Added covariance ellipse animatoin.

Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb

@@ -1,7 +1,7 @@
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  "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,

Chapter06_Multivariate_Kalman_Filter/Multivariate_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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   "name": "",
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+  "signature": "sha256:8dd8877926c460a830c170bd1b1320400c48afa047d9fa4f200279e5f3c4a52d"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -259,7 +259,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f45ace4df98>"
+        "<IPython.core.display.HTML at 0x7f56f45d49b0>"
        ]
       }
      ],
@@ -391,7 +391,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0f473f320>"
+        "<matplotlib.figure.Figure at 0x7f56f45d4a58>"
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       }
      ],
@@ -586,7 +586,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0f57b29b0>"
+        "<matplotlib.figure.Figure at 0x7f56f1553320>"
        ]
       }
      ],
@@ -633,12 +633,20 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d13579e8>"
+        "<matplotlib.figure.Figure at 0x7f56d0432a58>"
        ]
       }
      ],
      "prompt_number": 10
     },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "And for those of you viewing this online or in IPython Notebook on your computer, here is an animation.\n",
+      "<img src='ellipse.gif'>"
+     ]
+    },
     {
      "cell_type": "markdown",
      "metadata": {},
@@ -723,7 +731,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d13695c0>"
+        "<matplotlib.figure.Figure at 0x7f56f155c240>"
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@@ -750,7 +758,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d15bd9e8>"
+        "<matplotlib.figure.Figure at 0x7f56d046ab38>"
        ]
       }
      ],
@@ -777,7 +785,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d13f1780>"
+        "<matplotlib.figure.Figure at 0x7f56d0278160>"
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@@ -808,7 +816,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1259f60>"
+        "<matplotlib.figure.Figure at 0x7f56d00fbfd0>"
        ]
       }
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@@ -873,7 +881,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1240978>"
+        "<matplotlib.figure.Figure at 0x7f56d022a438>"
        ]
       }
      ],
@@ -1089,17 +1097,28 @@
      "metadata": {},
      "outputs": [
       {
-       "ename": "NameError",
-       "evalue": "name 'np' is not defined",
-       "output_type": "pyerr",
-       "traceback": [
-        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-2-d764da120a34>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'addition:\\n'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'\\nelement-wise multiplication\\n'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'\\nmultiplication\\n'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'\\ndot is also a member\\n'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-        "\u001b[1;31mNameError\u001b[0m: name 'np' is not defined"
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "addition:\n",
+        " [[ 2.  4.]\n",
+        " [ 6.  8.]]\n",
+        "\n",
+        "element-wise multiplication\n",
+        " [[  1.   4.]\n",
+        " [  9.  16.]]\n",
+        "\n",
+        "multiplication\n",
+        " [[  7.  10.]\n",
+        " [ 15.  22.]]\n",
+        "\n",
+        "dot is also a member\n",
+        " [[  7.  10.]\n",
+        " [ 15.  22.]]\n"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 19
     },
     {
      "cell_type": "markdown",
@@ -1125,6 +1144,7 @@
         "transpose\n",
         " [[ 1.  3.]\n",
         " [ 2.  4.]]\n",
+        "\n",
         "inverse\n",
         " [[-2.   1. ]\n",
         " [ 1.5 -0.5]]\n"
@@ -1342,19 +1362,8 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "ename": "ImportError",
-       "evalue": "No module named 'filterpy'",
-       "output_type": "pyerr",
-       "traceback": [
-        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-1-677e40b1808d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mfilterpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkalman\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mKalmanFilter\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
-        "\u001b[1;31mImportError\u001b[0m: No module named 'filterpy'"
-       ]
-      }
-     ],
-     "prompt_number": 1
+     "outputs": [],
+     "prompt_number": 23
     },
     {
      "cell_type": "heading",
@@ -1919,9 +1928,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d141aa20>"
+        "<matplotlib.figure.Figure at 0x7f56d00f60b8>"
        ]
       },
       {
@@ -1929,7 +1938,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1485c88>"
+        "<matplotlib.figure.Figure at 0x7f56d0448f60>"
        ]
       }
      ],
@@ -2091,9 +2100,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d13c11d0>"
+        "<matplotlib.figure.Figure at 0x7f56d02a1128>"
        ]
       },
       {
@@ -2101,7 +2110,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1267ef0>"
+        "<matplotlib.figure.Figure at 0x7f56d00ecf60>"
        ]
       }
      ],
@@ -2333,9 +2342,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d127cda0>"
+        "<matplotlib.figure.Figure at 0x7f56d0033f60>"
        ]
       }
      ],
@@ -2393,17 +2402,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d14995c0>"
+        "<matplotlib.figure.Figure at 0x7f56d00e22b0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d125e978>"
+        "<matplotlib.figure.Figure at 0x7f56d0118160>"
        ]
       }
      ],
@@ -2516,9 +2525,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d12633c8>"
+        "<matplotlib.figure.Figure at 0x7f56d00fb710>"
        ]
       }
      ],
@@ -2588,7 +2597,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d12f9da0>"
+        "<matplotlib.figure.Figure at 0x7f56d02400f0>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1446fd0>"
+        "<matplotlib.figure.Figure at 0x7f56d00e6dd8>"
        ]
       }
      ],
@@ -2687,7 +2696,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d12b6898>"
+        "<matplotlib.figure.Figure at 0x7f56d041be80>"
        ]
       }
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@@ -2716,7 +2725,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d156e748>"
+        "<matplotlib.figure.Figure at 0x7f56d01488d0>"
        ]
       }
      ],
@@ -2750,7 +2759,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d14e08d0>"
+        "<matplotlib.figure.Figure at 0x7f56d0168fd0>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1231630>"
+        "<matplotlib.figure.Figure at 0x7f56d00e1320>"
        ]
       }
      ],
@@ -2851,17 +2860,17 @@
       {
        "metadata": {},
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d12e9860>"
+        "<matplotlib.figure.Figure at 0x7f56d022aeb8>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d1459828>"
+        "<matplotlib.figure.Figure at 0x7f56d025c470>"
        ]
       }
      ],
@@ -2928,7 +2937,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7ff0d14327f0>"
+        "<matplotlib.figure.Figure at 0x7f56d022d470>"
        ]
       }
      ],

Chapter06_Multivariate_Kalman_Filter/animations.ipynb

@@ -0,0 +1,398 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:a32831d81465dc05ea4e456df090d3ec8c61f145c0cf2ded40441a9b44157792"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from __future__ import division, print_function\n",
+      "%matplotlib inline\n",
+      "import sys\n",
+      "sys.path.insert(0,'../code') # allow us to format the book\n",
+      "\n",
+      "# use same formatting as rest of book so that the plots are\n",
+      "# consistant with that look and feel.\n",
+      "import book_format\n",
+      "book_format.load_style()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "<style>\n",
+        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "\n",
+        "    div.cell{\n",
+        "        width: 850px;\n",
+        "        margin-left: 0% !important;\n",
+        "        margin-right: auto;\n",
+        "    }\n",
+        "    div.text_cell code {\n",
+        "        background: transparent;\n",
+        "        color: #000000;\n",
+        "        font-weight: 600;\n",
+        "        font-size: 11pt;\n",
+        "        font-style: bold;\n",
+        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
+        "   }\n",
+        "    h1 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "\t}\n",
+        "\t\n",
+        "    div.input_area {\n",
+        "        background: #F6F6F9;\n",
+        "        border: 1px solid #586e75;\n",
+        "    }\n",
+        "\n",
+        "    .text_cell_render h1 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 30pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1em;\n",
+        "        display: block;\n",
+        "        white-space: wrap;\n",
+        "    } \n",
+        "    h2 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h2 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 20pt;\n",
+        "        font-style: italic;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    } \n",
+        "    h3 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h3 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 18pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 2em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h4 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h4 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 16pt;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 0.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h5 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h5 {\n",
+        "        font-weight: 300;\n",
+        "        font-style: normal;\n",
+        "        color: #1d3b84;\n",
+        "        font-size: 16pt;\n",
+        "        margin-bottom: 0em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    div.text_cell_render{\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        line-height: 135%;\n",
+        "        font-size: 110%;\n",
+        "        width:750px;\n",
+        "        margin-left:auto;\n",
+        "        margin-right:auto;\n",
+        "        text-align:justify;\n",
+        "        text-justify:inter-word;\n",
+        "    }\n",
+        "    div.output_subarea.output_text.output_pyout {\n",
+        "        overflow-x: auto;\n",
+        "        overflow-y: scroll;\n",
+        "        max-height: 300px;\n",
+        "    }\n",
+        "    div.output_subarea.output_stream.output_stdout.output_text {\n",
+        "        overflow-x: auto;\n",
+        "        overflow-y: scroll;\n",
+        "        max-height: 300px;\n",
+        "    }\n",
+        "    code{\n",
+        "      font-size: 70%;\n",
+        "    }\n",
+        "    .rendered_html code{\n",
+        "    background-color: transparent;\n",
+        "    }\n",
+        "    ul{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li li{\n",
+        "        padding-left: 0.2em; \n",
+        "        margin-bottom: 0.2em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    ol{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ol li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    a:link{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:visited{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:hover{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:focus{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:active{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    .rendered_html :link {\n",
+        "       text-decoration: underline; \n",
+        "    }\n",
+        "    .rendered_html :hover {\n",
+        "       text-decoration: none; \n",
+        "    }\n",
+        "    .rendered_html :visited {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :focus {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :active {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .warning{\n",
+        "        color: rgb( 240, 20, 20 )\n",
+        "    } \n",
+        "    hr {\n",
+        "      color: #f3f3f3;\n",
+        "      background-color: #f3f3f3;\n",
+        "      height: 1px;\n",
+        "    }\n",
+        "    blockquote{\n",
+        "      display:block;\n",
+        "      background: #fcfcfc;\n",
+        "      border-left: 5px solid #c76c0c;\n",
+        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "      width:680px;\n",
+        "      padding: 10px 10px 10px 10px;\n",
+        "      text-align:justify;\n",
+        "      text-justify:inter-word;\n",
+        "      }\n",
+        "      blockquote p {\n",
+        "        margin-bottom: 0;\n",
+        "        line-height: 125%;\n",
+        "        font-size: 100%;\n",
+        "      }\n",
+        "</style>\n",
+        "<script>\n",
+        "    MathJax.Hub.Config({\n",
+        "                        TeX: {\n",
+        "                           extensions: [\"AMSmath.js\"]\n",
+        "                           },\n",
+        "                tex2jax: {\n",
+        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
+        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
+        "                },\n",
+        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
+        "                \"HTML-CSS\": {\n",
+        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
+        "                }\n",
+        "        });\n",
+        "</script>\n"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 1,
+       "text": [
+        "<IPython.core.display.HTML at 0x7fc031d109e8>"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import stats\n",
+      "import numpy as np\n",
+      "from matplotlib.patches import Ellipse\n",
+      "import matplotlib.pyplot as plt\n",
+      "from matplotlib import cm\n",
+      "from mpl_toolkits.mplot3d import Axes3D\n",
+      "\n",
+      "# this code lets me animate the 3d covariance. to be honest I do not find it\n",
+      "# very instructive or compelling so I am not using it for now.\n",
+      "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",
+      "    #print (minx, maxx, miny, maxy)\n",
+      "    \n",
+      "    minx = -9.57238091319 \n",
+      "    maxx= 13.5723809132 \n",
+      "    miny = -4.57238091319 \n",
+      "    maxy = 18.5723809132\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.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
+      "\n",
+      "    ax.set_xlabel('X')\n",
+      "    ax.set_ylabel('Y')\n",
+      "    ax.set_zlim([0,10])\n",
+      "    #ax.set_ylim([-5,20])\n",
+      "    #ax.set_xlim([-10,10])\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": 48
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "import mkf_internal\n",
+      "import matplotlib.pyplot as plt\n",
+      "from gif_animate import animate\n",
+      "\n",
+      "def mkf_animate(frame):\n",
+      "    global ax\n",
+      "    plt.cla()\n",
+      "    var = (31-frame) / 3\n",
+      "    plot_3d_covariance(ax, (2,7), np.array([[var,0],[0,4.]]))\n",
+      "    \n",
+      "    \n",
+      "def ellipse_animate(frame):\n",
+      "    \n",
+      "    plt.cla()\n",
+      "    cov = frame/15.\n",
+      "    P = np.array([[2,cov],[cov,2]])\n",
+      "    stats.plot_covariance_ellipse((2,7), cov=P, facecolor='g', alpha=0.2, \n",
+      "                              title='|2 {:.1f}|\\n|{:.1f} 2|'.format(cov, cov))\n",
+      "\n",
+      "fig = plt.figure()\n",
+      "#ax = fig.add_subplot(111, projection='3d')\n",
+      "animate('ellipse.gif', ellipse_animate, 30, 125)    "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc010a4e898>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAGzCAYAAAD5Z7qjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc010a4e080>"
+       ]
+      }
+     ],
+     "prompt_number": 47
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<img src='ellipse.gif'>"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "\n"
+     ]
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}

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')