[simulations] figure with normally distributed data

.gitignore

@@ -23,4 +23,6 @@
 *~
 *.zip
 *.vrb
+__*
 pointprocesses/lecture/pointprocessscetch*.tex
+

plotstyle.py

@@ -12,6 +12,31 @@ colors = {
 }
 
 
+def cm_size(*args):
+    """ Convert dimensions from cm to inch.
+
+    Use this function to set the size of a figure in centimeter:
+    ```
+    fig = plt.figure(figsize=cm_size(16.0, 10.0))
+    ```
+
+    Parameters
+    ----------
+    args: one or many float
+        Size in centimeter.
+
+    Returns
+    -------
+    inches: float or list of floats
+        Input arguments converted to inch.
+    """
+    inch_per_cm = 2.54
+    if len(args) == 1:
+        return args[0]/inch_per_cm
+    else:
+        return [v/inch_per_cm for v in args]
+
+
 def show_spines(ax, spines):
     """ Show and hide spines.
 

simulations/lecture/normaldata.py

@@ -0,0 +1,47 @@
+import numpy as np
+import scipy.stats as st
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+from plotstyle import colors, cm_size, show_spines
+
+if __name__ == "__main__":
+    # wikipedia:
+    # Generally, males vary in total length from 250 to 390 cm and
+    # weigh between 90 and 306 kg
+    n = 300
+    mu = 200.0
+    sigma = 50.0
+    rng = np.random.RandomState(22281)
+    indices = np.arange(n)
+    data = 50.0*rng.randn(len(indices))+200.0
+
+    fig = plt.figure(figsize=cm_size(16.0, 8.0))
+    spec = gridspec.GridSpec(nrows=1, ncols=2, width_ratios=[3, 1],
+                             left=0.12, bottom=0.17, right=0.97, top=0.98, wspace=0.08)
+    ax1 = fig.add_subplot(spec[0, 0])
+    show_spines(ax1, 'lb')
+    ax1.scatter(indices, data, c=colors['blue'], edgecolor='white', s=50)
+    ax1.set_xlabel('index')
+    ax1.set_ylabel('Weight / kg')
+    ax1.set_xlim(-10, 310)
+    ax1.set_ylim(0, 350)
+    ax1.set_yticks(np.arange(0, 351, 100))
+    
+    ax2 = fig.add_subplot(spec[0, 1])
+    show_spines(ax2, 'lb')
+    xx = np.arange(0.0, 350.0, 0.5)
+    yy = st.norm.pdf(xx, mu, sigma)
+    ax2.plot(yy, xx, color=colors['red'])
+    bw = 25.0
+    h, b = np.histogram(data, np.arange(0, 351, bw))
+    ax2.barh(b[:-1], h/np.sum(h)/(b[1]-b[0]), fc=colors['yellow'], height=0.9*bw, align='edge')
+    ax2.set_xlabel('pdf / 1/kg')
+    ax2.set_xlim(0, 0.01)
+    ax2.set_xticks([0, 0.005, 0.01])
+    ax2.set_xticklabels(['0', '0.005', '0.01'])
+    ax2.set_ylim(0, 350)
+    ax2.set_yticks(np.arange(0, 351, 100))
+    ax2.set_yticklabels([])
+
+    fig.savefig("normaldata.pdf")
+    plt.close()

simulations/lecture/simulations.tex

@@ -45,6 +45,16 @@ mean we just add the desired mean $\mu$ to the random numbers:
   x_i = \sigma \xi_i + \mu
 \end{equation}
 
+\begin{figure}[t]
+  \includegraphics[width=1\textwidth]{normaldata}
+  \titlecaption{\label{normaldatafig} Generating normally distributed
+    data.}{With the help of a computer the weight of 300 tigers can be
+    measured in no time using the \code{randn()} function (left).  We
+    then even now the population distribution, its mean and standard
+    deviation from which the simulated data values were drawn (red
+    line, right).}
+\end{figure}
+
 \begin{exercise}{normaldata.m}{normaldata.out}
   First, read the documentation of the \varcode{randn()} function and
   check its output for some (small) input arguments.  Write a little