SciPy_optimization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notebook to demonstrate SciPY optimization methods\n",
    "\n",
    "Mathematical optimization is at the heart of solutions to major business problems in engineering, finance, healthcare, socioeconomic affairs. Pretty much all business problems boil down to minimization of some kind of resource cost or maximization of some kind of profit given other constraints.\n",
    "\n",
    "An optimization process is also the soul of operation research, which is intimately related to modern data-driven business analytics. In this manner, it is also closely related to the data science pipeline, employed in virtually all businesses today. \n",
    "\n",
    "Although much has been written about the data wrangling and predictive modeling aspects of a data science project, the final frontier often involves solving an optimization problem using the data-driven models which can improve the bottom-line of the business by reducing cost or enhancing productivity.\n",
    "\n",
    "Python has become the de-facto lingua franca of analytics, data science, and machine learning. Therefore, it makes sense to discuss optimization packages and frameworks within the Python ecosystem.\n",
    "\n",
    "We cover optimization algorithms available within the SciPy ecosystem. SciPy is the most widely used Python package for scientific and mathematical analysis and it is no wonder that it boasts of powerful yet easy-to-use optimization routines for solving complex problems.\n",
    "\n",
    "For more information see\n",
    "\n",
    "#### [SciPy optimization reference guide](https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimize a simple scalar function: $\\text{sin}(x).\\text{exp}[(x-0.6)^2]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scalar1(x):\n",
    "    return np.sin(x)*np.exp(-0.1*(x-0.6)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_nice(x,y,title=None,xlabel='x',ylabel='y',show=True):\n",
    "    #plt.figure(figsize=(8,5))\n",
    "    if title!=None:\n",
    "        plt.title(str(title)+'\\n',fontsize=18)\n",
    "    plt.plot(x,y,color='k',lw=3)\n",
    "    plt.grid(True)\n",
    "    plt.xticks(fontsize=15)\n",
    "    plt.yticks(fontsize=15)\n",
    "    plt.xlabel(xlabel,fontsize=15)\n",
    "    plt.ylabel(ylabel,fontsize=15)\n",
    "    if show:\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-10,10,0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = scalar1(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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R5jgDy+Xx04HpjElr/rOefv36Ubt27UD1Bg0a5M3bpTcTS1Uh+TQGwnUwleeuC0tVNwEDgIuBLe40FDhHVX+MQ5zGpKw5c+Z482eccUbgeuecc443P3PmTA4dOhTTuEz1VSVGMsVpbBBKIpQ7K0VaAm8BC4Br3eKbgPdF5FT37Cm0znXAdQA5OTkVbl5aUFCQkk1TLa7opFNc/u0zMzMD11dVmjZtyrZt29i9ezcvvvii1/dbrGJLBIsrOgmJS1VTegK2AveFKS8A/lBGvceBdUAtX1ltYD3wdHnH7dWrl1bU7NmzK1w3niyu6KRLXNu3b1ecH2paq1Yt3bt3b1T1R4wY4dV/8sknYxpbolhc0alMXMB8DfDdXhUuu60g5N6O24y6HiH3gkJ0Ar5W1cKSAlU9CHwNtI9DnMakpM8//9yb7969u9eCLai+fft68x9//HHM4jLVW1VIPh8A54hItq9sOLAP+G8Z9dYDXUXEu7MqIplAV5wzImOqBX/HoKecckrU9UOTj1ov1yYGqkLy+SdwAJgoIme692VGAY+rr/m1iKwWkbG+ei8ArYD/iMh5InI+MAloCYxJWPTGJNlnn33mzQdpYh2qS5cuNG7stO3ZunUrq1atillspvpK+eSjqnnAQKAGMBnnAdMngPtCNq3pblNSbwEwCOdB09eAV4G6wFmq+mX8Izcm+VS11GW3iiSfjIwMfvazn3nLdunNxELKJx8AVV2mqmeoapaqtlTVe1S1KGSbdqo6MqRspqqerqpN3KmfquYmMnZjkmndunXs2LEDgMaNG9OhQ4cK7ee0007z5v1nUsZUVJVIPsaYivnyy8Mn+T169ECkYp17+M+Y/GdSxlSUJR9j0tjixYu9+e7du1d4P7179yYjw/m6WLp0KQUFBeXUMKZslnyMSWP+5HPCCSdUeD/169enc+fOABQXF7Nw4cJKx2aqN0s+xqQx/2W3ypz5AJx00knevF16M5VlyceYNLVz505vGIRatWrxP//zP5Xan933MbFkyceYNPXVV1958126dAnck3Uk/jMf/4OrxlSEJR9j0lSsGhuU6Nq1q9c1z4YNG/jxR+sc3lScJR9j0tSSJUu8+Vgkn5o1a3L88cd7y4sWLar0Pk31ZcnHmDS1bNkyb75Lly4x2WePHj28eUs+pjIs+RiThlSV5cuXe8uVbWxQwpKPiRVLPsakoa1bt5KXlwc4z+i0bt06Jvv1PytkycdUhiUfY9KQ/6ynU6dOFe5WJ1S3bt2oUcPpv3fVqlXW04GpsCqRfESks4jMFJG9IrJJRO4XkRrl1wQRGSoiX4jIPhHZLiIfiki9eMdsTDLF45IbQFZWFp06OWM7qmqph1iNiUbKJx8RaQzMwBnGdwhwP3AbztAK5dW9FngDZ0C6c4FrgVU4wy8Yk7bilXzA7vuY2KgKX8I3AFnAUHfwuOki0gAYJSKP+AeU8xORpjjj/tysqs/7Vv0n7hEbk2TxTj6vv/46YMnHVFzKn/ngnLFMDUky43ESUr8y6l3qvr4Sr8CMSVV25mNSXVVIPp2AFf4CVd0A7HXXRXIysBK4RkS+F5FCEZknIqfGL1Rjki8/P5+NGzcCTp9u7du3j+n+/S3eli5dysGDB2O6f1M9VIXLbo2BnWHK89x1kbQAjgPuBu4AtruvH4rIsaq6JbSCiFwHXAeQk5NDbm5uhQIuKCiocN14sriiU1Xj8p/1tGrVijlz5sQ8hhYtWrB582YKCwt55ZVXOPbYYwPFliwWV3QSEpeqpvQEFAK/DVO+EXiwjHrTcRopDPKVNcBJWn8p77i9evXSipo9e3aF68aTxRWdqhrXyy+/rO5nXy+++OK4xHDRRRd5x3jppZcCx5YsFld0KhMXMF8DfLcHuuwmIheLyDW+5aNFZK6I7BSRt0WkUYxyYTh5QLj9NyT8GVGJHe5rbkmBOveNFgCdYxWcMakmnvd7Svj7ePP3IWdMUEHv+dyNc9ZQ4hmgKfAQ0BN4MMZx+a0g5N6OiLQB6hFyLyjEcpxfZqFP1wlQHMsAjUkliUg+3bp18+Yt+ZiKCJp8jgGWAIhIQ+Bs4Peq+hBwF/Dz+IQHOM/onCMi2b6y4cA+4L9l1HsPJ9EMKClwY+8F2JNxJm2tWHH4N5klH5Oqomntpu5rP6AI58FPgO+BZrEMKsQ/gQPARBE5020UMAp4XH3Nr0VktYiM9YJVnQ+8A4wVkatF5DzgXZx7SH+PY7zGJM2hQ4dYs2aNt9yxY8e4HKd9+/be2D6bN2+2sX1M1IImny+By91uaa4FZqvqAXddW2BrPIIDUNU8YCBQA5iM07PBE8B9IZvWdLfxuwKYBDwOvIWTeM5w92lM2tmwYQOHDh0CoGXLltSrF5+epGrUqFFqmAY7+zHRCtrU+s84X/xXAwU4l91KXAjEdUxdVV0GnFHONu3ClBUAN7qTMWlv9erV3nxJ8+d46datG/Pnzwec5HPGGWX+FzWmlEDJR1XniEhboCPwrar6W5m9CKwOX9MYk0irVq3y5jt06BDXY9l9H1MZgR8yVdXdwAJxtAK2quohVZ0Sv/CMMdHwn/lY8jGpLHCDAxEZLCLzgP3ABuB4t3yMiFwRp/iMMVFI9GW3El9//TXFxfYEgwku6EOmV+G0FFuB0/2Mv94q4Jpw9YwxiZXIM5+cnByaN28OwJ49e1i7dm1cj2fSS9Azn7uAR1X1auD1kHVfYz0GGJN0RUVFpZpZx7pD0XD8Zz9fffVV3I9n0kfQ5HMUTl9p4eyndO8Hxpgk+O6777wepnNycsjOzi6nRuXZfR9TUUGTz3dAjwjremOt3YxJukTe7ylhycdUVNDkMxa4z21YkOWWiYgMxBmm4PmINY0xCZHIZtYlrINRU1FBm1o/DLTBGRW0yC2bi9OjwHOq+nQcYjPGRCGRjQ1KdO7cGRFBVVm1ahUHDhwov5IxBH/IVIGbROQJnK5ujsAZsmCWqn4Tx/iMMQElI/nUrVuXDh06sGrVKoqLi1m/fn1CjmuqvqhGMlXV1dj9HWNSUjLu+YBz36fkkp+/tZ0xZQmUfERkcHnbWE8HxiRPcXEx3377rbeciGbWJbp168bEiRMB7FkfE1jQM5/3CD8wm/rmQ3uUjhkR6YwzgF0fnNFLXwBGq2pRmRUP188AvsAZ+O7nqvpevGI1Jhm+//57735Ls2bNaNiwYcKO7W/xZmc+JqigyefoMGVNcHq3Hgn8MlYBhRKRxjhjBy0DhgDtgb/itNS7O+BurgWOjEuAxqSARD9c6udPPnbmY4IK2uAg3F3E9cAiESnCGXLhglgG5nMDTvPuoe7gcdNFpAEwSkQe8Q8oF46bvB4E7sQ5YzIm7fi/9I8+OtxvxfgpGVhu3759bN++ne3bt3PEEUckNAZT9UQzkmkkiyhnrJ1KOheYGpJkxuMkpH4B6v8F+ASYGYfYjEkJyUw+NWrUoHPnwz1s2fM+JohKJR8RqY1z2e2HmEQTXiecDk09qroB2Ouui0hEjse5JHh73KIzJgX4k0+7du0SfvyuXbt685Z8TBBBW7t9QenGBQC1gXZANnG85wM0xmlkECrPXVeWZ4C/q+pqEWlX3oFE5DqcXrvJyckhNzc3qkBLFBQUVLhuPFlc0alKcS1evNibz8/PT3jcdevW9eanTp1a6j5QKqhK/5apICFxqWq5E/Ay8FLI9A+c3q67BNlHRSegEPhtmPKNwINl1BsBbAYauMvtcBLo+UGO26tXL62o2bNnV7huPFlc0alKcbVq1Urdz7euXr064TFNnTrVO36fPn0SfvzyVKV/y1RQmbiA+RrgOzZog4ORlc5yFZcHNApT3pDwZ0SISC3gUZxugTJEpBGHe96uJyLZ6ozMakyVt3//fjZt2gRARkYGbdu2TXgM/jOdpUuXoqqIhD6ZYcxhsWhwEG8rCLm3IyJtgHqE3AvyqQe0Bh7HSV55wJfuuvE4jSSMSQv+Lm1at25NrVq1Eh5DixYtvBZuu3fvtm52TLkinvmIyIQo9qOqOjwG8YTzAfCHkLOV4cA+4L8R6hQAA0LKWgBv4jQLnxWPQI1JhnXr1nnziW7pVkJE6Natm3efYMmSJUlp+GCqjrLOfJpFMTWPY4z/BA4AE0XkTLdRwCjgcfU1vxaR1SIyFkBVD6lqrn8CPnM3XaKq8+IYrzEJlcxm1n7W4s1EI+KZj6qGnjkkharmueMG/Q2YjHOf5wmcBORXkzh28WNMqkqV5GMDy5loRNWrdbKo6jLKeZBVVduVs34dP+2bzpgqz5KPqYoCJx8RycbpW60jUCd0vareEcO4jDEBpUry8V92W7lyJQcPHqR27dpJi8ektqAPmbbH6aKmLk5Lsh9xOhatidOSbBfOcNrGmARLleSTnZ1NixYt2Lx5M4cOHWLlypUp97CpSR1Bm1o/AcwHcnAuXQ3G6VvtCpyWZfFq6WaMKcPu3bvZvn07AJmZmbRs2TKp8RxzzDHevF16M2UJmnxO4nCrM4Daqlqkqm/gDG/wVDyCM8aUzX/Wc9RRR5GRkdxH9/zNqy35mLIE/aTWAfJVtRjYAbTyrVsKdI91YMaY8qXKJbcSduZjggqafL4BjnLnFwE3iEgdtxuba4BN8QjOGFM2Sz6mqgqafMYDJ7jz9wAnA/nAbpz7PaNjH5oxpjyplnzatGnjde+zYcMGdu3aleSITKoKlHxU9XFVvc2d/wzoCtyE08LtBFV9PX4hGmMiSbXkU7NmTTp1OtwV49KlS5MYjUllgZKPiNT1L6vqd6r6vKo+rar26TImSZI9iFw4oT1cGxNO0Mtu20TkXyJykYhkxjUiY0wgqppyZz5gPR2YYIImnztweoV+C9gqIq+JyHkiUiW65zEmHW3bto09e/YAUL9+fW9Ig2SzDkZNEEHv+fxNVfsBbYD7gPbAuziJaKyInBXHGBGRziIyU0T2isgmEblfRMrsRFREThSRl9zerveKyEoRuU9EftI1kDFVUehZT6oM3hZ65uMMbmlMaVE9kaaqm1T1SVU9FTga+F9gEM6YO3EhIo2BGThD9A4B7gduo/wWdsNxkuTDOD0y/B24FRgXr1iNSaRUvOQG0LZtWxo0cAYOzsvL80ZZNcavQpfNRKQDzpf7cKAl8F0sgwpxA05XPkPd8Xumi0gDYJSIPOIf0yfEw6r6o285V0T2A8+JyFGqakMtmiotVZOPiNC1a1fmzp0LOGc/Rx55ZJKjMqkm8JmPiLQTkTtEZAGwEqepdS7QV1WPKrNy5ZwLTA1JMuNxElK/SJVCEk+JkuGz4zn4nTEJkarJB6zRgSlf0F6t5wG9cbrWmQjcDuRqYi7mdiJk2GtV3SAie911k6PY16lAMU7yNKZKS4XhsyOx5GPKE/Sy23KchgbTVbUojvGE0xhn9NJQee66QESkBXAX8FoZl+qMqTKqypnPl19+mcRITKqSVG+JIiKFwO2q+lRI+UbgZVW9K8A+auM0WmgN9FLVvAjbXQdcB5CTk9Nr/PjxFYq5oKCA+vXrV6huPFlc0UnluOrWrcugQYMoLCwEYMqUKWRlZSU5ssPv2Z49ezj//PMBqFGjBlOmTEnqwHKp/G+ZbnENGDBggar2LndDVU3pCdgK3BemvAD4Q4D6gnOPaDvQKehxe/XqpRU1e/bsCteNJ4srOqkc13fffac4LUC1adOmyQ7J43/P2rdv78U4f/785AWlqf1vmYoqExcwXwN8xyZ38I9gVuDc2/GISBucEVVXBKj/BE4T7SGqGmR7Y1JeKl9yK9GjRw9vftGiRWVsaaqjqpB8PgDOEZFsX9lwYB/w37IqisifgJuBK1R1TvxCNCaxLPmYqq4qJJ+SEVQnisiZ7n2ZUcDj6ms44PZkMNa3/Auch2BfBTaKyCm+qVli/wRjYsuSj6nqUr5vNlXNE5GBwN9wmlXvxLmUNipk05qAv8uds93Xke7k90vg5dhGakziVLXk8+WXX1JUVESNGmX2imWqkcDJR0R6A0NxWoyF9o+mqjo8loGF7HwZcEY527QLWR7JT5OOMWkhFYdSCNWiRQtatGjB5s2b2bt3L6tWrSo11o+p3oKO53MjMA+4Fqe/tGYhk/UYYEwCVYUzHyh99rN48eIkRmJSTdB7PrcWFyCKAAAgAElEQVQDLwGtVPVnqjogdIpjjMYYn8LCQjZu3Ag4/agddVQ8e7eqnBNOOMGbt/s+xi9o8mkOvKmqh+IZjDGmfFu3bqW4uBiAVq1akZmZuuM7WqMDE0nQ5PMBcHI8AzHGBLN582ZvPpUvucFPk4+meI8qJnGCNjj4OzBGRGoB0wnT15rbKMCYhDh48CDff/89P/74I7Vr16Zly5a0aNEi2WElhD/5pGpjgxLHHHMMDRs2ZNeuXWzbto3169enfMwmMYImn9nu633AvSHrBKcLDWtDaeJq1apVjB8/ng8++IAFCxZw8ODBUutbtWrFkCFDuP766+nevXuSooy/H374wZtP9TOfjIwMTjzxRGbMmAHA559/bsnHAMEvuw3wTWeETCVlxsScqvLuu+/Sp08fOnbsyL333sunn376k8QDsGnTJv7xj39wwgkn8Mtf/pJt27YlIeL4q0rJB+Ckk07y5j///PMkRmJSSaAzH1UtsxsbY2KtqKiIiRMn8sADD/DVV1+F3aZVq1a0bNmSwsJCVq9ezd69e711L7/8MtOnT2fy5Mml7jukgy1btnjzVeEswp985s2bl8RITCqJqnsdETlZRG4TkQfdV2uEYGLq0KFDvP7663Tt2pVLL720VOKpXbs2Q4YM4Y033mDr1q1s3LiR+fPn8+WXX5Kfn8/s2bO54IILvO03btxI3759yc3NTcJfEj9V+cxnwYIFHDpkjWZN8IdM64nIFOBT4P+AX7mvc0XkfRGpG8cYTTVw8OBBxo4dS6dOnbjyyitZseJwB+R169bltttuY926dUyaNInLLruMZs1Kd89Xo0YN+vfvzzvvvMM777xDw4YNAdizZw9DhgxJmwHN9u3bx44dOwDnb27dunWSIypfy5YtadOmDeDE//XXXyc5IpMKgp75PAL0welNuo6qtsTpYmeEW/5wfMIz6W7fvn1MmjSJY489lmuvvZZvv/3WW5ednc2f//xn1q9fz2OPPUbLli0D7fOCCy5g7ty53vb5+fkMHjw4Le4BrV+/3ptv06YNNWumfPeMgN33MT8VNPlcDPxRVf+tqsUAqlqsqv8G7gSGxStAk562bdvG6NGjadu2LU899RQbNmzw1jVu3Jj777+f9evX8+CDD9K0adOo99+5c2c+/PBD7wxo06ZNXHPNNVX+OZOq0q1OKEs+JlTQ5NMQ+C7Cuu+ABrEJJzwR6SwiM0Vkr4hsEpH7RaTcpt0i0lBEXhKRPBHZJSLjROSIeMZqIlNV5s+fzw033EDbtm0ZNWpUqbOR5s2b8/DDD7N+/XruueceGjduXKnjHX/88bzxxhve8rvvvsvzzz9fqX0mW1VNPieffPj2sDU6MBA8+XwJ3Cgi4i90l29018eFiDQGZuA8SzQEuB+4DRgdoPq/gP44HaKOBE4EJsUjThPZ6tWreeyxx+jevTsnnngizz33HPv27fPW5+Tk8OSTT7J27VruuOMOsrOzy9hbdAYPHswtt9ziLd95551V+vLbunXrvPmqlHx69epFRobzdfP1119TUFCQ5IhMsgW9YPxnnC52VojIf4AtOP29XQS0A86NS3SOG4AsYKg7eNx0EWkAjBKRR/wDyvmJSB/gHKCfqn7klm0E5onImao6I44xV2s7duxg7ty5fPTRR7z//vssWxa+84sePXrwhz/8gebNmzNw4MC4xfPQQw/x3nvvsWbNGvLy8vjzn//MmDFj4na8eKoKQymEU79+fTp37szSpUspLi5m/vz59O/fP9lhxUxBQQE//vgjO3fuZOfOnRw4cAAR8aasrCwaNGhAgwYNyM7OpkGDBtSqVSvZYSdV0Od8ZolID5zeDYYBLYEfcIZZGBrnrnXOBaaGJJnxOI0c+uEMMBep3paSxAOgqp+LyFp3nSWfStizZw8//PADmzdvZu3atSxfvpzly5ezbNkyvvnmm4j1srKyGDZsGL/61a84/fTTEZG4N4XOysriqaee4uc//zkAL7zwAjfffDPdunWL63HjoapedgPo06cPS5cuBWDOnDlVNvns2LGD3Nxc5s6dy+eff86qVatKdXkUVJ06dcjKyqJp06Y0aNCAhg0bljllZ2dTp04d6tSpQ2Zmpvfqn69ZsyYZGRneFHKxKqUEbirjJpgRcYwlkk7ArJBYNojIXnddpOTTCVgRpny5uy7mbr31VsaMGUNxcbHXCsn/66dkikV5kG1LPnwlr3v37iU7O7vUB7O8VxHhwIED7Nmzx5t27drFnj17Ar8vderU4ayzzuLCCy/kkksuoUGDuN4iDOv8889n8ODBTJkyBVVl9OjRvPXWWwmPo7KqcvI57bTTvHtuc+bMSXI00dm3bx/jx49n/PjxzJo1KybPKu3fv5/9+/eTl5cXgwgj8yej0ClScmrfvj0LFiyIa1xVoZ1mY8J0ZArkuesqUu+YGMT1E/v374/qSzld1axZk549e3Laaadx+umnc+aZZ1KvXr1kh8UDDzzAlClTAHj77bdZvHhxqfFmUl1+fr73jE9mZmaV60i1b9++3vzcuXOrxLDaO3fu5Mknn+TZZ5/lxx9/jLhdrVq1aNGiBY0bN6Zx48ZkZmaiqt60d+9e8vPz2b17N/n5+eTn53vDYsRbcXFx1Mfy35ONl4jJR0QmAH9S1W/d+bLEdRhtnMYGoSRCeYXrich1wHXg3ASP9nJQyQBf1UGtWrVo0qQJTZo0oWnTphx11FG0bdvWe61T5/BI61988UWZ+yooKEhYLwR9+/bl448/BuB3v/sdo0aNSom4gvA/A9W8eXM++uijMrZOjrLeM1WladOmbNu2jd27dzN27Fg6duyY9LjCKSoqYsqUKYwdO5Zdu3b9ZH2nTp3o0aMHnTt3pn379jRv3jyqRKqq7N+/30toBQUFpa4u7Nmzh4KCAvbu3VuqrLCwkMLCQg4ePOi9lswXFhZ6iUZVK5XciouL4/7ZL+vMpxlQckesOeV/0cdLHtAoTHlDwp/Z+Os1C1PeKFI9VR0DjAHo3bu3RntN+pRTTqGwsJCPPvqIvn37lvrlUzK5x6lUeTTb+j+IX3zxBT179vSW/evKes3MzKRu3brUq1ePevXqkZ2dTcOGDWN2PTk3Nzdh1/+feeYZ72zn448/5uijj444Emgi4wrC/yXYuXPnlIqtRHnv2Zlnnsn48eMB59d1ov6GaP4tv/32W6644go+++yzUuVt2rThN7/5DSNGjKBt27YJj6si/P/XQ6eioqKI9ebOnRv3f5uIycc/NLaqxjeKsq0g5B6NiLQB6hH+no6/Xt8w5Z2IU3PrkpuB9erVS8p9jfLk5eXRs2fPZIeRVN27d2fgwIHMnDmT4uJinnnmGR577LFkhxVIVW1m7de3b18v+Xz88cf89re/TXJEpY0bN44bb7yR3bt3e2Vt27blwQcfZPjw4VWuhZqIUKNGjagvb9atG/8e04L27XaviLSKsK6liISO8RNLHwDniIj/4Y/hwD6grN62PwBaiMhpJQUi0hvnfs8H8QjUVA2///3vvfnnn3++yjxzUlWbWfv57/vk5uYm7L5HeYqLi/nTn/7EFVdc4SWemjVrct9997FixQquuOKKKpd4Ul3Qh0zvAyL1YNjKXR8v/wQOABNF5Ez3vswo4HF/82sRWS0iY0uWVfVTYCrwqogMFZELgXHAHHvGp3o799xzvXsN+fn5/Otf/0pyRMFU5ZZuJbp06ULz5s0B2L59e0p0+Lp//35+8Ytf8NBDD3llHTp0YO7cuYwaNYqsrKwkRpe+giafsm7ut8a5vxIXqpoHDMQZKXUyTs8GT/DThFeTn46mOgLn7OhF4FVgAc6DsaYay8jI4IYbbvCWX3jhhSRGE1w6XHbLyMgo9UBxyQinybJ//34uuuiiUj9AzjvvPBYuXMiJJ56YxMjSX8TkIyJXi8gsEZmFk3j+UbLsm+YCr1P25a9KU9VlqnqGqmapaktVvUdVi0K2aaeqI0PKdqrqL1W1kao2UNVfqGrV7VvFxMyVV17pXUb57LPPvIcfU5WqpsVlN3AaHZRIZvLZv38/Q4cO5cMPP/TKbrrpJiZNmhTTLp5MeGWd+ewFtruTALt8yyXTWpzhFq6Lb5jGxFbTpk258MILveWxY8eWsXXy7dixw7sXUadOnQr19J0q/Mnn448/Zv/+/QmPoaioiBEjRvDBB4dv/957770888wzVWaYiqouYvJxh08YpqrDgFeAa0uWfdPlqvoXVd2euJCNiY1rrrnGmx8/fnyZTU+TzX/JrWXLlindbUp52rZty7HHHgs4za0/+eSThMdw66238s4773jL99xzD6NGjarS72tVE/Sez2+BsD9P3NZu9WMXkjGJMXDgQO/m9+bNm1Pyoc0S/ktuVa1ng3DOPvtsb/79999P6LGfeuopnn76aW/5tttuY/To0ZZ4Eixo8nkBZyiDcEa5642pUmrWrMmwYYfHQSx5/iQVpVvyKenkFZxxlhI1yN+kSZNKNbUfNmwYjzzyiCWeJAiafE4HIv08meKuN6bKGTHicF+5b7/9NoWFhUmMJrI1a9Z480GHE09l/fv3p35954LJt99+y/Lly+N+zOXLl3PllVd6ie7UU0/llVde8cYZMokVzUimeyOs20/ZHXwak7JOPfVUWrd2HmHbvn07M2fOTHJE4fn7dWvVKuzz3lVKZmYmgwYN8pbffffduB5v3759XHzxxd4Dxe3bt+edd96xZ3iSKGjyWQWcF2HdYODbCOuMSWkZGRlceuml3nKqXnpLt+QDcMEFF3jzkybFb4BhVeXRRx/1zq6ysrKYOHFilW4xmA6CJp9ngN+IyKMi0kVEmrivjwA3AU/FL0Rj4st/6e0///kPBw8eTGI0P1VYWMj69eu95XRJPoMHD/aaNc+bN6/UpcVYeuaZZ5g9e7a3/Nxzz3H88cfH5VgmuEDJR1Wfx+lR4P8BXwE/uq83AXe7642pknr37u09tJmfn89//xvXZ6ajtmHDBq8ZeKtWrcjMzExyRLFxxBFHcM4553jLb7zxRsyPMXfuXG677TZv+YYbbuDKK6+M+XFM9ALfaVPVB3D6cTsPuMp9baWqD5VZ0ZgUJyIMGTLEW548OdLguMnhv+TWvn37JEYSe5dffrk3P27cuJi2etu6dSvDhg3zRh3t3bs3Tz75ZMz2byonqmYeqrpLVT9U1XHu609HWTKmCvLff0hk098g0jn5DBkyxGv1tmLFChYuXBiT/R46dIjLLruMTZs2AdCgQQPeeuuttDlrTAeBk4+I1BGRs0XkVyLy/0KmG+MZpDHx1rdvXxo2bAjA+vXrWbJkSZIjOiydk0/dunW56KLDff3+4x//iMl+7777bmbNmgU4Z7Z33XVXxEEDTXIEHc/nNGAD8CHOA6V/CzPFjYj8WkRWich+EVkgIgMD1LleRKaLyBYR2SUin4jI2eXVM9VTrVq1OPfcc73leDf9jUY6Jx+gVA/j48aNY9u2yvX9O3HiRB5++GFv+b777uOkk06q1D5N7AU983kapzl1DyBTVTNCpuiGyYuCiIzAGdPnVeBc4GvgPRHpWk7Vu3A6Pr0euARYDXwoIheUWctUW6GX3lJFuiefPn360Lt3b8Dpafr55yvefmnlypWMHDnSWx48eDD33HNPZUM0cRA0+RwHjFLVL1U10Y+AjwZecTswnQ2MxEkkd5ZTr6eqXqeqk1R1uqpeDXwG/L6ceqaaGjRokNf094svvmD79uT3l6uqpZogp2PyERFuueUWb/mpp55iz549Ue8nPz+foUOHer1/H3300bz22mvWg0GKCvqv8hWQ8A6lROQYoCMwoaRMVYuBf+OcBUUUYdyeRUDzWMZo0kfjxo05/fTDPUXNmzcvidE4tmzZ4n0RN2zYkCZNmiQ5ovi49NJLOfLIIwHnb3788cejql9YWMgll1zCsmXLAGfYibfffjtt3690EDT53Aj8XkT6xTOYMDq5rytCypcDTUSkWZT76wMsq3RUJm357/vMnz8/iZE4Qi+5pWsHmJmZmYwePdpbfuSRR9iyZUuguqrK9ddfz/Tp072yMWPG0KNHj5jHaWIn6KhJ04G6wCwRKQTyQzdQ1XicUZT0GbczpDzPt/7HIDsSkV/h3LO6rYxtrsMdGC8nJ4fc3NxoYvUUFBRUuG48WVzla9z4cDeF8+fPZ+bMmdSoEbdbmuWaOnWqN5+dnU1ubm5KvV+hKhNbu3btOOqoo1i/fj0FBQUMHTqUBx54oMyEq6o899xzpYbBHjlyJG3atCkVR6q+Z9U6LlUtd8IZNuG+sqYg+3H31RDnjKbMyd32cpwhvBuG7OMst/zYgMfsBewBngwaZ69evbSiZs+eXeG68WRxla+4uFhbtmyp7udL582bl9R47r33Xi+WO++8U1VT6/0KVdnYpk6d6v29gD711FMRty0sLNSbbrqp1PYjR47U4uLimMcVL+kYFzBfA3zHBjrzUdVR0ae1iIYBQZqzCIfPcBrhDOONbxl+ekb00504943eB2ZSxlmPMeDc/D777LN55ZVXAJg2bVpSm+mme0u3UGeffTa33HKLN9jb7373OzIzM7n++utLbffdd98xcuRI71kegAsvvJAxY8ak7aXJdJPwZiCq+oKqSnmTu3nJvZ5OIbvpBOxQ1TIvuYlIc2AqsB4YoaqpO06ySRn+UTb9l72SobolH4CHH36Ynj17As6VmRtuuIHhw4czefJkpkyZwi233MJxxx1XKvEMHz6cCRMmUKtWrWSFbaIU6MxHRL7AOa2NSFVj/vNQVdeIyDc4Z0tT3Vgy3OUPyqrrDu09xV08X1UjjUdkTClnnXWWN//pp5+Sn59PgwYNkhLLN99848136NAhKTEkWp06dZg+fTqDBg3iiy++AGDChAlMmDDhJ9uKCKNGjeLuu++2JtVVTNB/ra/DTD8A7YAcYGk8gnONAn4pIneLyADgReBYwOvQVET6icihkNZ4E4Hjce5JtReRU0qmOMZq0kCzZs28X95FRUWlfmEn0rZt29ixYwfgdENT0hS5OmjSpAkzZswoNdxFqB49epCbm8u9995riacKCnrPZ2S4cvfs4l1gbgxjCj32m+5x/gjcg5P4zldVf8IToIb7WqLk5+u4MLu1i8KmTOecc47XyeXUqVO58MILEx7DypUrvfmOHTtWuy/YBg0a8Oabb3Lrrbcybtw4lixZQlFREd26deOCCy7gjDPOSGpLRFM5QZtah6WqBSLyV5y+3V6ITUhhj/M8ZTRSUNVcQhKK776RMVE7++yz+b//+z/AaXSQDP5Lbscdd1xSYkgFJ554IieeeGKywzAxFoufUo04/DyOMWnh1FNPJSsrC4A1a9awevXqhMfgP/OpzsnHpKegDQ4GhymuDfwPTl9ps8OsN6bKql27Nj169GDuXOeK8rRp0xJ+wz/0spsx6STomc97wGT3tWSaiNMYIBen52hj0kqvXr28+ZkzZyb8+HbmY9JZ0Hs+R4cp2w9sdZ9oNSbt+JPPrFmzKCoqStgN7qKiolKX+uzMx6SbQGc+qro+zLTFEo9JZ23btqVVq1YA7Ny5M2ZDPAexbt06Cgud0UtatmyZtOeMjImXiMlHRKaJyHEhZWeISL34h2VM8okIZ555prfs7zU53uySm0l3ZZ35nInTCSgAIlIDp3dr+59gqg1/8pkxY0bCjmuNDUy6i7aptT07Y6qVgQMHevOffPIJe/cmppcme8bHpLvq9ci0MVFq1aoVnTt3BuDgwYPMmTMnIce1y24m3ZWXfMI1KLBGBqZaScalN0s+Jt2Vl3ymishWEdmK05EowMySMv8U5ziNSRp/L9eJSD67d+9m06ZNANSqVYt27drF/ZjGJFpZz/mMLmOdMdVGv379qFGjBkVFRSxatIht27bRtGnTuB1vxYoV3nyHDh2oWbNSXTAak5IifqpVNWWSj4j8GrgDaIPTq/Udqhr4kXMR6QHMB/JUNX7fGiYtZWdnc8opp/DJJ58ATm8Hw4cPj9vxli493GF7165d43YcY5Ip5RsciMgI4J/Aq8C5OMnnPREJ9L9SnDF1/waUOeqpMWVJ5H2fr7/+2pvv0qVLXI9lTLKkfPLBufz3iqr+RVVnAyOB1cCdAetfgTPg3YvxCc9UB6EPm8azcw878zHVQUonHxE5BugIeOPnqmox8G+cs6Dy6mcDDwO3AwfjFKapBk4++WTq168PwPr161mzZk3cjmXJx1QHKZ18gE7u64qQ8uVAExFpVk79e4Hlqjop5pGZaqVWrVr063d4lPZ4XXrbuXMnGzduBJxhHdq3bx+X4xiTbKnejKZkkLqdIeV5vvVh7+W4/dLdBJwc9GAich1wHUBOTg65ubnRxOopKCiocN14sriiExqXv8nzm2++GZfnb5YsWeLNt2nTJuxDran6fkHqxmZxRSchcalqQiec/uI6lTe5216O81Brw5B9nOWWH1vGcT4EnvUtjwK2BY2zV69eWlGzZ8+ucN14sriiExrXkiVL1P3caZMmTfTQoUMxP+Zzzz3nHePyyy8PFFcqSdXYLK7oVCYuYL4G+I5NxpnPMOD5ANsJh89wGgG7fOsaua+hZ0RORZFzgZ8BvxGRkm3rOKukEbBPVQ9EG7ip3rp06UJOTg5btmxhx44dLF68uNSYP7Hgv99jLd1MOkv4PR9VfUFVpbzJ3bzkXk+nkN10AnaoaqTm08cB9YFVOAksD/gj0MSd/0NM/yhTLSRiiIXFixd789bYwKSzlG5woKprgG9wzpYAEJEMd/mDMqq+BQwImV4B8t351+IUsklz8exqp7i4uFTy6dmzZ0z3b0wqSfUGB+Dcq3ldRNYBnwBXA8cCvyjZQET6ATOBgar6X1X9HvjevxMR6Q8UqmpuQqI2ack/xMKcOXPYt28fWVlZMdn3mjVr2L17NwDNmjXzRlE1Jh2l9JkPgKq+CdyA83Dph8DxwPmqutS3mQA1sPGGTJy1bt2aTp2cq8AHDhzwutyJhUWLFnnzPXr0wOmcw5j0lPLJB0BVn1fVDqqaqao9NaRfN1XNde8V5Zaxj1Fq/bqZGIhXVzsLFy705nv06BGz/RqTiqpE8jEmlcQr+YSe+RiTziz5GBOl/v37k5Hh/NdZuHAh27dvr/Q+VbVU8rHGBibdWfIxJkoNGzbkpJNOApykMXv27Ervc9OmTWzd6ozJmJ2dbd3qmLRnyceYCoj18z7z5s3z5k844QTvzMqYdGWfcGMqINZDLHz66afe/KmnnlqpfRlTFVjyMaYCTjnlFOrVqwfA2rVrSw19XRFz58715vv06VOpfRlTFVjyMaYCMjMzOeecc7zld955p8L7OnDgAAsWLPCWLfmY6sCSjzEVNGTIEG++Msln0aJFHDjg9HPbvn17mjdvXunYjEl1lnyMqaDzzjuPGjVqAE6Dgc2bN1doP/77PXbWY6oLSz7GVNARRxzBaaedBjhNridPnlyh/fi76LHkY6oLSz7GVEJlL70VFRUxa9Ysb7lv374xicuYVFclko+I/FpEVonIfhFZICIDy68FIlJXRB4WkQ1u3TUicke84zXVhz/5zJgxg4KCgqjqL1y4kLw8Z8zEFi1a2Bg+ptpI+eQjIiOAfwKvAucCXwPviUiZ/0tFpAYwBRgC3AUMAh6Mb7SmujnmmGO8hHHgwAHef//9qOr7H1A966yzrCdrU22kfPIBRgOvqOpfVHU2ztAKq4E7y6n3a6A7cLqqvub2fD1WVR+Jb7imuhk2zBvrkHHjxkVVd9q0ad68f6A6Y9JdSicfETkG6AhMKClT1WLg3zhnQWX5FTBBVbfGL0Jj4PLLL/fmP/jgA7Zt2xaoXkFBQamHS/29JhiT7lI6+QCd3NfQx8eXA01EpFm4SiJSG+gBfC8i40Rkn4jsEpGXRKRBHOM11VD79u29VmqHDh1iwoQJ5dRwTJs2jcLCQgC6du1Ky5Yt4xajMakm1ZNPY/d1Z0h5Xsj6UEfgDBF+B1APuAC4Fef+zwsxjtGYUmc/L730UqA648eP9+YvuuiimMdkTCqTynaIGPUBRRoC5f7EU9UVInI58DrQSFV3+fZxFjAN6Kiqq8Ic40jge+A7oL2qFrrlVwGvAB1U9dsw9a4DrgPIycnp5f9yiEZBQQH169evUN14sriiE01cu3btYtiwYd6ZzN///nc6d+4ccfu9e/cydOhQr2eDl156iXbt2sU8rkRL1dgsruhUJq4BAwYsUNXe5W6oqgmdgGsBLW9ytx3sLh8Vso9hbnmzCMeo665/M6S8tVv+8/Li7NWrl1bU7NmzK1w3niyu6EQb19VXX+19fi+//PIyt3399de9bbt16xbXuBIpVWOzuKJTmbiA+RogFyT8spuqvqCqUt7kbl5yr6dTyG46ATtU9ccIx9gLrA+zqmS/xZX+Q4wJcfPNN3vzEyZM4Icffoi47WuvvebNX3bZZXGNy5hUlNL3fFR1DfANzpkOACKS4S5/UE7194DT3MYHJQbiJJ4lMQ7VGHr16uU1PCgsLOQvf/lL2O1WrFjB1KlTARARRowYkbAYjUkVKZ18XKOAX4rI3SIyAHgROBZ4qGQDEeknIodEpJ+v3qNANvC2iJzr3s95AnhRVTckLnxTndx1113e/JgxY8KO8/PQQ95Hl5///OccffTRCYnNmFSS8slHVd8EbsB5uPRD4HjgfFVd6ttMgBocvqyGqq4HzgQaAROBv+A0NrgZY+Jk8ODBDBgwAHD6bfvtb39bapTThQsXlrrkdvvttyc8RmNSQconHwBVfV5VO6hqpqr2VNWZIetz3XtFuSHl81W1r6pmqWqOqv5OVfcnNHhTrYgIjz32mLc8bdo07r//fgB27tzJlVdeSXGxc8tx0KBB1pGoqbaqRPIxpirp2bMnt912m7c8atQoBg4cSM+ePVm2bBkAWVlZPP3008kK0Ziks+RjTBz87//+b6nucmbNmmrorPAAAA8ZSURBVMXatWu95eeee45jjz02GaEZkxIs+RgTB7Vr1+add95h5MiRpcrr16/Pq6++ypVXXpmcwIxJETWTHYAx6apu3bq89NJL/PGPf2TOnDnUq1ePc845hyZNmiQ7NGOSzpKPMXHWqVMnOnUKfU7amOrNLrsZY4xJOEs+xhhjEs6SjzHGmISz5GOMMSbhLPkYY4xJOEs+xhhjEs6SjzHGmIRL+DDaVYWI/Ej4AemCaApsi2E4sWJxRcfiil6qxmZxRacycR2lqs3K28iSTxyIyHwNMoZ5gllc0bG4opeqsVlc0UlEXHbZzRhjTMJZ8jHGGJNwlnziY0yyA4jA4oqOxRW9VI3N4opO3OOyez7GGGMSzs58jDHGJJwlnyiJyHARmSgiP4iIisjICNsdKSL/EZECEdkmIn8TkboB9p8pIn8Vka0iskdE3heRdlHG2M6NLdy0spy6oyLUGxRNDOUcIzfCMeoEqPszEZknIvtEZK2I3BKjmBqIyGgR+VxEdonIZvffr2OAuiMj/D03VCCOziIyU0T2isgmEblfRGoEqNdQRF4SkTw3/nEickS0x4+w72Ei8q6IbHQ/zwtE5LIA9cK9J5/FIiZ3/xV63+P5Xrn7j/T5VhHpE6FOpP+z4ysRRwcReU5EvhSRIhHJDbONiMifReQ79//URyJyQsD9DxGRJSKyX0SWicjwaOKz8XyidwnQDngPuDbcBiJSE5gKHASGA42Ax93XK8rZ/9PuMX4P/AiMAqaLSDdV3R8wxh+A0A95FjAN+CBA/V1AaLJZHvDYQc0G/hxSdqCsCiLSAed9fQ/4E3AS8LiI7FXVFyoZT1vg18BY4C6grnuMeSJyvKp+F2AfZwD7fMtroglARBoDM4BlwBCgPfBXnB+Jd5dT/V/AcTifyWLgYWAS0DeaGCK4FViL85ncBgwG3hCRpqr6TDl1/wq85VveHYN4QkX7vsfzvQL4f0CDkLL7gR7AF+XUvR34xLdcmWeAuuD8W30G1I6wzZ3APcAfgBU4/9YzRKSrqm6OtGMROQ14G3gWuMU9zpsikqeq0wJFp6o2RTEBGe5rfUCBkWG2uQwoAo72lV2K80E/tox9twYOAVf5yo7ESWLXVjLuS914Ty5nu1HAtji/h7nAWxWo9xzwDVDTV/Ys8B3u/ctKxFQPyAopawIUAPeVU3ek+97Wr2QMfwLygAa+sjuAvf6yMPX6uMc/3Vd2klt2Zgz+vZqGKXsDWFtOPQV+E8fPUdTve7zfqwjHrA3sAP5Rxjbt3BjOj+FxM3zzbwG5Ievr4PzQvNdXVg/nR+8D5ex7KjArpGwKMCdofHbZLUqqWhxgs3OBL1R1ra9sEk4SKevy1dnu60Tf8TYCc9x9VsYInC+LeZXcTzKdC0xU1UO+svE4SbtrZXasqntUdV9I2Q6cXi6aV2bfUTgXmKqq+b6y8Thnrf3KqbdFVT8qKVDVz3HOVir7uUFVw/36XkTi3pdYiut7FcEgoDHwZpz2H1aA76pTcc7QJvjq7AEmU8Z7ISKZwAB/Pdd4oI+INAwSnyWf+OiEcwrrUdWDwLfuurLqfa+qBSHly8upVyYRaYDzYQr64W8kzn2qQhFZJCJDK3rsMpzt3tfYKyJTReT4sjYWkXpAG0LeVw5fDoz5ONUi0gzogHMZLIhvReSQiKwUkesrcMhwn5sNOGc+5X1uQt8XqOTnphynEux9GeW+J9tE5EURaRKHWKJ535PxXo0ANgIfB9j2Jff+zA8i8riIZMUpJnD+3iJgVUh5ee9Fe6AW4f8vZgDl3icFu+cTL42BnWHK89x1sa5XngtxTrGD3LxcjXOpZzHOpcXrgbdF5GJVnVhmzeD+C7ziHusonHssH4tId1VdF6FOI/c19P3Jc18r8/5E8lecy27lvW8//P/2zj/2q6qM4693lBDOxMZSScAcTqMtzdC5dAnBNFNQUgRmKPZrmcqotsxylkqttMQynVISqQkOjJSSH/6Yhoo6nJpZ1rSZmWjyw1B+xfLpj+d88HK5n8+9nx/f28rntd3B59xz7nm+zz33Puee85zz4OPmjwD98GHXayUNNLPZbdTXF+3mgDbqr4Sksfic1KdLsv4c70W/AozCdXSIpCPM7N89EKUTvdetq4HAeGCOpbGpJmwDrsbnZTcCo4Hz8Rf9Sb2WK7EX8HrBvdgADJS0W+o0F5WDLp/Ft7zxSZ+I+5blM7Oi3lLLIkXVNUmvUg5JpT2zJnJOBZ4ysycrlL9pp4qlJcCDwEVkhgNzedrSoZl9M5O8UtJdeC9qZjpaXqZqejf3VtLZuHPIKWa2rqT8cnwMvMHSNDRxoaQfVhyq3XG5grRu2k1PF/LJPS9vBm4zs3ktBTKbnvn5W0l/xOcFxuPD0F3Rhd5r0VViPN6JaznqYGZrgHMzSfdKehm4RtKhZvZ4H8gGLd43Tc61Klu1HBDGB2AS8JMK+VSeZQcbeLOnnmUQxb2uKuWMah5nO8mZXEjH4Y4EbWNmJumXwPck9WvSY+1Kh2b2kqQHgMNalG3oLa+fZr2wjuWSNAG4CjjfzBZXKF/EItzJY3+qe701u/97Ut5uinYRLmtvbZGGzJYCz1PutVnEMvxL8jB6YHyaUKb3WnSVYQrwjJmt7qDsItyh5jB8JKLXbAD2KHiuBwGbzWx7i3KNfFmajU4U8paf8zGzn5qZyo42L/s0uTFTSbvhn/WtvqCeBoam+Y0sBwMPdSjnqXgno+P1AommvZke6rBVHZtwr7b811/j9y567UQuSR/BdXWtmV1eQeYy2ulNF7WbobgHUlm7Kfoqbja/0TZp+OjXuOfWCel+tEVm2KmObVWa1dHnumqQvrzbmWvN09f6ehofrhyRSy/TxbPAdoqfxTdwj9RS3vLGp49YChwuaXgmbQLQH+/9NaPhHz+xkSBpCL7+oMr6nCKmAo+Y2bOdFJakJM8TPRqnL6pjb+Ao4NGSrEuBidp50eVk3Cj9vgdyfAB/wS7D1y50wyn4Go12YkItBY6TtEcmbTK+huW+knL7pLUXAEgahXd2Om03O0jr1hYCBwLHm9k/OrzOx/EhqLL73A1leu9TXeWYiD/znRqfU9O/faWvB/H5pUmNhMwcVVNdmNk2fJ3epNypycAqM/tnpdqr+mTHscOXfSTeKD6F90h+nH4fk8nzDvxl+Ci++Goq8BJwU+5adwN359Kuwx+eabiL5kO4N8qADmQdgnuzzGxy/hh8XVFW9vvwF++x+MNzB96bmdAj/X0Q+A2+RmMMcCbey1oPDCuRbQQ+bHNzKvtVvAfW1RqodO334EbseXyy98jMMTKTbzi7rsW6FZ8cPh44EbgxtY3z2pRhL3wS/U58qPTz6e+dlcv3DHB9Lm0ZPsz0SdzB5E/Ayh7dsznp75mR08uRQP+itpxkn4MPgX0MXzz5KvAw0K9HcpXqvW5dFdTzeJNzO8mFD4v/IMk0Dl+UugW4tYv6B+LvplOBVcBTmd8DU54LcG/Kc4Cx6dlcC+yduc4Zqc0Pz6QdndKuTM/LZfh74tjK8vVa4f/vR2okVnDcm8u3Hz6u/TqwDvdkGZjLc29Buf74bgivAJvwl//7OpR1Jm58hjQ5PzrJPjqTdn16MLek+lfivd1e6e+96W9ag697WpdeIgeXyZbSj8a9m7YCzwEzeiRXo76W95Y3FwNOz6R9J73ANie9PQpM61COkcA96TprgEvJvazT3z0vlzYI+Bn+gt+IG+hdFod2KNNzLXSzf1Fbxl9kD6T7ux037D8C9uxhWyrVe926ytQxOP3dX2uh03mZ31OA1fiiz3/hxukSknHvUIZGW21134R7m76QdLgS+FDuOtOzZTLpJ+Od7G14B3JKO/LFrtZBEARB7cScTxAEQVA7YXyCIAiC2gnjEwRBENROGJ8gCIKgdsL4BEEQBLUTxicIgiConTA+QfA/SCbs8on/bVmCoBPC+ARBEAS1E8YnCIIgqJ0wPkHQAZIGSXpB0g259Nsl/Tlt0Jgvs7ukTZK+WHButaQb0//3TVE//yJpS7rerLQzeiuZTNK5ubRvSVqbSxsmaYGk9ZlIsgfl8lwg6RlJWyW9LGmZpH3KNRME1QjjEwQdYGavAp8Bpkk6GUDSWcAJ+L5vmwvKbMJ3zZ6cTZd0APBh4JaUNBjfaPXL+OaylwNn4TGGuiLF5LkfOAj4Ar7x5+7AXY2QzZLOAL6O7zF4HHA2vtdYPtRHEHRMBJMLgg4xs+WS5gDXSforMBv4vpk92KLYAmCRpCFm9mJKm4wH6FqRrvskvgs0ACnQ3iZgrqTzrDi0cVW+hBuRQ81sfeb6z+Fhsa8GjgBWmNk1mXK9CqEeBEB8+QRBt3wFNwyr8J2BLwKPgyTp7Zmj8awtxXc6z8ZCmQwsbhiVVHampD9I2oLvjvwLfMfzYV3KOw4P2bCxIRvwGr4j9KiU53HgE5IulnRELn5SEPSEMD5B0AVm9jo+lNYfj8+yLZ06EzcajWNuyr8VuI009JbmWg5h50izM/HYLouBk/AvkXPSuQFdijw41b09d4wBhqY8c/Fht9Pw+DsvS7o0jFDQS2LYLQi6IEXBPBt4DLhQ0nwzewlYAhyeyZqd9L8FWCJpGG4IXsFj+DSYBCw0s29k6hlZQZxteJjrLO/O/V4P3I7HCcrzGoCZvYEPIc5OYbxPB74N/B24toIcQVBKGJ8g6BBJA4AbgOX4V8ITePTOCWa2Dg+kVsQKfI7nNNz4LLKdQ5S/EzckWU6vINILwPsz8r0NjyKa5e5U71NmtqXsgmb2N+C7yZmiigEMgkqE8QmCzpkF7AOMNbPNks4EVkqabmbzmhUys+2SFuPebPsCedfrO4EZkh4GnsUNz4gK8iwGzpH0GB6N9rPAu3J5rsBDwN8j6Sr8a2ZvPGz5/WY2X9J1+BfSQ3hkzTHAgXjI6iDoCTHnEwQdIOko3HPsXDNbA5C83K4ArpS0X8klFuCG50U8dHGWS4D5uHGbj4dVnlFBrIuBhancPNxxYG42g5mtBY7Ewx7Pxr/CLgP2BH6Xsq0CPoqHmr4DmAh8zsx+VUGGIKhEhNEOgiAIaie+fIIgCILaCeMTBEEQ1E4YnyAIgqB2wvgEQRAEtRPGJwiCIKidMD5BEARB7YTxCYIgCGonjE8QBEFQO2F8giAIgtr5DxIWpJAp1rK+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_nice(x,y,title=\"Objective function\",xlabel='x-values',ylabel='Function values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use `optimize.minimize_scalar()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = optimize.minimize_scalar(scalar1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result['success']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum occurs at:  -1.2214484245210282\n"
     ]
    }
   ],
   "source": [
    "print(\"Minimum occurs at: \",result['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: -0.6743051024666711\n",
      "    nfev: 15\n",
      "     nit: 10\n",
      " success: True\n",
      "       x: -1.2214484245210282\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bounded search (bound on the independent variable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = optimize.minimize_scalar(scalar1,bounds=(0,10),method='Bounded')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When bounded between 0 and 10, minimum occurs at:  4.101466164987216\n"
     ]
    }
   ],
   "source": [
    "print(\"When bounded between 0 and 10, minimum occurs at: \",result['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other function-based constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constraint1(x):\n",
    "    return 0.5-np.log10(x**2+2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constraint2(x):\n",
    "    return np.log10(x**2+2) - 1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constraint3(x):\n",
    "    return np.sin(x)+0.3*x**2-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "cons = ({'type':'ineq','fun':constraint1},\n",
    "        {'type':'ineq','fun':constraint2},\n",
    "       {'type':'eq','fun':constraint3})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = optimize.minimize(scalar1,x0=0,method='SLSQP',constraints=cons,options={'maxiter':100})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: 0.7631695862891654\n",
      "     jac: array([0.59193639])\n",
      " message: 'Iteration limit exceeded'\n",
      "    nfev: 1254\n",
      "     nit: 101\n",
      "    njev: 101\n",
      "  status: 9\n",
      " success: False\n",
      "       x: array([0.8773752])\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = optimize.minimize(scalar1,x0=-20,method='SLSQP',constraints=cons,options={'maxiter':100})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: -0.28594944567686104\n",
      "     jac: array([-0.46750661])\n",
      " message: 'Iteration limit exceeded'\n",
      "    nfev: 1233\n",
      "     nit: 101\n",
      "    njev: 101\n",
      "  status: 9\n",
      " success: False\n",
      "       x: array([-2.37569791])\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = optimize.minimize(scalar1,x0=-20,method='SLSQP',constraints=cons,options={'maxiter':3})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: -0.4155114388552631\n",
      "     jac: array([-0.46860977])\n",
      " message: 'Iteration limit exceeded'\n",
      "    nfev: 12\n",
      "     nit: 4\n",
      "    njev: 4\n",
      "  status: 9\n",
      " success: False\n",
      "       x: array([-2.10190632])\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multi-variate case: Sum of Gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = [-1,0.3,2.1]\n",
    "sigma = [2.1,0.8,1.7]\n",
    "add=np.zeros(1000)\n",
    "plt.figure(figsize=(8,5))\n",
    "for m,s in zip(mu,sigma):\n",
    "    x=np.arange(-5,5,0.01)\n",
    "    y=np.exp(-(x-m)**2/(2*s**2))\n",
    "    add+=y\n",
    "    plot_nice(x,y,show=False)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_nice(x=np.arange(-5,5,0.01),y=add)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian(m,s):\n",
    "    x = np.arange(-5,5,0.01)\n",
    "    return np.exp(-(x-m)**2/(2*s**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian_mixture(x):\n",
    "    \"\"\"\n",
    "    Computes the resultant Gaussian mixture from an input vector and known mean, variance quantities\n",
    "    \"\"\"\n",
    "    return -(np.exp(-(x[0]+1)**2/(2.1**2))+np.exp(-(x[1]-0.3)**2/(0.8**2))+np.exp(-(x[2]-2.1)**2/(1.7**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0233691172715331"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian_mixture(np.array([3,-2,2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([0]*3)\n",
    "result = optimize.minimize(gaussian_mixture,x0=x0,method='SLSQP',options={'maxiter':100})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -2.999999618263914\n",
       "     jac: array([-8.10027122e-05, -2.40206718e-04,  7.11023808e-04])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 42\n",
       "     nit: 8\n",
       "    njev: 8\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([-1.00017856,  0.29992313,  2.10102744])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bounds with multiple variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([0]*3)\n",
    "x1_bound = (-2,2)\n",
    "x2_bound = (0,5)\n",
    "x3_bound = (-3,0)\n",
    "result = optimize.minimize(gaussian_mixture,x0=x0,method='SLSQP',options={'maxiter':100},\n",
    "                           bounds=(x1_bound,x2_bound,x3_bound))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -2.217414055755018\n",
       "     jac: array([-2.89082527e-06,  3.60012054e-04, -3.15965086e-01])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 31\n",
       "     nit: 6\n",
       "    njev: 6\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([-1.00000644e+00,  3.00115191e-01, -8.03574200e-17])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  }
 ],
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