Add exercise 13

exercises/ex13/golf_reference.txt

+ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
+AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz
+-----------------------
+| A a B b C c D d E e |
+| F f G g H h I i J j |
+| K k L l M m N n O o |
+| P p Q q R r S s T t |
+| U u V v W w X x Y y |
+| Z z                 |
+-----------------------
+['a: ', 'apple']
+['b']
+['c']
+['d']
+['e']
+['f']
+['g: ', 'grape']
+['h']
+['i']
+['j']
+['k']
+['l: ', 'lemon']
+['m']
+['n']
+['o: ', 'olive']
+['p']
+['q']
+['r']
+['s']
+['t']
+['u']
+['v']
+['w']
+['x']
+['y']
+['z']
+apple begins with a, grape begins with g, lemon begins with l, olive begins with o

exercises/ex13/plot_skeleton.py

+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+#
+# Programming Techniques for Scientific Simulations, HS 2020
+# Exercise 13.2
+
+from __future__ import (division, print_function)
+
+import numpy as np
+import scipy.stats as st
+import scipy.linalg as la
+import matplotlib.pyplot as plt
+
+
+def get_samples(n=500):
+    return np.random.rand(n, 2) * 2 - 1
+
+
+def get_r(samples):
+    return la.norm(samples, axis=1)
+
+
+def calculate_pi(samples):
+    num_inside = np.sum(get_r(samples) < 1.)
+    num_total = len(samples)
+    return 4 * num_inside / num_total
+
+
+def create_scatter_plot(samples):
+    # TODO: Create a scatter plot of the samples.
+    pass
+
+
+def create_contour_plot(samples):
+    density_func = st.gaussian_kde(samples.T, bw_method=0.2)
+    # TODO: Create a contour plot showing the interpolated density.
+    pass
+
+
+def main():
+    np.random.seed(42)
+    samples = get_samples()
+    pi_estimate = calculate_pi(samples)
+    print('Pi ~= {}'.format(pi_estimate))
+
+    create_scatter_plot(samples)
+    create_contour_plot(samples)
+
+
+if __name__ == '__main__':
+    main()