fixes due to code directory

code/mkf_internal.py

@@ -0,0 +1,189 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May  1 16:56:49 2014
+
+@author: rlabbe
+"""
+import numpy as np
+from matplotlib.patches import Ellipse
+import matplotlib.pyplot as plt
+from matplotlib import cm
+from mpl_toolkits.mplot3d import Axes3D
+
+import stats
+
+def show_residual_chart():
+    plt.xlim([0.9,2.5])
+    plt.ylim([1.5,3.5])
+
+    plt.scatter ([1,2,2],[2,3,2.3])
+    plt.scatter ([2],[2.8],marker='o')
+    ax = plt.axes()
+    ax.annotate('', xy=(2,3), xytext=(1,2),
+                arrowprops=dict(arrowstyle='->', ec='#004080',
+                                lw=2,
+                                shrinkA=3, shrinkB=4))
+    ax.annotate('prediction', xy=(2.04,3.), color='#004080')
+    ax.annotate('measurement', xy=(2.05, 2.28))
+    ax.annotate('prior estimate', xy=(1, 1.9))
+    ax.annotate('residual', xy=(2.04,2.6), color='#e24a33')
+    ax.annotate('new estimate', xy=(2,2.8),xytext=(2.1,2.8),
+                arrowprops=dict(arrowstyle='->', ec="k", shrinkA=3, shrinkB=4))
+    ax.annotate('', xy=(2,3), xytext=(2,2.3),
+                arrowprops=dict(arrowstyle="-",
+                                ec="#e24a33",
+                                lw=2,
+                                shrinkA=5, shrinkB=5))
+    plt.title("Kalman Filter Prediction Update Step")
+    plt.axis('equal')
+    plt.show()
+
+
+def show_position_chart():
+    """ Displays 3 measurements at t=1,2,3, with x=1,2,3"""
+
+    plt.scatter ([1,2,3], [1,2,3], s=128, color='#004080')
+    plt.xlim([0,4]);
+    plt.ylim([0,4])
+
+    plt.xlabel("Position")
+    plt.ylabel("Time")
+
+    plt.xticks(np.arange(1,4,1))
+    plt.yticks(np.arange(1,4,1))
+    plt.show()
+
+
+def show_position_prediction_chart():
+    """ displays 3 measurements, with the next position predicted"""
+
+    plt.scatter ([1,2,3], [1,2,3], s=128, color='#004080')
+
+    plt.xlim([0,5])
+    plt.ylim([0,5])
+
+    plt.xlabel("Position")
+    plt.ylabel("Time")
+
+    plt.xticks(np.arange(1,5,1))
+    plt.yticks(np.arange(1,5,1))
+
+    plt.scatter ([4], [4], c='g',s=128, color='#8EBA42')
+    ax = plt.axes()
+    ax.annotate('', xy=(4,4), xytext=(3,3),
+                arrowprops=dict(arrowstyle='->',
+                                ec='g',
+                                shrinkA=6, shrinkB=5,
+                                lw=3))
+    plt.show()
+
+
+def show_x_error_chart():
+    """ displays x=123 with covariances showing error"""
+
+    cov = np.array([[0.003,0], [0,12]])
+    sigma=[0.5,1.,1.5,2]
+    e = stats.covariance_ellipse (cov)
+
+    stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
+    stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
+    stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)
+
+
+    plt.ylim([0,11])
+    plt.xticks(np.arange(1,4,1))
+
+    plt.xlabel("Position")
+    plt.ylabel("Time")
+
+    plt.show()
+
+
+def show_x_with_unobserved():
+    """ shows x=1,2,3 with velocity superimposed on top """
+
+    # plot velocity
+    sigma=[0.5,1.,1.5,2]
+    cov = np.array([[1,1],[1,1.1]])
+    stats.plot_covariance_ellipse ((2,2), cov=cov, variance=sigma, axis_equal=False)
+
+    # plot positions
+    cov = np.array([[0.003,0], [0,12]])
+    sigma=[0.5,1.,1.5,2]
+    e = stats.covariance_ellipse (cov)
+
+    stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
+    stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
+    stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)
+
+    # plot intersection cirle
+    isct = Ellipse(xy=(2,2), width=.2, height=1.2, edgecolor='r', fc='None', lw=4)
+    plt.gca().add_artist(isct)
+
+    plt.ylim([0,11])
+    plt.xlim([0,4])
+    plt.xticks(np.arange(1,4,1))
+
+    plt.xlabel("Position")
+    plt.ylabel("Time")
+
+    plt.show()
+
+
+
+def plot_3d_covariance(mean, cov):
+    """ plots a 2x2 covariance matrix positioned at mean. mean will be plotted
+    in x and y, and the probability in the z axis.
+
+    Parameters
+    ----------
+    mean :  2x1 tuple-like object
+        mean for x and y coordinates. For example (2.3, 7.5)
+
+    cov : 2x2 nd.array
+       the covariance matrix
+
+    """
+
+    # compute width and height of covariance ellipse so we can choose
+    # appropriate ranges for x and y
+    o,w,h = stats.covariance_ellipse(cov,3)
+    # rotate width and height to x,y axis
+    wx = abs(w*np.cos(o) + h*np.sin(o))*1.2
+    wy = abs(h*np.cos(o) - w*np.sin(o))*1.2
+
+
+    # ensure axis are of the same size so everything is plotted with the same
+    # scale
+    if wx > wy:
+        w = wx
+    else:
+        w = wy
+
+    minx = mean[0] - w
+    maxx = mean[0] + w
+    miny = mean[1] - w
+    maxy = mean[1] + w
+
+    xs = np.arange(minx, maxx, (maxx-minx)/40.)
+    ys = np.arange(miny, maxy, (maxy-miny)/40.)
+    xv, yv = np.meshgrid (xs, ys)
+
+    zs = np.array([100.* stats.multivariate_gaussian(np.array([x,y]),mean,cov) \
+                   for x,y in zip(np.ravel(xv), np.ravel(yv))])
+    zv = zs.reshape(xv.shape)
+
+    ax = plt.figure().add_subplot(111, projection='3d')
+    ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)
+
+    ax.set_xlabel('X')
+    ax.set_ylabel('Y')
+
+    ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)
+    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)
+
+
+if __name__ == "__main__":
+    #show_position_chart()
+    #plot_3d_covariance((2,7), np.array([[8.,0],[0,4.]]))
+    show_residual_chart()