Added covariance ellipse animatoin.

Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:1ca55361c7aabbb0d220744306919e1ec1a557e86f8de4612e37ee74aa2390ae"
+  "signature": "sha256:5d9e7c75a6f88ccdf422d155a9c5fb789b7b07e02f1a84790c3c8191465f131b"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -252,6 +252,66 @@
      ],
      "prompt_number": 1
     },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def plot_3d_covariance(ax, mean, cov):\n",
+      "    \"\"\" plots a 2x2 covariance matrix positioned at mean. mean will be plotted\n",
+      "    in x and y, and the probability in the z axis.\n",
+      "\n",
+      "    Parameters\n",
+      "    ----------\n",
+      "    mean :  2x1 tuple-like object\n",
+      "        mean for x and y coordinates. For example (2.3, 7.5)\n",
+      "\n",
+      "    cov : 2x2 nd.array\n",
+      "       the covariance matrix\n",
+      "\n",
+      "    \"\"\"\n",
+      "\n",
+      "    # compute width and height of covariance ellipse so we can choose\n",
+      "    # appropriate ranges for x and y\n",
+      "    o,w,h = stats.covariance_ellipse(cov,3)\n",
+      "    # rotate width and height to x,y axis\n",
+      "    wx = abs(w*np.cos(o) + h*np.sin(o))*1.2\n",
+      "    wy = abs(h*np.cos(o) - w*np.sin(o))*1.2\n",
+      "\n",
+      "\n",
+      "    # ensure axis are of the same size so everything is plotted with the same\n",
+      "    # scale\n",
+      "    if wx > wy:\n",
+      "        w = wx\n",
+      "    else:\n",
+      "        w = wy\n",
+      "\n",
+      "    minx = mean[0] - w\n",
+      "    maxx = mean[0] + w\n",
+      "    miny = mean[1] - w\n",
+      "    maxy = mean[1] + w\n",
+      "\n",
+      "    xs = np.arange(minx, maxx, (maxx-minx)/40.)\n",
+      "    ys = np.arange(miny, maxy, (maxy-miny)/40.)\n",
+      "    xv, yv = np.meshgrid (xs, ys)\n",
+      "\n",
+      "    zs = np.array([100.* stats.multivariate_gaussian(np.array([x,y]),mean,cov) \\\n",
+      "                   for x,y in zip(np.ravel(xv), np.ravel(yv))])\n",
+      "    zv = zs.reshape(xv.shape)\n",
+      "\n",
+      "    ax = plt.figure().add_subplot(111, projection='3d')\n",
+      "    ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
+      "\n",
+      "    ax.set_xlabel('X')\n",
+      "    ax.set_ylabel('Y')\n",
+      "\n",
+      "    ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)\n",
+      "    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 1
+    },
     {
      "cell_type": "code",
      "collapsed": false,

code/gif_animate.py

@@ -8,7 +8,7 @@ Created on Sun Sep 14 12:41:24 2014
 from matplotlib import animation
 import matplotlib.pyplot as plt
 
-def animate(filename, func, frames, interval, figsize=(6.5, 6.5)):
+def animate(filename, func, frames, interval, fig=None, figsize=(6.5, 6.5)):
     """ Creates an animated GIF of a matplotlib.
 
     Parameters
@@ -43,7 +43,8 @@ def animate(filename, func, frames, interval, figsize=(6.5, 6.5)):
             return
         func(frame)
 
-    fig = plt.figure(figsize=figsize)
+    if fig is None:
+        fig = plt.figure(figsize=figsize)
     forward.first = True
     anim = animation.FuncAnimation(fig, forward, frames=frames, interval=interval)
     anim.save(filename, writer='imagemagick')