN+PCcOEMEwDcrmcTb0ekySQJIo4TlsOMxmTRiMkipLu430/wXEMqlUf34/x/bSV0PdjcjkH34/Wv9RikXjQYKzeLRi9WsiU15JZvogMEXYS4muTzKhdqNXC7mtFUQIofD+iWHTx/RjHscjlbDzPTMc7VwNc16JS6TmOWGuNZZkUCmZnADBtS9ywvdD3Y1pbXSzLIgzB99cHAQEsCzzPwDRtarX17YO2bZDPm4RhOm64Wg14+eU6Bx/cglIOjdUNePIZivf9GXfhQioUmHPyIaw5dh/ULkNIyiV838WIEuKawbJ5i5kx5QmcF37HjZcdzYjdjuL++y3OOCOipWXLfhOr/e15+HmTeQ+fybIlb3DYYYd9YDPhipriimk2Jw6P2XPAB4cFb1ljcssai4OLCcZmFIL+owcGJ0yYwH777cdWW231aS/l4yRhQSGEEEIIIYQQQgghhBBCCCGEEEKIDUhY8B+AZVl8/vOf58wzz+SII46gUCh85Gv2KsLeuyScfVjE8ftFlHLwxGyDmx+xue4Bi+VrFdv00/QubvpahxxyCI8/NJEn563jgL0HM2ZMiZ2GJyTAnLkGM58wWblSUWyBYhGCBBIf/KYia2mGbduf6bOeZ8WSNey66wiCQBGEilxe4ykwTU0YQRgbZFxNpcMgkzEZvbvLrrt6rFzp8/zzTebO9SkWLbJZB9NMSBJNNqvIZFRn+186ZjeO6RxdnG6r12O0Tsfhaq0oFExsW+F5Bo5jYJoGmYyF1knnMelzN5uaYrFrlPB6YajJZs2NRgWHYdpo2BXO62orBMjl7B7thUopwjDGdS3qlkcw5xV8LHwskpWraQ4cTGGrtu57G4Yik0mfHZLuscNdgcQoSoN9vh9SKrmEoSaX62oZTMcYN5sRlpU2BHY9Yy5nk8nYRBE0GhGOo4gi0Hp9w6BhGNTrmiBIiKKIQsHEMAw8z6LZBN+n8/1CoeDw/PM+fQsBQ195FG/C3XiLF1FN8lR33JV5/3kia/bYFct0sEOLemjjNhOqfsgrU2by9vQHGKseYvKd/8eee+7JW28aTJiQhgX79t2y38B9z5nMmGfw3RM6uOaaq1m9ejWHHnro+wYGJ79lcu/rFpfsHbJVQb/nMV3Of9thSaA4u+/mjyv+Rw4M3n777Xzxi1+kV69en/ZSPk4SFhRCCCGEEEIIIYQQQgghhBBCCCGE2MAHz+UUfPWrX6Vv377suuuu77lfa803v/lNhg0bxogRI5g1a9aHus+QIUP41a9+xZlnnonv+x9lyRvZabDmR6eFvHJ9k/v/p8khu8dc96DFZ87LcNQPXSbPNHqMtH03y7K467or6EWTW266kVq5g7Y+cOgXEi68IOKQoyMWLVLcPN7irtsMVq5UeAWNAhq+ItFFDjzgcBa9PYuFb7yEUunNKk2DWEG9amAChWxCYihsV6MUNBqKQsHlK1/py8knF0iSkD/9aTUPPdSB79uAolbTlMuachmiyMW2IZuFYlGRzyssy+0cFaw7Q3Oa9va0KbBcjqhUIqrViPb2GNt2CMOk+1jDUNRqSed43zTo57oGrmuSJAb5vNMZ/jMxzfSnFIYK27YIQ02zmQYVq9WIdesCkkRTqQTUaiFBkAYY6/WQ7I5DSXbbDQ0YJGSSJqXX5qCUplcvD9s2iOOEej2iXPapVEIqFZ9sdv1cXqXS0cKlkksQhGSzJtVqSKUS9Ag1NpshhYJBsehgmia1Wky5HHY3BVarAcWioli0AZNyOabRSFAqvUc+bxOGCZYFjcb6dsFi0QEcCkkDUHTc/zRMeY5qbBLvNBTj26fyyo9OZmXfvtiRRsUGlbpJoZmwdPkypk6czJpnxvOTYxSP/PVPDBw4EIBGM1236275937OAoMdB2t++IP/5Dvf+Q5/+MMf+O53v4t+ny/7g2+a9PI0n+n3wa2Cs2oGL9RNTum9+UHBLoZh4DgOAGEYbvH5fy/r1q37VwsKCiGEEEIIIYQQQgghhBBCCCGEEEKId5FmwU1obW3lq1/9KhMmTOAb3/jGRvsnTZrEpEmTmDZtGrvvvjsXXHAB55xzzoe619ChQ1m7di133HHHBzagfVhKwbb9NcfuE3PWFyJa8prJM0yun2Rz77MmpZxm58Ea4z0ipNlshu2Hbs1dTy7g7bkvM3b3UWkIz1AM2hr22zNCmYq5rxpMf85g3TuKbQcnKCNtqOvXvz/z3lzIvDlvMHrkaIo5hW1DSNpCmMSKwE8/XkZjW+B5aagrCAwGD7bZeWeXOFbMmNHgpZea7LCDTZ8+kGavFL6ftulVqwFBoAkCje9rHMciSSJc18DzjM5xuiaOk47XBbqDhMViOjK469Wn28F1Fc1mRBxroij9aK3QWhNFcXcALQ0ZGhgGPUYBA4RhQiZjYFkGrmvheRael7bLZVuz6BmziDGIMAmXr6Y5YDANO0smY/UI/GmtcV0L100bEUF1j0TuahkMgohCwSEIks5RwTa2bXSGGCNAo7VBkqTX62oYjGM6Ry/HOI5JFIHnWWSzNlGkaDYhiiAIErJZRS7n0GiY+CvaMR57nJaHJvCU3p1WGgzaqTf2l46h48CDmLZNb+qOIh+B6lAYjiJc3mT2C7NYMGUKO4f3Mfnm73HkkUf0+N5PnmzyxBMml10adv47b54ghO/8zuHQPWMO2yvhwAMPpFqtcs0111CtVjnkkEN63KfDhwsmO5ywU8SRwz44LPjdxTZLA8V1QwPcDxG33rBhMI7jf4iGwd///vdceOGFH/v/OZ8yaRYUQgghhBBCCCGEEEIIIYQQQgghhNiANAtuwv777/+BjVsTJ07k9NNPRynF2LFjaW9vZ/ny5R/6ft/+9rcpl8vccsstH/oam6NfK3zvxIhXrm8y/mIfreGrV7qM/obHXU+ZJO+Rlzp8zDZ85fjDWfbOSm778wPUOhTZRFOwNG5RsfdnE75xXsTYzya8ONfgl1fbvDBNkXc0rq343Oe+QHttKdOmz6RSMaiVFbEPpV4J+azubhysNwxMW1OpGASBwnU1hqFoazMYNy7Paae1kiSK3/62yowZAdVqQhDE2HZ6fmurQ6Fg4LoK0DQakMtlaDRiqtWYcjmmoyPG902aTU0YapIkDUk2m5rW1gy5nEU+b1Mo2BQKFrZtUyrZFItW9yeTMcnnHUolh2LRoVh0KRad7nHBhYJFNpu2EVoWaJ2OSdYaarW09a9cDqhUAtaVBpD5zC4AKIAkRi1chFJpmK9QcCmVXHI5G8sy8P2Yjo6ASsUHeoYS05ZBB6WgVEoDg+VyQLUadocam82QTCYds+w4NvV6QrkcEkXp/ijS2HZCS4tFva4pl9PxzqDJ59Pnq1ah/c3lZO+/gz7XXk5h9gzqSR7DsGHX3ciecTKL+m3LC3kbXTJxOgzC1QplaxbPXsGUxx9nzYwJXPrFdUx95I/suOOOG33nXn7JYNCghHx+y77fj79oUGkoDtsr7n4nP/3pT/n617/Or3/9a370ox/1aBi8cY5FPVJ8dUT0gdedVTOYsM7i/H4RxY+Q8etqGFRKEQQByXv94D4h06dPJ45jjPdKCQshhBBCCCGEEEIIIYQQQgghhBBCiH8Z1qYPER9k6dKlDB48uPvvgwYNYunSpQwYMGCLr6W1ZuXKlZx11lmcd955PP3009RqNX70ox+9Z5Dq4+DY8JVDYk4+KOavU01+fKvNGf/r8n8TYn5+dsjeu6wPMRkGnDZuRxauOIrHJ97HM33a2G+//cAHw9C05BIaluLggxJGjUqY/LDJQw9bvPRywlFHxeyy/TbsOHxnnpnyKCNHjiSbyRLHio6agR0CEeTzGmWAHypsWxOGiiBIP4bhYJoNhg2zuOiiFv70p3buuafOvvua7LdflihSVKsaMMlmY3w/ARSuq9Ba0drqkSQRUZQGBIMgIZdzqdUaKKVIErobCbNZg1ot6PGuXNckCBobjbHN5ayNju3aXq83e2yLY41pgmWp7mAepKN8gz3H0jr7RZJEo1E0O96hrqFejzDNuDsk+O7r2XZCoeCglEEYJjQaEbXa+tBbsehSqYQopchmbUzToNGIqVTS67quS9dE3FzOxjBUd6gS4s62RchmHep1nb7j1auwpkyh+MrzxFi0qxzeyOFkDvoczV9amMUScxOLFf0sdE6hlgEJREGT2U+8yup5s9nBeZrbb7uInXba6T2/m0kCTz1tcsABWz7u94bJFn1KmoNHrf/+KqW44oorCMOQq666Ctd1ueSSS6gF8KsZNgcMiflM//efx51o+M4imzZLc1H/jz5CuCswGAQBURRhWdanEth77LHHWLRoUfcahBBCCCGEEEIIIYQQQgghhBBCCCHEvyZJhvyDiOOYMWPG0NbWxvbbb89pp53Gbbfdxk033cSwYcP+7vc3DPji3jFHjom54wmTy26x+fx/eJx8UMTPzg5oK6XHjRyYcMT+e7F22QKefvop2tra2GmnnUgSRWhCs6rIZTTF/nDKiRHzdlP89U6L6/9occThMfvvfyTzXv4FM6b8jSOPPpxaE5JE4eQ1QVNRraT30RqKxYSMTogiRaOhSBJFJuNSrfoopfjSl1p56KEKzzxTIY4jjj66RJKA70MY2igVozX4fjqOWCkDz4NGoytApggCKJUyxHGAYfQcwZrLJWitiWM6xw0n5PMZKpUakI4gVkpRrYYUCg71ehogS8fMpu18LS0ZgiDsHk2c9gamgcY0tBgThukI4bDPAGqnnkPxpeepvTAX9eJLmPWAZOwY4kGDMAyN46QjlC1LdY5Ijmk0IuIYlDIJgp4NdbZtApqWFpeOjohaLQ0AdonjBKViWlocqlVNrdZz3HEu5wAKpeJ01PGSldhTnqH42os08aioEnrECKwD94Z+/Vm8JAFjDcloh+W9rXRMbwWCCFa8uYBXX36VeNFULjk1z/f+/TcfGE577jmDVasUhx22ZWHB15coHphm8u9finDsnvuUUvzyl78kCAJ++tOfYts2wT6XsKquuGPfDw4A/n6VxfSayfht/PdtFbzBahCiOTvKYLDpkb4bBgbjtLrxEw8MXnzxxdx666185Stf4dZbb8W27U2fJIQQQgghhBBCCCGEEEIIIYQQQggh/ulIWPAj2mqrrVi8eHH335csWcJWW221xdcxTZOZM2f22LbXXntx6aWXcs8992CaH2Hm6RatI20aPGafmCv/YvPLuy0eeT7Dr74RcOy+MZ4N2/XWHDruBNYs/C33TbiTlrPOpX///lQDRTarqdcVNEApzegRCUP7Bdz6J5t777UYO7Yfu+2+L89Nn8qokftSaimSy6UjiLMFTb2SBqWUgnLZIJ+LqdfT/blcur5SyaBcTjAMOOywApaleO65tVhWmf32S+fVWhYUiw5a+2htEMeaZhOiyEappLsdMAw17e2aQsGkXPZ7vAvPM/H9BhsWCVYqMcVihnK5iVJdYTBFpRJRKtmUy2mTYGfuC9+HYtHe6NqQtviFYQwbhMr0oEGUBw8il81hTJmC+foczDfn4p9zDn7/QYAmDCMajfWLUkoRhukYZs+zsSyzc6RyjO/HhGEamiyVPDo6IpSCbDYdZ9xoxNRqMVrXKZU8ymVwHAPPs2k0Eup1DcSwfAXmlCfp9/rLNCjQYbSSjBqJe+A+mH3aqFSgWVEsX5fAAX1p9MtQChKavkW9o8or016gvGYxI/IzuXnC19h+++03+V286WaLXE5zxOFbFhb8yW02GQe+cfR7h/8Mw+Dqq68mDEMuu/p2TOMHnLBTxJiB7z8K+NWG4odLbcYVY07p/d7rmWGE/NSucXDscM4WrPfTDgyuXbuWESNGMHbsWJ544gk+//nPf2L3FkIIIYQQQgghhBBCCCGEEEIIIYQQn5xPfublv5ijjz6am2++Ga01U6dOpVQqfagRxO/lyCOPZN999+Wyyy7baPTth/HUIoO5qzfddgaQ8+BHp4U8+39NhvRLOPVyl/N/7dDwYY9tE0zT4vQzzsSzWrn7lptRQRlDaczM+mtorahUDUqtiq+eHDFmVMzUZ0wa9cNQrskTTz4JWlGrKiodBgkKz9UUC5psJg1uhZGBUmnTYK0G5TLUaha2HZHLxZRKCccem2W33Yo8/XSd115Lw3pRBB0dCq1NKpWAej0kSUKSJKZQsMnlFMWiQbFokM+bJImJ6xqkrX+pZjNtEnz3u+/oiCgUvO6/K9UVbozIZp2N3mVHR0A+v3671hrDUERRQmurR6FgUyy6FIsOuZyNbZv4TpYEqOLSntjUXl1AEMQEQYJpGhhG2mzouiaFgkuh4KGUSRTFBEFMuRwQBDFdeUbDUCRJQq9eDpZlUa8nlMsRYZg+m2mm/xUUCgZaG5TLMWGoUUuX0XLXbbTe8HvC1xfxjtmLyug9yf/neRROPIa620alosjlLOJchue8PGZflwGuTXMdvD33FaY+8ATNpdO46quaZyf9bLOCgsuWKe680+TUr0Tk85s8vNuUlw3uetriwmMi+ra8/3GmaXLNtb+n19l/Ja6X2ent8e97bDWG0950yRlw7bZ+9zvd0BIV83W3zCBtcEWQR21Gq+CGugKDSiniOCZJ3j+4+HFbt24dvXr14uKLL5agoBBCCCGEEEIIIYQQQgghhBBCCCHEvzDz0ksv/aD9H7jz/w9OPvlkfvjDH7J48WLGjx9PqVRi+vTpzJw5kz322IPtt9+e5557jm9+85s89NBDXHfddQwcOPBjubdSiv33359rrrkGy7LYeeedP/S1tIaT73P5+VQby4AxAxOMzcgztbXAaZ+LiRP47X02k583OXbvmHqoWOt7bDNwMDNmzuHNN5YwYuddyLgGSmvCUHWHqoJYkbU0g7YCy4BZ02169dqBhW/9hZ12GkUulwUgihWZDFTaFWGosEyN52nyuXSkb5KozmdR5HIG1WqI72vCULPddjZvvx0ye3aZz342Sz6v0FoRBAamGZMkuvs9+L7G8wwqlRDf7xwBHGps2yKOA0xTYdsK103vl8/bOI6B6xq4ronnmSil8DwT1zVxHLP7z6Zp4HlGj32OY5IkkMlYJIlG63QdadthjOdZlMtBZwtgQhxrdBBgzX0Zk4TYckj22xe3rbW7EdC2zc7n0wRBQhDExLEmSTRKgWUZOI5JNutgmgZhmB7XbEZksyZRlAYc83kXx7EJgvS9BEGCUprCqsVk778P9benaL5Tx7ey6D33IHval2CXkdQih0bDp7XVJJOxWBZ7zDUtXl4Y06YdbP0Os6ZOZ/W8tBhKWwAAIABJREFUtzhw+0X87dZT2H+fPTZoY/xg//mfNnPmGNx4Y0DLB4T+NtQM4Ev/7ZJxNTd+L8DZRG/qT55zeXRlX/ZY8lvuuPJbtLW1MXr06B7HJBrOesvh2arBn4f57JbdOLTbTsJXvDIVpbnNLzGAD9cCmo6vNkiShCRJUEpt9vv6KObNm8fy5cs59NBD/+73+oRd9mkvQAghhBBCCCGEEEIIIYQQQgghhBDiH4naRGPdR6+zEx/ZunXrOPjgg7nuuusYPnz4h77Omjpc/KjDPa9bHDAk5sYjfPrmNv/8SdMNzrrCpZDVXPvtgGlvmxTthKnPvca9905gxIiRHHHEEZRc8Kvgupp6pIhiRc7R1Nakwadp0w0ee8zE0NPYach8Tj/zy0RaU28obAviOt3BQEjHGVtWgFLgeaC1ge+DYQQ0m1H3cWvXxlx33XJ22MHg2GNLAJimIpfTaB10tralrYNRlGCaaQvfhopFRblc67Gt676NRtRju+MYRFG4UQuc65qEYdAdUOxi2wZaJ0RRz+O11hSLDpVK2BlCNLCnT8f560SSbA7/1NOptw3g3T/VbNam2Uw676PJZNIRxFrT2UBobrRmwzDI5WwgDVL6/gbjjIH8ysUYjz9BfcEK8vj4TpF4r8/iHrQfdZUjitL1FgoOcWxRb8Bix2NVxuPtlRGvT/XJe8uovrOAVpbxu//aiSMPHcuWmD1Hse++Hv92bsSVV773KOH38v/9weY399pM/O8mn9v9g5v5HnzT5EsTXM7YLeJXB1U59dRTeeCBB7jmmms488wzu4/7ryU2V62w+dmggG/2jza6Tg3NaW4Hc42Im/wiY5OezZId+LxoruGAePNHkydJQhiGaK0xTfPvPpJ44sSJvP322/zgBz/YovO22WYbCoUCpmliWRYzZ85k7dq1nHjiibz99ttss8023HnnnbS2tqK15qKLLuLBBx8km81y4403svvuu/+dnqjb3z9pKYQQQgghhBBCCCGEEEIIIYQQQgjxT0TGEP8TaG1t5aabbuLcc8+lvb39Q1+nTxZuPirgt1/wmbbMYL9bPV7azLHEAIftlfDI/zaJE8VX/9fFjhK0hp133pl99tmXOXNmM2PGDCohRDGUOwyiGuQMjaHA6xwtPGavhDFjYhI1hlfmmcyft4p6h4EZg2tpSq0a01wfYtNa4XkWQaAplzWVStw5Ytcgn08oFjWZDPTpY7L33i28+mrAihVpsCuONeUyKGVRLkfUahG+HxFFCZZlkMkk5PNQKimKRYXWUCq5ZDImjmNgmum2KEpH/24oCBIymY3HDvt+TDbr9hhfbJoKw4BcziGbtTrHDqejhwsFlzBMyOdtkiShOX8h9QceoQOPciMh0Zp3554MI21uLBYtCgUPw7BoNBIqlZBqNSQIYnw/JJMxcd30frmcS5IoKpWISiUkigKyWUUuZ1NcthD75ttoXn8H9QUrSByP6OBDUN+9CPfIcTSMHHEMhYKD52WpVi0aoWJBschClSXxY96c4UO1Tm3Vq5y6n89bT5yyxUHBKIILL3To1QsuuWTzg4IPTjP5zb02/3ZEuMmg4MurFWfd7/CZfjFXHRzgOA633HIL48aN44ILLuDWW28F4JqVFletsPlaW8iF/TYOCtbRnO2WmWNE/DoobBQUXKua/MibwXjnFd5Rzc1+FsMwsG37ExtJ3DWG+MP429/+xosvvsjMmTMBuPzyyznkkEOYP38+hxxyCJdffjkAkyZNYv78+cyfP5/x48fz9a9//WNbvxBCCCGEEEIIIYQQQgghhBBCCCGE2DwSFvwnMWLECL773e9y7rnnEsfxpk94H0rBGbvFPHpyk1jDuNs9nl2y+V+D3bbVTL68iWXAb++xWbbcoMXRHHXIfuy0/TAefexR3njjLXLF7jtSqysqHQrLUuRsTSGj+dzBMYMGReAex2OPpUGjOFZUywYdHQpNQiYTUyrFZLMJ1apBJtNznY2G6gwBxjQaEUkSse++LrZt8eKLNXK5dJyw1ppq1cS214+HVQrqdY1tO1SrIR0dAeVyQKUSUK2mo4mDICKOY7ROiOO4cwSwxnHSEcWZjIHWmlLJI5NJxw+7roHjKHw/oqUlg2Gk949jje8ndHQEGIZJR0eTctmnXA6oVgOazfQZPM9CLVwEnQExrTX6zbcplRyKRadzJLJJHCfUaiHt7T5x3DNUZ5oG+Xx6bBzHOI7RHZTsumY2a5PPuUQvvYbz26tp3ngHeskyTM8hN+4AzG9/i8rYQ6jpDNVq0BmqNNHaQGswihlmGi0sDyzaFy7h0UkLiFcqhmTfZPotY/n9z4/CcTYOUm7KlVdaPP+8yS+uCmht3bxzXl+i+NpVDiO3S/jp1z44YLikrDj2bpeCq7nzmICMnW53XZfbb7+dgw46iPPOO4/zH5zF9xY7HN0S8YshIe+eBlwl4Sy3g+lGyC+CAl+I3R77V6o6P3SnsUY1+L6/O721t7mvAPhkA4Nr166lT58+H8u1Jk6cyBlnnAHAGWecwb333tu9/fTTT0cpxdixY2lvb2f58uUfyz2FEEIIIYQQQgghhBBCCCGEEEIIIcTmkbDgP5GTTjqJHXbYgSuuuIJNjI/epM/00zxxik+/nOaYu12mLdv8r8L2W2nuvaxJram4d4pJM1aU2w2O/Nwx9MvlmPjnm1m0ajWG0XONFV8RRVBZp9A+nHRMgtImby8czIoVK7qPSxJFPq9oNKCjIw31QYJpKorFmFwu6Q5v1Wo2prnhyGLFzjtneekln46OgDAMMc0Y143JZi0KBSgUDLJZhWVBuQyeZ/VYZxyD6zrd71gpSBJNtRqRybidrX1puK9ej2hvTwOAzWbaWhgEMWGY0N4ekM2mga8NVashpVJmgy0a2zZwHItMxqJkBhRp4hFiovHdTGcoUHe3Bm54Td+PKRZNikUHz7OIooRqNQ0/BkFCudwknzfIZCyKRQ/HcmjMepXaL36P/vNfqC5dTTGbUDz8AJoXfIf2PQ4kMFw8z6JYzKC1R7mcjiw2DFjSsJga2aytvsOsSU/y0vOvwJLebOus4JVHxzB8h76b/V3a0NNPG/zkpzZf/nLE8cdvXiB2TQccf5mLY8OfL/HxPiCfuKoGR93lUg0UE473GVjo+f30PI8///nPbH/Rz7ixz96MaCzlxqEB1ruCgu0knOaWed6I+GVQ4Oh3BQXfUh1c4k2lpiL+y9+TXZPe3fuaNDbrueCTCwy2t7fTu3fvTR/4Lkopxo0bx+jRoxk/fjwAK1euZMCAAQD079+flStXArB06VIGDx7cfe6gQYNYunTpx7B6IYQQQgghhBBCCCGEEEIIIYQQQgixuSQs+E9EKcXPf/5zpkyZwsMPP/yRrzeoqJl0YpN+Oc0J97i81b75I4lHDNVce1HA4tUGj7xg4nkax3Y54fgzUUkLd1z/FxyjRs5JgM7QHeB0BbS0wrEVe+4egzGavz02k2JBk82mx1eqCttefz+toVo1SBJFrRaitY/rBuTzEaWShefRfZ8ddnAJQ5vly9MmvSSBRiOhoyMBTCqVgHo9JIoiIEIpg0xGkc8bnaE7E9M06NUrQz5vkc2aneN8jc7RwyamqVAq/ZimIgw1jmNhWQrbNnBdk2w2bTIsFBwKBZtCwe5sCLSJ44SWFhfbNgBFGCY0GiHt65qEM1+khkMTmwQDVU8DZrVaSD5v43kmhYJLoeDiODZRpGlvDwiCiDBcH6Q0TYNCwaNQyNBoaEwDatNmo68dj3nPPeRWLaGQd1HjDmXN+f/BmpFjybValEo22WyGRsOiXAbXNcnnPZq+y+y1GV6NY2Y9O4eZD8ykWYkYoHdErVjGnTcM3CgYubkWL1acdrrLsO00v/6/YLPOqTbSoOCydxR3/sBncN/3D9CursORf/FYXFbcdZzPbm3vfezN1SKvH/sftLwxnbnH7cTDD/y1x/6lKuZLXgevGBG/fY+g4ExjFf/lTcfSBv/THMMOSUv3vkXGIn6f+R1zzNmb9XzwyQQG165d+6HGED/zzDPMmjWLSZMmcc011/DUU0/12N/1+xBCCCGEEEIIIYQQQgghhBBCCCGEEP8YJCz4T8a2bf70pz9x6aWX8tZbb33k6w3Iw73H+2jglIkufrT5556wf8zRe0c8O9eg2nleqVTihONPoL2jwk233U1lrcYMoGgnZJ2ESlNhu+uDWnt/1kCZMQsW9mH+66uoVw0MIJeBfEHjebpHi2IQOKSxQ/B9Tbkcs3atRqkIpQI8L2THHQ0gYd26NHC44fn1uoFh9AwwNRoa27apViPK5bDzE9DeHhNFCfV6SKMR4vtpc2AcK7SO0TpC64gkiQmCCNNMA11hGOH76TnVaoDvx9RqAZWK3z1+uFYLaG/3O8OC6xmPP45fruMSYRGRt2IKw4dSKDi4rkW1GmJZFpVKQKXSs2XQ9yNyObNzLLJHHJtUKjHVckDy4hwaV15Dy4Rb6bXmbZxiicq4Y1n7jX8n2GMMTs6jVMrg+ybt7QFKRRSLBvm8R6Nh0143eaFm8tic+Ux59FnWLaiwxw5bcfExI1g+p50fXdLG8OFbNmq3S7kMx5/g4vtwxx0+hcKmz2n4cOL/uLzwhsFN3wsYs/P7h+hW1OCwP3u82a74y7E++wza+Fit4afLLL6zyOHIlogXj9iWPXbbhdNOO42HHnoIgJdVxPFuBytVwk1+iXEbBAU1mvusBfzcncXAJMfPmmMZpPPd+2ZZM7nDvY2M9hiUDNqi9/P3DgyuXbv2QzULbrXVVgD07duXY489lunTp9OvX7/u8cLLly+nb9++3ccuXry4+9wlS5Z0ny+EEEIIIYQQQgghhBBCCCGEEEIIIT4ZEhb8GD300EPsuOOODBs2jMsvv3yj/TfeeCNtbW2MGjWKUaNG8Yc//OFD3adfv36MHz+es846i1qt9lGXzXatmusO83lptcHPnrM3fcIGrjo3xIjhsRdMlJmG8gYPHsyhhx7KmwuW8NSUB4kjRbnDoN5uYPqQz2nyWY1haLJZ2G67BKxRPP30M0A6hrhaVaxba5IkIZYVks+HFAoxpqkpFKyN1qGUR5JAs5mQJAmWlbBqVYRpakwzxvMS8nlNLgelkksuZ+C6CqPzF1AuazKZntfVGrS2eXc5WhAkZLPeRqOgG42YQmHjwFwQxGQyDl3Nh10MI209zOdtikWX0pI3aJn2FBlCfOVg77UHHaecSUdrfyqVAL8zyVmt+uTzDkpBNmtTLHpksy5gUi6nAUWlNMQx6sXZFH5/Nb3/+hcy61bRUdqKNYcdh/W9C2Gv0RRac2SzHr5vUi5rkiR9P2FoUKlEBEGD9sTn9hcWMfmJp1i1aBnb996Gq761B7/+j+24+hfL2W+/HN/+dtvmfmV68H046WSXefMUt97qs+OOmx6v3RUUfHKOwe++FXDk2PcfWbywQzHudo9FZcU9x/kctPXGQbswgQsWOvxkmcOpvSNu2y6grVRgwoQJ7Lbbbpx88sn870vTOdFrxwT+0iwxNln/O/GJ+Y3zEjc78xgT9+PH/hhaSb8HISEPOPfzsDOZbZNtOb15Fr10Gsyrq2Wb/Z7+noHBdevWbXFYsFarUalUuv/88MMPs+uuu3L00Udz0003AXDTTTfxxS9+EYCjjz6am2++Ga01U6dOpVQqdY8rFkIIIYQQQgghhBBCCCGEEEIIIYQQn4yNU1fiQ4njmPPPP59HHnmEQYMGseeee3L00UczfPjwHsedeOKJXH311R/5fmPGjOHcc8/lggsu4Prrr8cwPlru87DtEk4ZHvGrGRZn7BaxbcumQ1sAA/tojtknYsJjFkeOiMg4EKIZOWIUq1at4tnn/kZLYTCjRo0CII4V7RVQTdAJ5PKakbso3ni9wOvz32b16tW0tXUFzxSua1OpBFSrGkgDUpYFuVza5Ke1ge8rajVNoeB0BuXAcdLRwIZhE8chzeb659Eacrm0iU9rME2FZSlM0+y+rlIKrVVnIM8jDCO01p0BQkgSTamU6RxlnG5TCuJY09LivWeYq7U1QxCkbYVdn2YzwnFM4jiCqS9ikLbVaRTVTAv5nYdSLvsoBa5r4TgWSqVji/N5h2o1RuueYbkkirBnP0+/J5+g3BHSxKTROoh478+id92VXDGDNszuMc/1eoLnmbiuTbWqKZfB80ySJOCOpxbyejkg6WgyaOA2fG6P7fj+eR6eE3HAAW9QKJjccMNgTHPLx82GIZx+hsOTT5pcd53PIQdvOgBXbcCXfuzy9EsGv/1mwCkHv39QcPYqxXF3u/ix4q9f8hkzcOPrt0dw2lsuj5dNvjcg5Hu9Krz+6lvMnz+f+fPnM2CrrXjtiH25dsxQ+i9dzYTWHem7QcZ6papzpfsib6syJwbDOD7aDqOz+fId9Q73unezWq1m32A/9on2Q6HQxCyw7uIt+05GBv9BW7zXZr2vrsBgGIbEcdy97aOq1+tks9ktOmflypUce+yxAERRxCmnnMKhhx7KnnvuyZe//GWuv/56tt56a+68804ADj/8cB588EGGDRtGNpvlhhtu+MjrFkIIIYQQQgghhBBCCCGEEEIIIYQQW0bCgh+T6dOnM2zYMIYOHQrASSedxMSJEzcKC36czj77bKZPn861117L+eef/5Gv99/7h9w9z+QX0y1+My7c7PPOPy7mrkdtZi8w2blNo5TCdTTHHXYwa1ct5cGH76F3794MHjwYAK0VhRZN+R1FrQLFHBCCYQ5i+vRJnHTSKTQaBlFkUKmYuK6B768PekURZLMO5XITSENTppkG9orFBDCIohjbhlpNUyx6VCp+9/lKQRSZKBUBmiTRBIEmCKBYtCmX6xs9YzarqNd7vpM0lJjg+/G7tisch422a60pFu3u7V3jg4MgJpu1aG49BP3661jEuKaC4UPRClpbPTo6Qnxf4/s915DL2dTrCZmMhaVjkqkzaD45lXq1Qg0otrXQvvcheKNHYjkO9bqmVkuDl+n6Nfm8iVI2tZrG82yq1Sb3/HUmc9bUSYr96Oe2MXq/YZx5TJ7DD05oNBKOPHIhy5dHTJ48lAEDtqyNEtKg4JlnOtx/v8VVVwaccvL7h/66rOmA4y9LRw//4dsBJx30/udMfsvg9L+6tHiav36pyfA+68OiSZKwbNkyHn9jKf9ljeQd22H4g1dx511Xc+WiRd1BT1Uq0nbH1eQPPYDmLffwP/2H0/f/sXfn4VFV9x/H33edmWSyBwgk7CRhERAFNxBFrFStOypqcW9tXapd3OvSutZqrbS1al3qhtiitmAtSkHFDVBwF0yQRRL2BDL73O38/piQEAKKW/1pv6/nmUdy59xzzr1zZ/zn83y/o9vDeQuN9fzJfheAy7J7sGfQte29d413eM6ehYnFCdlJ9Av6A5DWNvC+/Xu2GEuo8A6gxB/6me7bVxUY1LYvn/kp+vXrx9tvv93peFlZGXPmzNnh/H/6058+9/6EEEIIIYQQQgghhBBCCCGEEEIIIcQXJ2HBL0ljY2NbGA6gqqqKBQsWdBr3xBNPMG/ePGpqarj99ts7nPNZaZrGzTffzPjx49m8eTO2bTN69GhGjx79uebrHlVMGuwz7QOTmw50idq7dt7I2oCiYsVHa3RG9fdIxjUcR8NxTI46dBIPrZvCE4/dz3kXXIAVKQE0kg5omkIpjWhBbp5ePUfw9tv3su++GykpKSEU0giHc1X/lFJks+2hpkTCwDA0fD8XAgsCSCahsNBkw4YUjuOQn29jmi6ep1FYuDUMpeF5Ct+HggKLlpZsh6BULJYLzGUyHUN5nqe1tQ3eKldN0ELTgg4tiXMVCA10PSAI2o9rmkYi4REOmyilWisa6m37j44eSWb2c3gYZA86BFVSATEHgMLCEC0tDpqWq3YYiViYpo7vQ0T3cF94FefV+WipJBqgunQhPH4s3rBhhAMdpUxisdw+IxGLUMgkkVDE46BpAdEoJJNxZs16lTeWfowqG06P/oMYUD6QA0flcc7JAcVFAa6rmDz5YxYuTPHII70YNeqzVaQDyGRg8qk2zzxj8pvfOPzoR96nnrN8rcYx14Ro2KTx2JUOh++946CgUnDnYpPLXrAYXOrxq9rFvD37PabX17Ns2TLq6ur46KOPSO0+Hq58GDIO4asOw8puYOTIkZx00klUV1djjhjCHbtVsNaAK5x8Tj/uB2itFQNdAh6xPuRf1ir6+YX83Nmdbip3HzJkeM6exQfm+/T0e3GkcxQFqhCFYp3xIkvtvwCKIdmL6O4fgEKRNZ5CaZsJe2fu0v3bNjDoeR6maX7uwOD2rbSFEEIIIYQQQgghhBBCCCGEEEIIIcS3l4QF/4uOOOIITjrpJEKhEHfffTennXYac+fO/VxznXzyySxZsoT8/Hxqamq4//77ufLKK+nbt+8X2uNJgz0efNfkPysNjq759GpvALoOIwYFLF2qdXqiIuEIE084i7/+6V4e/MuTnH7GZIpLLTRDQysOiG02MFpzTr169aWhIcyrr77G9753WGu1v1yYKRRysCxFOKyj6zq+r2MYNrFYtsN6iYTBpk25fXfpYuD7inRaYVl6p7GOk6sY6PsBpqmh67n2w7puYlmKrRnCra2H8/PDOE7HYFsuuJdrU6xpsG2BNsMI4bq58UGg2loP+36AUp0rD2oNayjFpYUQxpw5+BUVBJWVhEK5cGFZWYh0WpHJBKRSPmTT6IsWoS9YQCgdx8JH61GFf9DBJHrXkFAaJAIgwDR9iosjeF6u1XAmk7sn+fk2K1duZMaMubz3wSIo24Nuw49nYL++9O1SwA9O8Bm+mwJybZ1PP/1jZs2KM2VKD44+umiXno9ttbTApJNCzJtncPvvHH74w08PCs5fonPidSECBU9fn2Xfwe2JTdd1WbFiBfX19XxQt5xHtuzHsoL9sZc/w3vXn8BxThLIBez69OlD/5parPN+y+JBExjgt3Bf9yR7zn2qLTCqUDxqZrjaSlKqdB7LFjAyaK+c2Kgl+H3oHVboMQ51e3GqOxCrtS3xx/oqnrZnEtdi7O+MZV9vNDo6Di0ste9mg/kaxf4ghjgXElHdCFhPyv4lrvkspr8fIe90NHYt9PdlBQYTiQTRaPQznyeEEEIIIYQQQgghhBBCCCGEEEIIIb55JCz4JamsrGT16tVtfzc0NFBZWdlhTFlZWdu/zz77bC655JLPvd69995LXl57Vbe5c+dy1VVXccopp3zuOQH26REQMRWvNuq7HBYE6F2hePNdDd8F01J4bntqrqysnFNOP5r7736Sf/7jaY499thcq96QTijk4ro6YFBYZDF8+GjefHMuY8fuT2FhQdsclhUim02TSPhsbT2saYq8vFxIzzB0lALX1WhoyJ1TVdVeGjEWU4RCRoeAXq4yoEk2m8ZxOrZhLSzUW9scs814RUGBTiLhbHccotHOx3PzWJ1CikGgiERMgiDoUKnQevFFfDTKSeIFJpm1H5Pq1RPH8XEcv3W+MKnmFMaixegLFxLNxDDxyVb1IbbfgeSPGEIs5qOpXPgxGg3h+xrJZMCWLT6a5lNcHAZCLF68ggULFrBixRKMvEp67ncOffsMpDwvwvcOgIlHBOj61lbJAWecsZp//CPGzTd356yzyvisGhs1jpsYYskSjfvuyzLpxE9/vh6ZY3DBH2y6l7pcddQClsx/m38+VMeyZcuor69nxYoVuXa8Rb3gxOlQOYrKZfdzkDaP6l9eSk1NDdXV1fTt25dmLcwZy20WJwxOL/e4rZdFWG9vHbyFgMvtBLNMhwN8i9uyBZS1hvcUiufM1TxoLSWEwaXZPRjl5851cZlnvcjr5gJKVAmTs6fRI8h999cbr7LUvhuPFAOcyfT2jgJ0ssZ00vavUGSIOFcQ8n6A5m/BSM3BLzh+l+7nlxEYbG5u7vC7JIQQQgghhBBCCCGEEEIIIYQQQgghvr0kLPglGTVqVFt4qbKykmnTpjF16tQOY9auXUv37t0BmDFjBoMGDfrc620bFAQ46KCDeOutt7jkkku44447OrTW/SwsAxaclqGq4LO1Jw1ZCs3UyGzRKCoIUDq4gSLl6GgaVPWrZfz4g5jznzm89NJLjB07FierEY1qrG5QgE9hgcfAcXuwaNEsFi2ay/jxR7WF6eJxnUhEJ5NpT9cppWEYFvF4hq0BQqUUb7+dpHdvg7IyMAxtm7Hg+z6el6uUB5BKKQoLw8TjHQN98XjncKGmaaTTuWCi7wfbHM+11jVNA8/rGICLxVzy8mxSKQdNA8syME0Nw9AJh0M4Tq7KoPfcXIJVq0hgkyBEkeGR7N4LtW0b43Qa9eqLdHvtZdysIkWIeM9qgtGjUX37ggaplEtpaRjfz7UdjsUUkKsiGInYxOMeL7zwFq+//hobN64hkteVvQ8+mbze+1CghxlZo3HmSYqSkvZrSKUCJk/OVRS8+ebuXHBB+Wd6NgDeelvj+ONDxOMa06dn+c7BQacxyWSS+vp66uvr+bBuOdPf2pv69GEYsRdZ9fwxnP34ZgDC4TD9+/dn6NChHHPMMWR6HsSD8fEozeDew7N8b8AkYFKHuWdt0TlnZYhUAPf0yXJKecfP6RXd4ed2gmYt4Aonj7O8CHrrM9KkZfiz/R5vGZsY7pdxfnYoJYQBaNQbecaeSZPexAh3D8a547GxybKZD+2/sMF8jQK/P0OcC4iq3vjax6TsK/CMeRj+SPKd32IE/TDij2NvuhSCGJnIaJTZY5fu6xcNDG7evFnCgkIIIYQQQgghhBBCCCGEEEIIIYQQ/yMkLPglMU2TP/7xj0yYMAHf9znzzDMZMmQIV199NSNHjuTII49kypQpzJgxA9M0KS0t5a9//euXuoeLLrqIU045hQcffJDTTz/9c8/Tv+SzBQUB4imNaJGipFgRi2sEKVBKx7IUkahCGRrjDxnFxg2bePnllyjvUs73xucXAAAgAElEQVTgQYMJAp01jbn1unZV2HYxQ4eO5fXXX2bUqDGUl0exLL2tPXA2m0Wp9iBkPK4RDhtkMrnwV2OjS1NTwP77F5JMtlch3CoaVSQSDqapYxgapqmjlKKoyECp9hAhKHTdxjCy7S1qW2+LbYfIZp3WtsUAuf+aponrum3V+IJAoRT4viIcNkmn3dYqge37KSy0SfxrLsZLLwEawf77g66zqVdPiof0IwhASyZRL75MZv5iMq5LBoNI3574+4/Hq+xJJGJh2yaeB6mUz+bNLobhEY3agE0Q6DQ2NvP222/z1luvk0ql6Nq1P9878kzCFfuQCEL0LjL5wcmKQQM7fq7NzR4nnLCK+fNTTJnS43NVFPzHPwx+8EOb0lLFrH+nKCxcwbPP1rcFA7e+1qxZ03qDu8OQaVA8liqe4LCRc6k56Uqqq6upqamhqqoKXddxfLj2JYs/vGExtEvAo0dmOz276QCuarD48waL3SIBD/bLMjDSPiaD4hYryQNWhv6Bwb2ZYnZTZusToHjRWMP99hI8As52BjPB64mG1qGaYKEq5MTMSfQN+qFQrDHmUGf/FZ8M/Z3v09s7Go2AjHkXaet3gEHEuY6QNxndWY694QiM9PP4oZE43f6ICvIxVjyJ3/fYXbq/XyQw2NzcTGlp6S6NFUIIIYQQQgghhBBCCCGEEEIIIYQQ32yaUp8YDPvsqTHxtUomk4wbN45bb72VkSNH/tfW/c4lIQB+fbzL3HkGBWFFfEvH6obhSEDgOzzwwF9obNzI5FN/TPeK7jz6qCKdhrPP9gBoamri7rtvYb/9xnLggQe0na8URCIZtlbKAx3f1zGMgFgsF+qbPn0Lq1Y5nH9+OSUlAamU22EPtq3huim2f+wLCozWCoXbH9eJx9Odju+ovXDuuN2pfTFAOGzgOG6HtsMA+ssvUzJvFg42+qSJqN13x/MU2ayHtyVG6Zvzic9/G83L3ZugXz8Yuz+Rmn4YhoHv662tmXM0DfLzbcAgHndZtqyeN998g2XLlgNRBgwYyv77701e2RDq10ToUmpw1EFw2CGwfTHKFSscjjtuJStWONx3X0+OPbao03XtiFKKpqYmli6t5/bfFzNr1p6UFC+lrOwHfPzxQpxt0pLFxcVUV1e3vbL5Y7j7pQPIuiZ/vMDhxAN33Kp42WaNM562Wbze4AfDXW4e5xLeLvr8ZlLjBytCLMno/Liry/VVLuFtMnSLdZeL7QTLdZ/T3DCXuvlEtqkmeLf9PouNjQz0iznPGUp3lQ/ASn0Fs+xn2KJvYXd3BOPc8YQIkdQaWWrfxWbjPYr9QQxyziNfVeLpr5Oyr8TXl2J53yHPvQ7dL8bafCvm5ttBi+CWXYtXeAbGR49jL7oKMs1kJr6Pilbt0j0HCIIA13UJgmCXA4PTp09nw4YNXHrppbu8zjfI5yuvKoQQQgghhBBCCCGEEEIIIYQQQgjxLSWVBb9l8vPzefTRRznuuOOYMWMGXbt2/crX9Hx4Z4XOyQd5DBsS8OIrOv4OYjqZtE5enslRR03mgQceYPrfH2XyqWezalUx48ZtDZBplJWVUVu7N4sWvcY+++xDOJwLIuaq94VIJFLbtSNW5Od7NDQ41NUlGD++gPLyXMU101Tkcna5DTmOorAwQizWMQAYi3nk5Vmk0x3DhYmEwrYNHKdjaC0e93Z4vKXFIRq1SCbb51FK4TgB0WgY3/cxDA1t1SrUc//B/2gFLeSRf+LRtPQbDDEHYjH01+ZjvfUmcd+niAxu7W5oB4/HqehJOu21BgRzaxcWhvE8HcOwSKV8Vq/ezFtvvc3bb79BKpWgoKCC/ff/LmPG7IUVKqd+XSGbNppM2E/jtEmKSKTzh/Xaa0kmTVqF78OMGX3Yf/9opzHpdJqPPvqIZcuWUV9fT11dXdu/N2/Wgamg7Ymm3U+XLr+npqY3RxxxXodwYHl5OZqm4Xpw42MWv/2bSW2V4pHLMwzq1TmrrBQ8+K7BJc/b2AZMPTLLUTUdPwM3gFvXmdy81qKLqfhndYaDi9qflzSK31kp7jfTVCidhzOFjAlsAAIUs83VPGJ9SACc4Qzku15vDDRSJJlrz+E9811KglJOznyfXkFvfLJ8ZE1lpfkUBiEGZn9MpX8wis0k7YtxzMfRgh7kZ/+C5X0HMzkTa+Nl6N7HeAWTcMpvQN+yhtAzEzA2LsDvMgrn4CfR1q/BWPQs3gFndboPO/J5KgxKG2IhhBBCCCGEEEIIIYQQQgghhBBCiP8dEhb8FqqurubGG2/kzDPP5KmnnsKyrK90vYVLdRJpjf2HBuTnwZDagHc+0AlHFJl0xyCaYehEo/kcf/zxPPTQQzz04Apgd4YNy6BpAZGIjmkaHHzwnvzpTy+xePFi9ttv37bz43GNSKS97TCApmkoZTJz5gYikYDddzeJx3NV/woKIBbLYlkGpqlhGBpKaRQV6a3VBTWUUgQBmKaGUh6apre1EFYKwuEQQZBubS+cazms6xq2rWGaGrquoeu5sbnqfIqiIgvXDfC8ANcNCAKfWMynsDBE/P1lGI88iqYCFCbBmDG09B9MgZskMXseee8sJhzkwpPZwUNp2mcsBdW9iScCVDpXYVDXdfLzbZTSSCR8HCfJ0qUfsmjRBzQ2LgdCDBgwlJEjRzBs2GAcx2JTPMyKhii1VRpn/USjT+8dF1578MFmLrxwDb17Wzz+eC/y8jYyZ84C6uvrWbZsGXV1ddTX17N69Wq2rUzavXt3qqurGT3mEl566VySyXyuuKKBn/9sIqY5aafPz/K1GmfeavP6hwanHeLx2x865Ic7j1ubgJ/MtnnmI5MDevn85VCHyoKOgcJ3UxrnrAzxdkrnhFKP3/VyKNnmV26+7nCZnWCVHnCyG+ZyN48ouUDdai3O3fb7LDW2MMwv44fOECpUHgrF28ZbPG/PxSHLfu5o9nVHY2GxSV/Eh/a9pPV1VHhjqXZOx6aArPkwGetWFElC7jlE3IvQsx9jbzoKIzWXwB5MpnIWAdXY86/FqH8EwuVkx/yZoPRArCevwVzwN4KyXnj7nQJmqHPpxx34rIHBzZs307dv30+dVwghhBBCCCGEEEIIIYQQQgghhBBCfPNJWPBb6vDDD2fRokVcc8013HDDDWi7EDT6vJ54ySBkKcaPyAX4hg9RvPsmhIsVluXjZHUyGQ1N04gnNEwTKiq6ceihRzNzZj8KCtdSUVFCPJ4hlcpVzCsqKqNv38EsXPgsBx44vDWwp+G6GqZpAx0rA77ySprGxoDDD48SCrWHozIZHV3X8LygtcJgTjSqk0jsqL2w2amNsOtCQYHdqR1xOr3zdsSRiEkm43Zqd9yytpnSZ54ioQJAEcbHIIv+7AyCRW9SSkALETKD9sQfvR+0VoaMxTKUlEQIAhPPg1TKp6kpTV1dHe+//x7Ll9ehFHTpUsmECd9l2LC9KC3tQiKhkc7YLFudTzjf5KLTNPbbt/OzsGXLFt5/v57rr08yb14ZXbuuwLJuZ8yYd0mn2687Go1SXV3N3nvvzeTJk6murmbAgAFUV1cTiUT53e0m111n0auX4l//yjJi99JOa22lFDw02+CSv9gYOjx0aZbj9u/cdlgp+PtSg5/PsUl5cPOBDuft6aFvcxnZAG5Za3HrOpNSAx7rn+XIkva5thBwk53kb2aWXoHO1Ewh+7ZWE8ziM91axgxzJXmYnJ8dygF+DzQ01mvreM5+lkajgSq/JxOcQ+miupDS1vG+dT+bzNfJCyrZI/MrSoNhuPp84vbV+PpSTH80ec6vMbwyrKZrMFvuAT2K0+W3ePmnYi75M6G3J0KQxdvtQtyB52HNvgd79k9BKdzDLsbb7VjsX5xFsPcBeCf/cKf3clufJTDY3NwslQWFEEIIIYQQQgghhBBCCCGEEEIIIf5HSFjwW0rTNH75y19yzDHH8MQTTzBx4sSvZJ1EGh573uSIfX2K8nPHevZUlJVBc7MGKILAx7YhHM5V5tN1jS1bAjY11QIG8dhMZs8exOjRw/D99nTd6NFjeOSRN3n11cWMHLln2/FsVlFQEKAUGIbGhg0ec+bE6dcvj912szvsz3UVhYXhTgHAeNwnP98mlXI6Hd9Re+FEwsO2TRzH63A8FnPJy7NIpTq2L06nPQoKQsRiaWzbxDQN7HUNGI88gmqJUYRPC3lkNAtefh0NUJqNGjKEvO8cQCxcTDhsEQqZBIFGJuOzZYuH46T4+OPlvPNOPR99tATX9Sgs7Mbeex/MbrsNoX//ngSBQSIRoJSiORZhSyyfww7ROOy7LqtWreTppzu2DK6rq2PTJhO4ERiMpj1MNPosvXsP4OCDz+7QNriiomKHwdOGBo3jT7CZN89g4nEeU6Y4FBXt9LFhbTNc8IcQ/37dYOwwn3sucujZtXPb4bUJ+Ol/bGYuMxnV3efu7zrUlnUc92pc54JVNkszOieXedzc06Gs9ZdNoXjKyHKDnaQFxY/cCD9x84igoVC8YWzkfusDNuoZxnmVTHZqKcQmQ5p51ou8aS4mTITDs0ewmz+UoLXl8CrzH2gYDHBOpZf3PZS2loT9I1zzGfSgkvzsXVjewVgt92I13QhBC17RmbilV2Ksmkv4uZHoydV4vb6HO+JXGG+/ROTq/dDiG/H2PgH3wAswH3+U8DX7gx0m2HM/0kuWEBk0aOc3dRu7GhiUNsRCCCGEEEIIIYQQQgghhBBCCCGEEP87JCz4LWYYBg8++CAHHXQQgwYNYsiQIV/6Gvf926QlqXHeke0hOk2DESMCZs82KCzUicUCXDcX3AOFYSji8QwLF9rsPsLDdcLMnTuXXr2i9OjR3hK1Z8+eVFXtxvz5LzNixO4YhrF1BZQySSTSuK7i4Yc3Yxg+hx1WSHExZLMupqm3tgfOBdsKCtpbC/t+7qWUDgRAe4hKKYVpmmSzXodQnFJgmiau6wG5dsZbX6apUVBgtXWJDQIIgoBs1qOwMEw8lsWf/zru7NloQYCyomjFReRtXENK2ShNJxg2FHvc/lgVXQgCKDYMtmxxyWY9Wlpira1/61i1ahlKKfLyith995FUVw9n4MD+2LZFMgmJBCiVZcXKJMs/tgnbr2Bqf+faq5dw+qkr8f32EGSXLl2oqalh6NDzeO21g9E0g+uvNznzzOux7Vt26fNXCv7+d4Of/szGdeHOO7OcOtnfacdcpeDxFwwuvscmlYXf/MDh3CM8ts+xKQUPvWdw+Qs2GQ+uH+vwk5Eexjbjmj24usHmgU0mveyAp6ozHFIUtL1fr3lcbSeZb7iM8E1ucKIMUrmfvLVakgfspSw2NtIriPLrzF4MDkoJCHjTXMw86wUyZBjh7clYdywhQqwzXmSZ9TBZvTnXctg9DVtZpK1byZr3ATph5+eE3R9iJv+DtWkUursMPzIOp8vNaM1NhP59HMamxQSlw8mMuQttXYzQ705CX1eHXz0a94Lp6HNeJDzpUMim8SaegXv+FVDeDXf2bIJ4nPy99tqlz2ZXAoPNzc2Ulu68+qMQQgghhBBCCCGEEEIIIYQQQgghhPj20NT2fVI7+sQ3xec3a9YsLrzwQnzf5+yzz+ayyy7r8H42m+XUU09l0aJFlJWV8fjjj9OnT5/Ptda7777Lqaeeyr/+9S+Ki4u/hN3nbEnAsB9GGN4/YOZ1HVvxptMwZYqJYUAm43UIjwUBTJvms3atxznnuIRCLg899BCbN6/jvPPOoGvXCjxPI5PRqK//iL/97W4OP/w4hg8f1jaHUhAOO0yfvpl3381w/PFFVFeHsG0Nx0kCHdNqBQV6pzbCAIWFBrFYFl3X0DRaXxqRiEY67aJULmC49b/RqEE87nSaJz/fJJnMdloXx6HouadJvbO0fe8oInjYOrDXSDKjDyQVLmTrd9F1XRoaGmhsXMHSpSvYsGENYFBWVkl1dS21tTV069aFVCrB+vWbaW5uZuPGzWza1Mz69Wl8eoDWDN5UIpF0W5vgrS2Da2pqGDBgAKFQIVdcsZZ77mlmxIgIDz3Uk379Qrv02QNs2gQ/+5nNE0+a7LWXz71/cejff+c/GY2bNC78k82/XzfYe6DPXRc51FR1Hl/XrPGT52xeajDYv8rnjxMcBpS0j1MKpjYZXNFgs9mD87p5/LKHS35rljRBwBQrzQNmmnw0LnHzmOSF0dFI4/Gk9REzzZVY6JzgDuBQrzcmOqv0VcyxZ7NBX09PvxcHO4fQTXVji76EOusBYkY9hf4AatyzKAr645jTSFu3o7RN2N5xRNxLMNMNWBuvxMi8QmAPxCm7HuX0xF50DUbDLIL8Ktw9riaIjMB+8DyM5QsJKmpxJ16HP/ww0DSs265C+3g57kXXovpWb3PduaSrZn62jHcQBLiuSxAEnQKD48eP5+WXX8a27U+Y4Rvrq+u9LoQQQgghhBBCCCGEEEIIIYQQQgjxDSRhwa+B7/vU1NQwe/ZsqqqqGDVqFI899hiDBw9uG3PnnXfyzjvvcNdddzFt2jSeeuopHn/88c+95rRp03j44YeZNm3aNhX6vphf3G1x19MmL/8+w+47CInNnKnzzjsGkYhHOt3+/iuv6rz4gsbhh8cZPjxXCS4Wi3P//fcTDqc57bQfEolEALBtnbvu+iOeF+enP/0FQaCTzUIQaLzxRoLnnmtizJh8xo7Nb5u/sFB1ajsMEA4HZDId2wXnqg/6eF6wk+Md2xEDRCI66bTX6Xhhod1hXW3TJvKe+jvhjWsx8PExcDFIG2H8ESMI9tkHraiIcNhg2bLVrFy5ipUrl9PQsBLf99C0EBUVPejevYJQqIhsNs3mzU1s2rSZeNwn9/V0AYuiogqKivrTtVsFhxwSZ999elBdXU1lZeUO28++9Vaas89ezZIlWX7yk3KuvbYboVDncTszY4bBTy602bIFrrzC5ac/9dhZhi0I4N5/m1z9VwsvgGsmu5x7hMf2j2HahVsXWPzudZM8E244wOHUoT76NpGv91IaP/vY5pWEwV75Pnf0dhiWl3u2FIp/GFlutlJs1AKO90Nc6uRTik6AYp6xhketOjbrWcZ6PZjs1FBCmM1aM89bc6kzP6QwKGKcexAD/UGktXUssx5hg/kqoaCU/u4pVPgH4BlzSFs3E+jLMP29ibi/xMrkYzX9CjPxJMroilt6JV74aOzXr8BYNhXsQtyhP8cbfC6YEdiylvBvD8WdcBH+6O+DYXa8YTv4zL6IIAjwPI8gCDAMA13XSSQSHH744SxevPhLXev/EQkLCiGEEEIIIYQQQgghhBBCCCGEEEJsQ8KCX4PXXnuNa6+9lmeffRaAm266CYDLL7+8bcyECRO49tpr2XffffE8j4qKCjZu3NihNe5noZTi4osvJhwOc/nll3/uebZasERn/CUhfniYx+9+7O5wTGOjYto0n7w8DcdRZDI6H31kMHWqwcCBilNOSZJKtYfuGhoaeeSR++jZs5JJkyZhtPacXbJkKU89dT9HHz2JwYMHoRS8/36WGTNiDBtmcNJJxeRaE2sErZm/dDpFENDhOvPydJLJVKdrj0ZNEonO4cJo1CQe7zzetg08z8UwdExTQ9d1DGNrq2LIZgP8N98meOIfbeeY+OimSXqPvUgMG0pjSwuNjY00NjawZs0qXDcLhIlEigmFQvi+TzKZJAhcwAMMwuFiSkur6NKlhIqKrhQWVlBe3pWSkkp8v4jvftdir70+OWTmeYrf/34j11+/gbIyg7vuquI73yn4xHO2tWED/PznNk8+ZTJ8eMA9d2fZbbed/0y8t1Ljgj/YLPzQYNzuPn8436FvRefxs5brXDzXZvkWnRMHedx0oEO39vwnWzy4fo3F3RtMSkz4daXDqeXtQcJ3dJdfWUkWGx7DfJNfufnsHlgALNU384C1hI+MGAP8Is50B1ETFJMmzavWKywyX8fAYB93P/by9kaRZoU1nQbz32gY9PaOpo97NEp/n7R1I57xOnrQj4h7BZazB3bTdZgtD4AWwiu5CLfkQtCjELiEZ4zBrxyPO+wXENqu3e9XEAr8JNsHBs877zzmzZvHxx9//F/bw3+ZhAWFEEIIIYQQQgghhBBCCCGEEEIIIbbx2fpZii9FY2MjPXv2bPu7qqqKBQsW7HSMaZoUFRXR1NREeXn551pT0zRuuukmDj30UGbNmsWhhx5KJpMhHA5/rvm6lSiO29/n2tN2HBQE6NEDioth/foAXXfYtAmeesqivFznxBMVtq2RydAW8KuqquSww47h6acf4j//+Q8TJhwCwMCBtZSX9+OVV15i0KCBfPihw8yZLfTpYzNxYvEntBfOYJoahqG1thkOKC21cV2/reVwLmQYUFxsEbRuRNNobT0cUFYWJpv1UUrh+4ogULiuRzRqEYtlcN32PJLx2DSMVSuwlY+r2kNgCljesy8LDcWK9xaTWjgP0Ml9/UKA1frKks1miUYjVFZ2oaysG9FoF8rLyygtLaNbtxKUMgAdXbdQKkQ6nc+IETYHH2yg65+cjaqry3LOOatZuDDNMccUcscdlZSV7dpPgFLw8CMGV1xhk0zCNVc7/PSnHpa14/GJNNz0mMUf/2lSnA9/+VmWk8b5bJ9RXbFF47IXLJ5eZlJTGvD08RnG9W6v8ugreHCTwa8abZo9OKuLx9WVLqWt216n+fzWSvGkmaVcadySjXKcH0JHY72W4mHrQ+ab6ykNQpyfHcpYvwcBPgvM+bxqvUKWDMP84Yx1DiCCzcfmDFZaT+KToYd/EP2dkzC1TaTt83HN59BUF/KcG7C9k9AwgWbMxD/wis7CLb0MzG7tF6dbZI58BfSd3OP/YlAwt5yOaZp4nofv+9xyyy0MGjSIu+++m3POOee/uhchhBBCCCGEEEIIIYQQQgghhBBCCPHfJ2HB/wHr16/n9ddfp66ujsrKSk477TSqqqro27cvTzzxxOeas0+F4sFLnE8co2kae+yh88wzPppm8ve/58J2xx6bxXEUjgOWlcI0NUIhA03T2W+/IWzZsj8vv7yQrl27MmLE7miaxr77jmHmzId44YWVzJ+fT48eFhMnFpFOQ16eRTrdMbSYSAQYhobnBXjbdAx2HB3Pc9i+oKZt544HQcc3dF3DMBSu27FNcTzuUlQUJhbL4nke+tTHMBtWowAfRRgHA5iD4kU0MquXkwsEBoBFJFJMly5dKC8vp6yslO7du9CtWzcKC4vRNJNUKrdeXp6NYVgkk4pkEqLREI5jAmFqa/OZMMHEsj45JOh5ij/+cRPXXbeeSETngQd6csIJxZ94zrbq6jQuvMhm3jyD/fb1+cMfHAYO3HE1QaXgH68YXHqvReMmndMO8fj1aQ7lRR3HpVz43UKL3y00MTT41f4OPxnpYW/TmnheTOeS1TbvpnVGR31u6eWwe2vL4RSKe6wU95hpfOBHboRz3QgF6MRxmG59xLPmxxjonOgM4AivDyEM3jfeY571IjG9hX5+Pw50xlOuSlljzOVN63GyejPl3igGuN8nqnoBkDbvwzVeJez8grB3FhrblDw0Skn3+QD0bY5ta2dBwa/JtoHBdDrNiBEjmDlzJv369eM73/nO1709IYQQQgghhBBCCCGEEEIIIYQQQgjxFfr/lWT5H1FZWcnq1avb/m5oaKCysnKHY6qqqvA8j5aWFsrKyj7Xeh988AHz58+npqaGc889l+9///tcfvnlPPjgg1/oOnbFkCEa//63xgMP2DQ3ZznpJI+ysvagWSQSIhbL4DjtYbwxY8axbt0KZs2aRmVlhAED+rPvvrXMnbsHr70WIhyOUVHRwOLFEaLRKOXlEQzDJBKJEAqFME2TINAoLAwRi3WsOui6AYWFYWKxjm2HHWfr8fbxvh8Qj6cIggzNzVtIJlOkUilaWmJs2rSJlpZNxOPNuK7LTSgswEcni4lCYxYWbxQWU1FaSkVFdyoqulFaWkqXLmWUlBQABr4PqZTXFl5MpXzy8nSKi0MoZRKLKWxbJxoNkU7rQJhBgyIceKBFXt6nV6Z79900557byOLFab73vULuuKMHFRU7KQe4nXQabrvN4rbfmeTlwZQ7HM44w9tpQbylqzV+cbfN828ZDO0b8NClGfYZ1DFkqRT8fanBL+dZNMZ1jh/occMBLpUF7c/EsozGVQ0WM7aY9LIDHuqX5diSXFVCD8V0I8vtVooNesBhns2lbj69lEEWn6fM5fzDWk4aj3F+FSe6AyhRIZbrH/Gi/Twb9A10Cyo4LHM4fYK+ADSYs1hq302RP5DdMj+jJBjSYc9h98eE3LPQ2a6N8FY7Cwr+PxMEAQ0NDdTV1fHhhx+ycOFCmpubefbZZzFN+V+BEEIIIYQQQgghhBBCCCGEEEIIIcS3naa2L7HW0Se+KT4fz/Ooqalhzpw5VFZWMmrUKKZOncqQIe0hpT/96U+8++673HXXXUybNo0nn3ySv/3tb1/aHu69916ee+457r//fvSvsB1qOg0Hjdd5552Ak0/K0qdPxwqAuaVTnSr6GUaGO++8i1QqxRlnnMHy5TazZsWx7Q2EQs+TSjXj+w65RzQAMuRa+2pomo5thwmFQoTDOpYVwTByJes0TQcUuu4BBpqWayvsuk7rK4nn+ThOFs9zaf8KeOSytVrrOltL4PmEwxFO8hU93W2vTcM6+zSyFT1RCiIRE9PUtwkHqtZwYq7sYV6ejWmapNO5Koa6rpGfH8LzdAzDJhIJ0b9/HnvtFaKg4NODXalUwE03bWDKlI0UFxvcdlsPjjuuCG37PsA7MWuWzi8utlmxQueEEzxuvsmhW7cdj92SyLUcvutpk/wwXP19l7MP8zCNjuNeX6tz2fMW89cY7N4t4JZxDqOr2sOETR7ctMbiLxtNQhpc3N3l/G4eER0Uiud1l5vtJPW6zwjf5Eo3nz0DC5+AF4w1PG7V06xn2cPvwmSnhp6qAICZ9j9533yP4qCYse6BDPIHo9F+H3yyNGlCM+0AACAASURBVOvvUB6M7HD8myqRSFBfX099fT11dXXU19ezYsUKfN+nZ8+e1NbWUltbS//+/enZsycDBgz4urf8Vfnmf5hCCCGEEEIIIYQQQgghhBBCCCGEEF8iCQt+TZ555hkuuugifN/nzDPP5Morr+Tqq69m5MiRHHnkkWQyGSZPnsybb75JaWkp06ZNo1+/fl/a+kopfvSjH9GvXz8uuOCCL23ebaVScOKkEHPnBEycuJm991Y4jiKb1XFd1RZcKyjwiMeznfaXSq3jrrvuR9dHkU7X0L9/iBNOKMIwHHxfkc1mSSQSJJNJHCdGS0sCx8niOA6O45DNZgmCJKmUQxAErdX7FEopdN3BdcH3c2G9IAjwPA/PS5PNujhOxxbL4XCY0tIopaVd6dq1K2VlZZSWllJcXEw0GiKb9dAenYaxagXh4ijaiScQ9OqF7+eqGbru9u2NdfLybHRdJwhM4vFtQ4M2iURAJBLCNG122y2PffeNEA5vl77bieeei/Ozn61hxQqHyZNLuOGGCsrKdq1y3PLlGhdfYjNrlkFtTcDttzsccECww7G+D399zuTXD1s0xeH0Q3yuOdWhy3Yth1e1aFz7ssXflph0y1dcM8bh+0N8jNaMajqAO9eb3LbOIu7D6eUeV1a6bC2A+KbucpOV5HXDo0+gc4mbz3d9Gw2NN/QNPGR/yBo9SbVfxGS3lsFBxwqAS40lpLQkw70RGOzaPfz/LggCGhsbqaurawsE1tXV0dTURH5+flsgcNCgQdTW1tKvXz9s2/5K9zRr1iwuvPBCfN/n7LPP5rLLLvtK19sFEhYUQgghhBBCCCGEEEIIIYQQQgghhNiGhAX/h2WzWQ4++GCuvPJKxo4d+6XO3dICJ5wQ4tXXdP78ZweNzaxY4RIOe2SzAYahEQoZWJaBptFayU8jl9HLZXzCYcV9933EqlUmhYXr+PGPh2IYOoWFEItlO60ZjSoSiY4hP6XANLM0NGygqamJ5uZmmpqaaWpqYvPmBrYtBmiaFqWlpVRUFFJQ0IWyslLKysooKSkhHA5jWXprqNDHNHVCIRPD0NA00DSNdNonm/U7Ve+zLANd1zAMA9M08TxFKuW3vR8KmUQiIZSycF0Nw7AwzRDV1XmMGhWmuHjXAm6NjS6XXbaWJ59soaYmxO9/34MDDoju0rmJBPz2VospU0xsGy6/3OXcH3vsLF/2n8U6V9xv8/5KnTG7+dx8tsOIAR1/LjZn4NYFFncuNtE1+MlIj5/t5VLQOqen4NEmgxvXWDQ4OocW+fy6ymFwJDdPneZxq5VitulQrjQudPM40QtjbZMB+5e5ktlmAye71Yzyu34rKgNuK5lMdqoSuHz5cjzPo6qqioEDB3YIBZaXl+9y9cgvk+/71NTUMHv2bKqqqhg1ahSPPfYYgwcP/q/vZRvfrodBCCGEEEIIIYQQQgghhBBCCCGEEOILkrDg/7iGhgYOPfRQnnjiCaqqqr6UOdeth2OOCfPBBxr33eswcaLPhx86TJ8ep7BQ+9Sgn23rZDKKRx/dwurVKQYObGbp0kcYO/Ygxo07GKU0giBLsE3BO9/3SaVaWLdubVsoMBcMbCKZbCaXG8q9iouLKC0to7y8mLKyYoqLc6HAgoICNA1MUyMc1gkC1RoG1ABFECh0HZJJF9/v/NWIRm0SCa/t70jExLIMggDSaZ+8vBDxuAtohEImoZBNNquRyfiEwxahUAjPMxk4MMo+++RTUrJrIUHHCfjDH5q4+eb1BAFcfHEXfvrTLoRCn95eOghg6mMG115rsXatzkkneVz3a5fu3Xf81X9/pcZVf7V59g2DPt0Crj/D5ejRPtvm07Ie3P2WyS3zLbZk4OQhPteMcaksyM2pFDy9xeBXjRZLMjp75vlcX+UytrD9A12p+YwPbyYfjR+4Ec70IuTvIPvlEaChYXyDcmFLly6ltra2LdSnlGLNmjV8+OGHHUKBGzduJD8/n+rqagYOHNj26t+//1deJfCzeu2117j22mt59tlnAbjpppsAuPzyy7/ObX1zHgohhBBCCCGEEEIIIYQQQgghhBBCiP+CXetNKr61qqqqmDJlCqeffjpPP/004XD4C82XTML48WE2btSYPj3Ldw7OBcCqqy0KCw3icR9dp0PQD8D3dZTKtSZesSLLE09sIZNRnHJKCb16FfHvf49k3rx5RKNRSkpKSKU2sm7dJpqaNtHUtJHm5maU8oEMoJOfn09ZWTkDB1ZSXj6cbt3KKCsrp7S0FMMwybUjzgUDs1mXIAjwfYXnBXieRiajUMrfYSiwoMA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