juliaL26a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA (Part 1)\n",
    "\n",
    "CPSC 340: Machine Learning and Data Mining\n",
    "\n",
    "The University of British Columbia\n",
    "\n",
    "2018 Winter Term 1\n",
    "\n",
    "By Mike Gelbart (converted to Julia by Jason Chau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyCall, PyPlot, Statistics\n",
    "plt = pyimport(\"matplotlib.pyplot\")\n",
    "SkDecomposition = pyimport(\"sklearn.decomposition\")\n",
    "using PyPlot\n",
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a synthetic data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 12\n",
    "d = 2\n",
    "\n",
    "x1 = range(0,stop=5,length=n) + randn(n)*0.05\n",
    "x2 = x1.*0.7 + randn(n).*0.5\n",
    "x1 = x1.-Statistics.mean(x1)\n",
    "x2 = x2.-Statistics.mean(x2)\n",
    "\n",
    "X = hcat(x1,x2)\n",
    "\n",
    "plt.scatter(x1,x2)\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run PCA with k=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1\n",
    "pca = SkDecomposition.PCA(n_components=k)\n",
    "pca.fit(X);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x0000000032B3FA90>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function make_plot(pca, X)\n",
    "    W = pca.components_\n",
    "    Z = pca.transform(X)\n",
    "\n",
    "    # visualize the subspace spanned by W\n",
    "    grid = range(minimum(X[:,1])-0.3,stop=maximum(X[:,1])+0.3,length=1000)\n",
    "    gridplot = (grid.-pca.mean_[1])/W[1,1]*W[1,2].+pca.mean_[2]\n",
    "\n",
    "    # visualize the reconstructions\n",
    "    Xhat = pca.inverse_transform(Z)\n",
    "    # xhat = Z@W + pca.mean_ # the same\n",
    "\n",
    "    plt.scatter(X[:,1],X[:,2], label=\"original data\")\n",
    "    plt.xlabel(\"x_1\")\n",
    "    plt.ylabel(\"x_2\");\n",
    "    plt.plot(grid, gridplot, \"black\", label=\"model\")\n",
    "    plt.scatter(Xhat[:,1],Xhat[:,2], c=\"red\", label=\"reconstructions\")\n",
    "    plt.axis(\"equal\");\n",
    "    \n",
    "    for i in 1:size(X)[1]\n",
    "        plt.plot((X[i,1],Xhat[i,1]),(X[i,2],Xhat[i,2]), \"red\")\n",
    "    end\n",
    "    \n",
    "    plt.legend()\n",
    "end\n",
    "    \n",
    "make_plot(pca, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line gives us a new, 1D coordinate system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Moving to $d=3,k=2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 12\n",
    "d = 3\n",
    "\n",
    "x1 = range(0,stop=5,length=n) + randn(n).*0.05\n",
    "x2 = -x1.*0.1 + randn(n).*2\n",
    "x3 = x1.*0.7 + randn(n).*3\n",
    "\n",
    "X = hcat(x1,x2,x3)\n",
    "X = X .- [Statistics.mean(X[:,i]) for i in 1:size(X)[2]]';"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.09109821416582614, 0.01220484645882519, 'x3')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pygui(true)\n",
    "p = PyPlot.scatter3D(X[:,1],X[:,2],X[:,3])\n",
    "xlabel(\"x1\")\n",
    "ylabel(\"x2\")\n",
    "zlabel(\"x3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at what PCA gives us"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.09113564449804984, 0.012209861172471081, 'x3')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pygui(true)\n",
    "# fit PCA\n",
    "pca = SkDecomposition.PCA(n_components=2)\n",
    "pca.fit(X)\n",
    "\n",
    "# get grid for visualizing plane\n",
    "z1 = range(-7,stop=7,length=10)\n",
    "z2 = range(-7,stop=7,length=10)\n",
    "z1grid = repeat(z1',10,1)\n",
    "z2grid = repeat(z2,1,10)\n",
    "Zgrid = hcat(z1grid'[:],z2grid'[:])\n",
    "Xgrid = pca.inverse_transform(Zgrid)\n",
    "Xgrid_re = reshape(Xgrid, 10,10,3)\n",
    "\n",
    "# get reconstructions of original points\n",
    "Z = pca.transform(X)\n",
    "Xhat = pca.inverse_transform(Z)\n",
    "\n",
    "for i in 1:n\n",
    "    PyPlot.plot3D((X[i,1],Xhat[i,1]),\n",
    "                    (X[i,2],Xhat[i,2]),\n",
    "                    (X[i,3],Xhat[i,3]),\n",
    "                    color=\"blue\")\n",
    "end\n",
    "PyPlot.scatter3D(X[:,1],X[:,2],X[:,3],color=\"blue\")\n",
    "PyPlot.scatter3D(Xhat[:,1],Xhat[:,2],Xhat[:,3],color=\"purple\")\n",
    "PyPlot.plot_surface(Xgrid_re[:,:,1],Xgrid_re[:,:,2],Xgrid_re[:,:,3],color=\"g\",alpha=0.5)\n",
    "\n",
    "\n",
    "xlabel(\"x1\")\n",
    "ylabel(\"x2\")\n",
    "zlabel(\"x3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also make a scatter plot of these $Z$-values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pygui(false)\n",
    "plt.scatter(Z[:,1],Z[:,2])\n",
    "plt.xlabel(\"z_1\")\n",
    "plt.ylabel(\"z_2\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: this is projecting and rotating the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$d=3,k=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <mpl_toolkits.mplot3d.art3d.Path3DCollection object at 0x00000000022EF208>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pygui(true)\n",
    "n = 12\n",
    "d = 3\n",
    "\n",
    "x1 = range(0,stop=5,length=n)  + randn(n)*0.05\n",
    "x2 = -x1.*0.1 + randn(n).*2\n",
    "x3 = x1.*0.7 + randn(n).*1.5\n",
    "\n",
    "X = hcat(x1,x2,x3)\n",
    "X = X.-[Statistics.mean(X[:,i]) for i in 1:size(X)[2]]'\n",
    "\n",
    "# fit PCA\n",
    "pca = SkDecomposition.PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "\n",
    "# get grid for visualizing plane\n",
    "Zgrid = reshape(range(-7,stop=7,length=100),100,1)\n",
    "Xgrid = pca.inverse_transform(Zgrid)\n",
    "\n",
    "# get reconstructions of original points\n",
    "Xhat = pca.inverse_transform(pca.transform(X))\n",
    "\n",
    "for i in 1:n\n",
    "    PyPlot.plot3D((X[i,1],Xhat[i,1]), \n",
    "                    (X[i,2],Xhat[i,2]), \n",
    "                    (X[i,3],Xhat[i,3]),\n",
    "                    color=\"blue\")\n",
    "end\n",
    "PyPlot.plot3D(Xgrid[:,1],Xgrid[:,2],Xgrid[:,3],color=\"black\")\n",
    "\n",
    "PyPlot.scatter3D(Xhat[:,1], Xhat[:,2], Xhat[:,3],color=\"purple\")\n",
    "\n",
    "PyPlot.scatter3D(X[:,1], X[:,2], X[:,3],color=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspecting the values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1\n",
    "pca = SkDecomposition.PCA(n_components=k)\n",
    "pca.fit(X);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12×3 Array{Float64,2}:\n",
       " -2.54405    1.36684    -1.77997 \n",
       " -2.01072   -1.17758    -1.6467  \n",
       " -1.5881     0.38777    -0.990278\n",
       " -1.06855   -0.211153   -2.18929 \n",
       " -0.75367   -0.947349    0.729205\n",
       " -0.196069   1.93066    -0.777257\n",
       "  0.318893  -0.345653    1.65795 \n",
       "  0.606889  -1.74889    -1.90289 \n",
       "  1.06283    0.575541    2.72211 \n",
       "  1.67985    0.0633328   0.96964 \n",
       "  1.97405   -1.78406     2.17391 \n",
       "  2.51865    1.89054     1.03357 "
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12×1 Array{Float64,2}:\n",
       "  3.0452099292442005 \n",
       "  2.5602725966197317 \n",
       "  1.807053771858783  \n",
       "  2.333531482892965  \n",
       " -0.03798736881432807\n",
       "  0.7253537978811908 \n",
       " -1.4410838745414303 \n",
       "  0.9743696685274146 \n",
       " -2.718620148732364  \n",
       " -1.8491739830310623 \n",
       " -2.954721546880222  \n",
       " -2.444204325024879  "
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = pca.transform(X)\n",
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Array{Float64,2}:\n",
       " -0.67574  0.0103443  -0.737067"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = pca.components_\n",
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 3)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(Z)+length(W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We sometimes call this \"compression\" because we've reduced the number of values we're storing ($15<36$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12×3 Array{Float64,2}:\n",
       " -2.05777     0.0315006    -2.24452  \n",
       " -1.73008     0.0264843    -1.88709  \n",
       " -1.2211      0.0186927    -1.33192  \n",
       " -1.57686     0.0241388    -1.71997  \n",
       "  0.0256696  -0.000392953   0.0279992\n",
       " -0.490151    0.00750328   -0.534635 \n",
       "  0.973798   -0.014907      1.06218  \n",
       " -0.658421    0.0100792    -0.718176 \n",
       "  1.83708    -0.0281222     2.00381  \n",
       "  1.24956    -0.0191284     1.36297  \n",
       "  1.99662    -0.0305646     2.17783  \n",
       "  1.65165    -0.0252836     1.80154  "
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xhat = pca.inverse_transform(Z)\n",
    "Xhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why you need to center the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KcAMAraiuaTnYdKQfgK5HuAGAVsRH2zu1H4CuR7gBgFakJsbK5bCrpRu+bbp211RqYmwoywLQCsINALQiMsKmFeluSWoScBrOV6S72e8GCCOEGwC4gRlJLmXPHy2nI3jqyemwK3v+aPa5AcIMm/gBQBvMSHJpmtvJDsVAN0C4AYA2ioywKW1wnNVlALgBpqUAAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEYh3AAAAKMQbgAAgFEINwAAwCiEGwAAYBTCDQAAMIql4WblypWy2WxBh9PpbPWa/fv3a8yYMbLb7brzzjv1yiuvhKhaAADQHVj+VPDhw4dr3759jeeRkZEt9i0vL9esWbP0+OOPKycnR++9956efPJJ9e3bVw8//HAoygXCXl19QCXlF1RdU6v4aLtSE2MVGWGzuiwACBnLw02vXr1uOFrT4JVXXtHtt9+udevWSZLuvvtuHTx4UL/85S8JN4Ck/DKPMvNOyOOtbWxzOexake7WjCSXhZUBQOhYvubm9OnT6t+/vxITE/Xoo4/qzJkzLfYtKirS9OnTg9ruv/9+HTx4UH/5y1+avcbv98vn8wUdgInyyzxaknM4KNhIUpW3VktyDiu/zGNRZQAQWpaGm3Hjxmnr1q16++23tWnTJlVVVWnChAn64osvmu1fVVWlfv36BbX169dPV69e1fnz55u9JisrSw6Ho/FISEjo9M8BWK2uPqDMvBMKNPNaQ1tm3gnV1TfXAwDMYmm4mTlzph5++GGNGDFC9913n3bt2iVJev3111u8xmYLXjsQCASabW+QkZEhr9fbeFRWVnZS9UD4KCm/0GTE5noBSR5vrUrKL4SuKACwiOVrbq7Xp08fjRgxQqdPn272dafTqaqqqqC26upq9erVS3Fxcc1eExUVpaioqE6vFQgn1TUtB5uO9AOA7szyNTfX8/v9OnnypFyu5hc+pqWlae/evUFte/bsUUpKir7xjW+EokQgLMVH2zu1HwB0Z5aGm+XLl2v//v0qLy/XBx98oO9///vy+XxatGiRpGtTSgsXLmzsv3jxYn3yySdatmyZTp48qddee02//vWvtXz5cqs+AhAWUhNj5XLY1dIN3zZdu2sqNTE2lGUBgCUsDTeffvqp5s6dq6FDh+p73/ueevfureLiYg0aNEiS5PF4VFFR0dg/MTFRb731lgoKCjRy5Ei9+OKL2rBhA7eBo8eLjLBpRbpbkpoEnIbzFelu9rsB0CPYAg0rcnsIn88nh8Mhr9ermJgYq8sBOhX73AAwVXt+v8NqQTGAmzMjyaVpbic7FAPo0Qg3gGEiI2xKG9z83YMA0BOE1d1SAAAAN4twAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABgFMINAAAwCuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEYh3AAAAKMQbgAAgFEINwAAwCjtCjdHjx7VqlWr9J//+Z86f/580Gs+n0//+I//2KnFAQBaV1cfUNHHX2hH6VkVffyF6uoDVpcEWM4WCATa9H/Cnj17lJ6eriFDhqimpkZfffWVfve732nKlCmSpHPnzql///6qq6vr0oJvls/nk8PhkNfrVUxMjNXlAECH5Zd5lJl3Qh5vbWOby2HXinS3ZiS5LKwM6Hzt+f1u88jNypUrtXz5cpWVlenPf/6zfvrTn+rv//7vlZ+ff9MFAwDaJ7/MoyU5h4OCjSRVeWu1JOew8ss8FlUGWK/N4eb48eON0042m00/+clPtHHjRn3/+99XXl5elxUIAAhWVx9QZt4JNTfs3tCWmXeCKSr0WL3a2jEqKkoXL14Maps7d64iIiL06KOP6t///d87vTgAQFMl5ReajNhcLyDJ461VSfkFpQ2OC11hQJhoc7gZOXKk3nnnHY0ZMyaofc6cOaqvr9eiRYs6vTgAQFPVNS0Hm470A0zT5nCzZMkSFRYWNvva3LlzJUkbN27snKoAAC2Kj7Z3aj/ANG0ON9/97nf13e9+V/v27dN9993X5PW5c+fK5/N1anEAgKZSE2PlcthV5a1tdt2NTZLTYVdqYmyoSwPCQrs38XvggQf0z//8z7py5Upj2+eff6709HRlZGR0anEAgKYiI2xake6WdC3IXK/hfEW6W5ERX38V6BnaHW4KCwuVl5ensWPH6vjx49q1a5eSkpJ06dIlHT16tMOFZGVlyWaz6dlnn22xz5YtW2Sz2ZoctbXMKwPoWWYkuZQ9f7ScjuCpJ6fDruz5o9nnBj1am6elGowbN05HjhzR4sWLNWbMGNXX12vVqlX6yU9+IputY/9KOHDggDZu3Kjk5OQb9o2JidGpU6eC2ux25pUB9Dwzklya5naqpPyCqmtqFR99bSqKERv0dO0ON5J06tQpHThwQAMHDtRnn32mDz/8UF999ZX69OnT7ve6dOmS5s2bp02bNmnVqlU37G+z2eR0Otv8/n6/X36/v/GcdUEATBIZYeN2b+Br2j0ttWbNGqWlpWnatGkqKyvTgQMHdOTIESUnJ6uoqKjdBSxdulQPPPBAs4uUm3Pp0iUNGjRIAwcO1IMPPqgjR4602j8rK0sOh6PxSEhIaHeNAACg+2h3uFm/fr1+//vf6z/+4z9kt9s1fPhwlZSU6Hvf+54mT57crvfKzc3VoUOHlJWV1ab+w4YN05YtW7Rz5069+eabstvtmjhxok6fPt3iNRkZGfJ6vY1HZWVlu2oEAADdS5sfnNng/Pnz+pu/+ZtmX9u/f7/+7u/+rk3vU1lZqZSUFO3Zs0f33HOPJGny5MkaOXKk1q1b16b3qK+v1+jRozVp0iRt2LChTdfw4EwAALqf9vx+t3vNTUvBRlKbg40kHTp0SNXV1UE7HtfV1amwsFAvvfSS/H6/IiMjW32PiIgIjR07ttWRGwAA0LN0aEFxZ5g6daqOHTsW1PajH/1Iw4YN03PPPXfDYCNJgUBApaWlGjFiRFeVCQDoInX1Ae70QpewLNxER0crKSkpqK1Pnz6Ki4trbF+4cKEGDBjQuCYnMzNT48eP15AhQ+Tz+bRhwwaVlpbq5ZdfDnn9AICOyy/zKDPvRNADQF0Ou1aku9mjBzfNsnDTFhUVFYqI+Oua54sXL+qJJ55QVVWVHA6HRo0apcLCQqWmplpYJQCgPfLLPFqSc7jJoyOqvLVaknOYTQhx09q9oLi7Y0ExAFinrj6ge9f+IWjE5noNz8V697nvMEWFIO35/W73reAAAHRUSfmFFoONJAUkeby1Kim/ELqiYBzCDQAgZKpr2vYswLb2A5pDuAEAhEx8dNueBdjWfkBzCDcAgJBJTYyVy2FXS6tpbLp211RqYmwoy4JhCDcAgJCJjLBpRbpbkpoEnIbzFeluFhPjphBuAAAhNSPJpez5o+V0BE89OR12bgNHpwjrfW4AAGaakeTSNLeTHYrRJQg3AABLREbYlDY4zuoyYCCmpQAAgFEINwAAwCiEGwAAYBTCDQAAMArhBgAAGIVwAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABgFMINAAAwCuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEbpZXUBAACEQl19QCXlF1RdU6v4aLtSE2MVGWGzuix0gbAZucnKypLNZtOzzz7bar9t27bJ7XYrKipKbrdb27dvD1GFAIDuKr/Mo3vX/kFzNxXrmdxSzd1UrHvX/kH5ZR6rS0MXCItwc+DAAW3cuFHJycmt9isqKtKcOXO0YMECHT16VAsWLNAjjzyiDz74IESVAgC6m/wyj5bkHJbHWxvUXuWt1ZKcwwQcA1kebi5duqR58+Zp06ZN+ta3vtVq33Xr1mnatGnKyMjQsGHDlJGRoalTp2rdunUhqhYA0J3U1QeUmXdCgWZea2jLzDuhuvrmeqC7sjzcLF26VA888IDuu+++G/YtKirS9OnTg9ruv/9+vf/++y1e4/f75fP5gg4AQM9QUn6hyYjN9QKSPN5alZRfCF1R6HKWLijOzc3VoUOHdPDgwTb1r6qqUr9+/YLa+vXrp6qqqhavycrKUmZm5k3VCQDonqprWg42HemH7sGykZvKyko988wz+s1vfiO73d7m62y24JXtgUCgSdv1MjIy5PV6G4/KysoO1wwA6F7io9v2+9LWfugeLBu5OXTokKqrqzVmzJjGtrq6OhUWFuqll16S3+9XZGRk0DVOp7PJKE11dXWT0ZzrRUVFKSoqqnOLBwB0C6mJsXI57Kry1ja77sYmyem4dls4zGHZyM3UqVN17NgxlZaWNh4pKSmaN2+eSktLmwQbSUpLS9PevXuD2vbs2aMJEyaEqmwAQDcSGWHTinS3pGtB5noN5yvS3Ubsd1NXH1DRx19oR+lZFX38RY9eJG3ZyE10dLSSkpKC2vr06aO4uLjG9oULF2rAgAHKysqSJD3zzDOaNGmS1q5dq9mzZ2vHjh3at2+f3n333ZDXDwDoHmYkuZQ9f7Qy804ELS52Ouxake7WjCSXhdV1jvwyT5PP5zLo87VXWO9QXFFRoYiIvw4uTZgwQbm5uXrhhRf085//XIMHD9Zvf/tbjRs3zsIqAQDhbkaSS9PcTiN3KG7Yx+fr4zQN+/hkzx/d4wKOLRAI9KhxK5/PJ4fDIa/Xq5iYGKvLAQCgw+rqA7p37R9avN29YU3Ru899p9sHufb8flu+zw0AAOgY9vFpHuEGAIBuin18mke4AQCgm2Ifn+YRbgAA6KYa9vFpaTWNTdfumupp+/gQbgAA6KZ60j4+7UG4AQCgG2vYx8fpCJ56cjrsPfI2cCnM97kBAAA3ZvI+Ph1BuAEAwACRETalDY6zuoywwLQUAAAwCuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEYh3AAAAKMQbgAAgFEINwAAwCiEGwAAYBTCDQAAMArhBgAAGIVwAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABgFMINAAAwiqXhJjs7W8nJyYqJiVFMTIzS0tK0e/fuFvtv2bJFNputyVFbWxvCqgEAQDjrZeUfHzhwoNasWaO77rpLkvT6669r9uzZOnLkiIYPH97sNTExMTp16lRQm91u7/JaAQBA92BpuElPTw86/8UvfqHs7GwVFxe3GG5sNpucTmcoygMAAN1Q2Ky5qaurU25uri5fvqy0tLQW+126dEmDBg3SwIED9eCDD+rIkSOtvq/f75fP5ws6AACAuSwPN8eOHdOtt96qqKgoLV68WNu3b5fb7W6277Bhw7Rlyxbt3LlTb775pux2uyZOnKjTp0+3+P5ZWVlyOByNR0JCQld9FAAAEAZsgUAgYGUBV65cUUVFhS5evKht27bpv/7rv7R///4WA8716uvrNXr0aE2aNEkbNmxoto/f75ff72889/l8SkhIkNfrVUxMTKd9DgAA0HV8Pp8cDkebfr8tXXMjSb17925cUJySkqIDBw5o/fr1evXVV294bUREhMaOHdvqyE1UVJSioqI6rV4AABDeLJ+W+rpAIBA00nKjvqWlpXK5XF1cFQAA6C4sHbl5/vnnNXPmTCUkJKimpka5ubkqKChQfn6+JGnhwoUaMGCAsrKyJEmZmZkaP368hgwZIp/Ppw0bNqi0tFQvv/yylR8DAACEEUvDzblz57RgwQJ5PB45HA4lJycrPz9f06ZNkyRVVFQoIuKvg0sXL17UE088oaqqKjkcDo0aNUqFhYVKTU216iMAAIAwY/mC4lBrz4IkAAAQHtrz+x12a24AAABuBuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEYh3AAAAKMQbgAAgFEINwAAwCiEGwAAYBTCDQAAMArhBgAAGIVwAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABgFMINAJa1fIkAAAzlSURBVAAwCuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADCKpeEmOztbycnJiomJUUxMjNLS0rR79+5Wr9m2bZvcbreioqLkdru1ffv2EFULAAC6A0vDzcCBA7VmzRodPHhQBw8e1He+8x3Nnj1bx48fb7Z/UVGR5syZowULFujo0aNasGCBHnnkEX3wwQchrhwAAIQrWyAQCFhdxPViY2P1b//2b3rssceavDZnzhz5fL6g0Z0ZM2boW9/6lt58881m38/v98vv9zee+3w+JSQkyOv1KiYmpvM/AAAA6HQ+n08Oh6NNv99hs+amrq5Oubm5unz5stLS0prtU1RUpOnTpwe13X///Xr//fdbfN+srCw5HI7GIyEhoVPrBgAA4cXycHPs2DHdeuutioqK0uLFi7V9+3a53e5m+1ZVValfv35Bbf369VNVVVWL75+RkSGv19t4VFZWdmr9AAAgvPSyuoChQ4eqtLRUFy9e1LZt27Ro0SLt37+/xYBjs9mCzgOBQJO260VFRSkqKqpTawYAAOHL8nDTu3dv3XXXXZKklJQUHThwQOvXr9err77apK/T6WwySlNdXd1kNAcAAPRclk9LfV0gEAhaAHy9tLQ07d27N6htz549mjBhQihKAwAA3YClIzfPP/+8Zs6cqYSEBNXU1Cg3N1cFBQXKz8+XJC1cuFADBgxQVlaWJOmZZ57RpEmTtHbtWs2ePVs7duzQvn379O6771r5MQAAQBixNNycO3dOCxYskMfjkcPhUHJysvLz8zVt2jRJUkVFhSIi/jq4NGHCBOXm5uqFF17Qz3/+cw0ePFi//e1vNW7cOKs+AgAACDNht89NV2vPffIAACA8dMt9bgAAADoD4QYAABiFcAMAAIxCuAEAAEYh3AAAAKMQbgAAgFEINwAAwCiEGwAAYBTCDQAAMArhBgAAGIVwAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABglF5WFwAAALq/uvqASsovqLqmVvHRdqUmxioywmZJLYQbAABwU/LLPMrMOyGPt7axzeWwa0W6WzOSXCGvh2kpAADQYfllHi3JORwUbCSpylurJTmHlV/mCXlNhBsAANAhdfUBZeadUKCZ1xraMvNOqK6+uR5dh3ADAAA6pKT8QpMRm+sFJHm8tSopvxC6okS4AQAAHVRd03Kw6Ui/zkK4AQAAHRIfbe/Ufp2FcAMAADokNTFWLoddLd3wbdO1u6ZSE2NDWRbhBgAAdExkhE0r0t2S1CTgNJyvSHeHfL8bwg0AAOiwGUkuZc8fLacjeOrJ6bAre/5oS/a5YRM/AABwU2YkuTTN7WSHYgAAYI7ICJvSBsdZXYYkpqUAAIBhCDcAAMAohBsAAGAUwg0AADAK4QYAABjF0nCTlZWlsWPHKjo6WvHx8XrooYd06tSpVq/ZsmWLbDZbk6O2NrTPrQAAAOHJ0nCzf/9+LV26VMXFxdq7d6+uXr2q6dOn6/Lly61eFxMTI4/HE3TY7aF9bgUAAAhPlu5zk5+fH3S+efNmxcfH69ChQ5o0aVKL19lsNjmdzjb9Db/fL7/f33ju8/k6ViwAAOgWwmrNjdfrlSTFxrb+gK1Lly5p0KBBGjhwoB588EEdOXKkxb5ZWVlyOByNR0JCQqfWDAAAwostEAgErC5CkgKBgGbPnq0vv/xSf/zjH1vsV1xcrI8++kgjRoyQz+fT+vXr9dZbb+no0aMaMmRIk/7NjdwkJCTI6/UqJiamSz4LAADoXD6fTw6Ho02/32ETbpYuXapdu3bp3Xff1cCBA9t8XX19vUaPHq1JkyZpw4YNN+zv9Xp12223qbKyknADAEA30TA4cfHiRTkcjlb7hsWzpZ566int3LlThYWF7Qo2khQREaGxY8fq9OnTbepfU1MjSUxPAQDQDdXU1IR3uAkEAnrqqae0fft2FRQUKDExsUPvUVpaqhEjRrSpf//+/VVZWano6GjZbNY8rTQcNSRiRrS6Ft9z6PBdhwbfc2jwPV/7va+pqVH//v1v2NfScLN06VK98cYb2rFjh6Kjo1VVVSVJcjgcuuWWWyRJCxcu1IABA5SVlSVJyszM1Pjx4zVkyBD5fD5t2LBBpaWlevnll9v0NyMiIto9OtSTxMTE9Nj/cUKJ7zl0+K5Dg+85NHr693yjEZsGloab7OxsSdLkyZOD2jdv3qwf/vCHkqSKigpFRPz1pq6LFy/qiSeeUFVVlRwOh0aNGqXCwkKlpqaGqmwAABDGLJ+WupGCgoKg81/96lf61a9+1UUVAQCA7i5y5cqVK60uAuEhMjJSkydPVq9eYbHO3Fh8z6HDdx0afM+hwffcdmFzKzgAAEBnCKsdigEAAG4W4QYAABiFcAMAAIxCuAEAAEYh3PRwhYWFSk9PV//+/WWz2fT73//e6pKMlJWVpbFjxyo6Olrx8fF66KGHdOrUKavLMk52draSk5MbNzpLS0vT7t27rS7LeFlZWbLZbHr22WetLsU4K1eulM1mCzqcTqfVZYU9wk0Pd/nyZd1zzz166aWXrC7FaPv379fSpUtVXFysvXv36urVq5o+fbouX75sdWlGGThwoNasWaODBw/q4MGD+s53vqPZs2fr+PHjVpdmrAMHDmjjxo1KTk62uhRjDR8+XB6Pp/E4duyY1SWFPW6W7+FmzpypmTNnWl2G8fLz84PON2/erPj4eB06dEiTJk2yqCrzpKenB53/4he/UHZ2toqLizV8+HCLqjLXpUuXNG/ePG3atEmrVq2yuhxj9erVi9GadmLkBrCA1+uVJMXGxlpcibnq6uqUm5ury5cvKy0tzepyjLR06VI98MADuu+++6wuxWinT59W//79lZiYqEcffVRnzpyxuqSwx8gNEGKBQEDLli3Tvffeq6SkJKvLMc6xY8eUlpam2tpa3Xrrrdq+fbvcbrfVZRknNzdXhw4d0sGDB60uxWjjxo3T1q1b9e1vf1vnzp3TqlWrNGHCBB0/flxxcXFWlxe2CDdAiP3TP/2T/u///k/vvvuu1aUYaejQoSotLdXFixe1bds2LVq0SPv37yfgdKLKyko988wz2rNnj+x2u9XlGO36ZQMjRoxQWlqaBg8erNdff13Lli2zsLLwRrgBQuipp57Szp07VVhYqIEDB1pdjpF69+6tu+66S5KUkpKiAwcOaP369Xr11Vctrswchw4dUnV1tcaMGdPYVldXp8LCQr300kvy+/2KjIy0sEJz9enTRyNGjNDp06etLiWsEW6AEAgEAnrqqae0fft2FRQUKDEx0eqSeoxAICC/3291GUaZOnVqkzt2fvSjH2nYsGF67rnnCDZdyO/36+TJk/rbv/1bq0sJa4SbHu7SpUv66KOPGs/Ly8tVWlqq2NhY3X777RZWZpalS5fqjTfe0I4dOxQdHa2qqipJksPh0C233GJxdeZ4/vnnNXPmTCUkJKimpka5ubkqKChocrcabk50dHST9WJ9+vRRXFwc68g62fLly5Wenq7bb79d1dXVWrVqlXw+nxYtWmR1aWGNcNPDHTx4UFOmTGk8b5jDXbRokbZs2WJRVebJzs6WJE2ePDmoffPmzfrhD38Y+oIMde7cOS1YsEAej0cOh0PJycnKz8/XtGnTrC4N6JBPP/1Uc+fO1fnz59W3b1+NHz9excXFGjRokNWlhTVbIBAIWF0EAABAZ2GfGwAAYBTCDQAAMArhBgAAGIVwAwAAjEK4AQAARiHcAAAAoxBuAACAUQg3AADAKIQbAABgFMINAKN4PB79wz/8g4YOHaqIiAg9++yzVpcEIMQINwCM4vf71bdvX/3sZz/TPffcY3U5ACxAuAHQrXz++edyOp1avXp1Y9sHH3yg3r17a8+ePbrjjju0fv16LVy4UA6Hw8JKAViFp4ID6Fb69u2r1157TQ899JCmT5+uYcOGaf78+XryySc1ffp0q8sDEAYINwC6nVmzZunxxx/XvHnzNHbsWNntdq1Zs8bqsgCECaalAHRLv/zlL3X16lX97ne/029+8xvZ7XarSwIQJgg3ALqlM2fO6LPPPlN9fb0++eQTq8sBEEaYlgLQ7Vy5ckXz5s3TnDlzNGzYMD322GM6duyY+vXrZ3VpAMIA4QZAt/Ozn/1MXq9XGzZs0K233qrdu3frscce0//+7/9KkkpLSyVJly5d0ueff67S0lL17t1bbrfbyrIBhIgtEAgErC4CANqqoKBA06ZN0zvvvKN7771XklRRUaHk5GRlZWVpyZIlstlsTa4bNGiQ/vznP4e4WgBWINwAAACjsKAYAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAAMAohBsAAGAUwg0AADAK4QYAABiFcAMAAIxCuAEAAEb5f/valLSziGNLAAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pygui(false)\n",
    "n = 12\n",
    "d = 2\n",
    "\n",
    "x1 = range(0,stop=5,length=n)  + randn(n).*0.05\n",
    "x2 = x1.*(-0.7) + randn(n).*0.5\n",
    "x1 = x1.-Statistics.mean(x1).+3\n",
    "x2 = x2.-Statistics.mean(x2).+5\n",
    "\n",
    "X = hcat(x1,x2)\n",
    "\n",
    "plt.scatter(x1,x2)\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lZWWm4wAhiyIDAD7W0dGhqqoqSVJtba3i4uIMJwJCF0UGAHysqKhIx44dU3p6uubPn286DhDSKDIA4EO7d+/W5s2bNW7cODU2NjLAF/AzigwA+Eh/f7/y8vIkSdnZ2Zo2bZrhREDoo8gAgI+sXbtWra2tSkhI0PLly03HAcICRQYAfKCzs1Pl5eWSpBUrVigxMdFwIiA8UGQAwAdKS0vV3d2ttLQ0LVy40HQcIGxQZABgjFpaWvTQQw9JkhobGxUREWE4ERA+KDIAMAYDAwPKycmRZVlasGCBZs6caToSEFYoMgAwBps2bVJzc7Pi4uJUU1NjOg4QdiJNBwBCkXfAUvPbH6rzo080IS5GV6YkKGIc64mEmu7ubhUXF0uSKioqlJycbDgREH4oMoCPPdd2RPdue0NH3J8MHkuOj1HFzZfo+ql80YWSyspKdXV1KTU1Vbm5uabjAGGJW0uADz3XdkR3PfrqkBIjSUfdn+iuR1/Vc21HDCWDr7W1tamxsVGS1NDQoKioKMOJgPBEkQF8xDtg6d5tb8g6yWvHj9277Q15B072DgQTy7KUl5cnr9erefPmKSMjw3QkIGxRZAAfaX77wxOuxHyWJemI+xM1v/1h4ELBL7Zs2aJdu3YpJiZGq1evNh0HCGsUGcBHOj8avsScyftgT729vVqyZIkkqaSkRE6n02wgIMxRZAAfmRAX49P3wZ6qq6vV0dEhp9OppUuXmo4DhD2KDOAjV6YkKDk+RsNNsnbo09lLV6YkBDIWfKi9vV2rVq2SJNXX1ys2NtZwIgAUGcBHIsY5VHHzJZJ0Qpk5/rzi5ktYTyaIFRYWqq+vT5mZmZo9e7bpOABEkQF86vqpyVqbNV1J8UNvHyXFx2ht1vRRryPjHbD00sEP9Ov9h/XSwQ+Y8WTQjh07tH37dkVGRmrNmjVyOCikgB2wIB7gY9dPTVbGJUljXtmXhfXsw+PxKD8/X5JUUFCg1NRUw4kAHEeRAfwgYpxDV1+UeMafP76w3j9ffzm+sN6ZXN3Bmaurq1N7e7uSk5NVVlZmOg6Az+DWEmAzLKxnLx0dHaqqqpIk1dbWavz48YYTAfgsigxgM75cWI8xNmNXVFSkY8eOKT09XfPnzzcdB8A/4dYSYDO+WliPMTZj19TUpM2bN2vcuHFqbGxkgC9gQ1yRAWzGFwvrsXnl2PX39w/uaJ2dna1p06YZTgTgZCgygM2MdWE9xtj4xtq1a9Xa2qqEhAQtX77cdBwAw6DIADYz1oX12Lxy7Lq6ulReXi5JWrFihRITz3wGGgD/osgANjSWhfXYvHLsSktL1d3drbS0NC1cuNB0HACnYPvBvocPH1ZxcbGeffZZ/f3vf9e//uu/asOGDZoxY4bpaIBfnenCemxeOTYtLS3asGGDJKmxsVERERGGEwE4FVsXmb/97W9KT0/Xtddeq2effVYTJkzQwYMH9bnPfc50NCAgzmRhveNjbI66PznpOBmHPr2yw+aVJxoYGFBOTo4sy9KCBQs0c+ZM05EAnIati0xNTY0mTZqkhx9+ePCY0+k0FwgIAsfH2Nz16KtySEPKDJtXntqmTZvU3NysuLg41dTUmI4DYARsPUbmN7/5jS6//HLdcsstmjBhgtLS0vTggw+e8jMej0c9PT1DHkC48fXmleGgu7tbxcXFkqSKigolJ3OOgGDgsCzLtnMwY2I+/SO8ePFi3XLLLWpublZBQYF+8Ytf6LbbbjvpZyorK3XvvfeecNztdrO0OMKOd8Aa8+aV4aKgoEBr1qxRamqqXn/9dUVFRZmOBIS1np4excfHn/b729ZFJioqSpdffrlefPHFwWN5eXlqaWnRSy+9dNLPeDweeTyewec9PT2aNGkSRQbAsNra2jRt2jR5vV49//zzysjIMB0JCHsjLTK2HiOTnJysSy65ZMixiy++WP/1X/817Geio6MVHR3t72hAyAuXqzmWZSkvL09er1dz586lxABBxtZFJj09XW+++eaQY2+99ZYmT55sKBEQHsJpn6YtW7Zo165diomJUV1dnek4AEbJ1oN9CwsL9fLLL2vlypVqb2/X448/rvXr12vRokWmowEhK5z2aert7dWSJUskSSUlJcyKBIKQrYvMFVdcoaeeekpPPPGEpk6dquXLl+tnP/uZ5s+fbzoaEJLCbZ+m6upqdXR0yOl0aunSpabjADgDtr61JEnf+MY39I1vfMN0DCAsjGafptEu1Gc37e3tWrVqlSSpvr5esbGxhhMBOBO2viIDILDCaZ+mwsJC9fX1KTMzU7NnzzYdB8AZosgAGBQu+zTt2LFD27dvV2RkpNasWSOHI/RmYwHhgiIDYNDxfZqG+1p36NPZS8G8T5PH41F+fr6kTxfBS01NNZwIwFhQZAAMOr5Pk6QTyozJfZq8A5ZeOviBfr3/sF46+MGYBhvX19ervb1dycnJKisr82FKACbYfrAvgMA6vk/TP68jk2RoHRlfrmnT0dGh5cuXS5Jqa2tZ7RsIAbbeosAXRrrEMYCh7LCy7/E1bf75j9TxFKPdAPPWW2/V5s2blZ6ert/97neMjQFsLCS2KABgTsQ4h9Ep1qdb08ahT9e0ybgkaUQFq6mpSZs3b5bD4ZDL5aLEACGCMTIAbGk0a9qcTn9/v3JzcyVJd955p9LS0nwVE4BhFBkAtuTLNW3Wrl2r1tZWJSQkDI6RARAaKDIAbMlXa9p0dXWpvLxckrRixQolJgb3isQAhqLIALAlX61pU1paqu7ubqWlpWnhwoU+zwnALIoMAFvyxZo2LS0t2rBhgyTJ5XIpIiLCD0kBmESRAWBbx9e0SYofevsoKT7mtFOvBwYGlJOTI8uytGDBAqWnp/s7LgADmH4NwNaun5qsjEuSRr2mzaZNm9Tc3Ky4uDjV1NQEKC2AQKPIALC90a5p093drZKSEklSWXm53jkWpeb9h40t7AfAfygyAEJOZWWlOjs7NSnl/9PWv0/Vzx98efC1M93eAIA9MUYGQEhpa2tTY2OjJKnviu/pr73eIa8fdX+iux59Vc+1HTERD4CPUWQAhAzLspSXlyev16vPXzJLMSknruB7fMuDe7e9MaZdtAHYA0UGQMjYunWrdu3apajoGJ397z8Y9n2j2d4AgL2Nqsi8/vrrqqqq0gMPPKD3339/yGs9PT26/fbbfRoOAEaqt7dXixcvliTN+8GPFRk/8bSfGek2CADsa8RF5vnnn9eVV16pzZs3q6amRhdffLF27do1+Prf//53bdq0yS8hAeB0qqur1dHRIafTqeycwhF9ZqTbIACwrxEXmcrKSt19991qa2vTO++8o6VLl+qb3/ymnnvuOX/mA4DTam9v16pVqyRJdXV1+srF/+KT7Q0A2N+Ii8yBAwcGbx05HA4VFRVp/fr1+o//+A9t27bNbwEB4HQKCwvV19enzMxMzZkzxyfbGwAIDiMuMtHR0eru7h5y7NZbb9WGDRv0ne98R0899ZTPwwHA6ezYsUPbt29XZGSk1qxZI4fj03Iylu0NAASPES+IN23aNO3atUszZswYcvzb3/62BgYG9L3vfc/n4QAEJ++ANeotBc6Ex+NRfn6+JKmgoECpqalDXj/T7Q0ABI8RF5m77rpLe/bsOelrt956qyRp/fr1vkkFIGg913ZE9257Q0fc/5gR5K/VdOvr69Xe3q6kpCSVlZWd9D2j3d4AQHBxWJbllxWhnnjiCX3zm9/UOeec448fP2I9PT2Kj4+X2+3W+PHjjWYBQt1zbUd016Ov6p//qBy//uHLWzodHR2aMmWKjh07pl/96lfKysryyc8FYA8j/f7224J42dnZ+utf/+qvHw/AZrwDlu7d9sYJJUbyz2q6RUVFOnbsmNLT0zV//nyf/EwAwcdvRcZPF3oA2FTz2x8OuZ30z3y5mm5TU5M2b94sh8Mhl8s1OMAXQPhhiwIAPjHSVXLHuppuf3+/cnNzJUl33nmn0tJO3E8JQPigyADwiZGukjvW1XTXrl2r1tZWJSQkaPny5WP6WQCCH0UGgE9cmZLg99V0u7q6VF5eLklasWKFEhOZjQSEO4oMAJ8IxGq6paWl6u7uVlpamhYuXHjGPwdA6Bh1kfnv//7vYV/7xS9+MfjfkydP1llnnXVmqQAEJX+uptvS0qINGzZIklwulyIiIsaUFUBoGPU6MtHR0crJyVF1dbWioqIkfXq59/bbb9f//M//6MMPxz4jwZdYRwYIPF+v7DswMKCrr75azc3NWrBggR555BEfpgVgR35bR2bPnj3atm2brrjiCh04cEDPPPOMpk6dqo8//livv/76mEIDCA3HV9OdPe1fdPVFiWPeEmDTpk1qbm5WXFycampqfJQSQCgYdZG56qqr9Nprr+myyy7TjBkzNHfuXC1ZskQvvPCCJk2a5I+MAMJYd3e3SkpKJEnl5eVKTmazRwD/cEaDfd988021tLToggsuUGRkpP74xz/q2LFjvs4GAKqsrFRnZ6dSU1OVl5dnOg4Amxl1kbnvvvt09dVXKyMjQ21tbWppaRm8QvPSSy/5IyOAMNXW1qbGxkZJUkNDw+C4vEDwDlh66eAH+vX+w3rp4Ac+21oBgG+NePfr49asWaOnn35aN9xwgyTp0ksvVXNzs0pLS3XNNdfI4/H4PCSA8GNZlvLy8uT1ejV37lxlZGQE7HcHcgdvAGMz6llL77//vs4777yTvtbU1KSvfvWrPgnmK8xaAoLTli1b9K1vfUsxMTH6wx/+IKfTGZDfG8gdvAEMz2+zloYrMZJsV2IABKfe3l4tXrxYklRSUhKwEhPoHbwBjB0r+wKwnerqanV0dMjpdGrp0qUB+72B3MEbgG9QZADYysGDB7Vq1SpJUl1dnWJjYwP2uwO1gzcA3xn1YF8A8KfCwkL19fUpMzNTc+bMCejv9tcO3r5e6RjAP1BkANjGjh07tG3bNkVGRmrNmjVyOAL7ZX98B++j7k9OOk7GoU/3jRrNDt7MgAL8i1tLAGzB4/EoPz9fklRQUKDU1NSAZ/D1Dt7HZ0D987ibo+5PdNejr+q5tiNjTAyAIgPAFurr69Xe3q6kpCSVlZUZy+GrHbyZAQUEBreWABjX0dGhqqoqSdKqVauMr/l0/dRkZVySNKZxLaOZAXX1RYk+SA2EJ4oMAOOKiorU29ur9PR0zZ8/33QcSf/YwftMMQMKCAxuLQEwqqmpSZs3b5bD4ZDL5Qr4AF9/8dcMKABDUWQAGNPf36/c3FxJUnZ2ttLS0gwn8p3jM6CGq2UOfTp7aTQzoACciCIDwJi1a9eqtbVVCQkJg2NkQoWvZ0ABODmKDAAjurq6VF5eLklasWKFEhNDb8Crr2ZAARgeg30BGFFaWqru7m6lpaVp4cKFpuP4jS9mQAEYHkUGQMC1tLRow4YNkiSXy6WIiAjDifxrrDOgAAyPW0sAAmpgYEA5OTmyLEsLFixQenq66UgAghhFBkBAbdq0Sc3NzYqLi1NNTY3pOACCHEUGQMC43W6VlJRIksrLy5WczGBXAGPDGBkAAVNZWanOzk6lpqYqLy/PdBxb8g5YDAwGRiGorshUV1fL4XCooKDAdBQAo9TW1iaXyyVJamhoUFRUlOFE9vNc2xHNqnlBtz74svI379etD76sWTUvsEs2cApBU2RaWlq0fv16XXbZZaajABgly7KUl5cnr9eruXPnKiMjw3Qk23mu7YjuevTVEzaaPOr+RHc9+iplBhhGUBSZjz/+WPPnz9eDDz6oz3/+86bjABilrVu3ateuXYqJiVFdXZ3pOLbjHbB077Y3ZJ3ktePH7t32hrwDJ3vHyH/HSwc/0K/3H9ZLBz8Y088C7CQoxsgsWrRIN910k6677rrTLmPu8Xjk8XgGn/f09Pg7HoBT6O3t1eLFiyVJJSUlcjqdZgPZUPPbH55wJeazLElH3J+o+e0Pz2g9mufajujebW8M+R3J8TGquPkSVhdG0LP9FZnNmzdr3759qq6uHtH7q6urFR8fP/iYNGmSnxMCOJXq6mp1dHTI6XRq6dKlpuPYUudHw5eYM3nfZ3HLCqHO1kXm0KFDys/P12OPPaaYmJFtdX/PPffI7XYPPg4dOuTnlACGc/DgQa1atUqSVFdXp9jYWDudryIAABo+SURBVMOJ7GlC3Mj+vo30fccF4pYVYJqtby3t27dPnZ2dmjFjxuAxr9erPXv2qLGxUR6P54SlzaOjoxUdHR3oqABOorCwUH19fcrIyNCcOXNMx7GtK1MSlBwfo6PuT05aOhz6dKPJK1MSRvVz/X3LCrADW1+R+drXvqbW1lbt379/8HH55Zdr/vz52r9/f8jvzwIEsx07dmjbtm2KjIxUQ0ODHA7WQhlOxDiHKm6+RNKnpeWzjj+vuPmSUa8n489bVoBd2PqKTFxcnKZOnTrk2DnnnKPExMQTjgOwD4/Ho/z8fElSQUGBUlNTDSeyv+unJmtt1vQTBuUmjWFQrr9uWQF2YusiAyA41dfXq729XUlJSSorKzMdJ2hcPzVZGZck+WxlX3/dsgLsJOiKzO7du01HAHAKHR0dg8skrFq1SuPHjzecKLhEjHP4bLzK8VtWdz36qhzSkDIzlltWgJ3YeowMgOBTVFSk3t5epaena/78+abjhL3jt6yS4ofePkqKj9HarOmsI4Og57AsK6Tn3fX09Cg+Pl5ut5t/GQJ+1tTUpGuuuUYOh0P79u1TWlqa6Uj4f9iMEsFmpN/fQXdrCYA99ff3Kzc3V5KUnZ1NibEZX96yAuyEW0sAfGLdunVqbW1VQkLCabcSAQBfocgAGLOurq7B2UkrVqxQYiL/8gcQGBQZAGNWWlqq7u5upaWlaeHChabjAAgjFBkAY9LS0qINGzZIklwuFytuAwgoigyAMzYwMKCcnBxZlqUFCxYoPT3ddCQAYYYiA+CMbdq0Sc3NzYqLi1NNTY3pOADCEEUGwBlxu90qKSmRJJWXlys5mYXVAAQeRQbAGamsrFRnZ6emTJmivLw803EAhCmKDIBRa2trk8vlkiQ1NDQoKirKcCIA4YoiA2BULMtSXl6evF6v5s6dq8zMTNORAIQxigyAUdm6dat27dqlmJgY1dXVmY4DIMxRZACMWG9vr5YsWSJJKikpkdPpNBsIQNijyAAYserqah06dEhOp1NLly41HQcAKDIARubgwYNatWqVJKmurk6xsbGGEwEARQbACBUWFqqvr08ZGRmaM2eO6TgAIIkiA2AEduzYoW3btikyMlINDQ1yOBymIwGAJIoMgNPweDzKz8+XJBUUFCg1NdVwIgD4B4oMgFOqr69Xe3u7kpKSVFZWZjoOAAxBkQEwrI6ODlVVVUmSamtrNX78eMOJAGAoigyAYRUVFam3t1fp6enKysoyHQcATkCRAXBSTU1N2rx5sxwOh1wuFwN8AdgSRQbACfr7+5WbmytJys7OVlpamuFEAHByFBkAJ1i3bp1aW1uVkJAwOEYGAOyIIgNgiK6ursHZSStWrFBiYqLhRAAwPIoMgCFKS0vV3d2ttLQ0LVy40HQcADgligyAQXv37tWGDRskSS6XSxEREYYTAcCpUWQASJIGBgaUk5Mjy7K0YMECpaenm44EAKdFkQEgSdq0aZNeeeUVxcXFqaamxnQcABgRigwAud1ulZSUSJLKy8uVnJxsOBEAjAxFBoAqKyvV2dmpKVOmKC8vz3QcABgxigwQ5g4cOCCXyyVJamhoUFRUlOFEADByFBkgjFmWpdzcXHm9Xs2dO1eZmZmmIwHAqESaDgDAnK1bt2rXrl2KiYlRXV2d6TiwGe+Apea3P1TnR59oQlyMrkxJUMQ49tyCvVBkgDDV29urJUuWSJKKi4vldDrNBoKtPNd2RPdue0NH3J8MHkuOj1HFzZfo+qkMBod9cGsJCFPV1dU6dOiQnE6niouLTceBjTzXdkR3PfrqkBIjSUfdn+iuR1/Vc21HDCUDTkSRAcLQwYMHtWrVKklSXV2dYmNjDSeCXXgHLN277Q1ZJ3nt+LF7t70h78DJ3gEEHkUGCEOFhYXq6+tTRkaG5syZYzoObKT57Q9PuBLzWZakI+5P1Pz2h4ELBZwCRQYIMzt27NC2bdsUGRmphoYGORwM3sQ/dH40fIk5k/cB/kaRAcKIx+NRfn6+JKmgoECpqamGE8FuJsTF+PR9gL9RZIAwUl9fr/b2diUlJamsrMx0HNjQlSkJSo6P0XDX6Rz6dPbSlSkJgYwFDIsiA4SJw4cPq6qqSpJUW1ur8ePHG04EO4oY51DFzZdI0gll5vjzipsvYT0Z2AZFBggTRUVF6u3tVXp6urKyskzHgY1dPzVZa7OmKyl+6O2jpPgYrc2azjoysBWHZVkhPYeup6dH8fHxcrvd/AsUYaupqUnXXHONHA6H9u3bp7S0NNOREARY2RcmjfT7m5V9gRDX39+v3NxcSVJ2djYlBiMWMc6hqy9KNB0DOCVuLQEhbt26dWptbVVCQsLgGBkACBUUGSCEdXV1Dc5OWrFihRIT+dc1gNBCkQFCWGlpqbq7u5WWlqaFCxeajgMAPkeRAULU3r17tWHDBkmSy+VSRESE4UQA4HsUGSAEDQwMKCcnR5ZlKSsrS+np6aYjAYBfUGSAELRp0ya98sorOvfcc1VbW2s6DgD4DUUGCDFut1slJSWSpIqKCiUns3gZgNBFkQFCTGVlpTo7OzVlyhTl5eWZjgMAfkWRAULIgQMH5HK5JEkNDQ2KiooynAgA/IsiA4QIy7KUm5srr9eruXPnKjMz03QkAPA7igwQIrZu3apdu3YpJiZGdXV1puMAQEBQZIAQ0NvbqyVLlkiSiouL5XQ6zQYCgAChyAAh4L777tOhQ4fkdDpVXFxsOg4ABIyti0x1dbWuuOIKxcXFacKECZozZ47efPNN07EAWzl48ODgWjF1dXWKjY01nAgAAsfWRaapqUmLFi3Syy+/rJ07d6q/v1+ZmZnq7e01HQ2wjcLCQvX19SkjI0Nz5swxHQcAAsphWZZlOsRIdXV1acKECWpqatK///u/j+gzPT09io+Pl9vt1vjx4/2cEAisZ599VjfeeKMiIyPV2tqq1NRU05EAwCdG+v0dGcBMY+Z2uyVJCQkJw77H4/HI4/EMPu/p6fF7LsAEj8ej/Px8SVJBQQElBkBYsvWtpc+yLEuLFy/WrFmzNHXq1GHfV11drfj4+MHHpEmTApgSCJz6+nr96U9/UlJSksrKykzHAQAjgubW0qJFi/TMM8/o97//vS644IJh33eyKzKTJk3i1hJCyuHDhzVlyhT19vbqkUce0YIFC0xHAgCfCqlbS7m5ufrNb36jPXv2nLLESFJ0dLSio6MDlAwwo6ioSL29vZo5c6aysrJMxwEAY2xdZI4vuf7UU09p9+7dSklJMR0JMK6pqUlPPPGEHA6HGhsb5XA4TEcCAGNsXWQWLVqkxx9/XL/+9a8VFxeno0ePSpLi4+NZKwNhqb+/X7m5uZKk7OxspaWlGU4EAGbZeozMcP/SfPjhh/X9739/RD+D6dcIJY2NjcrNzVVCQoLeeustJSYmmo4EAH4REmNkbNyxgIDr6uoanJ1UVVVFiQEABdH0ayDclZaWqru7W9OmTdOPfvQj03EAwBYoMkAQ2Lt3rzZs2CDp09tLERERhhMBgD1QZACbGxgYUE5OjizLUlZWltLT001HAgDboMgANvfII4/olVde0bnnnju4yzUA4FMUGcDG3G63iouLJUkVFRVKTk42nAgA7IUiA9hYZWWlOjs7NWXKFOXl5ZmOAwC2Q5EBbOrAgQNyuVySpIaGBkVFRRlOBAD2Q5EBbMiyLOXl5cnr9Wru3LnKzMw0HQkAbIkiA9jQ1q1b9cILLygmJkZ1dXWm4wCAbVFkAJvp7e3VkiVLJEnFxcVyOp1mAwGAjVFkAJu57777dOjQIU2ePHlwxhIA4OQoMoCNHDx4cHCtmPr6enZ5B4DToMgANlJYWKi+vj5lZGRozpw5puMAgO1RZACbePbZZ7Vt2zZFRkaqoaFBDofDdCQAsD2KDGADHo9H+fn5kqT8/HylpqYaTgQAwYEiA9hAfX29/vSnPykpKUnl5eWm4wBA0KDIAIYdPnxYVVVVkqTa2lqNHz/ecCIACB4UGcCwoqIi9fb2aubMmcrKyjIdBwCCCkUGMGjPnj164okn5HA41NjYyABfABgligxgSH9/v3JyciRJ2dnZSktLM5wIAIIPRQYwZN26dWptbVVCQsLgGBkAwOhQZAADurq6VFZWJkmqqqpSYmKi4UQAEJwoMoABy5YtU3d3t6ZNm6Yf/ehHpuMAQNCiyAABtnfvXv3yl7+UJDU2NioiIsJwIgAIXhQZIIAGBgaUk5Mjy7KUlZWl9PR005EAIKhRZIAAeuSRR/TKK6/o3HPPHdzlGgBw5igyQIC43W4VFxdLkioqKpScnGw4EQAEP4oMECCVlZXq7OzUlClTlJeXZzoOAIQEigwQAAcOHJDL5ZIkNTQ0KCoqynAiAAgNFBnAzyzLUl5enrxer+bMmaPMzEzTkQAgZFBkAD/bunWrXnjhBcXExKiurs50HAAIKRQZwI96e3u1ZMkSSVJxcbFSUlIMJwKA0EKRAfzovvvu06FDhzR58uTBGUsAAN+hyAB+cvDgQa1atUqSVF9fr9jYWMOJACD0UGQAPyksLJTH41FGRobmzJljOg4AhCSKDOAHzz77rLZt26bIyEg1NDTI4XCYjgQAIYkiA/iYx+NRfn6+JCk/P1+pqamGEwFA6KLIAD72s5/9TH/605+UlJSk8vJy03EAIKRRZAAfOnz4sJYvXy5Jqq2t1fjx4w0nAoDQRpEBfKioqEi9vb2aOXOmsrKyTMcBgJBHkQF8ZM+ePXriiSfkcDjkcrkY4AsAAUCRAXygv79fOTk5kqTs7GxNnz7dcCIACA8UGcAH1q1bp9bWViUkJKiqqsp0HAAIGxQZYIy6urpUVlYmSaqqqlJiYqLhRAAQPigywBgtW7ZM3d3dmjZtmn70ox+ZjgMAYYUiA4zB3r179ctf/lKS1NjYqIiICMOJACC8UGSAMzQwMKCcnBxZlqWsrCylp6ebjgQAYYciA5yhRx55RK+88orOPfdc1dbWmo4DAGGJIgOcAbfbreLiYklSRUWFkpOTDScCgPBEkQHOQGVlpTo7OzVlyhTl5eWZjgMAYYsiA4zSgQMH5HK5JEkNDQ2KiooynAgAwhdFBhgFy7KUl5cnr9erOXPmKDMz03QkAAhrFBlgFLZu3aoXXnhBMTExqqurMx0HAMJepOkAQDBxu90655xzdPfddyslJcV0HAAIew7LsizTIfypp6dH8fHxcrvdGj9+vOk4CAGHDx/W5z//eZ199tmmowBAyBrp9zdXZIBR+pd/+RfTEQAA/w9jZAAAQNCiyAAAgKBFkQEAAEGLIgMAAIJWUBSZBx54QCkpKYqJidGMGTP0u9/9znQkAABgA7YvMk8++aQKCgq0bNkyvfbaa/rKV76iG264Qe+++67paAAAwDDbryNz1VVXafr06Vq7du3gsYsvvlhz5sxRdXX1aT/POjIAAASfkX5/2/qKTF9fn/bt23fCfjaZmZl68cUXT/oZj8ejnp6eIQ8AABCabF1k3n//fXm9Xk2cOHHI8YkTJ+ro0aMn/Ux1dbXi4+MHH5MmTQpEVAAAYICti8xxDodjyHPLsk44dtw999wjt9s9+Dh06FAgIgIAAANsvUXBeeedp4iIiBOuvnR2dp5wlea46OhoRUdHByIeAAAwzNZXZKKiojRjxgzt3LlzyPGdO3dq5syZhlIBAAC7sPUVGUlavHixFixYoMsvv1xXX3211q9fr3fffVd33nmn6WgAAMAw2xeZb3/72/rggw/005/+VEeOHNHUqVO1Y8cOTZ48eUSfPz67nNlLAAAEj+Pf26dbJcb268iM1Z///GdddNFFpmMAAIAzcOjQIV1wwQXDvm77KzJjlZCQIEl69913FR8fbziNvfT09GjSpEk6dOgQiwX+E87N8Dg3w+PcDI9zc2qcnxNZlqWPPvpI559//infF/JFZty4T8czx8fH8z/HMMaPH8+5GQbnZnicm+FxbobHuTk1zs9QI7kAYetZSwAAAKdCkQEAAEErorKystJ0CH+LiIjQNddco8jIkL+TNmqcm+FxbobHuRke52Z4nJtT4/ycmZCftQQAAEIXt5YAAEDQosgAAICgRZEBAABBiyIDAACCVlgWGY/Ho2nTpsnhcGj//v2m4xj3zjvv6Ic//KFSUlIUGxuriy66SBUVFerr6zMdzZgHHnhAKSkpiomJ0YwZM/S73/3OdCTjqqurdcUVVyguLk4TJkzQnDlz9Oabb5qOZUvV1dVyOBwqKCgwHcUWDh8+rKysLCUmJurss8/WtGnTtG/fPtOxjOvv79dPfvKTwb+9X/ziF/XTn/5UAwMDpqMFlbAsMkuXLj3tksfh5I9//KMGBgb0i1/8QgcOHFB9fb3WrVun0tJS09GMePLJJ1VQUKBly5bptdde01e+8hXdcMMNevfdd01HM6qpqUmLFi3Syy+/rJ07d6q/v1+ZmZnq7e01Hc1WWlpatH79el122WWmo9jC3/72N6Wnp+uss87Ss88+qzfeeEOrV6/W5z73OdPRjKupqdG6devU2NioP/zhD6qtrdWqVavkcrlMRwsuVpjZsWOHlZqaah04cMCSZL322mumI9lSbW2tlZKSYjqGEVdeeaV15513DjmWmppqlZSUGEpkT52dnZYkq6mpyXQU2/joo4+sL33pS9bOnTutr371q1Z+fr7pSMYVFxdbs2bNMh3Dlm666Sbr9ttvH3Js3rx5VlZWlqFEwSmsrsj89a9/1cKFC/WrX/1KZ599tuk4tuZ2uwc33AwnfX192rdvnzIzM4ccz8zM1IsvvmgolT253W5JCsv/T4azaNEi3XTTTbruuutMR7GN3/zmN7r88st1yy23aMKECUpLS9ODDz5oOpYtzJo1S7/97W/11ltvSZJef/11/f73v9eNN95oOFlwCZvlAy3L0ve//33deeeduvzyy/XOO++YjmRbBw8elMvl0urVq01HCbj3339fXq9XEydOHHJ84sSJOnr0qKFU9mNZlhYvXqxZs2Zp6tSppuPYwubNm7Vv3z7t3bvXdBRb+fOf/6y1a9dq8eLFKi0tVXNzs/Ly8hQdHa3bbrvNdDyjiouL5Xa7lZqaqoiICHm9Xq1YsUK33nqr6WhBJeivyFRWVsrhcJzysXfvXrlcLvX09Oiee+4xHTlgRnpuPuu9997T9ddfr1tuuUV33HGHoeTmORyOIc8tyzrhWDjLycnR//7v/+qJJ54wHcUWDh06pPz8fD322GOKiYkxHcdWBgYGNH36dK1cuVJpaWnKzs7WwoULtXbtWtPRjHvyySf16KOP6vHHH9err76qTZs26f7779emTZtMRwsqQb9Fwfvvv6/333//lO9xOp36zne+o23btg35MvJ6vYqIiND8+fND8n+ckZ6b439433vvPV177bW66qqrtHHjRo0bF/Q9d9T6+vp09tlna8uWLZo7d+7g8fz8fO3fv19NTU0G09lDbm6unn76ae3Zs0cpKSmm49jC008/rblz5yoiImLwmNfrlcPh0Lhx4+TxeIa8Fk4mT56sjIwM/fKXvxw8tnbtWlVVVenw4cMGk5k3adIklZSUaNGiRYPHqqqq9Oijj+qPf/yjwWTBJehvLZ133nk677zzTvu+hoYGVVVVDT5/77339PWvf11PPvmkrrrqKn9GNGak50b6dHrktddeqxkzZujhhx8OyxIjSVFRUZoxY4Z27tw5pMjs3LlTs2fPNpjMPMuylJubq6eeekq7d++mxHzG1772NbW2tg459oMf/ECpqakqLi4O2xIjSenp6SdM03/rrbc0efJkQ4ns49ixYyf8rY2IiGD69SgFfZEZqQsvvHDI83PPPVeSdNFFF+mCCy4wEck23nvvPV1zzTW68MILdf/996urq2vwtaSkJIPJzFi8eLEWLFigyy+/XFdffbXWr1+vd999V3feeafpaEYtWrRIjz/+uH79618rLi5ucMxQfHy8YmNjDaczKy4u7oSxQuecc44SExPDfgxRYWGhZs6cqZUrV+pb3/qWmpubtX79eq1fv950NONuvvlmrVixQhdeeKEuvfRSvfbaa6qrq9Ptt99uOlpwMTllyqS3336b6df/z8MPP2xJOukjXP385z+3Jk+ebEVFRVnTp09nirFlDfv/yMMPP2w6mi0x/foftm3bZk2dOtWKjo62UlNTrfXr15uOZAs9PT1Wfn6+deGFF1oxMTHWF7/4RWvZsmWWx+MxHS2oBP0YGQAAEL7CcyAEAAAICRQZAAAQtCgyAAAgaFFkAABA0KLIAACAoEWRAQAAQYsiAwAAghZFBgAABC2KDAAACFoUGQAh48iRI/rud7+rKVOmaNy4cSooKDAdCYCfUWQAhAyPx6MvfOELWrZsmb785S+bjgMgACgyAGylq6tLSUlJWrly5eCxV155RVFRUXr++edP+Vmn06k1a9botttuU3x8vL+jArCBSNMBAOCzvvCFL+ihhx7SnDlzlJmZqdTUVGVlZenHP/6xMjMzTccDYDMUGQC2c+ONN2rhwoWaP3++rrjiCsXExOi+++4zHQuADXFrCYAt3X///erv79d//ud/6rHHHlNMTIzpSABsiCIDwJb+/Oc/67333tPAwID+8pe/mI4DwKa4tQTAdvr6+jR//nx9+9vfVmpqqn74wx+qtbVVEydONB0NgM1QZADYzrJly+R2u9XQ0KBzzz1Xzz77rH74wx9q+/btp/3s/v37JUkff/yxurq6tH//fkVFRemSSy7xd2wABjgsy7JMhwCA43bv3q2MjAzt2rVLs2bNkiS9++67uuyyy1RdXa277rrrlJ93OBwnHJs8ebLeeecdf8QFYBhFBgAABC0G+wIAgKBFkQEQNC699FKde+65J3089thjpuMBMIBbSwCCxl/+8hf93//930lfmzhxouLi4gKcCIBpFBkAABC0uLUEAACCFkUGAAAELYoMAAAIWhQZAAAQtCgyAAAgaFFkAABA0KLIAACAoPX/A+D/3f+Fk2w2AAAAAElFTkSuQmCC",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pygui(false)\n",
    "# mu=np.mean(X,axis=0)\n",
    "# X -= mu\n",
    "\n",
    "F = svd(X)\n",
    "W = F.Vt[1,:]'\n",
    "\n",
    "Z = X*W'\n",
    "\n",
    "# visualize the subspace spanned by W\n",
    "grid = range(minimum(X[:,1])-0.3,stop=maximum(X[:,1])+0.3,length=1000)\n",
    "gridplot = (grid.-pca.mean_[1])/W[1,1]*W[1,2].+pca.mean_[2]\n",
    "\n",
    "# visualize the reconstructions\n",
    "Xhat = Z*W\n",
    "# xhat = Z@W + pca.mean_ # the same\n",
    "\n",
    "plt.scatter(X[:,1],X[:,2], label=\"original data\")\n",
    "plt.xlabel(\"x_1\")\n",
    "plt.ylabel(\"x_2\");\n",
    "plt.plot(grid, gridplot, \"black\", label=\"model\")\n",
    "plt.axis(\"equal\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = [mean(X[:,i]) for i in 1:size(X)[2]]'\n",
    "X_centred = X .- mu;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F = svd(X_centred)\n",
    "W = F.Vt[1,:]'\n",
    "Z = X_centred*W'\n",
    "Xhat = Z*W\n",
    "\n",
    "grid = range(minimum(X_centred[:,1]).-0.3,stop=maximum(X_centred[:,1])+0.3,length=1000)\n",
    "gridplot = (grid.-pca.mean_[1])./W[1,1]*W[1,2]\n",
    "\n",
    "plt.scatter(X_centred[:,1],X_centred[:,2], label=\"original data\")\n",
    "plt.xlabel(\"x_1\")\n",
    "plt.ylabel(\"x_2\");\n",
    "plt.plot(grid, gridplot, \"black\", label=\"model\")\n",
    "plt.axis(\"equal\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: with centering, things look much better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.7.0",
   "language": "julia",
   "name": "julia-0.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}