GP Clustering 1d test.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "import numpy as np\n",
      "import matplotlib\n",
      "import matplotlib.pyplot as plt\n",
      "import scipy\n",
      "\n",
      "#data generator\n",
      "size = 300\n",
      "\n",
      "mu1, sigma1 = 1, 0.02 # mean and standard deviation\n",
      "s1 = np.random.normal(mu1, sigma1, size/3)\n",
      "\n",
      "mu2, sigma2 = 4, 0.1 # mean and standard deviation\n",
      "s2 = np.random.normal(mu2, sigma2, size/3)\n",
      "\n",
      "mu3, sigma3 = 2.2, 0.15 # mean and standard deviation\n",
      "s3 = np.random.normal(mu3, sigma3, size/6)\n",
      "\n",
      "mu4, sigma4 = 2.8, 0.1 # mean and standard deviation\n",
      "s4 = np.random.normal(mu4, sigma4, size/6)\n",
      "\n",
      "data =  np.concatenate((s1, s2 , s3 , s4)) \n",
      "\n",
      "\n",
      "print len(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "300\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plotScatter(X,title,c):\n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.plot(X,[0 for i in range(size)],c+'.')\n",
      "    ax.set_title(title)\n",
      "    plt.show()\n",
      "    \n",
      "def plotLine(data,X,Y,title,c):\n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.plot(X,Y,c+'-')\n",
      "    ax.plot(data,[0 for i in range(size)],\"r\"+'*')\n",
      "    ax.set_title(title)\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotScatter(data,\"scatter plot\",\"r\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEKCAYAAAD9xUlFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAHjFJREFUeJzt3HtwVPX9//HXhgSQIJcIJJINRnOBIBoi1GhHh6U0IFEo\n44WCgmkFpbSI0WmLTKdtsEWDyLQo1oGOIg7TCNoZk0rIlItRviLE1ghTEptAiWw2JFOaREVLEpbP\n74/95UOWzY1sJEt9PmZ22HPO+5x972c353XO7h4cxhgjAAAkhfV1AwCA0EEoAAAsQgEAYBEKAACL\nUAAAWIQCAMAiFIAQUVVVpbCwMJ07d66vW8E3GKEASMrJydHChQv95rlcLr388st91FHn2usX6A2E\nAtABh8MR1Poc8eOyZIDLUG5uromNjTVXXnmlGTt2rNmzZ48xxpizZ8+a1atXm4SEBHPllVeaSZMm\nmerqamOMMcuXLzdxcXFmyJAhZtKkSWbfvn3GGGN27txp+vfvbyIiIszgwYNNamqq+cUvfmH69etn\nBg4caAYPHmweffRRY4wx5eXl5rvf/a6JiooyY8eONdu3b7c9ZWVlmR/96Edm5syZJjIy0vbU1pQp\nU8yTTz5pbr75ZjNkyBDzve99z9TX1xtjjDl+/LhxOBzG6/UaY4zxeDxm1qxZJioqyiQmJpo//vGP\n7fY7ceLEr2mU8U1EKOCy88knn5i4uDhz8uRJY4wxn376qTl27Jgxxphnn33W3HDDDaaiosIYY8zh\nw4fNf/7zH2OMMVu3bjX19fXG6/WadevWmZiYGNPU1GSMMSYnJ8csXLjQ73FcLpd5+eWX7fTp06eN\n0+k0r776qvF6vaa0tNSMGDHClJWVGWN8oTB06FCzf/9+Y4wxZ86cCeh9ypQpJjY21hw5csR8+eWX\n5p577jELFiwwxgSGwu23325+8pOfmKamJvPxxx+bkSNHmr1793bYL9Ab+PgIl51+/fqpqalJR44c\nUUtLi8aMGaPrrrtOkvTyyy9r9erVSkpKkiTdcMMNioqKkiQ98MADGj58uMLCwvTEE0+oqalJ//zn\nPyVJxneAFPBYbee9/fbbuvbaa5WVlaWwsDBNnDhRd999t9544w1bM2fOHN16662SpAEDBgRsz+Fw\n6MEHH9T48eM1aNAg/eY3v9H27dsDHtvtdmv//v1as2aN+vfvr9TUVC1evFivvfZap/0CwSIUcNlJ\nTEzU73//e+Xk5Cg6Olrz58/XyZMnJfl2pgkJCe2u99xzz2n8+PEaNmyYhg8frs8++0ynTp3q9LHa\nfq/w6aef6uDBgxo+fLi9/elPf1JdXZ2tjYuL67L/tjVjxoxRS0tLQB81NTWKiopSZGSkX63H4+ly\n+0AwCAVclubPn699+/bp008/lcPh0IoVKyT5drhHjx4NqN+3b5/Wrl2rN954Q42NjWpoaNDQoUPt\n0XZ7XypfOG/MmDGaMmWKGhoa7O2LL77Qiy++eFG9nzhxwu9+RESERowY4VczevRo1dfX6/Tp0361\nTqezw36B3kAo4LJTUVGhvXv3qqmpSQMGDNDAgQPVr18/SdLixYv1y1/+UkePHpUxRocPH7Y71/Dw\ncI0YMULNzc166qmn9Pnnn9ttxsTEqKqqyu8jmejoaB07dsxO33XXXaqoqNDWrVvV0tKilpYWffjh\nh/rkk08kqVsf5xhjtHXrVpWXl+urr77Sr371K913330BO/m4uDh9+9vf1sqVK9XU1KTDhw/rlVde\n0YIFCzrsF+gNhAIuO01NTVq5cqVGjhypq6++WqdOndIzzzwjSXriiSc0d+5cTZ8+XUOHDtXDDz+s\nM2fOaMaMGbrjjjuUnJys+Ph4XXHFFRozZozd5n333SdJuuqqqzR58mRJ0mOPPaY333xTUVFRys7O\n1uDBg/XXv/5Vr7/+umJjY3X11Vdr5cqVam5uluQ7eu/qCN7hcGjhwoX6wQ9+oKuvvlrNzc16/vnn\n/Za3ysvLU1VVlUaPHq27775bTz31lL7zne902C/QGxwmyEONoqIiZWdny+v1avHixfY0vq3ly5dr\n586dGjRokF599VWlpaVJkhobG7V48WIdOXJEDodDr7zyim655ZZg2gFC2tSpU7Vw4UI99NBDfd0K\n0K6gzhS8Xq+WLVumoqIilZWVKS8vT+Xl5X41hYWFOnr0qCorK7Vp0yYtXbrULnvssceUmZmp8vJy\nHT58WCkpKcG0A1wW+MgHoSyoUCgpKVFiYqLi4+MVERGhefPmKT8/36+moKBAWVlZkqT09HQ1Njaq\nrq5On332mfbt22ePmMLDwzV06NBg2gEuC3xJjFAWHszKHo/H7+d1TqdTBw8e7LKmurpa/fr108iR\nI/XDH/5Qhw4d0qRJk7R+/XoNGjQomJaAkPbOO+/0dQtAp4I6U+juEc+Fp8sOh0Nnz57VRx99pB//\n+Mf66KOPFBkZqdzc3GDaAQAEKagzhdjYWLndbjvtdrvt76g7qqmurlZsbKyMMXI6nfrWt74lSbr3\n3nvbDYXExES/nwUCALqWkJDQ7jU7XQnqTGHy5MmqrKxUVVWVmpubtW3bNs2ePduvZvbs2fbS/AMH\nDmjYsGGKjo5WTEyM4uLiVFFRIUnavXu3rr/++oDHOHbsmL2kP5Rvv/71r/u8B/qkz8u1R/rs/VtP\nD6aDOlMIDw/Xhg0bNGPGDHm9Xi1atEgpKSnauHGjJGnJkiXKzMxUYWGhEhMTFRkZqc2bN9v1X3jh\nBT3wwANqbm5WQkKC3zIAwKUXVChI0syZMzVz5ky/eUuWLPGb3rBhQ7vrpqam6sMPPwy2BQBAL+GK\n5l7icrn6uoVuoc/edTn0eTn0KNFnqAj6iuavm8PhUIi3CAAhp6f7Ts4UAAAWoQAAsAgFAIBFKAAA\nLEIBAGARCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQCAMAiFAAA\nFqEAALAIBQCARSgAACxCAQBgEQoAAItQAABYhAIAwCIUAAAWoQAAsIIOhaKiIo0bN05JSUlas2ZN\nuzXLly9XUlKSUlNTVVpa6rfM6/UqLS1Ns2bNCrYVAECQggoFr9erZcuWqaioSGVlZcrLy1N5eblf\nTWFhoY4eParKykpt2rRJS5cu9Vu+fv16jR8/Xg6HI5hWAAC9IKhQKCkpUWJiouLj4xUREaF58+Yp\nPz/fr6agoEBZWVmSpPT0dDU2Nqqurk6SVF1drcLCQi1evFjGmGBaAQD0gqBCwePxKC4uzk47nU55\nPJ5u1zz++ONau3atwsL4agMAQkFQe+PufuRz4VmAMUZvv/22Ro0apbS0NM4SACBEhAezcmxsrNxu\nt512u91yOp2d1lRXVys2NlZ//vOfVVBQoMLCQp05c0aff/65HnzwQb322msBj5OTk2Pvu1wuuVyu\nYNoGgP85xcXFKi4uDno7DhPEYfrZs2c1duxY7dmzR6NHj9bNN9+svLw8paSk2JrCwkJt2LBBhYWF\nOnDggLKzs3XgwAG/7bz77rt67rnn9Je//CWwQYeDMwkAuEg93XcGdaYQHh6uDRs2aMaMGfJ6vVq0\naJFSUlK0ceNGSdKSJUuUmZmpwsJCJSYmKjIyUps3b+7wCQAA+lZQZwqXAmcKAHDxerrv5Gc/AACL\nUAAAWIQCAMAiFAAAFqEAALAIBQCARSgAACxCAQBgEQoAAItQAABYhAIAwCIUAAAWoQAAsAgFAIBF\nKAAALEIBAGARCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQCAMAi\nFAAAFqEAALCCDoWioiKNGzdOSUlJWrNmTbs1y5cvV1JSklJTU1VaWipJcrvdmjp1qq6//npNmDBB\nzz//fLCtAACCFFQoeL1eLVu2TEVFRSorK1NeXp7Ky8v9agoLC3X06FFVVlZq06ZNWrp0qSQpIiJC\nv/vd73TkyBEdOHBAL774YsC6AIBLK6hQKCkpUWJiouLj4xUREaF58+YpPz/fr6agoEBZWVmSpPT0\ndDU2Nqqurk4xMTGaOHGiJGnw4MFKSUlRTU1NMO0AAIIUVCh4PB7FxcXZaafTKY/H02VNdXW1X01V\nVZVKS0uVnp4eTDsAgCCFB7Oyw+HoVp0xpsP1Tp8+rXvvvVfr16/X4MGD210/JyfH3ne5XHK5XBfd\nKwD8LysuLlZxcXHQ2wkqFGJjY+V2u+202+2W0+nstKa6ulqxsbGSpJaWFt1zzz1asGCB5syZ0+Hj\ntA0FAECgCw+YV61a1aPtBPXx0eTJk1VZWamqqio1Nzdr27Ztmj17tl/N7Nmz9dprr0mSDhw4oGHD\nhik6OlrGGC1atEjjx49XdnZ2MG0AAHpJUGcK4eHh2rBhg2bMmCGv16tFixYpJSVFGzdulCQtWbJE\nmZmZKiwsVGJioiIjI7V582ZJ0vvvv6+tW7fqxhtvVFpamiTpmWee0R133BHkUwIA9JTDXPiBf4hx\nOBwB30kAADrX030nVzQDACxCAQBgEQoAAItQAABYhAIAwCIUAAAWoQAAsAgFAIBFKAAALEIBAGAR\nCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQCAMAiFAAAFqEAALAI\nBQCARSgAACxCAQBgEQoAAItQAABYQYdCUVGRxo0bp6SkJK1Zs6bdmuXLlyspKUmpqakqLS29qHUB\nAJdOUKHg9Xq1bNkyFRUVqaysTHl5eSovL/erKSws1NGjR1VZWalNmzZp6dKl3V4XAHBpBRUKJSUl\nSkxMVHx8vCIiIjRv3jzl5+f71RQUFCgrK0uSlJ6ersbGRtXW1nZrXQDApRVUKHg8HsXFxdlpp9Mp\nj8fTrZqampou1w1Z/ftLDkf3blFR0qef9nXHveuRRySXS8rMlBobg69/5BHp6qulAQOkYcOkjAwp\nOdl3f+BAadQo3zhGRkphYf7j27//+XkXLmudN3Sob5tDhpyfHxMjXXGFf11EhG97/ftLw4f71mnt\nd9w4Xz8jR3b+erY+17g4KTra13dGhpSVdf45tj5GR++ZsLCOl7ft2eHw9dyv3/mxOHy4/V7b9nXb\nbd1/7S5nnb3vHnlECg/v/t9xb95uuy2kxz48mJUdDke36owxwTyMcnJy7H2XyyWXyxXU9oLW0tL9\n2oYG35vA7f76+rnUKiqkd9/13X/kEWn79uDqKyqk2lrf/eZmafdu3x/s2bO+ef/+d8fbbvtatPc+\nM0b6/HPfNtuqqwusa308yfdHu3v3+X5ra6XPPvMt6+z1bPtcW+3e7dtBd/Y8Luylo/fYmTP+0217\nbmmR0tN9wXNhr237qq72/dud1+5y1tn7rqJC8nr7pq/33/9axr64uFjFxcVBbyeoUIiNjZW7zR+H\n2+2W0+nstKa6ulpOp1MtLS1drtuqbSiEBIej/R1Qe664Qvq///t6+7nUBg3y/Tt5srRpU/D1rctb\npaVJJ05I//mP76j53Dnf/H79ev6HPHGidOTI+Z1tZKT05Zedr5OWdr7fiIjzvXb2erY+lyFDfGHU\n+tgjRgQGU29zOKSDB6Vp0wJ7be1r6FBfYHT3tbucdfa+u/A9dymlpHwtY3/hAfOqVat6tiEThJaW\nFnPdddeZ48ePm6amJpOammrKysr8anbs2GFmzpxpjDHmgw8+MOnp6d1e1/hOMYJp8euxb58xDocx\nvmho/zZsmDExMcZUVfV1t72vocGY++7z/dsb9Q0NxsyZY0xmpu/fhgbfuDmdxhw6ZMz3vuebf+iQ\nb0xHjjRm1ChjMjJ862Rk+OZnZBhz222+8Q8P99VlZPjWb2jwrT9woG9eVZVv3VGj/LfVemvto1Vr\nP129nq3PtarKt43Wx25o8N1v+xgulzEDBhgzYoTv8ds+j9bnNWTI+ffU2rW+HrZvNyYszLfeoUO+\nuoEDffc76rVtXxfz2l3OOnvfNTT4xm3AAGOmTvW9FgMH+sY2PNw33v36+W6SMcnJ51+H1FRj+vc/\nPz1kiDETJwbuA4YMMebKK89Ph4f7HvMSjX1P952O/79yj+3cuVPZ2dnyer1atGiRVq5cqY0bN0qS\nlixZIkn2V0aRkZHavHmzbrrppg7XvZDD4Qj64ycA+Kbp6b4z6FD4uhEKAHDxerrv5IpmAIBFKAAA\nLEIBAGARCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQCAMAiFAAA\nFqEAALAIBQCARSgAACxCAQBgEQoAAItQAABYhAIAwCIUAAAWoQAAsAgFAIBFKAAALEIBAGARCgAA\nK6hQqK+vV0ZGhpKTkzV9+nQ1Nja2W1dUVKRx48YpKSlJa9assfN/9rOfKSUlRampqbr77rv12Wef\nBdMOACBIQYVCbm6uMjIyVFFRoWnTpik3Nzegxuv1atmyZSoqKlJZWZny8vJUXl4uSZo+fbqOHDmi\nQ4cOKTk5Wc8880ww7QAAghRUKBQUFCgrK0uSlJWVpbfeeiugpqSkRImJiYqPj1dERITmzZun/Px8\nSVJGRobCwnwtpKenq7q6Oph2AABBCioU6urqFB0dLUmKjo5WXV1dQI3H41FcXJyddjqd8ng8AXWv\nvPKKMjMzg2kHABCk8K4KMjIyVFtbGzB/9erVftMOh0MOhyOgrr157W2rf//+uv/++9tdnpOTY++7\nXC65XK4utwkA3yTFxcUqLi4OejtdhsKuXbs6XBYdHa3a2lrFxMTo5MmTGjVqVEBNbGys3G63nXa7\n3XI6nXb61VdfVWFhofbs2dPh47QNBQBAoAsPmFetWtWj7QT18dHs2bO1ZcsWSdKWLVs0Z86cgJrJ\nkyersrJSVVVVam5u1rZt2zR79mxJvl8lrV27Vvn5+Ro4cGAwrQAAeoHDGGN6unJ9fb3mzp2rEydO\nKD4+Xtu3b9ewYcNUU1Ojhx9+WDt27JAk7dy5U9nZ2fJ6vVq0aJFWrlwpSUpKSlJzc7OioqIkSbfe\neqv+8Ic/+DfocCiIFgHgG6mn+86gQuFSIBQA4OL1dN/JFc0AAItQAABYhAIAwCIUAAAWoQAAsAgF\nAIBFKAAALEIBAGARCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQC\nAMAiFAAAFqEAALAIBQCARSgAACxCAQBgEQoAAItQAABYhAIAwCIUAABWj0Ohvr5eGRkZSk5O1vTp\n09XY2NhuXVFRkcaNG6ekpCStWbMmYPm6desUFham+vr6nrYCAOglPQ6F3NxcZWRkqKKiQtOmTVNu\nbm5Ajdfr1bJly1RUVKSysjLl5eWpvLzcLne73dq1a5euueaanrYBAOhFPQ6FgoICZWVlSZKysrL0\n1ltvBdSUlJQoMTFR8fHxioiI0Lx585Sfn2+XP/HEE3r22Wd72gIAoJf1OBTq6uoUHR0tSYqOjlZd\nXV1AjcfjUVxcnJ12Op3yeDySpPz8fDmdTt144409bQEA0MvCO1uYkZGh2tragPmrV6/2m3Y4HHI4\nHAF17c2TpP/+9796+umntWvXLjvPGNOthgEAX59OQ6HtTvtC0dHRqq2tVUxMjE6ePKlRo0YF1MTG\nxsrtdttpt9stp9OpY8eOqaqqSqmpqZKk6upqTZo0SSUlJe1uJycnx953uVxyuVxdPS8A+EYpLi5W\ncXFx0NtxmB4eov/85z/XVVddpRUrVig3N1eNjY0BXzafPXtWY8eO1Z49ezR69GjdfPPNysvLU0pK\nil/dtddeq7///e+KiooKbNDh4CwCAC5ST/edPf5O4cknn9SuXbuUnJysvXv36sknn5Qk1dTU6M47\n75QkhYeHa8OGDZoxY4bGjx+v73//+wGB0No8AKDv9fhM4VLhTAEALt4lP1MAAPzvIRQAABahAACw\nCAUAgEUoAAAsQgEAYBEKAACLUAAAWIQCAMAiFAAAFqEAALAIBQCARSgAACxCAQBgEQoAAItQAABY\nhAIAwCIUAAAWoQAAsAgFAIBFKAAALEIBAGARCgAAi1AAAFiEAgDAIhQAABahAACwCAUAgNXjUKiv\nr1dGRoaSk5M1ffp0NTY2tltXVFSkcePGKSkpSWvWrPFb9sILLyglJUUTJkzQihUretoKAKCX9DgU\ncnNzlZGRoYqKCk2bNk25ubkBNV6vV8uWLVNRUZHKysqUl5en8vJySdI777yjgoICHT58WP/4xz/0\n05/+tOfPIgQUFxf3dQvdQp+963Lo83LoUaLPUNHjUCgoKFBWVpYkKSsrS2+99VZATUlJiRITExUf\nH6+IiAjNmzdP+fn5kqSXXnpJK1euVEREhCRp5MiRPW0lJFwubxT67F2XQ5+XQ48SfYaKHodCXV2d\noqOjJUnR0dGqq6sLqPF4PIqLi7PTTqdTHo9HklRZWan33ntPt9xyi1wul/72t7/1tBUAQC8J72xh\nRkaGamtrA+avXr3ab9rhcMjhcATUtTev1dmzZ9XQ0KADBw7oww8/1Ny5c/Wvf/2ru30DAL4OpofG\njh1rTp48aYwxpqamxowdOzag5oMPPjAzZsyw008//bTJzc01xhhzxx13mOLiYrssISHBnDp1KmAb\nCQkJRhI3bty4cbuIW0JCQo/27Z2eKXRm9uzZ2rJli1asWKEtW7Zozpw5ATWTJ09WZWWlqqqqNHr0\naG3btk15eXmSpDlz5mjv3r2aMmWKKioq1NzcrKuuuipgG0ePHu1piwCAi+QwxpierFhfX6+5c+fq\nxIkTio+P1/bt2zVs2DDV1NTo4Ycf1o4dOyRJO3fuVHZ2trxerxYtWqSVK1dKklpaWvTQQw/p448/\nVv/+/bVu3Tq5XK5ee2IAgIvX41AAAPzvCZkrmju7yE3y/Qxs6NChSktLU1pamn77299e8h4feugh\nRUdH64YbbuiwZvny5UpKSlJqaqpKS0svYXfnddVnKIylJLndbk2dOlXXX3+9JkyYoOeff77dur4c\n0+70GArjeebMGaWnp2vixIkaP368PSO/UF+/P7vTZyiMZyuv16u0tDTNmjWr3eV9PZ6tOuvzosez\nR99E9LKzZ8+ahIQEc/z4cdPc3GxSU1NNWVmZX80777xjZs2a1Ucd+rz33nvmo48+MhMmTGh3+Y4d\nO8zMmTONMcYcOHDApKenX8r2rK76DIWxNMaYkydPmtLSUmOMMV988YVJTk4OeN37eky702OojOeX\nX35pjDGmpaXFpKenm3379vkt7+uxbNVVn6EynsYYs27dOnP//fe320+ojKcxnfd5seMZEmcKnV3k\n1pbp40+6br/9dg0fPrzD5W0v6EtPT1djY2O712983brqU+r7sZSkmJgYTZw4UZI0ePBgpaSkqKam\nxq+mr8e0Oz1KoTGegwYNkiQ1NzfL6/UqKirKb3lfj2V3+5RCYzyrq6tVWFioxYsXt9tPqIxnV31K\nFzeeIREKnV3k1srhcGj//v1KTU1VZmamysrKLnWbXWrveVRXV/dhR+0LxbGsqqpSaWmp0tPT/eaH\n0ph21GOojOe5c+c0ceJERUdHa+rUqRo/frzf8lAZy676DJXxfPzxx7V27VqFhbW/mwyV8eyqz4sd\nz5AIhc4ucmt10003ye1269ChQ3r00Ufb/QlsKLgwkbvz3C61UBvL06dP695779X69es1ePDggOWh\nMKad9Rgq4xkWFqaPP/5Y1dXVeu+999r97xhCYSy76jMUxvPtt9/WqFGjlJaW1ulRdl+PZ3f6vNjx\nDIlQiI2NldvtttNut1tOp9Ov5sorr7SnnTNnzlRLS4vq6+svaZ9dufB5VFdXKzY2tg87al8ojWVL\nS4vuueceLViwoN03ayiMaVc9htJ4StLQoUN15513BvzXMaEwlm111GcojOf+/ftVUFCga6+9VvPn\nz9fevXv14IMP+tWEwnh2p8+LHs8gv9/oFS0tLea6664zx48fN01NTe1+0VxbW2vOnTtnjDHm4MGD\n5pprrumDTo05fvx4t75o/uCDD/r0i6fO+gyVsTx37pxZuHChyc7O7rCmr8e0Oz2Gwnj++9//Ng0N\nDcYYY7766itz++23m927d/vV9PVYdrfPUBjPtoqLi81dd90VMD8UxrOtjvq82PHs8RXNvSk8PFwb\nNmzQjBkz7EVuKSkp2rhxoyRpyZIlevPNN/XSSy8pPDxcgwYN0uuvv37J+5w/f77effddnTp1SnFx\ncVq1apVaWlpsj5mZmSosLFRiYqIiIyO1efPmS95jd/oMhbGUpPfff19bt27VjTfeqLS0NEnS008/\nrRMnTthe+3pMu9NjKIznyZMnlZWVpXPnzuncuXNauHChpk2b5vc31Ndj2d0+Q2E8L9T6sVCojeeF\n2uvzYseTi9cAAFZIfKcAAAgNhAIAwCIUAAAWoQAAsAgFAIBFKAAALEIBAGARCgAA6/8BtIHDmvpp\nPT0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7690198>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = 1\n",
      "#Calculate Covariance Matrix C\n",
      "def kernelFunction(x1, x2):\n",
      "    c = 0.\n",
      "    c += alpha * (x1 - x2) **2\n",
      "    c = math.exp(- 0.5 * c)\n",
      "    return c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#test kernel function\n",
      "print(kernelFunction(4,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.606530659713\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the whole covariance matrix \n",
      "def getCovarianceMatrix(data):\n",
      "    C = [[ 0 for i in range (size)] for j in range (size)]\n",
      "    for i in range (size):\n",
      "        for j in range (size):\n",
      "            C[i][j] = kernelFunction(data[i], data[j])\n",
      "    return matrix(C)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate variance of dataset\n",
      "def getVariance(data):\n",
      "    return np.var(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate matrix k for new data point x \n",
      "def getMatrix_k(x, data):\n",
      "    k = [ 0 for i in range (size) ]\n",
      "    for i in range (size):\n",
      "        k[i] = kernelFunction(x, data[i])\n",
      "    return matrix(k).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#test getMatrix_k\n",
      "k = getMatrix_k(0,data)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate inversion of Matrix A\n",
      "def getInversionMatrix(data, C):\n",
      "    var = getVariance(data)\n",
      "    return  (C + var * matrix(np.eye(size)) ).I \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calcalate the variance for a given point x\n",
      "def varianceFunction(x, data, invA):\n",
      "    k = getMatrix_k(x,data)\n",
      "    result = kernelFunction(x,x) - k.T * invA * k #here add var*I to add noise te covariance matrix\n",
      "    return result[0,0] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = [0 + 0.1 * i for i in range (55) ]\n",
      "variances = [0 for i in range (55) ]\n",
      "C = getCovarianceMatrix(data)\n",
      "invA = getInversionMatrix(data, C)\n",
      "for i in range (len(grid)):\n",
      "    variances[i] = varianceFunction(grid[i], data, invA)\n",
      "    \n",
      "plotLine(data,grid, variances , \"variance of the predictive value\" , \"g\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAEKCAYAAAAPVd6lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7728ef0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "var = getVariance(data)\n",
      "a = (C + var * matrix(np.eye(size)) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Gradient Descent"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#nabla_variance_function\n",
      "def getDeltaX(x, data, inv):\n",
      "    size = len(data)\n",
      "    k = matrix( [kernelFunction(x, data[i]) for i in range (size)]).T\n",
      "    nablaK = matrix([ (-kernelFunction(x, data[i]) * (x - data[i])) for i in range (size)]).T\n",
      "    delta_x =  nablaK.T * inv * k + k.T * inv * nablaK \n",
      "    return delta_x[0,0]\n",
      "\n",
      "#gradient descent iteration\n",
      "def gradientDescentIteration(x, data, inv, ita):\n",
      "    delta_x = getDeltaX(x,data,inv)\n",
      "    return ( x + ita * delta_x )\n",
      "\n",
      "def getEquilibriumPoint(x,data,inv,ita,maxIteration):\n",
      "    x_old = x\n",
      "    iteration = 1\n",
      "    for i in range(maxIteration):\n",
      "        x_new = gradientDescentIteration(x_old,data,inv,ita)\n",
      "        if( (x_new - x_old)/x_old < 0.00001):\n",
      "            break\n",
      "        else:\n",
      "            x_old = x_new\n",
      "            iteration += 1\n",
      "    print \"iteration: \" , iteration, \"x0: \", x, \"xt: \", x_new\n",
      "    return x_new,iteration"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C = getCovarianceMatrix(data)\n",
      "invA = getInversionMatrix(data, C)\n",
      "SEPs = array([getEquilibriumPoint(data[i], data, invA, 0.1, 1000) for i in range (size) ])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "iteration:  80 x0:  0.973841839434 xt:  1.02604988517\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 83 x0:  0.958862009343 xt:  1.02604956162\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  1.00155217224 xt:  1.02605456465\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.996944793149 xt:  1.02605266741\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 75 x0:  0.990307026992 xt:  1.02604690087\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 65 x0:  1.01048862684 xt:  1.02605339781\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59 x0:  1.01570847041 xt:  1.02604714254\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 77 x0:  0.987109597504 xt:  1.02605571588\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 76 x0:  0.988446615628 xt:  1.02605043057\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 79 x0:  0.979637470151 xt:  1.0260540685\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 57 x0:  1.01724785703 xt:  1.026048286\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 76 x0:  0.98972788965 xt:  1.02605453093\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 61 x0:  1.01422480285 xt:  1.0260494952\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  0.970038915681 xt:  1.02605128484\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 82 x0:  0.964064600331 xt:  1.02604917593\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 70 x0:  1.00252836412 xt:  1.02605005409\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 80 x0:  0.976109378986 xt:  1.02605500095\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 75 x0:  0.992106137974 xt:  1.02605315075\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 67 x0:  1.00728975336 xt:  1.02604929599\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 65 x0:  1.00993739087 xt:  1.02604907773\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.997583321363 xt:  1.02605530076\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 63 x0:  1.01288048964 xt:  1.02605506949\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.99735656268 xt:  1.0260543648\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 70 x0:  1.00199103965 xt:  1.02604723378\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 61 x0:  1.01422466474 xt:  1.02604949372\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64 x0:  1.01137531939 xt:  1.02605118118\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 45 x0:  1.02266362279 xt:  1.02605319829\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 75 x0:  0.99073477284 xt:  1.02604838274\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 69 x0:  1.00496957563 xt:  1.02605395656\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 68 x0:  1.00595569559 xt:  1.02605035661\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 52 x0:  1.01999520989 xt:  1.02604747044\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 76 x0:  0.989746747278 xt:  1.02605459144\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 72 x0:  0.998340923815 xt:  1.02604909976\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 65 x0:  1.01057791256 xt:  1.02605409849\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 53 x0:  1.01947493489 xt:  1.02604665671\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  0.994341813939 xt:  1.02605184044\n",
        "iteration:  1 x0:  1.04432866442 xt:  1.04308936172\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 70 x0:  1.00211750198 xt:  1.026047897\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 78 x0:  0.982307289716 xt:  1.02605154338\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  0.993423227944 xt:  1.02604836863\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 69 x0:  1.00514162383 xt:  1.02605493981\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 76 x0:  0.989816559956 xt:  1.02605481547\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 35 x0:  1.0244205673 xt:  1.02604704607\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 80 x0:  0.975697439059 xt:  1.02605406825\n",
        "iteration:  1 x0:  1.04136059039 xt:  1.04031742945\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 37 x0:  1.02424909476 xt:  1.02605413922\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 79 x0:  0.978150524333 xt:  1.02605040253\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  0.99350953047 xt:  1.02604869427\n",
        "iteration:  1 x0:  1.05674775287 xt:  1.05471569836\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64 x0:  1.01139489608 xt:  1.02605134713\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 69 x0:  1.00383715835 xt:  1.02604750215\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 85 x0:  0.950750244944 xt:  1.02605576096\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  1.00056802483 xt:  1.02604978907\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 42 x0:  1.02337050377 xt:  1.02605347614\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  0.99996832434 xt:  1.02604688842\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 80 x0:  0.974103348823 xt:  1.02605047289\n",
        "iteration:  1 x0:  1.02950130224 xt:  1.02926741231\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 72 x0:  0.99797509421 xt:  1.02604746992\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  1.00130751179 xt:  1.02605337563\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 72 x0:  0.999393999898 xt:  1.02605380497\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  1.00080976774 xt:  1.02605096035\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 75 x0:  0.992326172098 xt:  1.02605391822\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 68 x0:  1.00589818784 xt:  1.02605000158\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 68 x0:  1.00610530999 xt:  1.02605128067\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 69 x0:  1.00520074599 xt:  1.02605527786\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  0.994334691218 xt:  1.02605181347\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84 x0:  0.953053285951 xt:  1.02604977334\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64 x0:  1.01190230583 xt:  1.02605565318\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 67 x0:  1.00725993133 xt:  1.02604909671\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.997656688106 xt:  1.02605560377\n",
        "iteration:  1 x0:  1.03543563111 xt:  1.03479168569\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 76 x0:  0.987684567823 xt:  1.02604800173\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 44 x0:  1.02276656411 xt:  1.02604745213\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 83 x0:  0.961897906273 xt:  1.02605475923\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 55 x0:  1.01881968731 xt:  1.02605386795\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.995587706501 xt:  1.02604709322\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 61 x0:  1.0146947953 xt:  1.02605452803\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84 x0:  0.955251754101 xt:  1.02605319085\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 73 x0:  0.997676825314 xt:  1.02605568695\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 77 x0:  0.986587625645 xt:  1.0260541777\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 80 x0:  0.976359001641 xt:  1.02605556686\n",
        "iteration:  1 x0:  1.05476526333 xt:  1.05285672384\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 65 x0:  1.01024476682 xt:  1.02605148544\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 62 x0:  1.01339572545 xt:  1.02605057576\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 68 x0:  1.00599930575 xt:  1.0260506259\n",
        "iteration:  1 x0:  1.04091815375 xt:  1.03990445069\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 42 x0:  1.02337292343 xt:  1.02605358504\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 82 x0:  0.966266295009 xt:  1.02605330636\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 52 x0:  1.02001389696 xt:  1.02604786769\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84 x0:  0.952583769292 xt:  1.02604904703\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 46 x0:  1.0222363486 xt:  1.02604797042\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 80 x0:  0.974713881575 xt:  1.0260518473\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 78 x0:  0.980993869483 xt:  1.02604802029\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 71 x0:  1.00072952233 xt:  1.02605057142\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  0.971204127109 xt:  1.02605368679\n",
        "iteration:  1 x0:  1.03324871454 xt:  1.03275469637\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 67 x0:  1.00823762187 xt:  1.0260556428\n",
        "iteration:  1 x0:  1.02618885764 xt:  1.02618827862\n",
        "iteration:  1 x0:  1.02635563579 xt:  1.02634323422\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 70 x0:  1.00188262976 xt:  1.02604666551\n",
        "iteration:  1 x0:  4.13764863212 xt:  4.12744909744\n",
        "iteration:  1 x0:  4.03921924226 xt:  4.03698543262\n",
        "iteration:  1 x0:  4.0766795262 xt:  4.07165499661\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 60 x0:  3.97976046458 xt:  4.00498446444\n",
        "iteration:  1 x0:  4.17200648902 xt:  4.15858322481\n",
        "iteration:  1 x0:  4.10030487928 xt:  4.09336381792\n",
        "iteration:  1 x0:  4.14377889961 xt:  4.13301927526\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 96 x0:  3.82622662168 xt:  4.00496940637\n",
        "iteration:  1 x0:  4.0164110608 xt:  4.01571984738\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 83 x0:  3.9098663554 xt:  4.00498753969\n",
        "iteration:  1 x0:  4.12910490666 xt:  4.11967446728\n",
        "iteration:  1 x0:  4.15885049047 xt:  4.14668552111\n",
        "iteration:  1 x0:  4.0821777096 xt:  4.0767176516\n",
        "iteration:  1 x0:  4.14853759142 xt:  4.13733854041\n",
        "iteration:  1 x0:  4.02103150229 xt:  4.02003762338\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  3.91827578519 xt:  4.00497871735\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  3.94390243915 xt:  4.00495475513\n",
        "iteration:  1 x0:  4.13907537658 xt:  4.1287460967\n",
        "iteration:  1 x0:  4.08442663195 xt:  4.07878657355\n",
        "iteration:  1 x0:  4.16041165233 xt:  4.14809887291\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64 x0:  3.97122191781 xt:  4.00495702418\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  3.91611934854 xt:  4.00496127752\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 88 x0:  3.87888350096 xt:  4.00496360978\n",
        "iteration:  1 x0:  4.08189733485 xt:  4.07645964236\n",
        "iteration:  1 x0:  4.04795362332 xt:  4.04509723167\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84 x0:  3.90433558014 xt:  4.00498407268\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 107 x0:  3.7440386599 xt:  4.00498657333\n",
        "iteration:  1 x0:  4.10417817951 xt:  4.09691188302\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 91 x0:  3.86157924879 xt:  4.00497289185\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 46 x0:  3.99470162913 xt:  4.00498209299\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 84 x0:  3.9044148162 xt:  4.00498463679\n",
        "iteration:  1 x0:  4.08958353075 xt:  4.08352669105\n",
        "iteration:  1 x0:  4.13378409063 xt:  4.12393411372\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 55 x0:  3.98668061214 xt:  4.00498742842\n",
        "iteration:  1 x0:  4.15321446381 xt:  4.14157965236\n",
        "iteration:  1 x0:  4.0695042702 xt:  4.0650383256\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 78 x0:  3.92922168301 xt:  4.00495996784\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 72 x0:  3.95114629493 xt:  4.00496257961\n",
        "iteration:  1 x0:  4.07710805531 xt:  4.07204981324\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  3.91952667285 xt:  4.00498874784\n",
        "iteration:  1 x0:  4.03692385622 xt:  4.03485076198\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 78 x0:  3.9311816852 xt:  4.00497799514\n",
        "iteration:  1 x0:  4.03592283743 xt:  4.03391945123\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  3.9173969363 xt:  4.00497163254\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 83 x0:  3.90741078467 xt:  4.00496930183\n",
        "iteration:  1 x0:  4.09128168567 xt:  4.08508638058\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  3.946313357 xt:  4.00498146376\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 89 x0:  3.87695790456 xt:  4.00498900699\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 75 x0:  3.94200630466 xt:  4.0049722581\n",
        "iteration:  1 x0:  4.02320568279 xt:  4.02206764283\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 70 x0:  3.9575477497 xt:  4.00496911284\n",
        "iteration:  1 x0:  4.1044508539 xt:  4.09716154694\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 81 x0:  3.91553582293 xt:  4.00495652582\n",
        "iteration:  1 x0:  4.1362005379 xt:  4.12613230908\n",
        "iteration:  1 x0:  4.11880839636 xt:  4.11028656558\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 79 x0:  3.92660737451 xt:  4.00497424331\n",
        "iteration:  1 x0:  4.01521861305 xt:  4.01460469297\n",
        "iteration:  1 x0:  4.14329823869 xt:  4.13258277493\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 77 x0:  3.93504175126 xt:  4.00497698537\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 93 x0:  3.84554858634 xt:  4.00495841655\n",
        "iteration:  1 x0:  4.0899119439 xt:  4.08382837277\n",
        "iteration:  1 x0:  4.07494412652 xt:  4.07005571702\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  3.9451279085 xt:  4.00496836872\n",
        "iteration:  1 x0:  4.0671659118 xt:  4.06287958634\n",
        "iteration:  1 x0:  4.13751466027 xt:  4.12732728962\n",
        "iteration:  1 x0:  4.05004163046 xt:  4.04703383693\n",
        "iteration:  1 x0:  4.01444957981 xt:  4.01388532911\n",
        "iteration:  1 x0:  4.0332621901 xt:  4.03144295853\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 72 x0:  3.9525134286 xt:  4.00497927369\n",
        "iteration:  1 x0:  4.15497115638 xt:  4.14317168509\n",
        "iteration:  1 x0:  4.10775176815 xt:  4.10018271706\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 74 x0:  3.94643890625 xt:  4.0049828464\n",
        "iteration:  1 x0:  4.10425397547 xt:  4.09698128421\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 51 x0:  3.99074211749 xt:  4.00498362326\n",
        "iteration:  1 x0:  4.10092035681 xt:  4.09392781828\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 94 x0:  3.8439485899 xt:  4.0049872338\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 89 x0:  3.87462920518 xt:  4.00497499223\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 53 x0:  3.98819075784 xt:  4.00496299021\n",
        "iteration:  1 x0:  4.07206220291 xt:  4.06739840661\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 50 x0:  3.99125486077 xt:  4.00496736085\n",
        "iteration:  1 x0:  4.14898720057 xt:  4.13774642437\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 63 x0:  3.97387600519 xt:  4.00496996524\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 64 x0:  3.97208746026 xt:  4.00497319559\n",
        "iteration:  1 x0:  4.16645895847 xt:  4.15356976669\n",
        "iteration:  1 x0:  4.05983476312 xt:  4.05610378129\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 62 x0:  3.97541536667 xt:  4.00496337471\n",
        "iteration:  1 x0:  4.07242541444 xt:  4.06773340901\n",
        "iteration:  1 x0:  4.02652829255 xt:  4.02516780175\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 59 x0:  3.98089960138 xt:  4.00497482517\n",
        "iteration:  1 x0:  4.16429596567 xt:  4.15161364347\n",
        "iteration:  1 x0:  4.06758546706 xt:  4.06326700186\n",
        "iteration:  1 x0:  4.03906719306 xt:  4.03684406688\n",
        "iteration:  1 x0:  4.10243968765 xt:  4.09531974594\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 94 x0:  3.84311862577 xt:  4.00498286745\n",
        "iteration:  1 x0:  4.01032424907 xt:  4.01002404381\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 91 x0:  3.85968055571 xt:  4.00496194185\n",
        "iteration:  1 x0:  4.02803613472 xt:  4.02657384111\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 62 x0:  3.97587595507 xt:  4.00497299255\n",
        "iteration:  1 x0:  4.1202459422 xt:  4.11159847688\n",
        "iteration:  1 x0:  4.15807273322 xt:  4.14598124741\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 342 x0:  2.26581599599 xt:  2.50885880683\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 404 x0:  1.96914046207 xt:  2.50884679299\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 327 x0:  2.3124017447 xt:  2.50885560681\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 360 x0:  2.19285486499 xt:  2.50883877854\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 337 x0:  2.28089199845 xt:  2.50884647176\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 363 x0:  2.18012779849 xt:  2.50884125287\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 311 x0:  2.35251718725 xt:  2.50884951641\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 383 x0:  2.08430388221 xt:  2.50885040978\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 380 x0:  2.1012602456 xt:  2.50885679633\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 368 x0:  2.16113807606 xt:  2.50886172716\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 341 x0:  2.26716711328 xt:  2.50884379665\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 363 x0:  2.18085218469 xt:  2.50884529461\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 255 x0:  2.4402134663 xt:  2.50884418752\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 362 x0:  2.18774275344 xt:  2.50885917916\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 376 x0:  2.12280148583 xt:  2.50886291928\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 360 x0:  2.19513234185 xt:  2.50885189654\n",
        "iteration:  1 x0:  2.56172864205 xt:  2.56098715254\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 326 x0:  2.31553835094 xt:  2.50885846434\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 360 x0:  2.19383696536 xt:  2.50884443844\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 426 x0:  1.85834270033 xt:  2.50885739126\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 363 x0:  2.18383188303 xt:  2.50886189162\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 302 x0:  2.37101553777 xt:  2.50884014419\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 352 x0:  2.22846000158 xt:  2.50885492687\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 254 x0:  2.44152736213 xt:  2.50885148534\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 356 x0:  2.21271792277 xt:  2.50885661665\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 393 x0:  2.03285094467 xt:  2.50886112123\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 357 x0:  2.20878683784 xt:  2.50885774226\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 321 x0:  2.32810324151 xt:  2.50884980738\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 396 x0:  2.01532956452 xt:  2.50885643552\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 380 x0:  2.09793302801 xt:  2.50884083051\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 371 x0:  2.14357738057 xt:  2.50884413086\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 315 x0:  2.34246007606 xt:  2.50884247782\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 378 x0:  2.11097283571 xt:  2.50885431099\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 372 x0:  2.14174127489 xt:  2.50885943089\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 343 x0:  2.26274500583 xt:  2.50886161998\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 373 x0:  2.13700235874 xt:  2.50885998942\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 332 x0:  2.29768766061 xt:  2.50885507898\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 389 x0:  2.05319862211 xt:  2.50885466316\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 474 x0:  1.71047328628 xt:  2.50886167008\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 385 x0:  2.07336755946 xt:  2.50884871518\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 367 x0:  2.16543381157 xt:  2.50885997027\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 385 x0:  2.07397536915 xt:  2.50885154411\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 403 x0:  1.97579198613 xt:  2.50885206566\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 310 x0:  2.35540621091 xt:  2.50885642145\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 406 x0:  1.96014884622 xt:  2.50885554477\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 359 x0:  2.19995695652 xt:  2.50885511599\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 382 x0:  2.09230270062 xt:  2.50886343932\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 294 x0:  2.38666285361 xt:  2.50884553035\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 321 x0:  2.3271569529 xt:  2.50884085983\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 397 x0:  2.01032364084 xt:  2.50885868367\n",
        "iteration:  1 x0:  2.76813779955 xt:  2.76456358125\n",
        "iteration:  1 x0:  2.74514041556 xt:  2.7418534118\n",
        "iteration:  1 x0:  2.81649726547 xt:  2.81236417719\n",
        "iteration:  1 x0:  2.72916010589 xt:  2.72607919286\n",
        "iteration:  1 x0:  2.80634467779 xt:  2.80232308957\n",
        "iteration:  1 x0:  2.63950449563 xt:  2.63764890095\n",
        "iteration:  1 x0:  2.70477591377 xt:  2.70201810382\n",
        "iteration:  1 x0:  2.86039382797 xt:  2.85582191574\n",
        "iteration:  1 x0:  2.78847737049 xt:  2.78465986969\n",
        "iteration:  1 x0:  2.79382802585 xt:  2.78994840748\n",
        "iteration:  1 x0:  2.79855287975 xt:  2.79461910759\n",
        "iteration:  1 x0:  2.87890230165 xt:  2.87416951954\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1 x0:  2.73877581529 xt:  2.73557030267\n",
        "iteration:  1 x0:  2.68573715195 xt:  2.68323768368\n",
        "iteration:  1 x0:  2.69997594336 xt:  2.69728280889\n",
        "iteration:  1 x0:  2.77841963307 xt:  2.77472106836\n",
        "iteration:  1 x0:  2.96369991062 xt:  2.9584628687\n",
        "iteration:  1 x0:  2.69663720167 xt:  2.69398924179\n",
        "iteration:  1 x0:  2.89781342046 xt:  2.89293326108\n",
        "iteration:  1 x0:  2.65036081001 xt:  2.64835230118\n",
        "iteration:  1 x0:  2.66984794094 xt:  2.66756743654\n",
        "iteration:  1 x0:  2.79807375514 xt:  2.79414544395\n",
        "iteration:  1 x0:  2.87711461015 xt:  2.87239667228\n",
        "iteration:  1 x0:  2.71523790457 xt:  2.71234029937\n",
        "iteration:  1 x0:  2.79824713825 xt:  2.79431685007\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1 x0:  2.6592205531 xt:  2.65708795608\n",
        "iteration:  1 x0:  2.82067346962 xt:  2.81649552239\n",
        "iteration:  1 x0:  2.81119224601 xt:  2.80711699595\n",
        "iteration:  1 x0:  2.83584379417 xt:  2.83150813449\n",
        "iteration:  1 x0:  2.95992051756 xt:  2.95469663643\n",
        "iteration:  1 x0:  2.86887136043 xt:  2.8642238173\n",
        "iteration:  1 x0:  2.81909622287 xt:  2.81493514699\n",
        "iteration:  1 x0:  3.04569563617 xt:  3.04042947752\n",
        "iteration:  1 x0:  2.85849796804 xt:  2.85394340426\n",
        "iteration:  1 x0:  2.81429614434 xt:  2.81018693941\n",
        "iteration:  1 x0:  2.91154400616 xt:  2.90656849546\n",
        "iteration:  1 x0:  2.70955200291 xt:  2.70673016874\n",
        "iteration:  1 x0:  2.8584538831 xt:  2.85389972458\n",
        "iteration: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1 x0:  2.80883824382 xt:  2.80478895703\n",
        "iteration:  1 x0:  2.81253250757 xt:  2.80844255653\n",
        "iteration:  1 x0:  3.01387827301 xt:  3.00856235982\n",
        "iteration:  1 x0:  2.84117674157 xt:  2.83678768984\n",
        "iteration:  1 x0:  2.69249899914 xt:  2.68990723654\n",
        "iteration:  1 x0:  2.75608801666 xt:  2.75266280887\n",
        "iteration:  1 x0:  2.60569946974 xt:  2.60432491937\n",
        "iteration:  1 x0:  2.81042124172 xt:  2.80635447543\n",
        "iteration:  1 x0:  2.90913515479 xt:  2.90417563095\n",
        "iteration:  1 x0:  2.80321977639 xt:  2.79923317947\n",
        "iteration:  1 x0:  2.58617538677 xt:  2.58508117821\n",
        "iteration:  1 x0:  2.91584585232 xt:  2.91084259642\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "compare = matrix( [ [SEPs[i,0], data[i]]  for i in range (size)])\n",
      "print compare"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 1.02475978  0.97384184]\n",
        " [ 1.02475359  0.95886201]\n",
        " [ 1.02475607  1.00155217]\n",
        " [ 1.02475756  0.99694479]\n",
        " [ 1.02475776  0.99030703]\n",
        " [ 1.02475492  1.01048863]\n",
        " [ 1.02475872  1.01570847]\n",
        " [ 1.02475619  0.9871096 ]\n",
        " [ 1.02475151  0.98844662]\n",
        " [ 1.02475981  0.97963747]\n",
        " [ 1.0247578   1.01724786]\n",
        " [ 1.02475677  0.98972789]\n",
        " [ 1.02475667  1.0142248 ]\n",
        " [ 1.02475073  0.97003892]\n",
        " [ 1.0247537   0.9640646 ]\n",
        " [ 1.02475014  1.00252836]\n",
        " [ 1.02475616  0.97610938]\n",
        " [ 1.02475524  0.99210614]\n",
        " [ 1.02475302  1.00728975]\n",
        " [ 1.02475799  1.00993739]\n",
        " [ 1.02475686  0.99758332]\n",
        " [ 1.02475058  1.01288049]\n",
        " [ 1.02475637  0.99735656]\n",
        " [ 1.02476021  1.00199104]\n",
        " [ 1.02475665  1.01422466]\n",
        " [ 1.02475418  1.01137532]\n",
        " [ 1.02475211  1.02266362]\n",
        " [ 1.02475341  0.99073477]\n",
        " [ 1.02475667  1.00496958]\n",
        " [ 1.02475076  1.0059557 ]\n",
        " [ 1.02475645  1.01999521]\n",
        " [ 1.02475746  0.98974675]\n",
        " [ 1.02475248  0.99834092]\n",
        " [ 1.02475265  1.01057791]\n",
        " [ 1.02475441  1.01947493]\n",
        " [ 1.02475464  0.99434181]\n",
        " [ 1.04420473  1.04432866]\n",
        " [ 1.02475719  1.0021175 ]\n",
        " [ 1.02475584  0.98230729]\n",
        " [ 1.02475716  0.99342323]\n",
        " [ 1.02475766  1.00514162]\n",
        " [ 1.02476     0.98981656]\n",
        " [ 1.02475993  1.02442057]\n",
        " [ 1.0247557   0.97569744]\n",
        " [ 1.04125627  1.04136059]\n",
        " [ 1.02475979  1.02424909]\n",
        " [ 1.02475945  0.97815052]\n",
        " [ 1.02475052  0.99350953]\n",
        " [ 1.05654455  1.05674775]\n",
        " [ 1.02475602  1.0113949 ]\n",
        " [ 1.02475668  1.00383716]\n",
        " [ 1.02475357  0.95075024]\n",
        " [ 1.02475364  1.00056802]\n",
        " [ 1.02475544  1.0233705 ]\n",
        " [ 1.02475273  0.99996832]\n",
        " [ 1.0247561   0.97410335]\n",
        " [ 1.02947791  1.0295013 ]\n",
        " [ 1.02475517  0.99797509]\n",
        " [ 1.02475279  1.00130751]\n",
        " [ 1.02475384  0.999394  ]\n",
        " [ 1.02475636  1.00080977]\n",
        " [ 1.02475374  0.99232617]\n",
        " [ 1.02475704  1.00589819]\n",
        " [ 1.02475078  1.00610531]\n",
        " [ 1.02475134  1.00520075]\n",
        " [ 1.02475434  0.99433469]\n",
        " [ 1.0247515   0.95305329]\n",
        " [ 1.02475364  1.01190231]\n",
        " [ 1.02475085  1.00725993]\n",
        " [ 1.02475015  0.99765669]\n",
        " [ 1.03537124  1.03543563]\n",
        " [ 1.0247555   0.98768457]\n",
        " [ 1.02475359  1.02276656]\n",
        " [ 1.02475086  0.96189791]\n",
        " [ 1.02475527  1.01881969]\n",
        " [ 1.02475744  0.99558771]\n",
        " [ 1.02475161  1.0146948 ]\n",
        " [ 1.02475915  0.95525175]\n",
        " [ 1.02475111  0.99767683]\n",
        " [ 1.02475895  0.98658763]\n",
        " [ 1.02475248  0.976359  ]\n",
        " [ 1.05457441  1.05476526]\n",
        " [ 1.02475391  1.01024477]\n",
        " [ 1.02475474  1.01339573]\n",
        " [ 1.02475373  1.00599931]\n",
        " [ 1.04081678  1.04091815]\n",
        " [ 1.02475666  1.02337292]\n",
        " [ 1.02475898  0.9662663 ]\n",
        " [ 1.02475054  1.0200139 ]\n",
        " [ 1.02475369  0.95258377]\n",
        " [ 1.02475222  1.02223635]\n",
        " [ 1.02475101  0.97471388]\n",
        " [ 1.02475783  0.98099387]\n",
        " [ 1.02475206  1.00072952]\n",
        " [ 1.02475736  0.97120413]\n",
        " [ 1.03319931  1.03324871]\n",
        " [ 1.02475275  1.00823762]\n",
        " [ 1.0261888   1.02618886]\n",
        " [ 1.0263544   1.02635564]\n",
        " [ 1.02475412  1.00188263]\n",
        " [ 4.13662868  4.13764863]\n",
        " [ 4.03899586  4.03921924]\n",
        " [ 4.07617707  4.07667953]\n",
        " [ 3.99911673  3.97976046]\n",
        " [ 4.17066416  4.17200649]\n",
        " [ 4.09961077  4.10030488]\n",
        " [ 4.14270294  4.1437789 ]\n",
        " [ 3.99911352  3.82622662]\n",
        " [ 4.01634194  4.01641106]\n",
        " [ 3.99914098  3.90986636]\n",
        " [ 4.12816186  4.12910491]\n",
        " [ 4.15763399  4.15885049]\n",
        " [ 4.0816317   4.08217771]\n",
        " [ 4.14741769  4.14853759]\n",
        " [ 4.02093211  4.0210315 ]\n",
        " [ 3.99913803  3.91827579]\n",
        " [ 3.99913686  3.94390244]\n",
        " [ 4.13804245  4.13907538]\n",
        " [ 4.08386263  4.08442663]\n",
        " [ 4.15918037  4.16041165]\n",
        " [ 3.99913582  3.97122192]\n",
        " [ 3.99910938  3.91611935]\n",
        " [ 3.99912792  3.8788835 ]\n",
        " [ 4.08135357  4.08189733]\n",
        " [ 4.04766798  4.04795362]\n",
        " [ 3.99913548  3.90433558]\n",
        " [ 3.99912028  3.74403866]\n",
        " [ 4.10345155  4.10417818]\n",
        " [ 3.99913163  3.86157925]\n",
        " [ 3.99912285  3.99470163]\n",
        " [ 3.99914168  3.90441482]\n",
        " [ 4.08897785  4.08958353]\n",
        " [ 4.13279909  4.13378409]\n",
        " [ 3.99912329  3.98668061]\n",
        " [ 4.15205098  4.15321446]\n",
        " [ 4.06905768  4.06950427]\n",
        " [ 3.99911865  3.92922168]\n",
        " [ 3.99911829  3.95114629]\n",
        " [ 4.07660223  4.07710806]\n",
        " [ 3.99912933  3.91952667]\n",
        " [ 4.03671655  4.03692386]\n",
        " [ 3.99911383  3.93118169]\n",
        " [ 4.0357225   4.03592284]\n",
        " [ 3.99914061  3.91739694]\n",
        " [ 3.99914082  3.90741078]\n",
        " [ 4.09066216  4.09128169]\n",
        " [ 3.99910629  3.94631336]\n",
        " [ 3.99911909  3.8769579 ]\n",
        " [ 3.99911629  3.9420063 ]\n",
        " [ 4.02309188  4.02320568]\n",
        " [ 3.99912733  3.95754775]\n",
        " [ 4.10372192  4.10445085]\n",
        " [ 3.9991387   3.91553582]\n",
        " [ 4.13519372  4.13620054]\n",
        " [ 4.11795621  4.1188084 ]\n",
        " [ 3.99910471  3.92660737]\n",
        " [ 4.01515722  4.01521861]\n",
        " [ 4.14222669  4.14329824]\n",
        " [ 3.999111    3.93504175]\n",
        " [ 3.99912808  3.84554859]\n",
        " [ 4.08930359  4.08991194]\n",
        " [ 4.07445529  4.07494413]\n",
        " [ 3.99912274  3.94512791]\n",
        " [ 4.06673728  4.06716591]\n",
        " [ 4.13649592  4.13751466]\n",
        " [ 4.04974085  4.05004163]\n",
        " [ 4.01439315  4.01444958]\n",
        " [ 4.03308027  4.03326219]\n",
        " [ 3.99913992  3.95251343]\n",
        " [ 4.15379121  4.15497116]\n",
        " [ 4.10699486  4.10775177]\n",
        " [ 3.99912155  3.94643891]\n",
        " [ 4.10352671  4.10425398]\n",
        " [ 3.99912432  3.99074212]\n",
        " [ 4.1002211   4.10092036]\n",
        " [ 3.99911502  3.84394859]\n",
        " [ 3.99912487  3.87462921]\n",
        " [ 3.99911584  3.98819076]\n",
        " [ 4.07159582  4.0720622 ]\n",
        " [ 3.9991161   3.99125486]\n",
        " [ 4.14786312  4.1489872 ]\n",
        " [ 3.99912553  3.97387601]\n",
        " [ 3.99911074  3.97208746]\n",
        " [ 4.16517004  4.16645896]\n",
        " [ 4.05946166  4.05983476]\n",
        " [ 3.99910445  3.97541537]\n",
        " [ 4.07195621  4.07242541]\n",
        " [ 4.02639224  4.02652829]\n",
        " [ 3.99914018  3.9808996 ]\n",
        " [ 4.16302773  4.16429597]\n",
        " [ 4.06715362  4.06758547]\n",
        " [ 4.03884488  4.03906719]\n",
        " [ 4.10172769  4.10243969]\n",
        " [ 3.99910694  3.84311863]\n",
        " [ 4.01029423  4.01032425]\n",
        " [ 3.99913433  3.85968056]\n",
        " [ 4.02788991  4.02803613]\n",
        " [ 3.99912885  3.97587596]\n",
        " [ 4.1193812   4.12024594]\n",
        " [ 4.15686358  4.15807273]\n",
        " [ 2.45231599  2.265816  ]\n",
        " [ 2.36656738  1.96914046]\n",
        " [ 2.46366105  2.31240174]\n",
        " [ 2.43398229  2.19285486]\n",
        " [ 2.4560115   2.280892  ]\n",
        " [ 2.43068576  2.1801278 ]\n",
        " [ 2.47328489  2.35251719]\n",
        " [ 2.40438553  2.08430388]\n",
        " [ 2.40927615  2.10126025]\n",
        " [ 2.42569711  2.16113808]\n",
        " [ 2.45264824  2.26716711]\n",
        " [ 2.43087435  2.18085218]\n",
        " [ 2.49337996  2.44021347]\n",
        " [ 2.4326624   2.18774275]\n",
        " [ 2.41532204  2.12280149]\n",
        " [ 2.43456855  2.19513234]\n",
        " [ 2.56165449  2.56172864]\n",
        " [ 2.46441773  2.31553835]\n",
        " [ 2.43423523  2.19383697]\n",
        " [ 2.31477121  1.8583427 ]\n",
        " [ 2.43164885  2.18383188]\n",
        " [ 2.47768933  2.37101554]\n",
        " [ 2.4430351   2.22846   ]\n",
        " [ 2.49338072  2.44152736]\n",
        " [ 2.43906094  2.21271792]\n",
        " [ 2.38865691  2.03285094]\n",
        " [ 2.43806179  2.20878684]\n",
        " [ 2.46744125  2.32810324]\n",
        " [ 2.38292277  2.01532956]\n",
        " [ 2.4083262   2.09793303]\n",
        " [ 2.42099967  2.14357738]\n",
        " [ 2.47088225  2.34246008]\n",
        " [ 2.41202381  2.11097284]\n",
        " [ 2.4205034   2.14174127]\n",
        " [ 2.45155999  2.26274501]\n",
        " [ 2.41921777  2.13700236]\n",
        " [ 2.4601004   2.29768766]\n",
        " [ 2.39505641  2.05319862]\n",
        " [ 2.13472512  1.71047329]\n",
        " [ 2.40116192  2.07336756]\n",
        " [ 2.42683345  2.16543381]\n",
        " [ 2.4013426   2.07397537]\n",
        " [ 2.36905141  1.97579199]\n",
        " [ 2.47397398  2.35540621]\n",
        " [ 2.36312945  1.96014885]\n",
        " [ 2.435807    2.19995696]\n",
        " [ 2.40670811  2.0923027 ]\n",
        " [ 2.48140187  2.38666285]\n",
        " [ 2.46721395  2.32715695]\n",
        " [ 2.38124213  2.01032364]\n",
        " [ 2.76778038  2.7681378 ]\n",
        " [ 2.74481172  2.74514042]\n",
        " [ 2.81608396  2.81649727]\n",
        " [ 2.72885201  2.72916011]\n",
        " [ 2.80594252  2.80634468]\n",
        " [ 2.63931894  2.6395045 ]\n",
        " [ 2.70450013  2.70477591]\n",
        " [ 2.85993664  2.86039383]\n",
        " [ 2.78809562  2.78847737]\n",
        " [ 2.79344006  2.79382803]\n",
        " [ 2.7981595   2.79855288]\n",
        " [ 2.87842902  2.8789023 ]\n",
        " [ 2.73845526  2.73877582]\n",
        " [ 2.68548721  2.68573715]\n",
        " [ 2.69970663  2.69997594]\n",
        " [ 2.77804978  2.77841963]\n",
        " [ 2.96317621  2.96369991]\n",
        " [ 2.69637241  2.6966372 ]\n",
        " [ 2.8973254   2.89781342]\n",
        " [ 2.65015996  2.65036081]\n",
        " [ 2.66961989  2.66984794]\n",
        " [ 2.79768092  2.79807376]\n",
        " [ 2.87664282  2.87711461]\n",
        " [ 2.71494814  2.7152379 ]\n",
        " [ 2.79785411  2.79824714]\n",
        " [ 2.65900729  2.65922055]\n",
        " [ 2.82025567  2.82067347]\n",
        " [ 2.81078472  2.81119225]\n",
        " [ 2.83541023  2.83584379]\n",
        " [ 2.95939813  2.95992052]\n",
        " [ 2.86840661  2.86887136]\n",
        " [ 2.81868012  2.81909622]\n",
        " [ 3.04516902  3.04569564]\n",
        " [ 2.85804251  2.85849797]\n",
        " [ 2.81388522  2.81429614]\n",
        " [ 2.91104646  2.91154401]\n",
        " [ 2.70926982  2.709552  ]\n",
        " [ 2.85799847  2.85845388]\n",
        " [ 2.80843332  2.80883824]\n",
        " [ 2.81212351  2.81253251]\n",
        " [ 3.01334668  3.01387827]\n",
        " [ 2.84073784  2.84117674]\n",
        " [ 2.69223982  2.692499  ]\n",
        " [ 2.7557455   2.75608802]\n",
        " [ 2.60556201  2.60569947]\n",
        " [ 2.81001457  2.81042124]\n",
        " [ 2.9086392   2.90913515]\n",
        " [ 2.80282112  2.80321978]\n",
        " [ 2.58606597  2.58617539]\n",
        " [ 2.91534553  2.91584585]]\n"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotScatter(SEPs[:,0],\"SEPs plot\",\"r\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEKCAYAAAD9xUlFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIBQAAMb/AVNyTjThJs04AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7698518>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotScatter(data,\"scatter plot\",\"r\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEKCAYAAAD9xUlFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPT0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x78b7fd0>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}