typos

2020-01-02 11:07:07 +01:00
parent 5456959e12
commit 011f787528
8 changed files with 18 additions and 12 deletions
@@ -228,7 +228,7 @@ Note that the function <b>multivariate</b> returns also the covariance discussed
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">IPython.display</span> <span style="color: #008000; font-weight: bold">import</span> display
 n <span style="color: #666666">=</span> <span style="color: #666666">10000</span>
 mean <span style="color: #666666">=</span> (<span style="color: #666666">-1</span>, <span style="color: #666666">2</span>)
@@ -299,7 +299,8 @@ Our own code here is not very elegant and asks for improvements.
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># extract the relevant columns from the centered design matrix of dim n x 2</span>
+x <span style="color: #666666">=</span> X_centered[:,<span style="color: #666666">0</span>]
 y <span style="color: #666666">=</span> X_centered[:,<span style="color: #666666">1</span>]
 Cov <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #666666">2</span>,<span style="color: #666666">2</span>))
 Cov[<span style="color: #666666">0</span>,<span style="color: #666666">1</span>] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum(x<span style="color: #666666">.</span>T<span style="color: #AA22FF">@y</span>)<span style="color: #666666">/</span>(n<span style="color: #666666">-1.0</span>)
@@ -1034,7 +1034,7 @@ Note that the function <b>multivariate</b> returns also the covariance discussed
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
 <div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
-<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">IPython.display</span> <span style="color: #8B008B; font-weight: bold">import</span> display
 n = <span style="color: #B452CD">10000</span>
 mean = (-<span style="color: #B452CD">1</span>, <span style="color: #B452CD">2</span>)
@@ -1111,7 +1111,8 @@ Our own code here is not very elegant and asks for improvements.
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]</span>
+<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># extract the relevant columns from the centered design matrix of dim n x 2</span>
+x = X_centered[:,<span style="color: #B452CD">0</span>]
 y = X_centered[:,<span style="color: #B452CD">1</span>]
 Cov = np.zeros((<span style="color: #B452CD">2</span>,<span style="color: #B452CD">2</span>))
 Cov[<span style="color: #B452CD">0</span>,<span style="color: #B452CD">1</span>] = np.sum(x.T<span style="color: #707a7c">@y</span>)/(n-<span style="color: #B452CD">1.0</span>)
@@ -1014,7 +1014,7 @@ Note that the function <b>multivariate</b> returns also the covariance discussed
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
 <div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
-<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">IPython.display</span> <span style="color: #8B008B; font-weight: bold">import</span> display
 n = <span style="color: #B452CD">10000</span>
 mean = (-<span style="color: #B452CD">1</span>, <span style="color: #B452CD">2</span>)
@@ -1085,7 +1085,8 @@ Our own code here is not very elegant and asks for improvements.
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># extract the relevant columns from the centered design matrix of dim n x 2</span>
+x = X_centered[:,<span style="color: #B452CD">0</span>]
 y = X_centered[:,<span style="color: #B452CD">1</span>]
 Cov = np.zeros((<span style="color: #B452CD">2</span>,<span style="color: #B452CD">2</span>))
 Cov[<span style="color: #B452CD">0</span>,<span style="color: #B452CD">1</span>] = np.sum(x.T<span style="color: #707a7c">@y</span>)/(n-<span style="color: #B452CD">1.0</span>)
@@ -1019,7 +1019,7 @@ Note that the function <b>multivariate</b> returns also the covariance discussed
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">IPython.display</span> <span style="color: #008000; font-weight: bold">import</span> display
 n <span style="color: #666666">=</span> <span style="color: #666666">10000</span>
 mean <span style="color: #666666">=</span> (<span style="color: #666666">-1</span>, <span style="color: #666666">2</span>)
@@ -1090,7 +1090,8 @@ Our own code here is not very elegant and asks for improvements.
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># extract the relevant columns from the centered design matrix of dim n x 2</span>
+x <span style="color: #666666">=</span> X_centered[:,<span style="color: #666666">0</span>]
 y <span style="color: #666666">=</span> X_centered[:,<span style="color: #666666">1</span>]
 Cov <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #666666">2</span>,<span style="color: #666666">2</span>))
 Cov[<span style="color: #666666">0</span>,<span style="color: #666666">1</span>] <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum(x<span style="color: #666666">.</span>T<span style="color: #AA22FF">@y</span>)<span style="color: #666666">/</span>(n<span style="color: #666666">-1.0</span>)
@@ -1107,7 +1107,7 @@
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
-    "import matplotlib as plt\n",
+    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "n = 10000\n",
    "mean = (-1, 2)\n",
@@ -1240,7 +1240,8 @@
   },
   "outputs": [],
   "source": [
-    "# extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]\n",
+    "# extract the relevant columns from the centered design matrix of dim n x 2\n",
+    "x = X_centered[:,0]\n",
    "y = X_centered[:,1]\n",
    "Cov = np.zeros((2,2))\n",
    "Cov[0,1] = np.sum(x.T@y)/(n-1.0)\n",
@@ -781,7 +781,7 @@ Note that the function _multivariate_ returns also the covariance discussed abov
 !bc pycod 
 import numpy as np
 import pandas as pd
-import matplotlib as plt
+import matplotlib.pyplot as plt
 from IPython.display import display
 n = 10000
 mean = (-1, 2)
@@ -844,7 +844,8 @@ print(np.cov(X_centered.T))
 Note that the way we define the covariance matrix here has a factor $n-1$ instead of $n$.
 Our own code here is not very elegant and asks for improvements. 
 !bc pycod
-# extract the relevant columns from the centered design matrix of dim n x 2                                                      x = X_centered[:,0]
+# extract the relevant columns from the centered design matrix of dim n x 2
+x = X_centered[:,0]
 y = X_centered[:,1]
 Cov = np.zeros((2,2))
 Cov[0,1] = np.sum(x.T@y)/(n-1.0)