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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import scipy as sp\n",
      "import seaborn as sn\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "from __future__ import division\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cd ex1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C:\\Users\\Admin\\Dropbox\\Data science\\Coursera machine learning\\machine-learning-ex1\\ex1\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#load in the data, set header to None so that first line isn't assigned as header\n",
      "data = pd.read_csv('ex1data1.txt', header = None)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0</th>\n",
        "      <th>1</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 6.1101</td>\n",
        "      <td> 17.5920</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 5.5277</td>\n",
        "      <td>  9.1302</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 8.5186</td>\n",
        "      <td> 13.6620</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 7.0032</td>\n",
        "      <td> 11.8540</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 5.8598</td>\n",
        "      <td>  6.8233</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "        0        1\n",
        "0  6.1101  17.5920\n",
        "1  5.5277   9.1302\n",
        "2  8.5186  13.6620\n",
        "3  7.0032  11.8540\n",
        "4  5.8598   6.8233"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# assign the first and second columns to the variables X and y, respectively\n",
      "X = data.iloc[:,0]\n",
      "y = data.iloc[:,1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#check X\n",
      "X.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "0    6.1101\n",
        "1    5.5277\n",
        "2    8.5186\n",
        "3    7.0032\n",
        "4    5.8598\n",
        "Name: 0, dtype: float64"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#check y\n",
      "y.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0    17.5920\n",
        "1     9.1302\n",
        "2    13.6620\n",
        "3    11.8540\n",
        "4     6.8233\n",
        "Name: 1, dtype: float64"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#check that the length of y matches the MatLab file (97 rows), which it does. Assign this to the variable m\n",
      "m = len(y)\n",
      "m"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "97"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Plot a scatter of population size by profit\n",
      "plt.scatter(X,y, c = 'r', marker = 'x')\n",
      "plt.xlabel(\"Population of city in 10,000s\")\n",
      "plt.ylabel(\"Profit in $10,000s\")\n",
      "plt.title(\"Scatter plot of training data\")\n",
      "plt.xlim(4,24)\n",
      "plt.ylim(-5,25)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(-5, 25)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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gHIJUClIpEqecBoB/7RpSPY9zNywqwr91S9l0cbFbWq8lmQdWryL0ztukunUj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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc5a0048>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# X was automatically made into a series, so make it into a dataframe\n",
      "X = pd.DataFrame(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#insert a column of ones in the first column of X\n",
      "# This takes into account the intercept term, theta0\n",
      "X.insert(0, \"theta zero\",value =pd.Series(np.ones([m])))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#check this worked correctly\n",
      "X.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>theta zero</th>\n",
        "      <th>0</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1</td>\n",
        "      <td> 6.1101</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1</td>\n",
        "      <td> 5.5277</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1</td>\n",
        "      <td> 8.5186</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1</td>\n",
        "      <td> 7.0032</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1</td>\n",
        "      <td> 5.8598</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "   theta zero       0\n",
        "0           1  6.1101\n",
        "1           1  5.5277\n",
        "2           1  8.5186\n",
        "3           1  7.0032\n",
        "4           1  5.8598"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#initialize fitting parameters as stated in the homework\n",
      "theta = np.zeros([2, 1])\n",
      "iterations = 1500\n",
      "alpha = 0.01"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#this is how you calculate the hypothesis parameter\n",
      "hypothesis = X.dot(theta)\n",
      "hypothesis.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "   0\n",
        "0  0\n",
        "1  0\n",
        "2  0\n",
        "3  0\n",
        "4  0"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define a function that computes the cost function J()\n",
      "def costJ(X,y,theta):\n",
      "    '''where X is a dataframe of input features, plus a column of ones to accommodate theta 0; \n",
      "    y is a vector that we are trying to predict using these features, and theta is an array of the parameters'''\n",
      "    \n",
      "    m = len(y)\n",
      "    hypothesis = X.dot(theta) # if you're using a np array, you need to use flatten to remove nesting\n",
      "    a = (hypothesis[0]-y)**2 # otherwise this will give you completely the wrong answerX[:, 0]\n",
      "    J = (1/(2*m)*sum(a))\n",
      "    return J\n",
      "\n",
      "costJ(X,y,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "32.072733877455654"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define a function that will implement the gradient descent algorithm\n",
      "def gradDesc(X,y,theta,alpha,num_iters):\n",
      "    '''Implement the gradient descent algorithm, where alpha is the learning rate and num_iters is the number of iterations to run'''\n",
      "    \n",
      "    Jhistory = [] #initiate an empty list to store values of cost function after each cycle\n",
      "    theta_update = theta.copy()   \n",
      "    \n",
      "    for num_iter in range(num_iters):\n",
      "        #these update only once for each iteration\n",
      "        hypothesis = X.dot(theta_update)\n",
      "        loss = hypothesis[0]-y \n",
      "        \n",
      "        for i in range(len(X.columns)):\n",
      "            #these will update once for every parameter\n",
      "            theta_update[i] = theta_update[i] - (alpha*(1.0/m))*((loss*(X.iloc[:,i])).sum())\n",
      "\n",
      "        Jhistory.append(costJ(X,y,theta_update))\n",
      "        \n",
      "    return Jhistory, theta_update\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#try running the function \n",
      "Jhistory, theta_update= gradDesc(X,y,theta,alpha,1500)  \n",
      "Jhistory[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "[6.7371904648700083,\n",
        " 5.9315935686049572,\n",
        " 5.9011547070813872,\n",
        " 5.8952285864442207,\n",
        " 5.8900949431173322,\n",
        " 5.8850041584436461,\n",
        " 5.8799324804914157,\n",
        " 5.8748790947625746,\n",
        " 5.8698439118063845,\n",
        " 5.8648268653129296]"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# These are the final values for theta\n",
      "theta_update"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "array([[-3.63029144],\n",
        "       [ 1.16636235]])"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Check the output of Jhistory is decreasing towards a minimum\n",
      "plt.plot(Jhistory)\n",
      "plt.xlabel(\"number of iterations\")\n",
      "plt.ylabel(\"cost function\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "<matplotlib.text.Text at 0xf4e8518>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xf2a8f28>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Add a line which shows the outcome of the gradient descent after 1000 iterations\n",
      "plt.scatter(X.iloc[:,1],y, c = 'r', marker = 'x')\n",
      "plt.xlabel(\"Population of city in 10,000s\")\n",
      "plt.ylabel(\"Profit in $10,000s\")\n",
      "plt.title(\"Scatter plot of training data\")\n",
      "plt.xlim(4,24)\n",
      "plt.ylim(-5,25)\n",
      "plt.plot(X.iloc[:,1],X.dot(theta_update))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 209,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10833f28>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2VvWCXbvy63A6m473kTypvJYTZi7nw3nxexMXjbRZm3N7Viwn1u9wLHc27Ncb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\npZRSSimllFJKKaWU4v8B4xmEQ/enYX8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xfc78f98>"
       ]
      }
     ],
     "prompt_number": 209
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Next I want to make a contour plot that plots theta0 against theta 1 and the outcome of J\n",
      "# First initiate values for theta0 and theta 1\n",
      "theta0_vals = np.linspace(-10, 10, 100)\n",
      "theta1_vals = np.linspace(-1, 4, 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#they both have length 100\n",
      "len(theta1_vals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 280,
       "text": [
        "100"
       ]
      }
     ],
     "prompt_number": 280
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# initialize J_vals to a matrix of 0's\n",
      "J_vals = np.zeros([len(theta0_vals), len(theta1_vals)])\n",
      "J_vals.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "(100L, 100L)"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(theta0_vals)):\n",
      "    for j in range(len(theta1_vals)):\n",
      "        t = np.array([[theta0_vals[i]], [theta1_vals[j]]])\n",
      "        \n",
      "        J_vals[i,j] = costJ(X, y, t)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x000000000CAE3348>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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c/axUE97tjMEySsZFMbh3Db3dwFlYE9iB3FvDhK3v2axdZ2ejNJsaDuubg+l8\nSbQNIYDVKt5b/dbZ0RT923VaDlDK93USE7NS7aVkuukA2dsN5KgVQcMwfEcYhr8fhuE3wzB8NQzD\nv1Ln+5RBmKksJs/a9T7EugKyLMhSrQ6SbYIxoU0pk6Zsf2501kqKs1LNUDL2qGQun91A2vZyWkPd\nu4kA+KtRFL0PwCcA/AdhGL6n1hcatBqQ+nOZtesM7oTwvT66bnC4TFk7cFYpU7eYutlk+3mpOpu5\ntltzRmH2qWTUUA6gi5RMbzcgUetpiKLox1EUvbL79zWAbwN4rM53mjYIS1O2z9B0Ikn0mIPlw7Ob\nDeyDgYfDwzGOjiY4PBxjsRhjOg0a2SkkCUGSEAwGXi3pohAyuAPAdDrURmfIrlRqzCjMPkqm20M5\ncruBFOv1advLaQXa0pwwDJ8G8GEAX637XaYNwtKU7bbD+h7iLGMFVUvdrJ3udhXNZJCeJ3XmylHS\ndeXIv/F4gKOjKQ4ORtr19Ot1uveUqfPyo5QjSWQQ1sm3JwnbWzKboMFsmrh0eewGXCyXd66k3YCW\nuygMwxmA/wXAr+0y99owaRAms2KZtevMmJSlb12VRZN0jONg1zzkYLlMcHy8xd27G9y+vcZyGe8K\nwT4Wi7GWDtIilO3AdFqvmBrHZL9OnYXwODbXuGTfxCUXXXaA9DwPi4W0Gzg5udXJl1Md1L6DwjAc\nAPhtAL8TRdHfftjfFSXOrhACSZLsGolGcBvuXGKMgTEG13Xh+3oyYyHEXnblum6tzL146nQM9Sjz\nvQ+6bDrWce93V/1Onee6CEopOOda74sHgXOOJJHFZRP3/EXWc/fuXXDOcXR0hMGgW3UeIQRee+01\nrNdrPP300zg6Omp7SZXhlLyha939YRg6AD4P4E4URX/1vL8vhBC3bl3cz8H35daUUo40bf6NO59L\nnna1yqDrBR8EHqbTAHEsOzCrYjj0cHAwRhxne1755s05ypzP++HwcAzPc3Hnzubcvzsa+ZhMAriu\nA0IYlstESyY0GvmYzUYghOH0NK78PcOh5OwpZVguyykiHnYuZ7MBPM/dDdtu9j7M73mBNG1fiy05\n9gwyVAQXfmHquDd1gJAMb775fbiui0cffRKu202LjkceOSgVq+umBM8B+NcB/GIYhi/v/vlsze/c\ng1KxsxpwjVgNKF91nfI5WZytP4ijiSKq4wC+74GQixXIkoTi+HiLNKX7YqsONUqS0H0xtQ5PnmUM\naUrh+54SfZ+9AAAgAElEQVRW+mS7lRYUpigZZa9hByXT7aEcg8EQBwdH4Jzh9PRO28sxhloRLIqi\nL6PhJqcs4xiPPQyHLpKk2QxGzTAdDFykqQPO9WRncUwxnQ4xGg1qZe1JQvedm8pLpg7UVp+xi59X\nIcSui3SAyWSIxWKMzSbb1wGqYr1O4fsuxuPhbodW7fdtNhl838Vo5IMQactbF5xL7/bRyMd47O+5\n96aQphzjsYvh0Gl8h3AxDCA9ZCiE8Hb8e3cwnx9hu11js1liMpkjCMZtL6lxWH+FTFsNJIl+hUya\n5lOR6mTtSUJ2maM+9UdVxDHZUzGzWaBFkaKKqbNZUGvm63qtXwKZprlKpukBKLIrWqlkbMjau+0l\noxwgAeD4+GoUUq0P7EBuNWDCIIxSfc1FRSQJ2U3rqb6dl5kj3VkDt88VEsJwchKDUobxeFi74Yhz\nuRtwHKeWzS9juQRS59SlnJJp3pitSEOaSGjOR7cdIINgjOn0AJRmWK2O215O4+hEYFdWA65rympA\nbrV1NqckCd25B9YLCorK0cH3KqqpjvqCc4HT0xhZRhEEUhZZR5FCCMN2m8HzXMxm1V8UcUxAKUMQ\n6JNAKkrG1Dg91bhkj7a9u1k7ACwW13ej9I5BSNb2chpF+3fMBWGyaUlqirl2jxala6+TtTPG95rt\nug+XEPKc1t2ZCCFpFFUArRvct9sMhMigXOdcrdfZbmC1PhfI4jg9E5SMGh05HNpAyXTbAdJ1PRwe\n3gRw+bXtnQnspq0G1FQdvQoZvVm7DjDGtQWo9TpFHMviZd3gvlol4JxjOh1WXh/nYudLo9cFMo7N\nUTKESEpmMLCJkumu3cB4PMVoJEfpxbGWXkor0ZnADpzN2pt+oNTQDN93tWZmOrL2LKN7JUvd80Cp\nHPigK6PdbLIzwb3q96qB2EDeGVsFWabfBZJzgSQxR8mYrDGdh67bDTiOg8NDOUrv5OQ2OO/ey+ki\naP9OKQmTVgPK1lcn164ra9dlM6DkgL6v7zduNhm22/rBnVK+8113MZ9XNwvbbDJwLnXouqi1LDNH\nyXCe71btoWR8dFXbLkfpXQPnDCcnl1Pb3rnATqkA57KBo+msXfqhc3iengHVCrnzY/WgrC+wy4xF\n93CT7TbDZpPuDcaqXqs4JvuxelULxtIFMoXjOJhO9Q3CNk3JcC4pmZadBnZQDpAUQrTfIVsWs9kh\nBoMhttsl0rR6t7OtsOIWKQs1fNjE1rSJwdc6FDJqB+x5bi3XR0rV1Cr9BK60Ucjg+6qgWu17VqsU\njMmxelWzY0I4koTsmqD0dJCapmTsVcl0byjHvaP0urb+89D+HVIBjGHfdt109tLUMI7c+bFekNHR\nsEQIg+e5jWSdknMntYK76nYFgPm8Ot++3RLtgzlMUzJK9mvK0vph6LrdwHA4wnS6AKXk0mnbOxnY\nAbMFpeIwDn2djLS2X7vjOPuGpTpabULYrm7RjOxis0n3wf3goFo7t+LbPa8e364kkF1VyWSZomRs\nGcqhEpNuUjKLxbVLqW3vbGAvWg2Ymo+q22pAh1973rBUPVApE7DBoDk6YbNJ9+ZhVacmFfn2qrWF\nJrpSTTcuKSrSPkqmeyqZy6ptb//OqAGTTUtqGMdwqC9rL05ZqqocYYzv5XxVqQBK+f63NYnVKgEh\ncmpS1Yx5tUp3wzmGlf1kZFeqdNzUVTQ22bjEmLxmtgzl6LrdQFHbvt1eDm17pwN7G01Lum19deja\n9WTtMottegzccpl7y1SpLyi+va6fzGaT7iiZQNuLukjJNI00FdbMSe161l7Utp+e3gJj3Xs53YtO\nB3agKANr/gYv2vrqaujJs/bqpmOEsH0LftUsNsvkzTwcNhuUlP0AYxzTaVDpeEU/maryRcYE4pjs\nu1J1BKMiJWMquJtSh52HXNsOdNFuINe280vh297+HaEByk+jq1n7dltfIbPdysLPZFLtO7KM7qR0\nzQck1VXKucB8Xm3eqfKTGY0GldecJFSb747CWXvfZu9HxuScVN93jAzcPh9K286QZd0rRF4mbful\nCOzK4tRE8walAoTIrF3XgysHQqiMu3rWTqkMUlW+Q3qAM/i+V8sL/aJgjO8ljFWHZEs/GUmnVN3t\nbDbZ3gxN147P5MQlpQ6zx7dd0oGr1aqzlAzQfd/2SxHYAXmDAzCyLU0S/U1L2219nny7zXaZf7Xv\nSFPVzdp81g7Il9Fmk8J13Uoad2nylcJ1ncpe8JyL/bnXJYE0qZKxbyiHC8Db8dTd07af9W0/aXs5\nlXFpArvJSUucy6xdp9UApcqOt7qqQjbLsMoqG6X8MUHHKCQJLejTywfnNM3npVaVLyr//eFQn3e7\nomSCQK/18/1g31COwc7jv6vaduXbfheUdq9eAFyiwA6YbVpqNmuvp5Cpm7W7br2Gp7LYbrO9Pr1K\ncN5s0todpa7rgnPp3V7HbrgIsyoZuxwgZ7PZ7k/dU8lIbfsNAKKzlEz7d4FGmJy01ITVQFGTXnUn\noDpaR6NqWbvyoQ+C5vnhIuSAbL4f1l0GQuAey4Hyx3ccZ+ckqc+7XVk/Sz+fZl+URemvDQ6QQRCg\n29r2GYJgjDTdIo43bS+nNC5VYAck36j0vU2jCauBOK4/sDrn2ssHZ8b4rgir7zddBFIGGe+HWZfN\nvCnliGNSSwKZZWxPh+nasSRJfo/onKF7PyjprwkPpfNwWbTtgIOTk1vgvFuU0qUL7EBeTDIT3Omu\ncKVnu10c8FE1uORZ+6By1i5/k9msXcogpcysynCNogSyqh5fqWT0UjKSHptMzFAydmnbuztKbzAY\n4uDgCJwzLJfd0ra3f/UbgEnP9izjO92yvqalPGuvp2uXwaR85p+mRHv94KKoO1xjtUoghMz6q1wP\nqZLRS8lQao6SkUM5pN2ADQ6QXR+lN58fwfcHWK9PkWVJ28u5MC5lYAfMGiUlCds1Lel5aKXPt2zx\nrxpc05SC0mo+NEVNe9O+J/dDHBOkqSymlg2unAus11ICWdVsLE0ZskwvJRPH1Bglo+hIGxwgL8so\nPaBb2vZLG9ilUZIZ+SOlHJTynRGXnicpSchuGMegxvSh6ll7HMvOwbpe71WxXid7T5myNFea0tou\nkM1QMrS2m+dFYZ/dQHd920ejCSaTOQhJsdmctr2cC6H9q94gTMoflbRNF30hhAzussmlWnCqk7Ur\nXX0d58k6UJ4yqphathv2rAtklU5c2bgkKRk9tQZ1Tn1f76jF+8E+u4EBujxKb7G4DsdxcXp6B4zZ\n/3K61IHdpPyxiaYlOUKP70boVVt/vay9vq6+DiStIp0cyzYvCZF/djar1pWaprmXjE5KxtxQDtvs\nBrqrkvE8H4vFdQghcHJyu+3lnItLHdgBs/LHppqWZGCuk7VX86HJslxd0xZXm2VsNzfVLc2ZZxmr\n3ZV6lpKp9BVnIIQ5SqZoN2CDtl2Gm+5q26fTAwyHAeJ4jSTZtr2ch+LSB3bA3M3dRNNScaZm1S11\nrpApX0xMEtKK9LGIzSaXMZalpYpdqVXMzZSXjE6VDCHFmkyzj6BJg7zz0PWsXRZS1QDsW1ZTSlci\nsBflj03f3M00LVWnU4C88SYI/NKBJEnqSy91QDo5ckynw1K/QQhgvU53dE5VlUxOyeiaC2vSbiCn\nZNp/3Lvu2z4cBpjNDsEYwXJp7wDs9q+0ISj5oykfGZ2e7YTIoludDC/3ay/3cpBFXCm9NOkfcy84\nF1itUgAozbcTwvbDtOtSMtOpHkrGpAOkMsgzNWnsfOS+7V3Uth8cXIPn+Vit7B2AfWUCu0n5o9pq\n16FP7kXdQRqEsL0EsHzWnvPMbUIFaM8rz7fXNQrjPJ+4pOs8mHSAzDJzk8bOQ9e17a7r7kzCYO0A\n7CsT2AHz7o+APm9zxgTSlML3qzfNqJdDWS8VaXMgj62LiqiK7TYDpdUmJxWNwqogSXL5qC7lk2lK\nxlTT3nnovrY9H4Adx/YNwG7/ChtEUf7Y9JaUMaFds6ysBqpm7ZTm7pFlXw7KUrjtrB2orm8/axRW\nlZJJte5eTDpAFnetTct/LwZ1H3dP237WJOw2OLeLUrpSgR0w226tu2lJWQ24bnWrgaqBiTGONFWW\nwu1m7Wf17eV2H9tttpdwVqFkGMvtHqq+YO+FSQfIfNfafmDvukpGDsCWJmGnp3fbXs4Z1A7sYRj+\nvTAM3wzD8Bvn/d3j42MrLl6X5Y9xLK0GxuNBpXNZpHTKUhmKymlbIQPkGvUqBVFFyVRtXIpjsuPG\nfW3zYa+utt1Drm3vVtYO5CZhm41dJmE67sq/D+CzF/mLhBDYwKcVR4l1Wf5Y9SW53VYrhqpBIFUK\nsE2gakGUUr57Kbi1VDKOo9MB0pzdgL3a9syKxK8MbDUJq31Zoyj6QwAXEnTaNAfR9PBrnfLHNJVN\nS0KISmoKpfDwPLd09q1sBmzg2utMTtpssloqmeLLQdd1bcduoP0X9Flte/uJX1lIk7DZziRs2fZy\nABjm2ItzENuG1PZyI4UkQpRnuz5Zm3JfrBpg4zjbUTrldNmEsH2zjg1Zu/JvlxLIctRKkZKpkmlJ\nWkx1tda/rqpnQGcS8CDYq223I/Eri8XihlUmYUafzOIcRBsaE0z6yMSxXvkjIfLmr1rMlJ4lcqBE\nWWvezUY2ClUdQacbcUz2nbVlJicVs+4qEALYbEitruB7kWV5D0TTCYd92vbuFlKlSdg1CMFxetq+\nSZiWyxmG4dMAfiuKog887O8JIQSlFHfv3oXnebh27Zo2r+uqIISAEALf9zEcNksvUCrdGj3Pg6eh\nS0oIsZ/F6Lpu6XN578NT5vPFz7Z9DYHqv6XOOVBgjO0/62ogrTnnoFQmAoPBoNHzSylFlsmJVUEQ\ntH4tT09PkaYp5vM5xuNxq2spCyEEvvOd7yCOYzzzzDOYz+favtspeWGMzz47Po4BeGCM4datYzhO\n+wqL8dgFIQTLZYomEwXHAebzIQihuHu3vjvczZtzJAnBaDTAapUgTctvAYdDHwcHI6Qp3VMTF4Hn\nuTg6moAQhtPTuPRxm8BoNMBsFpT+LYOBh8ViDEoZTk7K/xbHcbBYjAAI3L270XIPjUZStbRaxUjT\nZne3o5HcRR8fr8E0HermzTlu3VqV/pwQMn6tViusVqT1F01ZzOfXEcc/wOuv/39429uebG39OuSO\nvwHgBfmv4ffDMPy3zv9UsTGh/S2XKR+ZpuWPVe6hLKOVDMJs0rUrJAlBllEEgV9KykmIjGa+71WS\ncgqh327ApLY9Tc11ZJ+HeymZrmE4HGE6PQClBKvVSWvrqJ2xR1H0q2U/I6V6A8gLR5D7RrQDxrCT\nPzqgFNqylvshTeUszSDwQAgDr1knklw5wXQ6xHg82HeIlsFmk+LwcILpNCiVfW+3GYLAx2QytCZr\nX69THB56mM2C3fm9eOLAGMdkMkSa0lKfA7Cb0SqzbOWmWRdxTDGdDjAe+9hsmgtyQgCEyMA+HDrI\nsraTLQ9SHSNNwhzHjsTholgsriOON1it7mIymcH3zbMSLb6i7ZpebjJr0S9/pIWGmfLZHaV59l3G\naqCYtbfp/FiEGmYtJyddvLjrOA42m/KfKyIfytG9UXqEmLO2Pg/dNwnzWp+21NoltO3imfSROTto\nQZ/7Yx11xnab7mxpy7smVvlck8gyusugy1EyWZY7YJbtygVyy4cq/QEPQtGWomm6Nk3NWVufh66b\nhE0mcwyHIyTJBnG8MX78Vq/g2YvXftZuUv6l20eGEI4sY5U5b+mBUr5pSQYz+bmqQ7ebwGajhlkH\npTjq9Tr/XJXCl7IbGI2q7Z7uhdS2m/RtN9PbcTF02yTs6Eh2pEprX7Prb//VbJl2lRBhJGvhXCDL\nuNYBFrlVQLUAu93KpqXJZFgqGBY/Z4uIgXOBzSaF65ajVuQovGz3uaq7H712A1nGtDe4PfhY5no7\nzkPXC6mDgZq2RI1PW2o9sNt28XIfGRNj9GSRbjTS4yNTpAKqZHdCSEqmLKVTp9mpSaQp3VMrZc5H\nkqiGp0Glly4hvLLR2oNgyre9aBIWBO0H96JJmA21uLKQ05Y849OWWg/sEsVCavtbLlM+GlL+qLeQ\nmiT15I9ymAQr7VyoKAh5XBsCgoSiViaTspRMUqt2kO9i9JwP6dvOjfi2mzTJOw9d70h1XReLhaJk\nbhtbvxWB3TaHt6KPRvNt3Xp9ZJT8sU4htapzoW4KQgeKlEyZdTGWG6VVOY9qFyOvgy7fdqrdKfRB\nsNMkrJuF1PF4iiAYI023xgqp7V+1HaRW1a5CquIaTRRSAWjbZqdpPsKtig9KcT5qGSpCHrd8s1PT\nSFO6p1bKFJbVUA5p8lX+90gXTr3nQ0llm6Zk7DQJA7paSFXWvqent/Y2IE3CnqcPgG1bLsU1mhij\np8aj6Srabjb13B/X66ryR5W12yN/BPLfM5sFpV7UVTTxRShtu65dzFmpbLOPr8lpY+fBNnl0WQwG\nQ8znR2CMYblsftqSVYFdXjz1ZrankGpiIEGS0N3WV49eWTUP+b5bWZNdhYoghBWaloxbET0QjOX2\nvmVeOvL3EAwGXiU5p5pY1YS23cwAbDMqsYvBRZenLR0cHMHzfKzXJ40XUm24WvdA+TLbU0gFmh/I\nUdQr61JSKPlj1UJqkYooU3jMm5bs4doBWXuglJWed7peF+Wc5U/kdit920cjX4vvC+di7zk0Gpkq\npDrQYEhaC10vpDqOu6dkpLa9ufVbF9htLKQSYqZpI9cru1oCgCqkShlidW17WWqlzoSmprFeSy/5\nMtSKEALbbfkCbBHKt13Xy06NXBwOr5pJWPcLqaPRBGkaI47XjR2n/St1H9hcSG0auotjSVLPRyYv\nPPqlCo9nJzTZUHyTyIdrlKNWlAy0bLavIAvS1TuD7weTA7AJsa2Q2t1pSzJrd3BychucNxPfrAzs\nEnZtuUxNdqdUaDd+qjt4uYofjGp2qtPB2RQ2m2odtsUCbBUoamw67a5JmD2FVLviQxn4/gAHB0fg\nvLlCqrWB/SoXUnX7yCj3Rt+v5sIos1xZiC1DrSRJNZlh0xCiqG2/eJDOz0M133bVGey6+igqVXRv\n2kcGsLmQ2v6uvizm80N43gDr9SkISbV/vw1X6CHoC6m6imPbLdn5yFTzc9luU3DOK2e5tskfixRT\nmZdd1fOgoNskjHMYK6Qy1hdSdUEWUm8AAI6P9RdSrQ7sfSGVayuOFaf8VJsSVI3SYSzP9m1yfwTO\n2gZc9N46ex6qUzI6B2CnKQNjV7mQCnS3kDpFliXYbsuPEXwY2r8658C2QiohfSG1fAdnWksu2BSK\nVsVlULWgrCAtlvUOKEkS0hdSLdjVl8Xh4Q04joPT0ztaC6nWB3YJe7ZcRfe7q11ILef+WNcKtylI\nsy4ZEExSTDk1pquQqv9eeRD6Qqo++P4A87n+QmonAntfSNU3QadYSK3iEli1gFi0wrWrkJrbL1Sl\nmGwppOouuj8MpgbAXwRyV9/lQuoRfF8WUrNMTyG1/atyYfSFVH0dqWTXkdpOIbWqXLAppKnkZ6tR\nTHoKqboa0swVUmFNIVWiu1m7NAmThVRdHamdCex9IVV2pOqx9hXYblUhtZolraJ0ygRpxngtK9ym\nUfalU7WgXMR223ek6kDXC6mjkd5CavtXpARsK6SatvbVOZAjt/b1KlrS0krWvlX9Z5qG4ziVZrcW\nC8p1O1J1FVL7jtS+kNqpwC5h15bLVCFVWfv6vj5r37qDMap0pKrP1bHCbQrSrEtNPbr45zab8v4z\nZ4+bm7XpQLEjtWlr376Qqg86C6mdC+z2zkg1Z+2rv5BabUZq1SlDWZYP8tBVN9ABqfXPdgXNi/+e\nov9MVYvkOrNq7wd1r1xta9/2d/VlMZ8faimk2nAlKqA4I7X9i2dyRqrStusKAGo2Z1VqpOqUITWL\ndDotN4u0aRRnt5ZZV+4DU26QR/G4nOujqIodqU3PSO07UvWh2JFap5DaycBu28UzOUYsy+QEneHQ\n0zJiS2nM68zmrDJl6OwsUrsomSqdpZyLvVa/amFYFVJ1adtVITUIvMZ3k30hVR+KhdSq1r7tX4WK\nsLGQaoprVNtsSvXctFnGQAjDcOhXam4hhCFJyk8ZqurX0jSyrKpVsZIvDiqpl4rXQfeM1Ka17ULY\nOCO124XU3Nq3/Po7G9gl7MnaAVlIMsE1ykKqvNi6ttmKSqiabW42uW1AOW17UovCaApqIEfZ86EK\nw3V8ZC7DjFQTA5sfBtt29WUhC6mHlQupnQ7s9hZSm+cak0Q11XiaZqTmBbzqJmHlqRXGRKVZpE1D\nzowlpWWIZ3c/5W+C4oxUXYXlvCO1+V2RKqQS0v7zeJlmpJZFpwO7hF2FVJNco+d5O72yrpb0epay\nVamVOJZ2A6PRwCpKJt/FlHvh5D4y1bJuWUitPqv2XnAud3ie5zZ+flVywxhrnNc/D13P2tWM1On0\noPRnOx/Y5cVTD1D7F89k04bruiCEYzDQp1eu20m5WiX7Ds4yQUlRMmU/1yTULsb3y2XPMtunu/F7\n5bNuqX6qN6v2XqQpBecya2/6/OY0Yfvh5TLMSD06eqT059o/8xogL54qpLZ/8Uw1bchuSb165bMm\nYdU02VIdUo5aUZRM2c81jSLnXa5pSY3fq/aiqmuxfC+kj4yZQirncjfpus3bbVwMuUKmi4XUKrgU\ngV1CZTZ2XDzlftd01sK50G78VNS2V/FPj2NSafBz8XO2OEBKX53yTUt5s1M1Px5A/0COLOP74S06\nXhYPw3A4NDa34DzYVoszgUsT2G3j0xiTfKMJkzA5QUffAysE9tOWqg5ezp0cR6U+t1rJz83n9lAy\nqnloNCrHeVdtdlKQAzmkj4yuF10cyx1t01m74zjG7DYuhtza14ZaXNO4NIFdoujLbEfWbipr0W38\npAqhVdUdeZt9ObsBxvg+Qy77UmgS+VjBctlz3aw7L+Dq4dqLnkNND+SgVFKSvu/0hVTDqH26wzD8\nbBiGfxyG4XfDMPxPdSyqKmyz9jU5bUk9sDqVD5uN4perqTM2m9xuoCwlo9Q1tnjJVM3apYsm2zUt\nlX/cJNWmV/5Y9BxqGmlq00AOu2pxTaLW2Q7D0APwdwB8FsB7AfxqGIbv0bGwqrCtndjktKUk0at8\n4FwNwK4+5We1Sio5Oa5WiXVeMlU97NWEpqruj7rlj8WBHE37yCi7Dc9zGuf1L4ZiLe7yZu11Q83H\nALwWRdHrURQRAP8QwC/XX1Zd2NVO3IZJWDMDsMuvn1I5XKPsKL2il4wt9r5JknPmZYrK0nO9+vDq\nZuSPuY+MCfljX0g1i7qR5nEA3y/8+Qe7/9YqbKNkTJqENdFCXn9KUArG5Ai5MllbcZiHroBWF3Fc\nzTBNedeXbXZS0C1/VN95NQdyFJsa20/8mkDdK1o6Yt68Oa95yIvj9PQUaZpiPh9gPB4bO+79IOVv\nMYZDFwcHI7iaeJn7nU8hBAghmE4HGAyqSRbvBeccvu/i+vVppbWrl+vR0RQALrwm9bnpNNj5yTQX\nGC5yb6r1jMfD3czYi69HCFlIvHFjVul3CCHAOcdiMYanwbNCGckNBh6uXw+03ZMKxfMphECSJNrv\n/6rIsgwnJyfwfYajo4NG76s2UDew/xDAOwp/fgdk1v5A3LpVf57fRSGEvFir1QqrFWn94nmeg9HI\nxWYTI0nqZwo3b84feD6DQHY9rtfJ3lemLhaLEVzXwcnJFoyV3wXNZgFGowE2mxRxfPFt8GDgYbEY\ng1KOk5Nt6eNeBA87l/ciCHzM5yNstxm22+zCx3BdB0dHE3AucHxc7XfM5wEGAw/HxxtQWv8e8jwH\ns9kQaZphvdZHTdzvfKr7f72OkaY2ZMoeKKW4desEjmNHkV4X6r42XwLwrjAMnw7DcAjgcwB+s/6y\n9MA2Po0xYayQlGvb9QzABvSM0sspmYvfeoQwxHEG33e1uR7WQZrSvT1vmVxBFaPLzlUtQr1IdDUt\nFdVUTcsfiwM52pY/Slxe+WOt0xtFEQXwHwL4XQDfAvCPoij6to6F6YNdJmFd1rYTUs9uQIhqQzkA\nyfNTyjEeD63oSlXFzLIBOo6zvb1xlQ2kcn+Us2/1nAeT8kdTQoKLQCZ+6je3n/jpRO0rGUXR7wD4\nHQ1raQSO40CIIYAU8s3stkrJqELScOhiOJTdeU1BZWPDoYcg8JCm9V9s222GwcDDZDIAIVJZUQZq\nKMdoNMB4PChFyaxWCQ4Px5jPRzg52ZY+tk4kCdnx7OV+g+zqzTCdBhiPh6WoHIU4JhgO5TXIsvrX\nVMkfRyNf233yICghgTSuc0Bp25myDzmoRxZSpVy6+7gcv+Ic2NaYkJuENa9tj2NaGI+mx25AByXD\neXlKhjGO9VpKIOfzdrtScwlieVqlrtWAGn4tj62r09ik/FFYK3+8LJTMlQjsEnaZhKnikYktqW5K\nJsvY3sOkqi57tZKUzHxejpJJU7ofw6eLZ66KOM52zprl+XL1cqwq49TdtASYG6MHmOvIvhi6PZDj\nfrgygd22NzPnkrM2oe2llIMQvf4gxVF6VagtWRCVjUtVxs9VsSrQDWWWVqXdv1iArbqTimOiddCK\n6oEw4f5Y9JFpW2loW2zQgSsT2CWKJmE2FFLNDcBW49HGY1+b3YBqsa/qAKkal8oGaJnxJwCw00S3\nFxmShNTO2qvuPNTLIQh8bedASWNNFVJ7H5lm0P4ZNQgb38z5ltSc3YA+XjZ3gKxOySgvmXKcOaUc\nm410gWyTb5dj56RSqKxaRxqE1esm3W5JpU7YB8Gk+yNjMDYj+GK4PD4yVyqwA/eahLUvcVLadnlz\nN5t5Zlm+1dZpN5BTMuU/L71kqmnUk4TsB063qW9Xqpgq2vTtNq2VtROSD8/WdU1Nuz+amhF8Hmzr\ne6mD9s9mK1AmYXZp24PAjLZd5yi9s5RMVZVMBkpZJY36apXu9e1tDcKmlINSKSstS4lkGdtZFFez\n9aPvdRcAAA4iSURBVAXyF4surt2k+6MQuY+SHWP0LoePzJUM7LZRMiZ928+O0rNjKAeQT06qMsw6\nH6DdHt+uCpnVsvZ63aSU8r17pK7mrV7+CNhgIFgVVzKwA4DjeLCpWGLSt13ZDQSBPvVDPpSjakel\nnJzkeeWHWRf17QcHo1ZUFmlK94M4ykLRKVWtkQHJteuctATkw69NDDuxSf54Nja0v6Ovgisb2CXs\n0rabbLdugpJR4+OqZp5qctJoNMBwWF4+KLl6r7WReur3t5G1q52Yzgla+fBrt/GdkE3yR4m8DtfF\nrP1KB3bbKBmTvu1F8yddPGqSyDFwQVCdklmvkz0lUzaYbDYZsowiCNrxb8+Lju1k7XFcXXr5ICQJ\n21FMzdcv7JM/2jOJrSzaP4Ot4+pq25OEabUbAID1ui4lI2rZBqxWyd5B0rRZmBBK+uhWUqjUzdql\n5znduUfq2YnJwrAa3NJ0smGb/NGuSWxlcOUDu21ZO5BnLiYomVwHbQ8lk6YUaSqLgWWzz2Lz0nw+\nMj5nM01ldleFl9aRtScJ2c291Wc1oGi7qyl/tEcaXQbtnz0LYJ+2XWZKnte8BKwpSkYFqDqUTBXv\ndkCeu7yYOjbK2WYZA+e8csGxftZe3VL4QeBcgBBuxLPdTvmj3NHbII2+KPrAvodd2vY0zSVgJuwG\ndFMydVUyRe/2KpRMmtK9ysZ0Z2qaSufFKi81PVm7UujosY9Q32nOs91W+aMdO/qLoA/sO9h4AU3Z\nDQD6HSCLlEzVxqXi5KSygzkAmf2mqRyGbbIzVdExVYOgytrrFEHz66m/aclEIxghNskfiz4y7Sd9\nF0Ef2AuwVdtuwm5ANrkw7ZN56njJAHlXahUJJCApHdWZakopowqOw2G1jJkQtlcXVd1BNWEQppqW\nRqPmm5bUzAJ75I92JX3noQ/sPwG7tO2qmGTCbkBu4eWDq6tJ6qyXTLXfsFxWl0AKASyXMRjjmE4D\nY7YDaUp2GWfVrF0VtavvNHTb+gIyuMvCvgn5o7kd63k4W0htP+k7D+2fMctgGyVj0m6g6ACpKxjo\n8JLhvJ4EknOB5TIB5wLz+ciIh3sddQwAZFnu/Fg1484ytjd905W1ZxkDY0Lrdz4I9g2/7o780YrT\nZR/s0rabtBsgJB/KoStTyr1kqk1cUt9RVQIJSNsBkx7uUkkiaajqgzTqTVmS36HX1hfIX/5msnYZ\nQO3J2rvh/tj+2bIQtmXtQDt2AzpVFZtNBs6lSqZqoCtKIKsqTpSH+2Ixbjy4q6y9quSzOGWpKo1V\ntPXVVafJawjNT1qS3dhS+mu6J+H+yMfo2aCeexD6wP4AyEq4PW9nOUpP7FQJzVMyulUVkpKpNwT7\nbPNRUCnYJQnBZpPC89zGNe6EyMBeh9fXlbUDwHisTxlkdtJSL38siz6wPxRFb+b2385FpYApSmYw\n0NeUkmVsT6dUDQiUShdIOTmpvAQSkIFOySgPDsaVvuMikBwxr2VtkBe0qwd2NfNWZth6riVjYk/Z\nNV2zECJPapr2ULoIuiB/7AP7QyDfzirLsePtnKa53UDT69E9JxWQGm3OpVFV1a11HBNkmdSnVw14\nm022f8nM56PGziUhDK7r1gqoeSdp9exYZe16uXa2o+zM6NqFEFYEdgm7s3ajgZ0xO99uD0NuN2CH\ntl1SMhyu64DSZtdzlpLRs+UWQgZVSclUy7gBOZiDc47pdFg5Y1ytkr0bZFMgRN7zdXY9uWtjdSpF\nZe3SzEvPY2/SagCwzbPdbvmj0cD+6quvgtL2+erysEvmpBwgCSEGGkU4COG76Tx6bhdCGJJEuiBW\n5Y6FEFitUgDS7KvqeVguZXCX31P9RfMgUCoDu+9Xz2qLro1VdfGA1MYD+kboAWatBuz0bLcnLhRh\nNLBzznF8/JaVW5eHwcZxWUoGZkYlQxqhZKTio/oQZkKYFj+Y5VIWZINgUMm64GFgTNkw16Mr4jir\n7bXOmOwu1pm1yz4Lc1YDdnm22yt/NHp2Dg4OkKYx4nht8rBaYNu4LMYAz/OMOEA2oZIBpHc7gFo+\nLjr4dgU1vUm3aRil0j2zzkuRc7EPynVeEnFc34fmXqQp20lxmw/sRc92O5qW7JQ/Gj01TzzxBBzH\nwcnJbXBuz0m4OIoFk/a3XsPh0JgDZE7J6ONTGeN7iqFOcNfBtzuOg+Uy3nPuBwf6gjtj8l6pq0hR\nQbnOC0zaNFPtWbsyCLvqTUs27OYBw4E9CAIcHFwD5wynp3dMHloLbLuIjuMgTYWxoRxNUDJxTGqP\n0/tJvr3a4qSvTLLfAegK7roCe1G2WKe5Ko5lTUF31q6sn5tOMopNSzZ4ttsofzT+ypvNDjEYDLHZ\nLJGmsenDa4BddgOMCVAqOk/JKO/2qgGryLfXDcjF4L5YjCu/KBQYkwmAjk7XJCG7GaR2ce2A7JSV\nSYa5pqVe/nh/GA/sjuPg8PARALgEhVQ7LqKyG+gqJaO6UusYhQEy+1fa9DquiIAM7klCMBh4ODwc\n12pn51xfYE9TNUSj3os170bV94LOMg7GOIbD5nss7Gtaskv+2ApJFQQjTKcLUEqwXN5tYwm1YNso\nvbMOkN2kZNKU7bnfOtI55SczHg9qK1HW63RvP7BYTCpntyrI1c38FZKE1m5Yai5rl7a+JnpW7Gta\nygN72zW41qoPi8V1eJ6H1eoYhGRtLaMG7BqlZ3IoR5GS0dnJqIzC6nSlKp4ckHx73Sw5jglWqwSO\nAywW40oZru5dlHqx1s/a9StkCJFZO+e8cZM1wMampXyeQ5toLbC7rovDw5sAukzJ2Gc3YGooRxP2\nvrIrVc45raMnZ6w4zLp+ATRNKU5P4507ZYCDg3INUSpTV5RMXQghkKYUvl9P+qgGmevO2pNEJjom\nrAbsa1oq+ku1l7VXvpphGP7FMAy/GYYhC8Pwz1T5jvF4htFoiixLsN2uqi6lNdhmN1CkZEwEdzUE\nezTytWmKCeFIEgLPc2vtBtKU7oy+PC0dpZRynJxs90XVw8PJhRtyVPBV6hgdSBI9HLmu7ymCUtlE\nNBg0b+sL2Jy1t5fw1XkcvwHgVwD8QZ0FHB7e2GvbGWs/OJaHXW3FOSXjwms4YWpi4hIgW98plQXC\nOhnpZpOBEIYgGNSmLYCc5tls1G5gfKGhHUHgQwixty7QgaL3Sx3Ko/g9upwfAdk8B5ix9c0nLTU/\niOYikM2MSjnXTkyofBqiKPrjKIqiugvw/QEWi+sQguPk5HbdrzMOG+0GFCVjopBKSD4EW2dzymaT\n7iWQdbbYq1Wyb16qW0xViGNyJnu/dm2K6XR438AYBD5830OWMei+NZT0sa68MFfI6AvCruuCEL5L\nMExk7fY0LUm0m7VbcRam0wWGwwBxvEaSbNpeTmmctRtof9dRlIKZ2J4qz/Ag0DcHk7F8Vmodvl3N\nOwX0FFOL61suE6xWCShlGI+HODqaYLEYYzodYjYLMJ8HmM0CcC6w2aRajluElD7WL6LmjU/6piwB\nZodxyKYlsZu01PjhzsXZpiXzMeGhZzwMw98D8Oh9/q+/EUXRb+lahNK237r1AxBCMNJr1WEIA8iG\npfYzdkAGds8Tu0DWvKY4jikmExkYdBUJlSbd82RhrGriQ6ksps5mAXzfRZbpUzGpWazDobenjoo7\nA/liibWdk3uRZdKSwXXrnXdV13BdV5tUUc19dZx61++iyDK+8+Rp/p6/GNqLCQ8N7FEU/TmdB3N0\nCXl79OjRo8cDoYuK6QN2jx49eliCygE5DMNfAfDfA7gB4BTAy1EU/XldC+vRo0ePHj169OjRo0eP\nHj169OjRo0ePHj169OjRo0cPk2hczRKG4V8E8DcBvBvAs1EU/T+F/++vA/i3IcWefyWKov+z6fVc\nJoRh+DcB/LsAbu3+01+Pouj/aG9F3UQYhp8F8LchO0p+PYqi/7rlJXUaYRi+DmAJ+VyTKIo+1u6K\nuoMwDP8egH8ZwFtRFH1g99+uAfhHAJ4C8DqAvxRF0cnDvsdE5+l9PWXCMHwvgM8BeC+AzwL4H8Iw\ntKITtkMQAP7bKIo+vPunD+olEYahB+DvQN6D7wXwq2EYvqfdVXUeAsBndvdkH9TL4e9D3otF/DUA\nvxdFUQjgC7s/PxSNB9KHeMr8MoDfiKKIRFH0OoDXAPQ3QXn0PQT18DEAr0VR9HoURQTAP4S8N3vU\nQ39fVkAURX8I4Pie//wXAHx+9++fB/Cvnvc9bWbIjwH4QeHPPwDweEtr6TL+ozAM/ygMw78bhuFh\n24vpIB4H8P3Cn/v7sD4EgP8rDMOXwjD899pezCXA26IoenP3728CeNt5H9DizqPRU8YGgwer8JBz\n+58B+B8B/Be7P/+XAP4bAP+OoaVdFvT3nH48F0XRj8IwvAng98Iw/ONdJtqjJqIoEmEYnnvPagns\nFT1lfgjgHYU/P7H7bz0KuOi5DcPw1wFoM2a7Qrj3PnwHzu4ke5REFEU/2v3vrTAM/wkk3dUH9up4\nMwzDR6Mo+nEYhm8H8NZ5HzBNxRR5t98E8K+FYTgMw/CnALwLwNcMr6fT2F1khV+BLFT3KIeXALwr\nDMOnwzAcQhb0f7PlNXUWYRhOwjCc7/59CuBfQH9f1sVvAvjLu3//ywD+6XkfMCF3fKCnTBiGfwNS\n7kgB/FoURb/b9HouE8Iw/AcAPgRJJ/wJgH+/wMX1uCDCMPzzyOWOfzeKor/V8pI6i12S9k92f/QB\n/E/9+bw4wjD8DQC/ABkv3wTwnwP43wD8zwCexAXljj169OjRo0ePHj169OjRo0ePHj169OjRo0eP\nHj169OjRo0ePHj169OjRo0ePHj169OjRo0ePHj169OhRGf8/ZDJZepggnBEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcb5fe10>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.contour(theta0mesh,theta1mesh,J_vals, np.logspace(-2, 3, 20))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x000000000D124948>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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c/axUE97tjMEySsZFMbh3Db3dwFlYE9iB3FvDhK3v2axdZ2ejNJsaDuubg+l8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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcade8d0>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sn.set_palette(\"Blues\")\n",
      "plt.scatter(theta_update[0], theta_update[1], )\n",
      "plt.contour(theta0_vals, theta1_vals, J_vals.T, logspace(-2, 3, 20))\n",
      "sn.set_style(\"darkgrid\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PluFQ6snqRajdbrZNMa+ASJ9CRAVEu4hFi+Iy3XwzZN4YAgfECfLkyQC9nodW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10de7128>"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#numpy.meshgrid takes two (or more) 1d x and y coordinate arrays, and returns a pair of 2d x and y grid arrays. \n",
      "theta0mesh, theta1mesh = np.meshgrid(theta0_vals,theta1_vals)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure()\n",
      "ax = fig.gca(projection='3d')\n",
      "ax.plot_surface(theta0mesh, theta1mesh, J_vals.T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x10e16da0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0dRlzg+y//9sceuixmd8q5V1DMplg48ZNxOMJy9IdDeiEZkZTt7SAi+ZbrafV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\nypYiCC6qqg4lK6rRaOOfMRjm4nC8itlsRBAMJJNGotFexOO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SQJpUKkUiYaC29nDgKHJH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       "text": [
        "<matplotlib.figure.Figure at 0x10ac0898>"
       ]
      }
     ],
     "prompt_number": 88
    }
   ],
   "metadata": {}
  }
 ]
}