Ran all notebooks to use new css settings.

2016-01-17 20:44:23 -08:00
1 parent 0a41e78aeb
commit 5240944dd4
@@ -0,0 +1,540 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<style>\n",
+       "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+       "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
+       "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
+       "@import url('http://fonts.googleapis.com/css?family=Fira+sans');\n",
+       "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
+       "    div.cell{\n",
+       "        width: 900px;\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: 12pt;\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",
+       "        text-align: left;\n",
+       "    } \n",
+       "    h2 {\n",
+       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "    .text_cell_render h2 {\n",
+       "        font-weight: 200;\n",
+       "        font-size: 16pt;\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: wrap;\n",
+       "        text-align: left;\n",
+       "    } \n",
+       "    h3 {\n",
+       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+       "    }\n",
+       "    .text_cell_render h3 {\n",
+       "        font-weight: 200;\n",
+       "        font-size: 14pt;\n",
+       "        line-height: 100%;\n",
+       "        color:#d77c0c;\n",
+       "        margin-bottom: 0.5em;\n",
+       "        margin-top: 2em;\n",
+       "        display: block;\n",
+       "        white-space: wrap;\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "    h4 {\n",
+       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+       "    }\n",
+       "    .text_cell_render h4 {\n",
+       "        font-weight: 100;\n",
+       "        font-size: 14pt;\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",
+       "\n",
+       "    .text_cell_render h5 {\n",
+       "        font-weight: 200;\n",
+       "        font-style: normal;\n",
+       "        color: #1d3b84;\n",
+       "        font-size: 16pt;\n",
+       "        margin-bottom: 0em;\n",
+       "        margin-top: 0.5em;\n",
+       "        display: block;\n",
+       "        white-space: nowrap;\n",
+       "    }\n",
+       "    div.text_cell_render{\n",
+       "        /*font-family: 'Vollkorn', verdana,arial,sans-serif;*/\n",
+       "        line-height: 150%;\n",
+       "        font-size: 130%;\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: 50000px;\n",
+       "    }\n",
+       "    div.output_subarea.output_stream.output_stdout.output_text {\n",
+       "        overflow-x: auto;\n",
+       "        overflow-y: scroll;\n",
+       "        max-height: 50000px;\n",
+       "    }\n",
+       "    div.output_wrapper{\n",
+       "        margin-top:0.2em;\n",
+       "        margin-bottom:0.2em;\n",
+       "}\n",
+       "\n",
+       "    code{\n",
+       "        font-size: 6pt;\n",
+       "\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",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
+       "                           },\n",
+       "                tex2jax: {\n",
+       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
+       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
+       "                },\n",
+       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
+       "                \"HTML-CSS\": {\n",
+       "                    scale:95,\n",
+       "                        availableFonts: [],\n",
+       "                        preferredFont:null,\n",
+       "                        webFont: \"TeX\",\n",
+       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
+       "                }\n",
+       "        });\n",
+       "</script>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#format the book\n",
+    "%matplotlib inline\n",
+    "from __future__ import division, print_function\n",
+    "import sys;sys.path.insert(0,'..')\n",
+    "from  book_format import load_style;load_style('..')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Interactions\n",
+    "\n",
+    "This is a collection of interactions, mostly from the book. If you have are reading a print version of the book, or are reading it online via Github or nbviewer you will be unable to run the interactions.\n",
+    "\n",
+    "So I have created this notebook. Here is how you run an interaction if you do not have IPython installed on your computer.\n",
+    "\n",
+    "1. Go to try.juptyer.org in your browser. It will launch a temporary notebook server for you.\n",
+    "\n",
+    "2. Click the **New** button and select `Python 3`. This will create a new notebook that will run Python 3 for you in your browser.\n",
+    "\n",
+    "3. Copy the entire contents of a cell from this notebook and paste it into a 'code' cell in the notebook on your browser. \n",
+    "\n",
+    "4. Press CTRL+ENTER to execute the cell.\n",
+    "\n",
+    "5. Have fun! Change code. Play. Experiment. Hack.\n",
+    "\n",
+    "Your server and notebook is not permanently saved. Once you close the session your data is lost. Yes, it says it is saving your file if you press save, and you can see it in the directory. But that is just happening in a Docker container that will be deleted as soon as you close the window. Copy and paste any changes you want to keep to an external file.\n",
+    "\n",
+    "Of course if you have IPython installed you can download this notebook and run it on your own computer. Type\n",
+    "\n",
+    "    ipython notebook\n",
+    "    \n",
+    "in a command prompt from the directory where you downloaded this file. Click on the name of this file to open it."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Experimenting with FPF'\n",
+    "\n",
+    "\n",
+    "The Kalman filter uses the equation $P^- = FPF^\\mathsf{T}$ to compute the prior of the covariance matrix during the prediction step, where P is the covariance matrix and F is the system transistion function. For a Newtonian system $x = \\dot{x}\\Delta t + x_0$ F might look like\n",
+    "\n",
+    "$$F = \\begin{bmatrix}1 & \\Delta t\\\\0 & 1\\end{bmatrix}$$\n",
+    "\n",
+    "$FPF^\\mathsf{T}$ alters P by taking the correlation between the position ($x$) and velocity ($\\dot{x}$). This interactive plot lets you see the effect of different designs of F has on this value. For example,\n",
+    "\n",
+    "* what if $x$ is not correlated to $\\dot{x}$? (set F01 to 0)\n",
+    "\n",
+    "* what if $x = 2\\dot{x}\\Delta t + x_0$? (set F01 to 2)\n",
+    "\n",
+    "*  what if $x = \\dot{x}\\Delta t + 2*x_0$? (set F00 to 2)\n",
+    "\n",
+    "* what if $x = \\dot{x}\\Delta t$?  (set F00 to 0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARAAAAEoCAYAAACQI67VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x71f6828>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from IPython.html.widgets import interact, interactive, fixed\n",
+    "import IPython.html.widgets as widgets\n",
+    "import numpy as np\n",
+    "import numpy.linalg as linalg\n",
+    "import math\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib.patches import Ellipse\n",
+    "\n",
+    "def plot_covariance_ellipse(x, P, edgecolor='k'):\n",
+    "    U,s,v = linalg.svd(P)\n",
+    "    angle = math.atan2(U[1,0],U[0,0])\n",
+    "    width  = math.sqrt(s[0]) * 2\n",
+    "    height = math.sqrt(s[1]) * 2\n",
+    "\n",
+    "    ax = plt.gca()\n",
+    "    e = Ellipse(xy=(0, 0), width=width, height=height, angle=angle,\n",
+    "                edgecolor=edgecolor, facecolor='none',\n",
+    "                lw=2, ls='solid')\n",
+    "    ax.add_patch(e)\n",
+    "    ax.set_aspect('equal')\n",
+    "    \n",
+    "    \n",
+    "def plot_FPFT(F00, F01, F10, F11, covar):\n",
+    "    \n",
+    "    dt = 1.\n",
+    "    x = np.array((0, 0.))\n",
+    "    P = np.array(((1, covar), (covar, 2)))\n",
+    "    F = np.array(((F00, F01), (F10, F11)))\n",
+    "\n",
+    "    plot_covariance_ellipse(x, P)\n",
+    "    plot_covariance_ellipse(x, np.dot(F, P).dot(F.T), edgecolor='r')\n",
+    "    #plt.axis('equal')\n",
+    "    plt.xlim(-4, 4)\n",
+    "    plt.ylim(-4, 4)\n",
+    "    plt.title(str(F))\n",
+    "    plt.xlabel('position')\n",
+    "    plt.ylabel('velocity')\n",
+    "                 \n",
+    "interact(plot_FPFT, \n",
+    "         F00=widgets.IntSlider(value=1, min=0, max=2.), \n",
+    "         F01=widgets.FloatSlider(value=1, min=0., max=2., description='F01(dt)'),\n",
+    "         F10=widgets.FloatSlider(value=0, min=0., max=2.),\n",
+    "         F11=widgets.FloatSlider(value=1, min=0., max=2.),\n",
+    "         covar=widgets.FloatSlider(value=0, min=0, max=1.));"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Covariance Ellipse\n",
+    "\n",
+    "See the effect of varying the variances and covariance of a covariance matrix of the form\n",
+    "\n",
+    "$$\\begin{bmatrix}\\texttt{var}_x & \\texttt{cov}_xy \\\\ \\texttt{cov}_xy & \\texttt{var}_y\\end{bmatrix}$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAEACAYAAACzsMNYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7427588>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from IPython.html.widgets import interact, interactive, fixed\n",
+    "from IPython.html.widgets import FloatSlider\n",
+    "from math import cos, sin, pi, atan2, sqrt\n",
+    "import  numpy.linalg as linalg\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib.patches import Ellipse\n",
+    "\n",
+    "def plot_covariance_ellipse(P):\n",
+    "    U,s,v = linalg.svd(P)\n",
+    "    angle = atan2(U[1,0],U[0,0])\n",
+    "    width  = sqrt(s[0]) * 2\n",
+    "    height = sqrt(s[1]) * 2\n",
+    "\n",
+    "    ax = plt.gca()\n",
+    "    e = Ellipse(xy=(0, 0), width=width, height=height, angle=angle,\n",
+    "                edgecolor='k', facecolor='none',\n",
+    "                lw=2, ls='solid')\n",
+    "    ax.add_patch(e)\n",
+    "    h, w = height/4, width/4\n",
+    "    plt.plot([0, h*cos(angle+pi/2)], [0, h*sin(angle+pi/2)])\n",
+    "    plt.plot([0, w*cos(angle)],      [0, w*sin(angle)])\n",
+    "\n",
+    "def plot_covariance(var_x, var_y, cov_xy):\n",
+    "    P = [[var_x, cov_xy], [cov_xy, var_y]]\n",
+    "    plot_covariance_ellipse(P)\n",
+    "    plt.xlim(-6, 6)\n",
+    "    plt.gca().set_aspect('equal')\n",
+    "    plt.ylim(-6, 6)\n",
+    "    plt.show()\n",
+    "\n",
+    "interact (plot_covariance,           \n",
+    "          var_x=FloatSlider(value=5., min=0, max=20.), \n",
+    "          var_y=FloatSlider(value=5., min=0., max=20.), \n",
+    "          cov_xy=FloatSlider(value=1.5, min=0.0, max=50, step=.2));\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# g-h Filter\n",
+    "\n",
+    "Experiment with various values for g-h filter parameters."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEACAYAAABRQBpkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7e26358>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "from IPython.html.widgets import interact, interactive, fixed\n",
+    "import IPython.html.widgets as widgets\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import numpy.random as random\n",
+    "\n",
+    "def gen_data(x0, dx, count, noise_factor):\n",
+    "    return [x0 + dx*i + random.randn()*noise_factor for i in range (count)]\n",
+    "\n",
+    "def g_h_filter(data, x0, dx, g, h, dt=1., pred=None):    \n",
+    "    x = x0\n",
+    "    results = []\n",
+    "    for z in data:\n",
+    "        #prediction step\n",
+    "        x_est = x + (dx*dt)\n",
+    "        dx = dx        \n",
+    "        if pred is not None:\n",
+    "            pred.append(x_est)\n",
+    "        \n",
+    "        # update step\n",
+    "        residual = z - x_est\n",
+    "        dx = dx    + h * (residual) / dt\n",
+    "        x  = x_est + g * residual     \n",
+    "        results.append(x)  \n",
+    "    return np.array(results)\n",
+    "\n",
+    "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n",
+    "\n",
+    "def interactive_gh(x, dx, g, h):\n",
+    "    data = g_h_filter(data=zs, x0=x, dx=dx, dt=1.,g=g, h=h)\n",
+    "    plt.plot(zs, color='r')\n",
+    "    plt.plot(data, color='k')\n",
+    "    plt.show()\n",
+    "\n",
+    "interact (interactive_gh,           \n",
+    "          x=widgets.FloatSlider(value=0., min=-50, max=50.), \n",
+    "          dx=widgets.FloatSlider(value=5., min=-50., max=50.), \n",
+    "          g=widgets.FloatSlider(value=0.1, min=0.01, max=2, step=.02), \n",
+    "          h=widgets.FloatSlider(value=0.02, min=0.0, max=0.5, step=0.01));"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}