Updated Table of Contents
Removed the Appendixes that I deleted, and added all of the supporting notebook.
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Roger Labbe committed
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@@ -1,5 +1,266 @@
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],
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"source": [
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"#format the book\n",
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"%matplotlib inline\n",
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"from __future__ import division, print_function\n",
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"import sys;sys.path.insert(0,'..')\n",
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"from book_format import load_style;load_style('..')"
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]
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},
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"cell_type": "markdown",
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"metadata": {},
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@@ -19,7 +280,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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@@ -29,8 +290,8 @@
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"output_type": "stream",
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"text": [
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"50000\n",
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"3.00043200502\n",
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]
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}
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],
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@@ -38,7 +299,6 @@
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"import numpy as np\n",
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"import numpy.random as random\n",
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"\n",
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"\n",
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"mean = 3\n",
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"std = 2\n",
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"\n",
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@@ -59,16 +319,16 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 3,
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"metadata": {
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"data": {
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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x79d6550>"
|
||||
"<matplotlib.figure.Figure at 0x7b851d0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -99,7 +359,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": true
|
||||
@@ -107,9 +367,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x46db518>"
|
||||
"<matplotlib.figure.Figure at 0x4b35ba8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -130,16 +390,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7fd8b00>"
|
||||
"<matplotlib.figure.Figure at 0x8a54e48>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -160,16 +420,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x82595f8>"
|
||||
"<matplotlib.figure.Figure at 0x8acabe0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -177,7 +437,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
@@ -190,16 +450,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEACAYAAAD4NNLwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XdcVvf99/HXhy2goKIgKA5wG/eMxp3EmDgymsQkzfg1\nxo6kbfq727R3992mu03bpEmaNLOZzWqWGrNMYl3gXrhFUUQQRQVkXd/7jwsNsSqXCpwLeD8fDx5y\nnesczpsjXG/Oub7nHHPOISIiEixCvA4gIiJSk4pJRESCiopJRESCiopJRESCiopJRESCiopJRESC\nSkDFZGZTzCzLzLaY2X2nef4mM1tT/bHIzPrXeG5X9fRVZra8LsOLiEjTY7Wdx2RmIcAWYBKwD8gA\nbnTOZdWYZySwyTlXZGZTgJ8550ZWP7cDGOKcO1RP34OIiDQhgewxDQe2OueynXMVwEvAjJozOOeW\nOueKqh8uBVJqPG0BrkdERCSgwkgB9tR4nMMXi+dUdwLzajx2wPtmlmFms889ooiINCdhdfnFzGwC\ncAcwpsbk0c65XDNrh7+gNjnnFtVcrqioSNdFEhFpwuLi4izQeQPZY9oLpNZ43LF62hdUD3h4DJhe\n8/0k51xu9b/5wBv4Dw2KiIicViDFlAGkm1lnM4sAbgTeqjmDmaUCrwFfds5trzE92sxiqz+PAS4D\n1tdVeBERaXpqPZTnnKsys7uBBfiL7Ann3CYzm+N/2j0G/BhoAzxsZgZUOOeGA4nAG2bmqtf1vHNu\nwdnWFxcXd2HfUROXmZkJwNChQz1OEvy0rQKnbRU4bavAFRUV1T7TaQT0HpNzbj7Q85Rpf6/x+Wzg\nvwY2OOd2AgPPK5mIiDRLGsYtIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJB\nRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUk\nIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJB\nRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBRcUkIiJBJczr\nACLNybody/lk9TsAtI5N4ObLvvmF57OyV1NeWQZAx3ZdadOqfYNnFPFaQMVkZlOAP+Pfw3rCOffb\nU56/Cbiv+uFR4OvOubWBLCvSnBw+WsCWPWsBaN865b+ef+mjhyk8cgCAWZO+wah+lzZoPpFgUOuh\nPDMLAR4CLgf6ArPMrNcps+0AxjrnBgC/BB47h2VFmr3Kqgr2FWSfLCWR5iyQPabhwFbnXDaAmb0E\nzACyTszgnFtaY/6lQEqgy4o0Z+8t/xeb96ylsCiPwqP5XscRCQqBFFMKsKfG4xz8hXMmdwLzznNZ\nMjMzA4gk2k6BC6ZtlZ27++Tnx48fZ+PWNews2ABAaXE5hw8cw+dztO3Qknf+8yL79+XTqU2PBssX\nTNsq2Glb1a579+7ntVydDn4wswnAHcCYuvy6Ik1Z7s5Cls3LImdbAc7nADCD5LQE9l1bwKwr5gAQ\n16ItoSH+X9mikoNUuUoAoiNiiQqP8Sa8SD0IpJj2Aqk1HnesnvYFZtYf/3tLU5xzh85l2ZqGDh0a\nQKTm68RfadpOtQvGbVW65gDLd/g/P1xcwLsvLGT1J/4JISFGUucEWrdMIGvTFvZuK+Dp377NysXr\nuWRmP64cfTNJcR2Ji2nLhx8/x96CXQDMvOQOxgwed0G5gnFbBSttq8AVFRWd13KBFFMGkG5mnYFc\n4EZgVs0ZzCwVeA34snNu+7ksK9JcvJ/5Om//51kAKiuqWPDPFWxfm0tIiDFoYjqDJ6aTnNSRn93x\nGB9nzuW+H97Lig+3sfaznRQdLMHnc4SFhzIgfZTH34lI/aq1mJxzVWZ2N7CAz4d8bzKzOf6n3WPA\nj4E2wMNmZkCFc274mZatt+9GJIjtztsKgHOO1XNz2b42l4ioMKbdNZLrps9iaK9xhIWGAxAbG8PI\nqb1J7dWed59YTvbGPD54YRWXf3mIl9+CSIMI6D0m59x8oOcp0/5e4/PZwOxAlxVpzvatqmDJxyuI\niAzjmrtH065jPGkpfUlP6ftf8yZ3a8vV37iYV/+yiK2r9hLfLgYLMQ9SizQcXZJIpAHl7izkjX/O\nx8yYcec42nWMP+18XZJ6cNPke7hp8j0kJMcx9X+GYQYZ729h7/aCBk4t0rBUTCINpOx4Oe8/vxLn\nHPfddx89BnQ647zt4jswsu8kRvadRGLrjqT2bM+QyT3AwfvPraT8eEUDJhdpWComkQby9ksfUlRQ\nTHrPNH72s5+d8/LDp/Ske69uHD1UyvL3ttR9QJEgoWISaQDbtm3jg38vAuAnv/w+kZGR5/w1QkND\n+Ob378IM1ny6g8L9R+s6pkhQUDGJNIBZt11LZWUVvYd3ot+APuf9dQYMvIjZs+/CV+Vj00Jdwkia\nJt32QqQeHTpawMPP/oHMxWsJjwhl1JXnXkrXT/wq5RXHAejQNpX77x/OCy+8wMql6+g2Ih4uqevU\nIt7SHpNIPSo+foTHHnoKgP5ju3Hr9LvpnHhu1w/r3rEffbsOpW/XobRp1Z6EhATuvfdeAJbO1WmB\n0vRoj0mkHq3IWMnurAOER4bx0x/9nIv7XUZ4WAQAv5z91Hl/3e985zv86YE/krO1gLUrNzBx8Iy6\niiziOe0xidSjvz3oPw99zOWDmDZu1slSulDx8fFced1kAF565o06+ZoiwULFJFJPtmzZwgfvfUho\nWAijLx9Y519/ytUTCQsPZdmiTNavX1/nX1/EKyomkXrywAMP4Jyj59BOxMZF1/nXj4tvSe8R/ov3\n//GPf6zzry/iFRWTSD04fPgwzzzzDACDxqfV23oGjU/DzHjxxRcpKNCliqRpUDGJ1IPnn3+e0tJS\nxlxyMW2SWtbbeuISYhh28SDKysp46qnzH0whEkxUTCJ1zDnH448/DsCsL99Q7+u78ppLAXjkkUeo\nqqqq9/WJ1DcVk0gdW7FiBWvWrKFt27ZcfsWl9b6+A7aJhMTW7Ny5kw8++KDe1ydS31RMInXsxN7S\ndddfw6bdK+ttPaEhoYD/luxpgxMBTr6v5Zyj8Ej+yY+KyvJ6yyFS11RMInXo2LFjvPDCCwCMmNSf\nBRmv1Nu6Zoy5jbum/RCAXkP9t9B45dV/sWHbKpzz8bOnZp/82LVfVyOXxkPFJFKHXn75ZY4dO8bo\n0aPp3PXz+y31TB1QL+trFdOaPp0H06ptNCnpCVRWVPHsc0+z58COelmfSEPQJYlE6tA//vEPAGbP\nnn1y2vhB05l5yR31sr7UxHTmzPgxR0oOkb3mavZu+5Tn/vk8pa2z62V9Ig1Be0wi56HwyAHmL3uZ\n+cte5q1Fz1Jy/BjrNqxh6dKltGzZki996UsNlsXMiItpw/CxgwiLCGXfjoMUFRQ32PpF6pr2mETO\nw8EjB5i79MWTjz9Y8ToZCzYDcNmUyeQf2cvuvG0NmimqRQRp/TuwOTOHrIw9jLiiV4OuX6SuaI9J\npA4459iyci8AvoR8/vjyd1m55bMGz9FrmP99razMPTifa/D1i9QFFZNIHTiYe5TC/UeJig6nQ3pr\nz3J07N6O2PgWHDlYQu6uQs9yiFwIHcoTqQNbV+UAkDYgmdBQ/99737j650SER9IqpuGKKiTE6D4o\nhVUfb2Pb6n0kd2vbYOsWqSsqJpELVPMwXo/BKbSL68B3bvgt0VEtMbMGy9E1qSfRkbEcGHiYVR9v\nY/vafVwysx8W0nAZROqCiknkAh3Yc5gjB0uIjYvmhqtvpV3rRGJatGrwHNeM+woA4wdO492nRnPs\ncCn7sw/RoWubBs8iciH0HpPIBTqxt3T11TO4YdIcJg6e6WkeMyN9QDIA29bs8zSLyPlQMYlcAOdz\nbF3lL6Yrpl3ucRq/mBatuPSKiQBsX7MP5xzLN36kq0FIo6FiErkAebsPUVx0nNj4Fgwc3N/rOAB0\nat+N33z3UVJSUjh6qJS83YdZtukj1m1f5nU0kYComEQuwI51+wHodlFSgw50qE1ISAjXXnst4N9r\nEmlMVEwiF2DHulwAul3UweMk/+26664DYF/WEZzTybbSeKiYRM5TYd5RDh04RmR0OMlpwXe+0MUX\nX0xSUhL79x0gP6fI6zgiAVMxiZynndWH8br0STx5Um0wCQ0NZeZM/wjBHev3e5xGJHDB99sk0kgE\n82G8E6ZPnw7Arg0qJmk8VEwi5+FAXj77sw8RGh5C517tvY5zRhMmTCCqRST5OUW88t7TfLZmrteR\nRGoVUDGZ2RQzyzKzLWZ232me72lmi83suJl955TndpnZGjNbZWbL6yq4iJc+ev9jAFJ7tOfLU7/F\njZO+QVLbTrUs1fCioqIYPNw/jH3nhv2s8OCK5yLnqtZLEplZCPAQMAnYB2SY2ZvOuawasx0E7gFO\nd8q7DxjvnDtUB3lFPLdm21Keff5pAEaMHcLF/S71NE9tZsyYyeJPMti5fj9c73UakdoFssc0HNjq\nnMt2zlUALwEzas7gnCtwzq0AKk+zvAW4HpFGYeuujezYlIMZ9BuS7nWcWt1xy2zMjJytBRwvLfM6\njkitAimMFGBPjcc51dMC5YD3zSzDzGafSziRYOFzPjZlr2JT9irmvvcOvipHSrf2zJx4i9fRatWu\nXTsGDRmAr8rH5jU7vY4jUquGuLr4aOdcrpm1w19Qm5xzi840c2ZmZgNEavy0nQJXF9vK56viuSW/\nBiBj8RoAhgwbTOlByDwY/P8X/Qf2Y2XmatYsyzrr9tDPVeC0rWrXvXv381oukD2mvLine truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x851f860>"
|
||||
"<matplotlib.figure.Figure at 0x9dbac88>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -207,7 +467,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"norm = stats.norm(mean, std)\n",
|
||||
"plt.plot(xs, norm.pdf(xs), color='k', lw=2)\n",
|
||||
"plt.show()"
|
||||
@@ -222,16 +482,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7a13710>"
|
||||
"<matplotlib.figure.Figure at 0x9de1780>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -260,16 +520,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 9,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x859ba90>"
|
||||
"<matplotlib.figure.Figure at 0x9e29ac8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -279,8 +539,8 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"mean = 13.96\n",
|
||||
"std = 2.81\n"
|
||||
"mean = 13.99\n",
|
||||
"std = 2.80\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -294,8 +554,8 @@
|
||||
"\n",
|
||||
"d_t = f(data) # transform data through f(x)\n",
|
||||
"\n",
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(data, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"\n",
|
||||
"plt.ylim(0, .35)\n",
|
||||
"plt.show()\n",
|
||||
@@ -324,16 +584,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 10,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEACAYAAAD4NNLwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8lNW9+PHPNzshJJCwJ+y7IIvsILiggEsF16pV61Lr\n5afdbG9ttdarrdflVlttr73iVrVudYdaEVSqsoct7BAMAbIQCJAQEhKynN8fz+SZmZBlkszMM5l8\n37588WznzDcDk++c85znHDHGoJRSSoWKCKcDUEoppTxpYlJKKRVSNDEppZQKKZqYlFJKhRRNTEop\npUKKJiallFIhxafEJCJzRWSXiOwRkfvqOX+FiGSIyCYRWSci0z3OZXue82fwSoWqVn5mGi2rVLiT\npp5jEpEIYA8wC8gD0oHrjTG7PK6JN8aUubbPBv5hjBnh2s8CxhtjjgfmR1AqtLTmM+NLWaXCnS8t\npklApjFmvzGmEngbmOd5Qe0HzCUBqPHYFx9fR6lw0ZrPTJNllQp3viSMVOCgx36O65gXEZkvIjuB\nxcDtHqcMsExE0kXkztYEq1Qb0ZrPjE9llQpnUf6qyBjzEfCRiJwL/B642HVqujEmX0S6YSWoncaY\nFZ5li4uLdV4k1aYkJSVJa+to5DPTJP3MqLamOZ8ZX1pMuUBfj/0017F6uZLOQBFJdu3nu/48AnyI\n1VWhVDhrzWemWWWVCke+JKZ0YLCI9BORGOB6YJHnBSIyyGP7HCDGGHNMROJFJMF1vCMwG9jmt+iV\nCk0t/sz4UlapcNdkV54xplpE7gGWYiWyl4wxO0XkLuu0WQhcLSK3AKeBU8B1ruI9gA9FxLhe6w1j\nzNLGXi8pKanlPw2wfv16ACZMmNCqetpDXaEYUyjXVVxc7NN1rfnMNFS2sddr7WcmkPz5/geaxup/\nvn5m6vLpHpMxZgkwrM6x5z22nwSerKfcPmBsiyJTqg1r6WemobJKtSc6jFsppVRI0cSklFIqpGhi\nUkopFVI0MSmllAopmpiUUkqFFE1MSimlQoomJqWUUiFFE5NSSqmQoolJKaVUSNHEpJRSKqRoYlJK\nKRVSNDEppZQKKZqYlFJKhRRNTEoppUKKJiallFIhRROTUirkffDBB5x//vm89tprToeigsCnhQKV\nUsopVVVV3HHHHRQVFbFixQomTpzIiBEjnA5LBZC2mJRSIW3btm0UFRUBUF1dzYMPPuhwRCrQNDEp\npULa6tWrvfaXLl2KMcahaFQwaFdeCPl8/QdUVJYTEx3HxROucjocpULCmjVrvPZLSko4fPgwPXr0\ncCgiFWiamELIZ+v+QUVlOdFRMZqYlHLZtGnTGccyMzM1MYUx7coLIacrKwCorDrtcCRKhY78/Pwz\njmVmZjoQiQoWTUxKqZBVVVXF0aNHzzi+Z88eB6JRweJTYhKRuSKyS0T2iMh99Zy/QkQyRGSTiKwT\nkem+llVKqYYUFhbWO9BBW0zhrcnEJCIRwF+AOcBI4AYRGV7nss+NMWOMMeOAO4AXm1FWKaXqVVBQ\nUO/x/fv3BzkSFUy+tJgmAZnGmP3GmErgbWCe5wXGmDKP3QSgxteySinVkMOHD9vb/fv3t7fru++k\nwocvo/JSgYMe+zlYCceLiMwHHgO6AZc1p6yn9evX+xBS0/xVTzDrMhifrmvONa2NSetyGzJkiB8i\nUc3h2WIaM2YM2dnZ9vGamhoiIvQ2eTjy29+qMeYjY8wIYD7we3/Vq5RqvzxbTP369aNz586ANSii\nsLDQqbBUgPnSYsoF+nrsp7mO1csYs0JEBopIcnPLAkyYMMGHkBpW+824tfU4UdfrK8VuNVV1KGbK\nyFkBjastv1dO1FVcXOzztSIyF/gT1pe/l4wxT9Q5fyNQOxioBPh/xpgtrnPZQDFWl3ilMabRXoZw\n5tli6tGjB7169bKnJ8rPz6d79+5OhaYCyJcWUzowWET6iUgMcD2wyPMCERnksX0OEGOMOeZLWVW/\n9bu/cjoE1UI+DvrJAmYaY8Zg9TAs9DhXA5xvjBnXnpMSeLeYunfvTq9evex9vc8UvppsMRljqkXk\nHmAp7m9/O0XkLuu0WQhcLSK3AKeBU8B1jZUN0M/S5sVEx1JRWe50GKr17EE/ACJSO+hnV+0FxhjP\neXbWYN2PrSXoM4YAHDlyxN7u1q0bvXv3tvc1MYUvn6YkMsYsAYbVOfa8x/aTwJO+llX1i4mO08QU\nHpo76OcHwKce+wZYJiLVwEJjzAv+D7Ft8Ow+7dy5s7aY2gmdK08pB4nIBcBtwLkeh6cbY/JFpBtW\ngtppjFnRUB3+HL0YKC2N0fMeU05ODlVVVfZ+RkZGQH72tvB+1gr1WFs6klW7C5TyP58G/YjIaKx7\nS1cYY47XHjfG5Lv+PAJ8SBOPWISzkydP2tsdO3YkJSXF3j927JgTIakg0BaTUv5nD/oB8rEG/dzg\neYGI9AXeB242xnzrcTweiDDGnBSRjsBs4OHGXswfIw4DpbWjIk+dOmVvz5gxg06dOtn7lZWVfv3Z\n/TmCM9DaSqzNGcnqSROTUn7m44ChB4Fk4DkREdzDwnsAH4qIwfp8vmGMWerMT+IsYwwnTpyw9xMT\nE72Gh3uO2FPhRRNTiNpzcAurti1j2qiLnQ5FtYAPA4buBO6sp9w+YGzAA2wDSktLqamxZjfr0KED\n0dHRXmswaWIKX3qPKYQdOnrA6RCUcoxnN1BSUhIAKSkpWA1MOHr0qNdgCBU+NDGFiMqq05x2DRXv\nkZzmcDRKOa9uNx5AZGQkXbt2tY97PuekwocmphCxcPGj9jNMowZMdDgapZxXX4sJ0PtM7YAmphAk\niNMhKOW4hhKT3mcKf5qYQsyC+Q/RKb6z02Eo5bj6uvLAu8XU0EKCqm3TxKSUCknaldd+aWJSSoUk\nTUztlyamEPbvzYvJytvV9IVKhSFfuvI0MYUnTUwh7vDxRtdVVCpsNZSYPAc/6D2m8KSJKQQN7XO2\n0yEo5bjS0lJ7OyEhwd7WFlP408QUglK7DWDyiAudDkMpR9WdWbyWJqbwp4kpBJwoLeLQsRynw1Aq\npHi2mBpLTMaYoMalAk8TUwj4cuOHFJ88Wu+5rzL+SUlZUZAjUsp5DXXlJSQkEB8fD0B5eTklJSVB\nj00FliamEBMbHee1n3tkH8dLCh2KRinnNNRiAu3OC3eamELIvHNvZWDvEQAM7TvG4WiUclZD95hA\nE1O408QUoiYOP4+07gOdDkMpxzTUlQeamMKdJialVEjytStPn2UKP5qYlFIhqbGuPJ1hPLz5lJhE\nZK6I7BKRPSJyXz3nbxSRDNf/K0RktMe5bNfxTSKyzp/BK6XCU01NDWVlZfZ+7Si8WtqVF96imrpA\nRCKAvwCzgDwgXUQ+NsZ4TuKWBcw0xhSLyFxgITDFda4GON8Yc9y/oSulwtWpU6fs7Q4dOhAZGel1\nXrvywpsvLaZJQKYxZr8xphJ4G5jneYExZo0xpnYq4DVAqsdp8fF1lFIKaLwbD7TFFO6abDFhJZmD\nHvs5WMmqIT8APvXYN8AyEakGFhpjXmjsxdavX+9DSE3zVz3BqOvQIesbX07OQdYb9/myUqsrY+fO\nnRw+eOZDtu3xvXKyriFDhvghEuWLxgY+gN5jCne+JCaficgFwG3AuR6Hpxtj8kWkG1aC2mmMWeHP\n11VKhZfGhoqDtpjCnS+JKRfo67Gf5jrmxTXgYSEw1/N+kjEm3/XnERH5EKu11WBimjBhgm+RN6D2\nm3Fr6wlmXTmntrIjD9LS+jBhvPv8l5lvcqwURowYQd8eg/0eV1t8r5ysy3PhOhVYTXXlpaSkICIY\nYzh69CiVlZVER0cHM0QVQL7c+0kHBotIPxGJAa4HFnleICJ9gfeBm40x33ocjxeRBNd2R2A2sM1f\nwSulwlNTXXlRUVGkpKTY+4WFOm1XOGkyMRljqoF7gKXAduBtY8xOEblLRH7ouuxBIBl4rs6w8B7A\nChHZhDUoYrExZqnffwqlVFhpKjGBd3feoUOHAh6TCh6f7jEZY5YAw+oce95j+07gznrK7QPGtjLG\ndm/Xgc2kdR9IhOjgRtU+eHbl1XePCSA1NZUdO3YAkJeXx7hx44ISmwo8/U3XBvxz1d8xNTVOh6FU\n0PjSYkpLS7O3c3J0PbNwookphPXvOazpi5QKQ5qY2jdNTCHsugvuIiIisukLVchp5TRejZZtD5oa\nLg5WV16t3NwzBgqrNkwTk1J+5jGN1xxgJHCDiAyvc1ntNF5jgN9jPWrha9mw19RwcdAWUzjTxKSU\n/7VmGq8my7YHze3K0xZTePHrzA+q+dJ3fcWXGz92OgzlX62Zxqu5Zf06dVOgNDfG/fv329tHjhyp\nt3xRUZHX9aE4RVeghXqsLZ3GS1tMDjPGt9F227M3BDgS5QSPabza5b2khnjOLl53yYtaSUlJxMbG\nAlYLy7P7T7Vt2mIKEWMHT+P8sZefcbymphqAj7/5G6MHTQ52WKplWjONl09lPfljuqVAaemUUDEx\nMfb22Wef3WD5AQMGsGuXtQJPly5dGDNmTAsj9e/0VYHWVmJt6TRe2mIKEdFRMURGnvk9Ia3bQAAd\nnde2tHgaL1/Ktge+3GMCKzHVysrKCmhMKng0MYW4W+b+zOkQVDO1ZhqvhsoG/YdwmC8zP4B3Ytq3\nb19AY1LBo115SgVAS6fxaqhse+Nri2ngwIH2traYwocmJqVUyGlJV96+ffsoLCvk7W1vk3sil+Fd\nh3PViKvoFNspoLEq/9PEpJQKOb525Xm2mDZXbmbAMwM4edpd9oEvH+Ctq99iRr8ZgQlUBYTeY1JK\nhRxfW0yDBg2yNkZC3vQ8r6QEkFuSy9w35rImZ01A4lSBoYlJKRVSKisrOX36NAAiQLine truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x95bb7f0>"
|
||||
"<matplotlib.figure.Figure at 0x8dc9eb8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -343,8 +603,8 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"mean = -1.57\n",
|
||||
"std = 2.10\n"
|
||||
"mean = -1.59\n",
|
||||
"std = 2.09\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -354,7 +614,7 @@
|
||||
"\n",
|
||||
"d_t = f2(data)\n",
|
||||
"plt.subplot(121)\n",
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"\n",
|
||||
"plt.subplot(122)\n",
|
||||
"kde = stats.gaussian_kde(d_t)\n",
|
||||
@@ -379,7 +639,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -390,7 +650,7 @@
|
||||
"-1.5*sin(x/3)*sin(1.5*x + 2.1) + cos(x/3)*cos(1.5*x + 2.1)/3 - 1.6"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -412,7 +672,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"execution_count": 12,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -423,7 +683,7 @@
|
||||
"-1.66528051815545"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -442,16 +702,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"execution_count": 13,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAaYAAAEACAYAAAD4NNLwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0xaa5bac8>"
|
||||
"<matplotlib.figure.Figure at 0x9e02b00>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -459,7 +719,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step')\n",
|
||||
"plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2)\n",
|
||||
"plot_normal(xs, f2(mean), abs(float(m)*std), color='k', lw=3, label='EKF')\n",
|
||||
"plot_normal(xs, d_t.mean(), d_t.std(), color='r', lw=3, label='MC')\n",
|
||||
"plt.legend()\n",
|
||||
|
||||
@@ -21,7 +21,7 @@
|
||||
"@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",
|
||||
"@import url('http://fonts.googleapis.com/css?family=Fira+sans');\n",
|
||||
"\n",
|
||||
".CodeMirror pre {\n",
|
||||
" font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
|
||||
@@ -116,9 +116,9 @@
|
||||
" white-space: nowrap;\n",
|
||||
" }\n",
|
||||
" div.text_cell_render{\n",
|
||||
" font-family: 'Fira sans', verdana,arial,sans-serif;\n",
|
||||
" font-family: 'Vollkorn', verdana,arial,sans-serif;\n",
|
||||
" line-height: 150%;\n",
|
||||
" font-size: 110%;\n",
|
||||
" font-size: 130%;\n",
|
||||
" font-weight: 400;\n",
|
||||
" text-align:justify;\n",
|
||||
" text-justify:inter-word;\n",
|
||||
@@ -264,11 +264,8 @@
|
||||
"#format the book\n",
|
||||
"%matplotlib inline\n",
|
||||
"from __future__ import division, print_function\n",
|
||||
"import sys\n",
|
||||
"sys.path.insert(0,'..')\n",
|
||||
"sys.path.insert(0,'../code') \n",
|
||||
"from book_format import load_style\n",
|
||||
"load_style('..')"
|
||||
"import sys;sys.path.insert(0,'..');sys.path.insert(0, '../code')\n",
|
||||
"import book_format; book_format.load_style('..')"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -293,7 +290,7 @@
|
||||
"data": {
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"image/png": 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truncated
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||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x22cc3fe0b00>"
|
||||
"<matplotlib.figure.Figure at 0x7bec9e8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -374,7 +371,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Derivation of ILS Equations (Optional)"
|
||||
"### Derivation of ILS Equations"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
@@ -1,92 +0,0 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Linearizing with Taylor Series\n",
|
||||
"\n",
|
||||
"Taylor series represents a function as an infinite sum of terms. The terms are linear, even for a nonlinear function, so we can express any arbitrary nonlinear function using linear algebra. The cost of this choice is that unless we use an infinite number of terms the value we compute will be approximate rather than exact.\n",
|
||||
"\n",
|
||||
"Before applying it to a matrix lets do the Taylor expansion of a real function since this is much easier to visualize. I choose sin(x). The Taylor series for a real or complex function f(x) at x=a is the infinite series\n",
|
||||
"\n",
|
||||
"$$f(x) = f(a) + f'(a)(x-a) + \\frac{f''(a)}{2!}(x-a)^2 + \\, ...\\, + \\frac{f^{(n)}(a)}{n!}(x-a)^n + \\, ...$$\n",
|
||||
"\n",
|
||||
"where $f^{n}$ is the nth derivative of f. To compute the Taylor series for $f(x)=sin(x)$ at $x=0$ Let's first work out the terms for f.\n",
|
||||
"\n",
|
||||
"$$\\begin{aligned}\n",
|
||||
"f^{0}(x) &= sin(x) ,\\ \\ &f^{0}(0) &= 0 \\\\\n",
|
||||
"f^{1}(x) &= cos(x),\\ \\ &f^{1}(0) &= 1 \\\\\n",
|
||||
"f^{2}(x) &= -sin(x),\\ \\ &f^{2}(0) &= 0 \\\\\n",
|
||||
"f^{3}(x) &= -cos(x),\\ \\ &f^{3}(0) &= -1 \\\\\n",
|
||||
"f^{4}(x) &= sin(x),\\ \\ &f^{4}(0) &= 0 \\\\\n",
|
||||
"f^{5}(x) &= cos(x),\\ \\ &f^{5}(0) &= 1\n",
|
||||
"\\end{aligned}\n",
|
||||
"$$\n",
|
||||
"\n",
|
||||
"Now we can substitute these values into the equation.\n",
|
||||
"\n",
|
||||
"$$\\sin(x) = \\frac{0}{0!}(x)^0 + \\frac{1}{1!}(x)^1 + \\frac{0}{2!}(x)^2 + \\frac{-1}{3!}(x)^3 + \\frac{0}{4!}(x)^4 + \\frac{-1}{5!}(x)^5 + ... $$\n",
|
||||
"\n",
|
||||
"And let's test this with some code:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"estimate of sin(.3) is 0.30452025\n",
|
||||
"exact value of sin(.3) is 0.295520206661\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"\n",
|
||||
"x = .3\n",
|
||||
"estimate = x + x**3/6 + x**5/120\n",
|
||||
"exact = np.sin(.3)\n",
|
||||
"\n",
|
||||
"print('estimate of sin(.3) is', estimate)\n",
|
||||
"print('exact value of sin(.3) is', exact)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This is not bad for only three terms. If you are curious, go ahead and implement this as a Python function to compute the series for an arbitrary number of terms.\n",
|
||||
"\n",
|
||||
"Now we can consider how to linearize a nonlinear "
|
||||
]
|
||||
}
|
||||
],
|
||||
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|
||||
"kernelspec": {
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"display_name": "Python 3",
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"pygments_lexer": "ipython3",
|
||||
"version": "3.5.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
@@ -0,0 +1,351 @@
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{
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{
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|
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},
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"outputs": [
|
||||
{
|
||||
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|
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"<style>\n",
|
||||
"@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
|
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"@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",
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||||
"\n",
|
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".CodeMirror pre {\n",
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" width: 900px;\n",
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" margin-right: auto;\n",
|
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" }\n",
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" div.text_cell code {\n",
|
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" background: transparent;\n",
|
||||
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|
||||
" font-weight: 600;\n",
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" font-size: 11pt;\n",
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" font-style: bold;\n",
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||||
" font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
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||||
" h1 {\n",
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" font-family: 'Open sans',verdana,arial,sans-serif;\n",
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||||
"\t}\n",
|
||||
"\t\n",
|
||||
" div.input_area {\n",
|
||||
" background: #F6F6F9;\n",
|
||||
" border: 1px solid #586e75; \n",
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||||
" }\n",
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"\n",
|
||||
" .text_cell_render h1 {\n",
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" font-weight: 200;\n",
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" font-size: 30pt;\n",
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" line-height: 100%;\n",
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" color:#c76c0c;\n",
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" margin-bottom: 0.5em;\n",
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" margin-top: 1em;\n",
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" display: block;\n",
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" white-space: wrap;\n",
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" text-align: left;\n",
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" } \n",
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" h2 {\n",
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" font-family: 'Open sans',verdana,arial,sans-serif;\n",
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" text-align: left;\n",
|
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" }\n",
|
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" .text_cell_render h2 {\n",
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" font-weight: 200;\n",
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" font-size: 16pt;\n",
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" font-style: italic;\n",
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" h3 {\n",
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" font-family: 'Open sans',verdana,arial,sans-serif;\n",
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" font-weight: 100;\n",
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" 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",
|
||||
" font-weight: 400;\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",
|
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" padding-left: 0.5em; \n",
|
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" margin-bottom: 0.5em; \n",
|
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" margin-top: 0.5em; \n",
|
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" }\n",
|
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" ul li li{\n",
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" padding-left: 0.2em; \n",
|
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" margin-bottom: 0.2em; \n",
|
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" margin-top: 0.2em; \n",
|
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" }\n",
|
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" ol{\n",
|
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" margin: 2em;\n",
|
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" }\n",
|
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" ol li{\n",
|
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" padding-left: 0.5em; \n",
|
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" margin-bottom: 0.5em; \n",
|
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" margin-top: 0.5em; \n",
|
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" }\n",
|
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" ul li{\n",
|
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" padding-left: 0.5em; \n",
|
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" margin-bottom: 0.5em; \n",
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" margin-top: 0.2em; \n",
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" }\n",
|
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" a:link{\n",
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" font-weight: bold;\n",
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" color:#447adb;\n",
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" }\n",
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" a:visited{\n",
|
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" font-weight: bold;\n",
|
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" color: #1d3b84;\n",
|
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" }\n",
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" a:hover{\n",
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" font-weight: bold;\n",
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" color: #1d3b84;\n",
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" }\n",
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" a:focus{\n",
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" font-weight: bold;\n",
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" color:#447adb;\n",
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" a:active{\n",
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" font-weight: bold;\n",
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" color:#447adb;\n",
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" }\n",
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" .rendered_html :link {\n",
|
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" text-decoration: underline; \n",
|
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" }\n",
|
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" .rendered_html :hover {\n",
|
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" text-decoration: none; \n",
|
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" }\n",
|
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" .rendered_html :visited {\n",
|
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" text-decoration: none;\n",
|
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" }\n",
|
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" .rendered_html :focus {\n",
|
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" text-decoration: none;\n",
|
||||
" }\n",
|
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" .rendered_html :active {\n",
|
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" 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",
|
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" preferredFont:null,\n",
|
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" webFont: \"TeX\",\n",
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" styles: {'.MathJax_Display': {\"margin\": 4}}\n",
|
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" }\n",
|
||||
" });\n",
|
||||
"</script>\n"
|
||||
],
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||||
"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": [
|
||||
"# Linearizing with Taylor Series\n",
|
||||
"\n",
|
||||
"Taylor series represents a function as an infinite sum of terms. The terms are linear, even for a nonlinear function, so we can express any arbitrary nonlinear function using linear algebra. The cost of this choice is that unless we use an infinite number of terms the value we compute will be approximate rather than exact.\n",
|
||||
"\n",
|
||||
"The Taylor series for a real or complex function f(x) at x=a is the infinite series\n",
|
||||
"\n",
|
||||
"$$f(x) = f(a) + f'(a)(x-a) + \\frac{f''(a)}{2!}(x-a)^2 + \\, ...\\, + \\frac{f^{(n)}(a)}{n!}(x-a)^n + \\, ...$$\n",
|
||||
"\n",
|
||||
"where $f^{n}$ is the nth derivative of f. To compute the Taylor series for $f(x)=sin(x)$ at $x=0$ let's first work out the terms for f.\n",
|
||||
"\n",
|
||||
"$$\\begin{aligned}\n",
|
||||
"f^{0}(x) &= sin(x) ,\\ \\ &f^{0}(0) &= 0 \\\\\n",
|
||||
"f^{1}(x) &= cos(x),\\ \\ &f^{1}(0) &= 1 \\\\\n",
|
||||
"f^{2}(x) &= -sin(x),\\ \\ &f^{2}(0) &= 0 \\\\\n",
|
||||
"f^{3}(x) &= -cos(x),\\ \\ &f^{3}(0) &= -1 \\\\\n",
|
||||
"f^{4}(x) &= sin(x),\\ \\ &f^{4}(0) &= 0 \\\\\n",
|
||||
"f^{5}(x) &= cos(x),\\ \\ &f^{5}(0) &= 1\n",
|
||||
"\\end{aligned}\n",
|
||||
"$$\n",
|
||||
"\n",
|
||||
"Now we can substitute these values into the equation.\n",
|
||||
"\n",
|
||||
"$$\\sin(x) = \\frac{0}{0!}(x)^0 + \\frac{1}{1!}(x)^1 + \\frac{0}{2!}(x)^2 + \\frac{-1}{3!}(x)^3 + \\frac{0}{4!}(x)^4 + \\frac{-1}{5!}(x)^5 + ... $$\n",
|
||||
"\n",
|
||||
"And let's test this with some code:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"estimate of sin(.3) is 0.30452025\n",
|
||||
"exact value of sin(.3) is 0.295520206661\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"\n",
|
||||
"x = .3\n",
|
||||
"estimate = x + x**3/6 + x**5/120\n",
|
||||
"exact = np.sin(.3)\n",
|
||||
"\n",
|
||||
"print('estimate of sin(.3) is', estimate)\n",
|
||||
"print('exact value of sin(.3) is', exact)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This is not bad for only three terms. If you are curious, go ahead and implement this as a Python function to compute the series for an arbitrary number of terms."
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
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"display_name": "Python 3",
|
||||
"language": "python",
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||||
"name": "python3"
|
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},
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"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
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"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
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"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.5.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
Reference in new issue
Block a user