Formatting and experiments.

Let this check in get away from me. Bunch of small formatting sttuf
in the various chapters, some experimental animations and code, etc.
Not a clearly delineated check in.

code/nonlinear_plots.py

@@ -1,62 +1,78 @@
-# -*- coding: utf-8 -*-
-"""
-Created on Sun May 18 11:09:23 2014
-
-@author: rlabbe
-"""
-
-from __future__ import division
-import numpy as np
-import matplotlib.pyplot as plt
-
-
-def plot_transfer_func(data, f, lims, num_bins=1000):
-    ys = f(data)
-    
-    
-    h = np.histogram(ys, num_bins, density=False)
-   
-    #plot output
-    plt.subplot(2,2,1)
-    plt.plot(h[0], h[1][1:], lw=4)
-    plt.ylim(lims)
-    plt.gca().xaxis.set_ticklabels([])
-    plt.title('output')
-
-    plt.axhline(np.mean(ys), ls='--', lw=2)
-
-    # plot transfer function
-    plt.subplot(2,2,2)
-    x = np.arange(lims[0], lims[1],0.1)
-    y = f(x)
-    plt.plot (x,y)
-    isct = f(0)
-    plt.plot([0,0,lims[0]],[lims[0],isct,isct],c='r')
-    plt.xlim(lims)
-    plt.ylim(lims)
-    plt.title('transfer function')
-
-    # plot input
-    h = np.histogram(data, num_bins, density=True)
-
-    plt.subplot(2,2,4)
-    plt.plot(h[1][1:], h[0], lw=4)
-    plt.xlim(lims)
-    plt.gca().yaxis.set_ticklabels([])
-    plt.title('input')
-
-    plt.show()
-
-
-
-if __name__ == "__main__":
-    from numpy.random import normal
-    import numpy as np
-
-    data = normal(loc=0.0, scale=1, size=500000)
-
-    def g(x):
-        return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x
-
-
-    plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
+# -*- coding: utf-8 -*-
+"""
+Created on Sun May 18 11:09:23 2014
+
+@author: rlabbe
+"""
+
+from __future__ import division
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def plot_transfer_func(data, f, gaussian, num_bins=300):
+    ys = f(data)
+    x0 = gaussian[0]
+    in_std = np.sqrt(gaussian[1])
+    y = f(x0)
+    m = np.mean(ys)
+    std = np.std(ys)
+    
+    in_lims = [x0-in_std*3, x0+in_std*3]
+    out_lims = [y-std*3, y+std*3]
+    
+
+   
+    #plot output
+    h = np.histogram(ys, num_bins, density=False)
+    plt.subplot(2,2,4)
+    plt.plot(h[0], h[1][1:], lw=4)
+    plt.ylim(out_lims[1], out_lims[0])
+    plt.gca().xaxis.set_ticklabels([])
+    plt.title('output')
+
+    plt.axhline(np.mean(ys), ls='--', lw=2)
+    plt.axhline(f(x0), lw=1)
+
+    # plot transfer function
+    plt.subplot(2,2,3)
+    x = np.arange(in_lims[0], in_lims[1], 0.1)
+    y = f(x)
+    plt.plot (x,y)
+    isct = f(x0)
+    plt.plot([x0, x0, in_lims[1]], [out_lims[1], isct, isct], color='r', lw=1)
+    plt.xlim(in_lims)
+    plt.ylim(out_lims)
+    #plt.axis('equal')
+    plt.title('function')
+
+    # plot input
+    h = np.histogram(data, num_bins, density=True)
+
+    plt.subplot(2,2,1)
+    plt.plot(h[1][1:], h[0], lw=4)
+    plt.xlim(in_lims)
+    plt.gca().yaxis.set_ticklabels([])
+    plt.title('input')
+
+    plt.show()
+
+
+
+if __name__ == "__main__":
+    from numpy.random import normal
+    import numpy as np
+
+    x0 = (1, 1)
+    data = normal(loc=x0[0], scale=x0[1], size=500000)
+
+    def g(x):
+        return x*x
+        return (np.cos(3*(x/2+0.7)))*np.sin(0.7*x)-1.6*x
+        return -2*x
+
+
+    #plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
+    plot_transfer_func (data, g, gaussian=x0,                        
+                        num_bins=100)
+    

experiments/bicycle.py

@@ -1,46 +1,43 @@
-# -*- coding: utf-8 -*-
-"""
-Created on Tue Apr 28 08:19:21 2015
-
-@author: Roger
-"""
-
-
-from math import *
-import numpy as np
-import matplotlib.pyplot as plt
-
-wheelbase = 100 #inches
-
-vel = 20 *12  # fps to inches per sec
-steering_angle = radians(1)
-t = 1 # second
-orientation = 0. # radians
-
-pos = np.array([0., 0.])
-
-
-for i in range(100):
-#if abs(steering_angle) > 1.e-8:
-    dist = vel*t
-    turn_radius = tan(steering_angle)
-    radius = wheelbase / tan(steering_angle)
-    
-    arc_len = dist / (2*pi*radius)
-    
-    turn_angle = 2*pi * arc_len
-    
-    
-    cx = pos[0] - (sin(orientation) * radius)
-    cy = pos[1] + (cos(orientation) * radius)
-    
-    orientation = (orientation + turn_angle) % (2.0 * pi)
-    pos[0] = cx + (sin(orientation) * radius)
-    pos[1] = cy - (cos(orientation) * radius)
-
-    plt.scatter(pos[0], pos[1])
-
-plt.axis('equal')
-   
-   
-   
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Apr 28 08:19:21 2015
+
+@author: Roger
+"""
+
+
+from math import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+wheelbase = 100 #inches
+
+vel = 20 *12  # fps to inches per sec
+steering_angle = radians(1)
+t = 1 # second
+orientation = 0. # radians
+
+pos = np.array([0., 0.]
+
+for i in range(100):
+#if abs(steering_angle) > 1.e-8:
+    dist = vel*t
+    turn_radius = tan(steering_angle)
+    radius = wheelbase / tan(steering_angle)
+
+    arc_len = dist / (2*pi*radius)
+
+    turn_angle = 2*pi * arc_len
+
+
+    cx = pos[0] - (sin(orientation) * radius)
+    cy = pos[1] + (cos(orientation) * radius)
+
+    orientation = (orientation + turn_angle) % (2.0 * pi)
+    pos[0] = cx + (sin(orientation) * radius)
+    pos[1] = cy - (cos(orientation) * radius)
+
+    plt.scatter(pos[0], pos[1])
+
+plt.axis('equal')
+