updated sensitivity intro notebook

sensitivity_examples.py

@@ -16,8 +16,6 @@
 import pandas as pd
 from _operator import index
 
-cp.Sens_m
-
 # start the linear model
 def linear_model(w, z):
     return np.sum(w*z, axis=1)
@@ -68,8 +66,7 @@ def evaluate_linear_model(A, B, C, w):
     # Set mean (column 0) and standard deviations (column 1) for each factor z. Nrv=nr. rows
     Nrv = 4  # number of random variables 
     zm = np.array([[0., i] for i in range(1, Nrv + 1)])
-
-    # TODO: LR decide if the following lines should be kept
+    # The above "list comprehension" is equivalent to  thenext four lines 
     # zm = np.zeros((Nrv, 2))
     # zm[0, 1] = 1
     # zm[1, 1] = 2
@@ -113,7 +110,7 @@ def evaluate_linear_model(A, B, C, w):
 
     print("\nTheoretical sensitivity indices\n")
     row_labels= ['S_'+str(idx) for idx in range(1,Nrv+1)]
-    print(pd.DataFrame(s**2, columns=['S anal'],index=row_labels).round(3))
+    print(pd.DataFrame(s**2, columns=['S analytic'],index=row_labels).round(3))
 
 
     #  Expectation and variance from sampled values

sensitivity_introduction.ipynb

@@ -42,7 +42,9 @@
     "plt.style.use(\"ggplot\")\n",
     "# import seaborn as sns # sets another style\n",
     "matplotlib.rcParams['lines.linewidth'] = 3\n",
-    "matplotlib.rcParams['figure.figsize'] = (7.0,5.0)\n",
+    "fig_width, fig_height = (7.0,5.0)\n",
+    "\n",
+    "matplotlib.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
     "\n",
     "# font = {'family' : 'sans-serif',\n",
     "#         'weight' : 'normal',\n",
@@ -66,9 +68,7 @@
     "from monte_carlo import generate_sample_matrices_mc\n",
     "from monte_carlo import calculate_sensitivity_indices_mc\n",
     "import pandas as pd\n",
-    "from _operator import index\n",
-    "\n",
-    "cp.Sens_m"
+    "from _operator import index"
    ]
   },
   {
@@ -225,8 +225,7 @@
     "    # Set mean (column 0) and standard deviations (column 1) for each factor z. Nrv=nr. rows\n",
     "    Nrv = 4  # number of random variables \n",
     "    zm = np.array([[0., i] for i in range(1, Nrv + 1)])\n",
-    "\n",
-    "    # TODO: LR decide if the following lines should be kept\n",
+    "    # The above \"list comprehension\" is equivalent to  thenext four lines \n",
     "    # zm = np.zeros((Nrv, 2))\n",
     "    # zm[0, 1] = 1\n",
     "    # zm[1, 1] = 2\n",
@@ -340,8 +339,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Note that the assumption of independent factors $Z_i$, we may sample\n",
-    "each $Z_i$ independently from their marginal distributions and store\n",
+    "Note that the assumption of independent factors $Z_i$ allows us to sample\n",
+    "each $Z_i$ independently from its own marginal distribution. We store\n",
     "all the samples for all the factors $Z_i$ in the the numpy array\n",
     "`Z[i,:]`, where $i$ corresponds to $Z_i$ as:"
    ]
@@ -487,7 +486,7 @@
     "\n",
     "$$\n",
     "\\begin{equation}\n",
-    " \\sigma_Y^2 = \\sum_{i=1}^{r} \\left(\\Omega_i^2 \\, \\sigma_{Z_i}\\right)^2\n",
+    " \\sigma_Y^2 = \\sum_{i=1}^{r} \\left(\\Omega_i \\, \\sigma_{Z_i}\\right)^2\n",
     " \\label{eq:Ss_model_ded} \\tag{10}\n",
     "\\end{equation}\n",
     "$$"
@@ -541,7 +540,7 @@
     "    \n",
     "    print(\"\\nTheoretical sensitivity indices\\n\")\n",
     "    row_labels= ['S_'+str(idx) for idx in range(1,Nrv+1)]\n",
-    "    print(pd.DataFrame(s**2, columns=['S anal'],index=row_labels).round(3))"
+    "    print(pd.DataFrame(s**2, columns=['S analytic'],index=row_labels).round(3))"
    ]
   },
   {
@@ -689,7 +688,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Further, the variance the output $Y$ may be decomposed into:"
+    "Further, the variance of the output $Y$ may be decomposed into:"
    ]
   },
   {