Minor updates to PythonSimpleFunctions module 3 notebook (to make matrices in python style in comments)

course/Module01-Entropy/PythonSimpleFunctions/Module_3_notebook.ipynb

@@ -81,14 +81,14 @@
     "        </tr>\n",
     "    </tbody>\n",
     "</table>\n",
-    "where we have a binary $x$ and $y$ we have <code>p=np.array([[0.2, 0.3],[0.1,0.4]])</code> where $p(x=0,y=0) = 0.2$, $p(x=0,y=1) = 0.3$, $p(x=1,y=0) = 0.1$, and $p(x=1,y=1) = 0.4$. If the variable $x$ can take more than two values for example, then we will have more than two rows in <code>p</code> (e.g. <code>p = [0.15, 0.1; 0.1, 0.3; 0.15, 0.2]</code>).\n",
+    "where we have a binary $x$ and $y$ we have <code>p=np.array([[0.2, 0.3],[0.1,0.4]])</code> where $p(x=0,y=0) = 0.2$, $p(x=0,y=1) = 0.3$, $p(x=1,y=0) = 0.1$, and $p(x=1,y=1) = 0.4$. If the variable $x$ can take more than two values for example, then we will have more than two rows in <code>p</code> (e.g. <code>p = np.array([[0.15, 0.1], [0.1, 0.3], [0.15, 0.2]])</code>).\n",
     "\n",
     "1. To fill in the template, you will need to call your existing functions `jointentropy(p)` for $H(X,Y)$ and `entropy(p)` for $H(X)$ and $H(Y)$ to provide the calculations needed. Note that to compute $H(Y)$ you will need to extract $p(y)$ from the $p(x,y)$ matrix by summing over all $x$ rows (as per the activity for conditional entropy in the previous module), whilst for $H(X)$ you will need to extract $p(x)$ from the $p(x,y)$ matrix by summing over all $y$ columns."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -150,7 +150,7 @@
    "source": [
     "2. Test that your code works, e.g. by running:\n",
     "    1. `mutualinformation(np.array([[0.2, 0.3],[ 0.1, 0.4]]))` and validating that you get the result 0.0349 bits. Recall that the conditional entropy computed for this $p(x,y)$ probability table in the previous module was 0.965 bits - is the result for MI sensible with respect to that result?<br/>\n",
-    "    Confirm that MI is symmetric with respect to the input variables by computing `mutualinformation([0.2, 0.1; 0.3, 0.4])`\n",
+    "    Confirm that MI is symmetric with respect to the input variables by computing `mutualinformation(np.array([[0.2, 0.1], [0.3, 0.4]]))`\n",
     "    1. `mutualinformation(np.array([[0.5, 0],[ 0, 0.5]]))` and validating that you get the result 1 bit.\n",
     "    1. `mutualinformation(np.array([[0.25, 0.25],[ 0.25, 0.25]]))` and validating that you get the result 0 bits. Can you explain this and the previous result?"
    ]

course/Module01-Entropy/PythonSimpleFunctions/completed/Module_3_notebook_solutions.ipynb

@@ -81,7 +81,7 @@
     "        </tr>\n",
     "    </tbody>\n",
     "</table>\n",
-    "where we have a binary $x$ and $y$ we have <code>p=np.array([[0.2, 0.3],[0.1,0.4]])</code> where $p(x=0,y=0) = 0.2$, $p(x=0,y=1) = 0.3$, $p(x=1,y=0) = 0.1$, and $p(x=1,y=1) = 0.4$. If the variable $x$ can take more than two values for example, then we will have more than two rows in <code>p</code> (e.g. <code>p = [0.15, 0.1; 0.1, 0.3; 0.15, 0.2]</code>).\n",
+    "where we have a binary $x$ and $y$ we have <code>p=np.array([[0.2, 0.3],[0.1,0.4]])</code> where $p(x=0,y=0) = 0.2$, $p(x=0,y=1) = 0.3$, $p(x=1,y=0) = 0.1$, and $p(x=1,y=1) = 0.4$. If the variable $x$ can take more than two values for example, then we will have more than two rows in <code>p</code> (e.g. <code>p = np.array([[0.15, 0.1], [0.1, 0.3], [0.15, 0.2]])</code>).\n",
     "\n",
     "1. To fill in the template, you will need to call your existing functions `jointentropy(p)` for $H(X,Y)$ and `entropy(p)` for $H(X)$ and $H(Y)$ to provide the calculations needed. Note that to compute $H(Y)$ you will need to extract $p(y)$ from the $p(x,y)$ matrix by summing over all $x$ rows (as per the activity for conditional entropy in the previous module), whilst for $H(X)$ you will need to extract $p(x)$ from the $p(x,y)$ matrix by summing over all $y$ columns."
    ]
@@ -150,7 +150,7 @@
    "source": [
     "2. Test that your code works, e.g. by running:\n",
     "    1. `mutualinformation(np.array([[0.2, 0.3],[ 0.1, 0.4]]))` and validating that you get the result 0.0349 bits. Recall that the conditional entropy computed for this $p(x,y)$ probability table in the previous module was 0.965 bits - is the result for MI sensible with respect to that result?<br/>\n",
-    "    Confirm that MI is symmetric with respect to the input variables by computing `mutualinformation([0.2, 0.1; 0.3, 0.4])`\n",
+    "    Confirm that MI is symmetric with respect to the input variables by computing `mutualinformation(np.array([[0.2, 0.1], [0.3, 0.4]]))`\n",
     "    1. `mutualinformation(np.array([[0.5, 0],[ 0, 0.5]]))` and validating that you get the result 1 bit.\n",
     "    1. `mutualinformation(np.array([[0.25, 0.25],[ 0.25, 0.25]]))` and validating that you get the result 0 bits. Can you explain this and the previous result?"
    ]