Added chart of multiple Gaussians

code/pf_internal.py

@@ -0,0 +1,55 @@
+import numpy as np
+import pylab as plt
+from matplotlib.patches import Circle, Rectangle, Polygon, Arrow, FancyArrow
+import book_plots
+import numpy as np
+from numpy.random import multivariate_normal
+from nonlinear_plots import plot_monte_carlo_mean
+
+def plot_random_pd():
+    def norm(x, x0, sigma):
+        return np.exp(-0.5 * (x - x0) ** 2 / sigma ** 2)
+
+
+    def sigmoid(x, x0, alpha):
+        return 1. / (1. + np.exp(- (x - x0) / alpha))
+
+    x = np.linspace(0, 1, 100)
+    y2 =  (0.1 * np.sin(norm(x, 0.2, 0.05)) +  0.25 * norm(x, 0.6, 0.05) + 
+           np.sqrt(norm(x, 0.8, 0.06)) +0.1 * (1 - sigmoid(x, 0.45, 0.15)))
+    plt.xkcd()
+    #plt.setp(plt.gca().get_xticklabels(), visible=False)
+    #plt.setp(plt.gca().get_yticklabels(), visible=False)
+    plt.axes(xticks=[], yticks=[], frameon=False)
+    plt.plot(x, y2)
+
+def plot_monte_carlo_ukf():
+
+    def f(x,y):
+        return x+y, .1*x**2 + y*y
+       
+    mean = (0, 0)
+    p = np.array([[32, 15], [15., 40.]])
+
+    # Compute linearized mean
+    mean_fx = f(*mean)
+
+    #generate random points
+    xs, ys = multivariate_normal(mean=mean, cov=p, size=3000).T
+    fxs, fys = f(xs, ys)
+ 
+    plt.subplot(121)
+    plt.gca().grid(b=False)
+     
+    plt.scatter(xs, ys, marker='.', alpha=.2, color='k')
+    plt.xlim(-25, 25)
+    plt.ylim(-25, 25)
+
+    plt.subplot(122)
+    plt.gca().grid(b=False)
+
+    plt.scatter(fxs, fys, marker='.', alpha=0.2, color='k')
+                
+    plt.ylim([-10, 200])
+    plt.xlim([-100, 100])
+    plt.show()