[simulations] figure for random numbers

plotstyle.py

@@ -102,6 +102,10 @@ def show_spines(ax, spines):
 # initialization:
 plt.xkcd()
 mpl.rcParams['figure.facecolor'] = 'white'
+#mpl.rcParams['axes.spines.left'] = True    # newer matplotlib only
+#mpl.rcParams['axes.spines.bottom'] = True
+#mpl.rcParams['axes.spines.top'] = False
+#mpl.rcParams['axes.spines.right'] = False
 mpl.rcParams['xtick.direction'] = 'out'
 mpl.rcParams['ytick.direction'] = 'out'
 mpl.rcParams['xtick.major.size'] = 6

simulations/lecture/randomnumbers.py

@@ -0,0 +1,65 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+from plotstyle import colors, cm_size, show_spines
+
+if __name__ == "__main__":
+    n = 21
+    nn = 10000
+    maxl = 5
+    
+    indices = np.arange(n)
+    rng = np.random.RandomState(19281)
+    x1 = rng.rand(n)
+    rng = np.random.RandomState(35281)
+    x2 = rng.rand(n)
+    rng = np.random.RandomState(35281)
+    x3 = rng.rand(n)
+
+    x = rng.rand(nn)
+    lags = np.arange(-maxl, maxl+1, 1)
+    corrs = [np.corrcoef(x[maxl:-maxl-1-l], x[maxl+l:-maxl-1])[0, 1] for l in lags]
+
+    fig = plt.figure(figsize=cm_size(16.0, 11.0))
+    spec = gridspec.GridSpec(nrows=2, ncols=2,
+                             left=0.10, bottom=0.12, right=0.98, top=0.97,
+                             wspace=0.4, hspace=0.6)
+    
+    ax = fig.add_subplot(spec[0, 0])
+    show_spines(ax, 'lb')
+    ax.plot(indices, x1, c=colors['blue'], lw=1, zorder=10)
+    ax.scatter(indices, x1, c=colors['blue'], edgecolor='white', s=50, zorder=20)
+    ax.set_xlabel('Index')
+    ax.set_ylabel('Random number')
+    ax.set_xlim(-1.0, n+1.0)
+    ax.set_ylim(-0.05, 1.05)
+    
+    ax = fig.add_subplot(spec[0, 1])
+    show_spines(ax, 'lb')
+    ax.plot(indices, x2, c=colors['blue'], lw=1, zorder=10)
+    ax.scatter(indices, x2, c=colors['blue'], edgecolor='white', s=50, zorder=20)
+    ax.set_xlabel('Index')
+    ax.set_ylabel('Random number')
+    ax.set_xlim(-1.0, n+1.0)
+    ax.set_ylim(-0.05, 1.05)
+    
+    ax = fig.add_subplot(spec[1, 1])
+    show_spines(ax, 'lb')
+    ax.plot(indices, x3, c=colors['blue'], lw=1, zorder=10)
+    ax.scatter(indices, x3, c=colors['blue'], edgecolor='white', s=50, zorder=20)
+    ax.set_xlabel('Index')
+    ax.set_ylabel('Random number')
+    ax.set_xlim(-1.0, n+1.0)
+    ax.set_ylim(-0.05, 1.05)
+    
+    ax = fig.add_subplot(spec[1, 0])
+    show_spines(ax, 'lb')
+    ax.plot(lags, corrs, c=colors['red'], lw=1, zorder=10)
+    ax.scatter(lags, corrs, c=colors['red'], edgecolor='white', s=50, zorder=20)
+    ax.set_xlabel('Lag')
+    ax.set_ylabel('Serial correlation')
+    ax.set_xlim(-maxl-0.5, maxl+0.5)
+    ax.set_ylim(-0.05, 1.05)
+
+    fig.savefig("randomnumbers.pdf")
+    plt.close()

simulations/lecture/simulations.tex

@@ -45,17 +45,25 @@ random numbers is generated by subsequent calls of the random number
 generator. This is in particular useful for plots that involve some
 random numbers but should look the same whenever the script is run.
 
-Figure XXX: three sequences - initial one, second different one with
-seed, third with same seed. Fourth panel with autocorrelation
-function.
-
 \begin{exercise}{}{}
   Generate three times the same sequence of 20 uniformly distributed
   numbers using the \code{rand()} and \code{rng()} functions.
 \end{exercise}
 
+\begin{figure}[t]
+  \includegraphics[width=1\textwidth]{randomnumbers}
+  \titlecaption{\label{randomnumbersfig} Random numbers.}  {Numerical
+    random number generators return sequences of numbers that are as
+    random as possible. The returned values approximate a given
+    probability distribution. Here, for example, a uniform
+    distribution between zero and one (top left). The serial
+    correlation (auto-correlation) of the returned sequences is zero
+    at any lag except for zero (bottom left). However, by setting a
+    seed, defining the state, or spawning the random number generator,
+    the exact same sequence can be generated (right).}
+\end{figure}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 \section{Univariate data}
 The most basic type of simulation is to draw random numbers from a
 given distribution like, for example, the normal distribution. This