nmf.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "from matplotlib import pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n",
    "\n",
    "from sklearn.datasets import make_biclusters\n",
    "from sklearn.datasets import samples_generator as sg\n",
    "# from sklearn.cluster.bicluster import SpectralCoclustering\n",
    "from sklearn.metrics import consensus_score\n",
    "from biclustering import DeltaBiclustering, MSR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['random']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAhCAAASKnADGgSJPAKgPAQhAAAIQgAAEIAABCEAAAhAo8SOCKVOmyBlnnCFT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qzHjBnjOXOXGTyd/Pnz5+XMmTNWX9ODDi9NQRoL2XTt6uqS999/3wouXnrppdb6RNdzGqR2curp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\nvEfADQFn1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U6mSVoIIIAAAggggIDXBQgOeL2FKB8CCCCAAAIIIIAAAggggAACLgsUuJw+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\nwASYABNgAkyACTABJsAEmMB4EPj/70iDvNB/qF4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image at 0x1117557d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import Image \n",
    "Image(filename='synteticBiclusters.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_dataset(option, noise=1, noise_background=True, shuffle=False):\n",
    "    shape = (150,150)\n",
    "    n,m = shape\n",
    "    \n",
    "    # values can't be a lot far...\n",
    "    centers = [20, 40, 60, 80, 100]\n",
    "    \n",
    "    y_row = np.zeros(150)\n",
    "    y_col = np.zeros(150)\n",
    "\n",
    "    if noise_background:\n",
    "        data = np.random.rand(n, m)*100\n",
    "    else:\n",
    "        data = np.zeros(n*m).reshape(shape)\n",
    "\n",
    "    if option == 'a':\n",
    "        data[60:110][:,70:140] = np.random.rand(50,70)*noise + centers[0]\n",
    "        y_row[60:110] += 1\n",
    "        y_col[70:140] += 1\n",
    "    elif option == 'd':\n",
    "        data[0:50][:,0:70] = np.random.rand(50,70)*noise + centers[0]\n",
    "        y_row[0:50] += 1\n",
    "        y_col[0:70] += 1\n",
    "\n",
    "        data[50:100][:,50:100] = np.random.rand(50,50)*noise + centers[2]\n",
    "        y_row[50:100] += 2\n",
    "        y_col[50:100] += 2\n",
    "\n",
    "        data[100:150][:,80:150] = np.random.rand(50,70)*noise + centers[1]\n",
    "        y_row[100:150] += 3\n",
    "        y_col[80:150] += 3\n",
    "    elif option == 'e':\n",
    "        data[0:70][:,0:50] = np.random.rand(70,50)*noise + centers[3]\n",
    "        y_row[0:70] += 1\n",
    "        y_col[0:50] += 1\n",
    "\n",
    "        data[50:100][:,50:100] = np.random.rand(50,50)*noise + centers[1]\n",
    "        y_row[50:100] += 2\n",
    "        y_col[50:100] += 2\n",
    "\n",
    "        data[80:150][:,100:150] = np.random.rand(70,50)*noise + centers[2]\n",
    "        y_row[80:150] += 3\n",
    "        y_col[100:150] += 3\n",
    "    elif option == 'f':\n",
    "        data[0:50][:,0:40] = np.random.rand(50,40)*noise + centers[4]\n",
    "        y_row[0:50] += 1\n",
    "        y_col[0:40] += 1\n",
    "\n",
    "        data[50:150][:,0:40] = np.random.rand(100,40)*noise + centers[0]\n",
    "        y_row[50:150] += 2\n",
    "\n",
    "        data[110:150][:,40:95] = np.random.rand(40,55)*noise + centers[2]\n",
    "        y_row[110:150] += 3\n",
    "        y_col[40:95] += 2\n",
    "\n",
    "        data[110:150][:,95:150] = np.random.rand(40,55)*noise + centers[1]\n",
    "        y_row[110:150] += 3\n",
    "        y_col[95:150] += 3\n",
    "    elif option == 'g':\n",
    "        data[0:110][:,0:40] = np.random.rand(110,40)*noise + centers[0]\n",
    "        data[110:150][:,0:110] = np.random.rand(40,110)*noise + centers[2]\n",
    "        data[40:150][:,110:150] = np.random.rand(110,40)*noise + centers[1]\n",
    "        data[0:40][:,40:150] = np.random.rand(40,110)*noise + centers[3]\n",
    "    elif option == 'h':\n",
    "        data[0:90][:,0:90] = np.random.rand(90,90)*noise + centers[0]\n",
    "        data[35:55][:,35:55] = (np.random.rand(20,20)*noise + centers[1]) + data[35:55][:,35:55]\n",
    "        data[110:140][:,35:90] = np.random.rand(30,55)*noise + centers[4]\n",
    "        data[0:140][:,110:150] = np.random.rand(140,40)*noise + centers[2]\n",
    "        data[0:55][:,130:150] = (np.random.rand(55,20)*noise + centers[3]) + data[0:55][:,130:150]\n",
    "    elif option == 'i':\n",
    "        data[20:70][:,20:70] = np.random.rand(50,50)*noise + centers[0]\n",
    "        data[20:70][:,100:150] = np.random.rand(50,50)*noise + centers[1]\n",
    "        data[50:110][:,50:120] = np.random.rand(60,70)*noise + centers[2]\n",
    "        data[120:150][:,20:100] = np.random.rand(30,80)*noise + centers[3]\n",
    "\n",
    "    if shuffle:\n",
    "        np.random.shuffle(data)\n",
    "        np.random.shuffle(data.T)\n",
    "\n",
    "    return data, y_row, y_col"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nonnegative Block Value Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "This is a coclustering algorithm called Block Value Decomposition (BVD) based on Nonnegative Matrix Factorization (NMF)\n",
       "technique.\n",
       "The goal is to find a factorization for the data matrix $X \\in \\mathbb{R}_{+}^{n \\times m}$, where $n$ is the number of objects\n",
       "and $m$ is the number of features of theses objects and the factorization takes the form: $X \\approx USV^T$, where\n",
       "$U \\in \\mathbb{R}_{+}^{n \\times l}$ is a matrix of rows factors representing features clusters,\n",
       "$S \\in \\mathbb{R}_{+}^{l \\times k}$ is a block matrix representing how blocks are related, and\n",
       "$V \\in \\mathbb{R}_{+}^{m \\times k}$ is a matrix of columns factors representing rows clusters."
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x10e3c2a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "This is a coclustering algorithm called Block Value Decomposition (BVD) based on Nonnegative Matrix Factorization (NMF)\n",
    "technique.\n",
    "The goal is to find a factorization for the data matrix $X \\in \\mathbb{R}_{+}^{n \\times m}$, where $n$ is the number of objects\n",
    "and $m$ is the number of features of theses objects and the factorization takes the form: $X \\approx USV^T$, where\n",
    "$U \\in \\mathbb{R}_{+}^{n \\times l}$ is a matrix of rows factors representing features clusters,\n",
    "$S \\in \\mathbb{R}_{+}^{l \\times k}$ is a block matrix representing how blocks are related, and\n",
    "$V \\in \\mathbb{R}_{+}^{m \\times k}$ is a matrix of columns factors representing rows clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "This algorithm solves the following optimization problem:\n",
       "$$\\textit{min } ||X - USV^T||^2 \\textit{ s.t. } U \\geq 0, S \\geq 0, V \\geq 0$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x1126dbfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "This algorithm solves the following optimization problem:\n",
    "$$\\textit{min } ||X - USV^T||^2 \\textit{ s.t. } U \\geq 0, S \\geq 0, V \\geq 0$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "The optimization problem can be solved using Lagrange multipliers ($\\lambda$), optimizing the following Lagrange function:\n",
       "$${\\cal L} = |X - USV^T||^2 - tr(\\lambda_1U^T) - tr(\\lambda_2S^T) - tr(\\lambda_3V^T)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x11286ba50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "The optimization problem can be solved using Lagrange multipliers ($\\lambda$), optimizing the following Lagrange function:\n",
    "$${\\cal L} = |X - USV^T||^2 - tr(\\lambda_1U^T) - tr(\\lambda_2S^T) - tr(\\lambda_3V^T)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Then ${\\cal L}$ must satisfy the K.K.T. conditions:\n",
       "$$\\frac{\\partial {\\cal L}}{\\partial U} = 0$$\n",
       "$$\\frac{\\partial {\\cal L}}{\\partial S} = 0$$\n",
       "$$\\frac{\\partial {\\cal L}}{\\partial V} = 0$$\n",
       "$$\\lambda_1 \\odot U = 0$$\n",
       "$$\\lambda_2 \\odot S = 0$$\n",
       "$$\\lambda_3 \\odot V = 0$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x1126dbb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "Then ${\\cal L}$ must satisfy the K.K.T. conditions:\n",
    "$$\\frac{\\partial {\\cal L}}{\\partial U} = 0$$\n",
    "$$\\frac{\\partial {\\cal L}}{\\partial S} = 0$$\n",
    "$$\\frac{\\partial {\\cal L}}{\\partial V} = 0$$\n",
    "$$\\lambda_1 \\odot U = 0$$\n",
    "$$\\lambda_2 \\odot S = 0$$\n",
    "$$\\lambda_3 \\odot V = 0$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Solving the derivatives and equal them to $0$, is possible to solve the optimization problem by applying gradient\n",
       "ascending on ${\\cal L}$ with the following update rules:\n",
       "$$U \\gets U \\odot \\frac{XVS^T}{USV^TVS^T}$$\n",
       "$$V \\gets V \\odot \\frac{X^TUS}{VS^TU^TUS}$$\n",
       "$$S \\gets S \\odot \\frac{U^TXV}{U^TU^TSV^TV}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x1126dbf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "Solving the derivatives and equal them to $0$, is possible to solve the optimization problem by applying gradient\n",
    "ascending on ${\\cal L}$ with the following update rules:\n",
    "$$U \\gets U \\odot \\frac{XVS^T}{USV^TVS^T}$$\n",
    "$$V \\gets V \\odot \\frac{X^TUS}{VS^TU^TUS}$$\n",
    "$$S \\gets S \\odot \\frac{U^TXV}{U^TU^TSV^TV}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nmtf(X, k, l, num_iter=1):\n",
    "    \"\"\"\n",
    "    Performs nonnegative block value decomposition\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X : array or sparse (CSR) matrix of shape (n_samples, n_features), or \\\n",
    "            array of shape (n_samples, n_samples)\n",
    "        A feature array, or array of distances between samples if\n",
    "        ``metric='precomputed'``.\n",
    "    k : int\n",
    "        number of rows clusters\n",
    "    l : int\n",
    "        number of columns clusters\n",
    "    num_iter : int, optional\n",
    "        number of iterations to make the factorization\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    U : array matrix of shape (n_samples, n_features_clusters)\n",
    "        matrix of rows factors representing features clusters\n",
    "    S : array matrix of shape (n_samples_clusters, n_features_clusters)\n",
    "        block matrix representing how blocks are related \n",
    "    V : array matrix of shape (n_features, n_samples_clusters)\n",
    "    \"\"\"\n",
    "    def scale(A):\n",
    "        return (A - A.min()) / (A.max() - A.min())\n",
    "\n",
    "    n, m = X.shape\n",
    "    \n",
    "    U = (np.random.rand(n,k))\n",
    "    S = (np.random.rand(k,l))\n",
    "    V = (np.random.rand(l,m))\n",
    "\n",
    "    X_norm = (X)\n",
    "    for i in xrange(num_iter):\n",
    "        U_delta = (X_norm.dot(V.T).dot(S.T)) / (U.dot(S).dot(V).dot(V.T).dot(S.T))\n",
    "        U_new = np.multiply(U,U_delta)\n",
    "\n",
    "        V_delta = (S.T.dot(U.T).dot(X_norm)) / (S.T.dot(U.T).dot(U).dot(S).dot(V))\n",
    "        V_new = np.nan_to_num(np.multiply(V,V_delta))\n",
    "\n",
    "        S_delta = (U.T.dot(X_norm).dot(V.T)) / (U.T.dot(U).dot(S).dot(V).dot(V.T))\n",
    "        S_new = np.nan_to_num(np.multiply(S,S_delta))\n",
    "\n",
    "        np.sum((X - U_new.dot(S_new).dot(V_new.T))\n",
    "\n",
    "        U = U_new\n",
    "        V = V_new\n",
    "        S = S_new\n",
    "\n",
    "    # normalization\n",
    "#     U_diag = np.diag(np.diag(np.ones(n).dot(U)))\n",
    "#     V_diag = np.diag(np.diag(np.ones(m).dot(U.T).T))\n",
    "    \n",
    "#     U = np.multiply(U, np.diag(S.dot(V_diag)))\n",
    "#     V = np.multiply(V, np.diag(U_diag.dot(S)))\n",
    "\n",
    "    return U, S, V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fast Nonnegative Matrix Tri Factorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "In this case, the goal is to optimize the following problem:\n",
       "$$\\textit{min } ||X - USV^T||^2 \\textit{ s.t. } U \\in \\Psi^{n \\times k}, S \\in \\mathbb{R}_{+}^{l \\times k}, V \\in \\Psi^{m \\times l}$$\n",
       "where $U$ and $V$ turns into cluster indicator matrices, with vectors $\\vec{u_i}$ and $\\vec{v_j}$ which contains $1$ in\n",
       "only one position, indicating the cluster that that this vector belongs, and $0s$ in the rest."
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x10357cf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "In this case, the goal is to optimize the following problem:\n",
    "$$\\textit{min } ||X - USV^T||^2 \\textit{ s.t. } U \\in \\Psi^{n \\times k}, S \\in \\mathbb{R}_{+}^{l \\times k}, V \\in \\Psi^{m \\times l}$$\n",
    "where $U$ and $V$ turns into cluster indicator matrices, with vectors $\\vec{u_i}$ and $\\vec{v_j}$ which contains $1$ in\n",
    "only one position, indicating the cluster that that this vector belongs, and $0s$ in the rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Similar to the other algorithm, it optimizes $S$ with a multiplicative update rule and the following subproblems:\n",
       "$$S \\gets (U^TU)^{-1}U^TXV(V^TV)^{-1}$$\n",
       "$$v_{ij} \\left\\{\n",
       "\\begin{array}{ll}\n",
       "        1 & j = \\textit{argmin}_l ||\\vec{x_i} - \\vec{\\tilde{u_l}}||^2 \\\\\n",
       "        0 & \\textit{otherwise}\n",
       "    \\end{array}\n",
       "\\right.$$\n",
       "$$u_{ij} \\left\\{\n",
       "\\begin{array}{ll}\n",
       "        1 & i = \\textit{argmin}_k ||\\vec{x_j} - \\vec{\\tilde{v_k}}||^2 \\\\\n",
       "        0 & \\textit{otherwise}\n",
       "    \\end{array}\n",
       "\\right.$$\n",
       "where $\\tilde{U} = US$ and $\\tilde{V} = SV^T$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex at 0x103594450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "Similar to the other algorithm, it optimizes $S$ with a multiplicative update rule and the following subproblems:\n",
    "$$S \\gets (U^TU)^{-1}U^TXV(V^TV)^{-1}$$\n",
    "$$v_{ij} \\left\\{\n",
    "\\begin{array}{ll}\n",
    "        1 & j = \\textit{argmin}_l ||\\vec{x_i} - \\vec{\\tilde{u_l}}||^2 \\\\\n",
    "        0 & \\textit{otherwise}\n",
    "    \\end{array}\n",
    "\\right.$$\n",
    "$$u_{ij} \\left\\{\n",
    "\\begin{array}{ll}\n",
    "        1 & i = \\textit{argmin}_k ||\\vec{x_j} - \\vec{\\tilde{v_k}}||^2 \\\\\n",
    "        0 & \\textit{otherwise}\n",
    "    \\end{array}\n",
    "\\right.$$\n",
    "where $\\tilde{U} = US$ and $\\tilde{V} = SV^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fnmtf(X, k, l, num_iter=1):\n",
    "    def scale(A):\n",
    "        return (A - A.min()) / (A.max() - A.min())\n",
    "\n",
    "    n, m = X.shape\n",
    "    \n",
    "    U = (np.random.rand(n,k))\n",
    "    S = (np.random.rand(k,l))\n",
    "    V = (np.random.rand(m,l))\n",
    "\n",
    "    # solve subproblem to update U\n",
    "    U_new = np.zeros(n*k).reshape(n,k)\n",
    "    X_norm = (X)\n",
    "    for i in xrange(num_iter):\n",
    "        S = np.linalg.pinv(U.T.dot(U)).dot(U.T).dot(X_norm).dot(V).dot(np.linalg.pinv(V.T.dot(V)))\n",
    "\n",
    "        U_tilde = U.dot(S)\n",
    "        for i in xrange(m):\n",
    "            subproblem_result = np.zeros(l)\n",
    "            for j in xrange(l):\n",
    "                subproblem_result[j] = np.linalg.norm(X[:][:,i] - U_tilde[:][:,j])\n",
    "            ind = np.argmin(subproblem_result)\n",
    "            U_new[i][ind] = 1\n",
    "\n",
    "        # solve subproblem to update V\n",
    "        for j in xrange(n):\n",
    "            subproblem_result = np.zeros(k)\n",
    "            for i in xrange(k):\n",
    "                optimization_result[i] = np.linalg.norm(X[j][:] - V_tilde.T[i][:])\n",
    "            ind = np.argmin(optimization_result)\n",
    "            V_new[j][ind] = 1\n",
    "\n",
    "        U = U_new\n",
    "        V = V_new\n",
    "        S = S_new\n",
    "\n",
    "    # normalization\n",
    "#     U_diag = np.diag(np.diag(np.ones(n).dot(U)))\n",
    "#     V_diag = np.diag(np.diag(np.ones(m).dot(U.T).T))\n",
    "    \n",
    "#     U = np.multiply(U, np.diag(S.dot(V_diag)))\n",
    "#     V = np.multiply(V, np.diag(U_diag.dot(S)))\n",
    "\n",
    "    return U, S, V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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PyfJxxPsu5re7fINW19wkA9z3s3v5mK7JxI6HuAlRht/ozcRJHALJ0jHEc29w9wOu/1JS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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1120b7710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11363b6d0>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f1c750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1136d3890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113155050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cvZrU2cnFxXpp22jsOBVq6QSw7ebVlZ6G9HACoiCjGCfgjqd4jVKV+wfFqH90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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112e62750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, _, _ = generate_dataset(option='a', noise=1.0, noise_background=False)\n",
    "\n",
    "plt.matshow(X, cmap=plt.cm.Blues)\n",
    "plt.title(\"Original Data\")\n",
    "plt.show()\n",
    "\n",
    "U, S, V = nmtf(X,2,2,1)\n",
    "\n",
    "plt.matshow(U, cmap=plt.cm.Blues)\n",
    "plt.matshow(S, cmap=plt.cm.Blues)\n",
    "plt.matshow(V, cmap=plt.cm.Blues)\n",
    "\n",
    "plt.matshow(U.dot(S).dot(V), cmap=plt.cm.Blues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11243d810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11266da50>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TUr70xacu+Gt8sgAHZBvLi9/62tJPsPDAid2ln7AytrEAWbaxXPLa71v6CRbedsPRpZ+w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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df5810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df5c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112651ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADXVJREFUeJzt3VuMXWUZxvGntAqlhIINp4iiQMHghZGDhrYwBDamEuCG\nvBfcQOAKxBBCICZAQG68IBgPUCEx8RAuMLwXoDEcp3ZmtIRwaKYxEmg5alQEm7YUArbU8WIGnJY9\ns781XYfv/fb/l5Cw2pW1n8K39rufvdasSgAAAAAAAAAAAMDQWdT2C5pZT9IdM5t3uPsf2s5QhZnd\nL+lUSQdJusrdX+s4UhIzO1jSFkl3ufu6rvMMYmbHS3pA0hJJz7n7jR1HmpeZXSHpOkkfSbrN3Td0\nHKmvJW2+mJkdJOlOSb2ZX3rCzDa4+1SbOapw92skyczOl3SzpGu7TZTsGkkvSMr2v+1+7pZ0q7s/\n3XWQRDdJ+rqkZZKekHR2t3H6a/UEl7RS0hZ3/0CSzOxVSSdL2tpyjoXYJWl31yFSmNmhki6U5JIO\n6zjOQGa2WNJJgU5uSXpR0oikYyU903GWObV9gn9O0g4z+9HM9k5JKxTjBL9a0k+6DpHoekn3Sjqm\n6yCJjpJ0iJk9IulwSfe4+8MdZxrkSUk3SPqspGwr0EEtv942SUdIukXSrTP//u+WM1RmZpdIetnd\nX+o6yyBmtlzSGnd/XB18x7JA2zT9Zn+ZpLWSbjGzpd1GmpuZnSjpYne/1N3XSro517xtn+CvSjpl\n1vZKd3+l5QyVmNkZkkbc/cddZ0m0WtPT8EFN9/CrzOy0jjPNy933SPqbpGPdfbek/3QcaZDFmvn0\na2aLJC1Vpt91dPEt+rck3T6zeae7P9V2hirM7DVNL77/Svqzu1/fcaRkZnalpGXu/rOuswxiZl+U\ndL+k5ZIecves65CZ3SJpjaaH5G/c/VfdJgIAAAAAAAAAAAAAoHy13ejy7HPPT727c0ddhwOQ6PDl\nR+gbZ53Z91yu7YdN3t25Q6tHLqjrcAASbRxfP+fvtX0vuiRpYnysi5c9INEyR8srkbkJnZzgANpR\nWwcfHR2d4iM60L6N4+vV6/X6nstMcKBgdPBE0TJHyyuRuQkDv0WP9hRUAP83bwefeQrqHzXrKaia\nfrrJp55eQQcHunEgHfyTp6DOPAn146egAghg0An+yVNQZ56E+vFTUA9I7r2ln2iZo+WVyNyEQSd4\npaegzv7DToyPFbW9eXIyqzyl5Z0YH9Pmycms8kTansugDr5Y0oSmO/giSU+5++p++9LBgW4suIO7\n+15N/1VDT2n6Qe/frz0dgMYMvA7u7k+6+5qZf2p5xHHuvaWfaJmj5ZXI3ATuZAMKxr3oQHDciw4M\nKe5FTxQtc7S8EpmbwAQHCkYHB4KjgwNDig6eKFrmaHklMjeBCQ4UjA4OBEcHB4YUHTxRtMzR8kpk\nbgITHCgYHRwIjg4ODCk6eKJomaPllcjcBCY4UDA6OBAcHRwYUnTwRNEyR8srkbkJTHCgYHRwIDg6\nODCk6OCJomWOllcicxOY4EDB6OBAcHRwYEjRwRNFyxwtr0TmJjDBgYLRwYHg6ODAkKKDJ4qWOVpe\nicxNYIIDBaODA8HRwYEhRQdPFC1ztLwSmZuwZNAOZna/pFM1/WZwlbu/1ngqALVI7uBmdr4kc/dr\n+/0+HRzoRl0dfJek3fVEAtCGKif41ZLuq+NFc+8t/UTLHC2vROYmJJ3gZnaJpJfd/aX59pv9h50Y\nHytqe/PkZFZ5Sss7MT6mzZOTWeWJtD2XgR3czM6QdLm73zTffnRwoBsH2sFd0llmtsHMflpvNABN\nGniZzN1PrPtFJ8bHdO7IeXUftlHRMkfLK5G5CdzJBhSMe9GB4LgXHRhS3IueKFrmaHklMjeBCQ4U\njA4OBEcHB4bUwOvgTcj92mE/VTKvuPyXjeVYumxp0n573npRnzn2tOTjHnzowQuNNK9VZ52QvO/b\nLz2vo79yZvL+7+z8YCGRBnr8u6uT9819LTPBgYJ1coLn/I43l2iZq0zvXFSZ3rnIfV0wwYGCcR08\nUbTMe956sesIlb390vNdR6gs93XBBAcKRgdPFC0zHbwdua8LJjhQMDp4omiZ6eDtyH1dMMGBgtHB\nE0XLTAdvR+7rggkOFIwOnihaZjp4O3JfF0xwoGB08ETRMtPB25H7umCCAwWjgyeKlpkO3o7c1wUT\nHCgYHTxRtMx08Hbkvi6Y4EDB6OCJomWmg7cj93XBBAcKRgdPFC0zHbwdua+LTh6bXLoTVn6+sWMv\nWdLMe3JTx33vwz2NHFeSFi2q7e/tKBYdPFG0zO+9sbnrCJVt2/JC1xEqy31d0MGBgtHBE0XLfNiX\nvtZ1hMpWnHJG1xEqy31dMMGBgtHBE0XLTAdvR+7rggkOFCzpMpmZHSxpi6S73H3dgb5o7r2ln2iZ\n6eDtyH1dpE7wayS9IGmqwSwAajbwBDezQyVdKOm3kmq5syD33tJPtMx08Hbkvi5SJvj1ku5tOgiA\n+s17gpvZcklr3P1xJUzv2e9mE+Njc26fO3LevL+f43aVP58kvf/mZr3/5ubGtt97Y/M+U3r/7Y9/\nLXX/Xa9Patfrk41tb9vywj4Tut/2bCn7b9+66ZPt7Vs31bqduj4+7uA5rM9+5j1pzewiSTdKekfS\nlzX9pdwV7v6pn0UcHR2dWj1ywcAXHAan3/5kY8eOdi/6MUcta+S4kvTh7r2NHPex61Y1ctymbBxf\nr16v1/dcnvf/qrs/6u49d79c0n2SftHv5K4q997ST7TMdPB25L4ukn+azN1/3WQQAPXjXvRE0TJz\nHbwdua8L7mQDCsa96ImiZaaDtyP3dcEEBwpGB08ULTMdvB25rwsmOFAwOniiaJnp4O3IfV3wVNUG\nvP7Y75o7+IovJO22d/urWvyPj5IPe9CRRy800bxOt7PSMxy+VMetSL/z7bW33l1IpKFCB08ULfPi\nI0/qOkJlx301/c0gF7mvCzo4UDA6eKJomfduf7XrCJX98y/PdR2hstzXBRMcKBgdPFG0zHTwduS+\nLpjgQMHo4ImiZaaDtyP3dcEEBwpGB08ULTMdvB25rwsmOFAwOniiaJnp4O3IfV0wwYGC0cETRctM\nB29H7uuCCQ4UjA6eKFpmOng7cl8XTHCgYHTwRNEy08Hbkfu6YIIDBaODJ4qWmQ7ejtzXBRMcKBgd\nPFG0zHTwduS+LniqagO+eeXlXUfIxuv/2tV1hKFGB08ULfOOVzZ1HaGy7VvjZc59XdDBgYLRwRNF\ny3zEyad3HaGyI1fGy5z7umCCAwWjgyeKlpkO3o7c1wUTHCgYHTxRtMx08Hbkvi6SroOb2fGSHpjZ\n/zl3v7HRVABqkTrB75Z0q7ufU8fJnXtv6SdaZjp4O3JfFwNPcDNbLOkkd3+6hTwAapTyEf0oSYeY\n2SOSDpd0j7s/fCAvmntv6SdaZjp4O3JfFykf0bdJ2inpMklrJd1iZkv77Tj748rE+NhQb+94ZdM+\nH5OHfXv71k37fATPfbvr9VN1ey6LBu4hycwelHSTu//dzP4k6UJ3/2D2PqOjo1OrRy5IOZwmxsey\nf+fbX5XMa+/d2GyYBDte2ZTFFF+8OP1CzfatmypN8ampqYVEGujR76xK3jeHtbxxfL16vV7fczn1\np8m+J+nnZrZc0kP7n9wA8pR0grv7XyVdVNeLdv2OtxDRMucwvauig9ePO9mAgnEveqJombkO3o7c\n1wUTHCgY96InipaZDt6O3NcFExwoGB08UbTMdPB25L4umOBAwTp5bHLuvaWfKpmXLGnufTP15q0V\np55Z8bjN3BVWBR28fkxwoGB08ETRMkfssxEz574umOBAwbgOniha5oh9NmLm3NcFExwoGB08UbTM\nEftsxMy5rwsmOFAwOniiaJkj9tmImXNfF0xwoGB08ETRMkfssxEz574umOBAwejgiaJljthnI2bO\nfV0wwYGC0cETRcscsc9GzJz7umCCAwWjgyeKljlin42YOfd1wQQHCkYHTxQtc8Q+GzFz7uuCCQ4U\njA6eKFrmiH02Yubc1wUTHChYJ09VzeHvVK6qSubfX3N2s2ESlP7fOBe5Z2aCAwVbVNeBRkdHp1aP\nXFDX4QAk2ji+Xr1er++5zAQHCsZ18ETRMkfLK5G5CUxwoGB0cCC4+Tr4wMtkZnaFpOskfSTpNnff\nUHM+AA1J+Yh+k6RVkr4t6Qd1vGjuvaWfaJmj5ZXI3ISUG11elDQi6VhJzzQbB0CdUk7wJyXdIOmz\nktbV8aI53/kzl2iZo+WVyNyEeT+im9mJki5290vdfa2km81s6Vz7z/64MjE+xjbbbLe0PZd5v0U3\ns5WSfujul5rZIknPSjrH3T/cf98q36Lnfv9uP9EyR8srkXmhFnwnm7tvlfSMmT0q6TFJ6/qd3ADy\nxHVwIDjuRQeGFPeiJ4qWOVpeicxNYIIDBaODA8HRwYEhRQdPFC1ztLwSmZvABAcKRgcHgqODA0OK\nDp4oWuZoeSUyN4EJDhSMDg4ERwcHhhQdPFG0zNHySmRuAhMcKBgdHAiODg4MKTp4omiZo+WVyNwE\nJjhQMDo4EBwdHBhSdPBE0TJHyyuRuQlMcKBgdHAgODo4MKTo4ImiZY6WVyJzE5jgQMHo4EBwdHBg\nSNHBE0XLHC2vROYm1PkRfUzSSF3HA5BsvNfrndd1CAAAAAAAAAAAYvkfxsBU36JaKnoAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111dc4650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.zeros(10*10).reshape((10,10))\n",
    "X[3:8][:,3:8] = X[3:8][:,3:8] + 20\n",
    "\n",
    "plt.matshow(X, cmap=plt.cm.Blues)\n",
    "plt.title(\"Original Data\")\n",
    "plt.show()\n",
    "\n",
    "U, S, V = nmtf(X,2,2,1)\n",
    "\n",
    "plt.matshow(U, cmap=plt.cm.Blues)\n",
    "plt.matshow(S, cmap=plt.cm.Blues)\n",
    "plt.matshow(V, cmap=plt.cm.Blues)\n",
    "\n",
    "plt.matshow(U.dot(S).dot(V), cmap=plt.cm.Blues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-5c5f31752c60>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m40\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m60\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "X = np.zeros(10*10).reshape((10,10))\n",
    "X[0:4][:,0:4] = X[0:4][:,0:4] + 20\n",
    "X[2:8][:,4:6] = X[2:8][:,4:6] + 40\n",
    "X[6:10][:,6:10] = X[6:10][:,6:10] + 60\n",
    "\n",
    "plt.matshow(X, cmap=plt.cm.Blues)\n",
    "plt.title(\"Original Data\")\n",
    "plt.show()\n",
    "\n",
    "U, S, V = nmtf(X,4,4,9)\n",
    "\n",
    "plt.matshow(U, cmap=plt.cm.Blues)\n",
    "plt.matshow(S, cmap=plt.cm.Blues)\n",
    "plt.matshow(V, cmap=plt.cm.Blues)\n",
    "\n",
    "plt.matshow(U.dot(S).dot(V), cmap=plt.cm.Blues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FNXIG9x05lEUd75xDmUyswsvfz6L5wYRCMwOllBMzVsH5yAIjOIT8iUuzsPwR\nyNaH5bqUw8sIVyHZ/TdFFs4vGLZfSCaJDFSWV1lWZ/nQkavnjz2s1XSSTzMrrsrzcwR0VORbYYHt\npNQ629yG5AfQ63e4bUKifqzhC9bMWhY9z1R4tg/zpx4tEzG7DFO/5H7vdf6Sxp7NyP3AZZF8n23+\nbRs8TILfZUyC62mxHXa5pvvK14Axhlqfe/cNTdqEiSaaCMA6z00gfX/moogDY7NjdWYBxhyETR+A\nHH/QcnVsZyC3bdxDsQ8IiKN85d18L2gbhWxbQPJFjnEP6B2K4+ZJZQGMDElq4FWNPRzuz67Y74OD\nrLuv0cgMmFpt0WoD5GW7CnnfijFcRk0EYvCO03tg39Cm2eUvGJtX2zbleq5gskxt8s20m1SmtU+o\nOWYxp7OKmTW3hfOK0ccM1Dc1dV6B1mqBCECx92zwwzK3tSysseO8MMj9pvEXkmjqwKKD5yylMAaq\nQ4A2aipiGp0VWbOdt+xlzUCm6sVGOERt4nqTvnZGA8uW1gJPaUNoEbMDmWV6xhI8q0o16Y1c68n6\nAbp+HmZSMxzivOwi5MnmvIvECBXbwEP7R9oXZttZ6+PhML2/CNnDa1SMByOicfskDeNCi/pFXlma\nYoto8k3YjnL3jo9AKnf7+/li+rZr4wxyfEOUXZbFAQBuAFImXrzZVoA5ib6PaoEXQFBzFMT5Oe/b\nOtg91TvN2YKaGcm3q71QzV6edyWg7CABtDtzetplmgam8aUOzLVwGqVndzzrxI7B9R2oiBIj3T+Z\nQntljGwoyG6B2exldvjWPsG1XaiIALY9fE99g15zClIHrk/vcAm2LjUTaq+NI7NmJ0/brysYIa3R\nN+HW1IagVXPeWQl91DEJ8jghsSIEX6a3aa6/+TWjRcgeryZkRYCSZ+nYZARV8skGS3z/2QcWGLbQ\nQFIigFSuctz4CCFnzcTw6hUv8mVOKxt78nnNKcgz7DGqxVE8A0ve5LNtq2EJ3qSZnwPiPGEzCnl3\ntCNu2yh/bounQjSLuYpnwOl58ec8PNWtp02R9J5YGKMOWsOH1dTyXIEmbcJEE00EYAfYGTAV1+Ji\nPCRcgQ6JLn+8Q/sigDyLgx2DYAZiLCRux+xrIHYGEVDlyt+8j/kvvYdsx1DsEpD9HVJ8OtKns+5f\nXmbfBEDrp4XYpl5YerlXOjGnmT9x1nQE6bK9/K0+3etEKcPzkRjaMn/iTMnPAozeTlxD06Ue0kfW\nnl/p77nkSSOVAAAgAElEQVTcoPP2wDnPx4H1+jaN5ysRY4k9aNti6pa/C4eiV/3gtFHZWwSVPsdM\nZFsN0VawKCXfqNYPRGu3QOQYACzWKra/IhqwWMHnH8pkBqBclWOMEJ8IFg1UHAJTN6ac3sRfcMVA\nqmdewQAt91rfBPUyoeykyipk/At0ReFSjX2uYRX52lj12WPhuD2eEZG1BGQjKE+UVexupb/sfTbo\nyelqi5BjyASYuhAWIIu1rYNdnLxFryb+1XxRRj4azfh+P4eKo2Dz4LZJ/ZcYHAFr5AzWdW7COnwi\nLib79anc9Ze5VeWujTNgGwJZ0GqegcrzkN6NMSojn8w9NP5On/Id10VxGIAyOmIOI29uhhvIGBgZ\nLKkIzRYdr5GH/DN6zeBYzaeAd2HPDNcrs4ZGe/UPGIOgTMt8MBgEBOpGRJZdlnvMYXjBW+3uzByG\nd9+W6+3irGWR9209hSvK7zhamRoYbAyZtK1DpQ5cfo3jY9rJXot3//Ed+rRkFARejkXjeAMSG0Af\nuxbyfXFaamhiim8B5yOYAeMAYnXIqszxeY36RhbxQlBiidSHScnuI4OiCmagOoZkfZE5WQ4csc+D\n7P410oGzPMnxCZQWwsjYWdaNJb1gFGxXr1Rg6VwAxhBGE4vbnttD8rTNM9d1Aa7Qz8vZAl56K/ZY\nDIQnI/dPbif5FBDNv3aKvkUY/6nE5/QzxhW872R9VKgt+VwGxmwscR0m34SJJppoVbogMaFt20sA\nfBbAL3dd976NnMT86r/+WgDaWIiJxQHe2QPdtzp+SdP32rVZsg8h4NXfVcplYDG7UcdiRszXyiWZ\n7qtTpK3NwUAqBiJQB+w81tueN+Cxsalx5d2BFZ09ez9cNrzGGgP+bsr1sabMI+Bz8E1g8SZQmy3g\nWANRPTPfGOH6FPRk38A7oHAJANTRcc0MLrjI49D2NWt/KE1qq9heOP1lPQ69ttaMkfi+8leZFxzK\nAo5MivPZejHhbQDuARA3ehKzqBCbwCq+wqLHWNLYTOR+WjDSnxgSBeiJyOKACl0WdD7yV6snUFSK\nnC6VPYg2pj7ZBZvdZJl9FjZdVFqscmT2kF1ymYXUFU1/zIp6cikvGlxeTuOww6zisgNbqc6irusq\ntNSlN4wXDSmX227zs3Vgdagqd4HowaJEVvE1um4sqnmigRWLJL2oF6U+LI7UWHqjwi1jyFEZW03F\nVooJbdteDuD7AXwQaQ5u6CTmyTdhKvdiKPdiauuFiAk/A+A3AHz78HtDJzHLTsz+CPo8hHLNvgOM\n6stvmHvyDmA2BwBuMBTznj19GRg2LqoDaw0aSs/1kTI+/P7/Bt/zuteP8txquv2Tn5jKXYF+7kMP\n5WvPm5aJFT2zJuD0A0dw4JqbAejj+rJ42ceRXYq8K+ljLLYrPeXBHrecftYEPHzsMPZfc7PKexGV\nZGfraVbKyVDbts8FcGvXdX+AMpc2fBIzkDrnXj5lOYTRKcr3H9GnJt9z1yHcc9ehLMPLqccy0e+5\n644SSQnlFOYQAm64+TXpOac/nPITMUVOaub8jx29My9g9w7PgSQO3HfkTtx35M68UN1H5cmguP2T\nn8jtuf2Tn9iW3zIxtqs8pt3U3rMPHsXZB49m1fbpE4fxyENH1fMzDxwBkCaopJ/3ES98+U04efww\nTj9wJEsVZx44gtMnDicxuAk488ARnHngSMagzj54FCePH875P/qpozj74JHhnA7g7INHcPbBVF6M\nwOkTR/DwsZL+4WOHSTKLOHX8ME4dP5zF7rMPHsEpyv/0icM4efzwSHtnaUXBTlPbtj8I4GcBfBnA\ndyBxGG8F8H6scBLzwYMH46VXvcqtQG1lZrsDV5cPDSyqHZqeexGY2W6AF1ob9MQ78VnUi5IPt0fy\nv+HFzxt3wkQ7ht7+/3wKAEbBabK9SfDtX3gszZqAc3NJU/K26b3x7R3mI+/26rfkM4YE5LnkdW4e\nXSe7H3nuI9VTmM+LM+i67iNd193Wdd2PIS0Av9V13XEkAPFjSAewvntRHuwj4FH2MxiARdEoiPZB\nVkXvDIUayS6eTmwueTYhKPsAtnVg8FEASgEpxe7Bq7eIEvM+jnbN7aKp3NVIQOLiaxKG71/EQxYv\n+z4OrvFpl5cJ3jQhT8Bs/9Lr9HLNxL4u8l4aWyXPfTN9pohXrixIvBAI1c75YLpgC8Su6/4dXa9+\nEnMsK5zqmmEVY9UiQBxEsDL+WPa3KzmvjPZMRmCs3uRrdqmWt2ociSVrfDTRziRvt5+R5Zns+EK8\n42ZtE+WRxke63jcr16mscp25UcMZcH3k0bk5ne3RhIEjBc71wEw0tQZ78LCKhf2wNMUW0MGDB+Ml\nVw5igqmB/OTFQOnyARdABPSk5BBodvJbsmwX14XtCYRqi4EN1SbXk5iws0nEBEAvBvLJ7U7usd+c\nXtTN9tq+4y0GKlwe/MUghKDu75sVjlaIF4NVxYQ1+iak/9VgpAFLJzEHPeEdn5H/2g6uOj3oye5t\n6CrSEWEDXP8YAeEfLD4x0c4ltQCgcAN5ksHYGonZehNG4wJIiTkwj1ATkPPnydoEzX3MSHj3tGI9\nHTZixQG92JR5tQqTujZz5IwZRH0eAduvCIkokdIU+UeMe+wZjLMmFL8D+osx5rMWmbhce95jOWuR\n66MXlVxWKHgDUOq822TovVauyOg8IflbyqIgJDJ6jBEPHzuMc3ONN8x77WMjxGNo36zE7hDVufzJ\nu+fm0cUYkkYjaR96KqunOgSzSAmWsIgm34SJJpoIwBoxg8tEtWjkfE9Nx/hBTX0HaLaodvwZr42s\nkmHVIqslc1poDIPFExYZbF0A4FXf8RerfTHR+kmMjtj4J/0u4p982lWwBPvMk+lrIqRVaXr5AFBq\nTBmLelwW0ZZByR9+ztmdhxl4jj6AjxMwCGijEtXjFoTRfe6gpP7TbGG+P+TJlo9SV0nrRUkC4RCj\n6MgT7XgKQeMB8vn2zcoEVRMOY81Cyieo+zJx2aLQqvnY/4WtF3kRUriW8r+R+mvNRckbqCvxC60d\nM9gL5e42GXoqd3USy8SLody1x0BMoAmvruW+EKP3FsmXa+uSHHN6qwkYtBAVAakWV7ExnERejRV3\nUV/5J9r5ZFXMcj3vyUK1qe++vFtnFp0ASFYPLuIaczYjbUWpQ7Fx0HVmC0R5edWhuKMwA8BXBbK5\nMJN1VRYKMA5DlWtdrpS53PTZ5sOaB6bJzmB30M9+sDgqsXzv2RywybIdu9a5DhjbDXg4hFVPlwWj\nbtqcy+mju9gw3sCY2Juft8nmyBNNNNHFR2s8N+HOkfPPIhNfttcWfSxQgJsai8N7dQghez+y70Mq\nTxsqZS4g634pWAnRIkcwqdtekqF3c7liOmx19tlPhURAGTfinaj0/cP7fa+5As7T5hMja7fSffZH\nsFyBYAYCbhafneJDwb4S+2ZhZC8xav8F9d4FEE84T4PAcj9b8wXieZS1FXyZh99NxiDFOcmT22qx\nDkYejCQ+5PvQrNykTdgdxKJBNnunzcGa/GqWvhj5eFaHzMZH1kI1dpEo70iac+Z4SCEZizFGsB2R\nVUty+iXeyynd8iSbT+zCXCOWy+1i4E0yuxh477KqcNFioEBDp1w2m7bnNHqLwWRnsLPpn3w4+SZY\n3TyDcbXFwAMNhTMQkne94CfAeDEQspgBv+uN3dpiwLQj7QyE7AQOdF0zNOKJ7ule2XiJARwVkYju\nK2OkWDv8lTQdSqtggEsydppodxDvmhx9iO0DhNi/gLmBOe00wqLL9SJTdnvfLiKeoZJ4K0oaqXNP\nosas0YZJq2i31m5nEMG+BiQjmfRx+LMYg8j0skMLfsBnJPL1PYcP5TL5/IWAMZvE6HBAwRUSdsDX\nBUuQeqb30/3dKkPvlXLlW/aDClF2fMamhM7Ny/kcMUYVQYjt/0sawrUCqwRL7IKaLH9uXtJy3YAU\nHcl7z6sz12FhP6zQVxNNNNEeoLVhBpdffSOAxSBgcFh9e7QZE4sVfI/NiOWVGn5gRRVPPGE8wxo1\ncVqpxqtfMmEGO5kknoGNAcCsey2oqZA1I67FPPBCqaV0GO6P8QRAu0uzaGztFYTYHiLGglu86dk7\nGTOoyFDR/laIfUlTnkPFEhAaxS0cHjHwV9NccPpA+SpVZigypw16soKYNtEOoAIMa3BQrvfNgosf\nWECQ8/Hu27iEzLUHGpe8YLBBUaRJr4OejOdQT9tYCLquNVo7ZrAXyt1tMvRU7uq0Lt+E0xejbwKg\nd33eZT1kntU/2pvR9xdgagYxQVB/Zvt9bQWJBtbOoMIB8Gq/SnSZidZPbHgmxDspx8gU4A8o6L2w\n6nzfL2ex6zLnme7pd4W4nk1TbF72zUK2O+B6rsIVADvANwHQtv3epAR8Od7GQqjJ97zAaDfkdJ8n\nPRNjA4s6irENvjfZGewO4kNUeAJ53zX9LtfeISYsr3P6mqGR3Wg8e4Wm0eIr2y54ixkT20wswgwm\nbcJEE00E4AIWg7ZtD7Rt+/G2be9o2/ZXh3u3Db/vaNv2+xa9L/p+oMSNT+BgsTXw9PeBrkt8QnHl\nHL9rOSQ+aUn0vGxnoIKmorCBfdQ2BExsx8D3hPaSDL0by/Xs//O5BWGcRnT5IWjMIJ+REP30tXKL\nPULhKpLbdMw+BVY0EPsGMY23vhFAuV41ZP+FYAa/AuAXuq77/wCgbdsG6RCV24bnf9i27ce7rlso\nsHBl5ZRkSyP1iWNezEg+p9f+4JEWiaiwCinVnmDDdfNUl7osjepOMQ12F0X6mNYdeJEfi3xr1hQw\nBrBMRQnSGjBm0DS+FkPc7KV8HusyfFk0sGcx1Oh8z1qcAfjLshAMtKFTmF91y63nU/QF0zrKXcch\npFO520P7h0NXL4Zyz5czeD6AS9u2/V0AzwHw6wAexQZOYS4gINtcax1uiTWnIx15aL8998DTAjD4\nWDtchTkMNlhi8FHn7wdcFY3FRDuf2IjIA5gBbejmIf8A7cTRBxC5LNYCWPsDbaeQ/rNPBEdeqpky\nx7i6FkHofBeDP0Oa7G8GMANwJ4D/Aunk5Z9Gmgu/iQWnMP+fv/0B/OhbfgoxRtwz6P5f/V2vxbyP\n+YTjG78r7eL3Hj6EgLKr33/kTgDADTe/Bk0IuPfwIcQYccPw/L7huaSX/F91y6245647ch1uoOeS\nf4yl/BtuuRUhlPIl/b2UXwRynjfccmuuj9QPAH79vf8Kr7z+enVKMIAt/y33tqs8+b3b2nv2wXTi\n8otecVM+Zn0+jzhw7c35eQjAgWtuxrl5xKkTCSfYf83N+bTkpgn5aHZODyCfuCy7+ZnhxGbJX3CH\n/fQ+AFx57c1ACPmE5yuH9CdPHMFX/vTTuP6NP4Fz84hHP5XSv/DlN+X8QgiUX3p/GTdx3kJt27a/\nA+DtXdedadv2EIA3IB26utIpzJ9+9Ok8+cpOH0Y7PLCambLNh4k5gPsOH8qLhKe6ZLLPPTUj1y1i\njBsAwBMnj62FheVjyqdy6yTmyCzrLzrOjOX30ycOY/81N5sQfHWbBSHGmix5qkLrXn32waPYf83N\nKl5CzUWasYRFLswXshhcBeADAJ4L4P/quu69bdu+AcA/HZL8Utd1H/PetfEMpBK2E4WsbYF32Kqk\nA8YiQDHi0CKDx8Wz/4Kd3MxCcvnZ2CnotsgAmWIg7mySeAZ2Mnm+ALWFgW0LamHQPfNjIQ/ss7YI\nNeJYh965CbywbclZi13XnQTwg+be6qcwD1ST3a18nzua8YNKehsGja3HQvmhOtoLaALo6MjMqXgx\nD0ZtmDCDXUHs0CNjou8jhpABapLNex1dKGufmlDd0ZcdbMJ14MUGFeckjrTFXApjHvYk6Mk3YYeU\nu9v07lO5q9N0bsImUAD5CDCbTSySrGWzYOLL0cpruQNg7JJsvRjFdDkv6qibMi8jFQCFym3CYtZu\nop1D5Tvp8xFYy8CHljKC7xkUMdoPIHsbxjQY3Tp45x2w3QPv9DFGzCjAaXS4Da5DXHEsrmW0Hjx4\nMF5yZcIMeNJYLIDve27JDOrV4hZYjGGj/ggeKGnZf8+FmcWfGyffhB1NAiA2QYcKE6rFIagFyeVN\nzcZF8EBJwFdFahWjAcXZOakiAnjiyeSbMNFEEy2lNZ6bkHwEInTYdCYx9ZRdX0Kdix23fUNYNo6l\nGKOOHXf/kUMjFr4JOgaiXI9W4+wLocsVG/YEJoYspkwxEHdHufL9+ljOF0hjZ2y8w2cfxBiV7C7j\nj9WM4m/QhMIxeFyB3E++MsXoiX0WOH4ix0BkPwj2t5E5A2ifhRqtPZ6BnXQeC5bEBJT7KHgAv8fa\nBGbvPSMtdnm2x6pLufbodT6D0RdJNtb2iXYGsf0/y+Ue1b6xDs2n1X1C6iRlY90qdYiU3moxNJ4x\nVsXHGFWEo436JqwNMxA7g1UWA2tn4AU9sQ3xZH3OX6kiK/lbJ6qazQHn44Von+wMdjbJWYvWiciT\n3dNvAvic+4Cv+wf02Z3eYrDI/oAXAyE2KLLOcZ4ac0eem+BNRGV9CBOJyAETVRy5oMFBb+IqN9Dg\ne6LZICkMVvI9DxQOlL5mPzHRziVlgUinGdUOXvUmuaRhjQCDj97kZvbdlsXPvPiJkRab3myJrAHx\n4XJNa8MMJJ6B3blZVcNyfH4OrR7MMhK9GwGFMUiaiHLGo6yiEssgonSXXOd85R5hGDBpbVfn+AzY\nfTL0Xi5Xxs2+WZG/bQg0vs/nJkhcATFEa4aJamMlAGNuWMbufMhD4hNwPgUzSP4GlotQxnJ9yVPE\nimV706RNmGiiiQDsADsDQDskeZS4geGaxAEb0GRGbFR+t6IX5sAoWgTwHaRq9gpcH+XaTO2Z7Ax2\nNolvAlB3PfacgZilT+nj6D1rvCTpbaATzqOGSbBhEvtEKACU7A+Ekqt1ur8lvgkXSt4CwLbhtbMP\nGkbsiELQ8n0VY6Dy1QJD+eQ8oSe3BgrLNS9CjGFYEWiinUkM3ukIx2UTKWNFn4PAEYqE7ETkaz6L\nwfMjsGAiGywJ8SKicYEFgVJXGIuTb8I20G6WoadyF9NWnF+wCl1UvgkCuvEuPgsgNp53dPNuRT3I\nMQpZtWP9FATpd8UKaK4i50/GRrxiI0YlhsiZDaxZmGhnE31Kd1e2x6Bl7pX0/ZbtV34EzZh7qBGf\n0QBos2N+PwSJflTq0/f+qUurlr02zEDOTbByuWdDAOiK1s5ZWBboRBuGaNFDuy3LfS1KeG7LFkvw\ngqZOmMHOJvFNALTcz3I5y/rWkAjwjILKBsF5eweb1PwamGygXls+oMUQ69gkdXvz8+qYwaRNmGii\niQDsAMzAAoUiPoztDwZ7cBQ7A04TzDX7CERi5e+56w61+ic2r9gcpPcLqCjXAXS+Q9C2BY1bXrm/\nl2To3V4u6+PZbiDbmJDOftYEPHzssELzhSuQ8dQbDoCvbbhz0UxJuUySdzPYOJw+cSTXU8al+Nwo\nDjnXZTmGuD4LROoIbjbX13MbtovHsrBk43y0GABokYRNkLlcVXdUWDkSWypu6xPtQNJmu+W+nlRy\nt2ADop5mmb28O+RtxhKD/5In4wEcHZnLZbVhD6h4BuwTkTE3BKWKXIV2BGbgVYZlcXt/mV+AleFr\ntggergDoRYXVkkIW5/DeBaYYiLuFOJ6B3SiAse0BqxM9lV8tbkENxKsduGPrwxyIhw1wGsBXMy7y\nTZgwg4kmmgjADvBNAIpBDy+cHBsAIB8A8jXwQqKL6MAqRMk/BODuu+4oGAG0r4M93s36IHi+DDZ4\nqrCNYh3Zx7irZei9UK7nC1DbxeXIs3Pz9M4jDx1F04RRKDSPYowKD2AsK5dr/CA4vcRaiDGVOyNO\nRLANr56r0trjGQDGyk+sphBHz4U8/X3N2o9VRH0fgQH8idBiguRZGwQCIArVcAW5K0FYJtr5xN6A\nMpPZO9Gy8KxyzBPagINZdif79pQPLwQ6P3vN+QDGmpEmvyeeNAFoaIFaJTryeWMGbdv+OIB/AOAc\ngF/suu7jbdveBuBdQ5J3dV33R9679twErowbO85MNq9ZtcXAHkBZ0sNdDHgC2wlvXU35GTA2gpK8\nXv2Syc5gJ5N3iApQXwyErDtzzU/BPWwVUItBDVfwjI5qcRR4MbAnL0s9F/kmXIiY8HYA3w3gBwC8\np23bgHQK8xuGv3cP9xZSoD9Aq0M4HFpW3VF6D/gTNVB2cw5FDOCQUiOXUhRRorCKkf5A4ol2kRaR\nQak6N9iZE62fsjVhxGhiCyvO3ACHK7MsvagfWXxgEdeq+6TMhsafqDKbwV2axQqP9lU4gVWsD4EL\nWwweAvA6AD8E4C5s8BTm+4/cmSe3/KlIMQ7rba8l1JnI/dzRQja+odg3WB91ntBybYkXKo6joPAJ\nsoeQj7rbZOi9Vq58V5HHZfIL8SYCaF3+qeOH1YEmWYSgSSyLhDgh5RBnIrLGEv9Anpc0xtw9aDsD\nPWd03WSB4UVoEV0IZvBRAP8IwLcgHbL6bdjAKcyffehEPvPwXjp4VX5HQD0PIYzS8+9o3u9jHKW/\nkZ4jAq8aDna97/AhIGBh/oj6INjRcwDXDwetSvk3Ds+P3X8/gO07+NROiu0+eHW3tVecfq667pb8\nO8ZyMOrpB46g76M6OBVIB7XK7xCAA9feop7b9Fe/sjxvmqAOSuWDWyW9PZhV8j/9wBF85YufHuWv\nD3aNqj6cf43Oi5tt2/YlAH6l67ofGX7fDuC/BvCPoU9h/u+7rvu8fZ/jGWjbar0fe/EEa2lsrIHa\nKsgh0Gp+4zUsgY2UsrwXfI6G8Y/JzmBn08996KF8zUNB2G4+q9A+9+z/xZJQrhmz8gyBbHquC4Ob\n7PDE3AiPX88palXfhPPlDGby7oALXAbg8wBeRmle6i0EttIWmBMSmQnQBkjsVGSdhBi8E6oZF/U0\no+3CwRqBfK+ybHrYg9RhkXw30c4hBvJmg+DcR4zQemA8DpQqmtJJPhbF1w5K8r8+odm4iAHNmpWi\nd2Zjj1Adv0znhRl0Xfc5AHe1bfsRAL8P4H1d1z2FBCB+DEmEePeiPNYVz+C+KZ7BVO4m0nTWIoCu\n697j3Fv5FGYGRpiNYtdgTivE9v/MdjGHwVwFo/z9gM5KcMmaf4EXR8GahnrqIlIpV/0XJtp5xLp5\nfYxauj9rfDVjEh/KoSgKlM5svx+5KIQ6V8GnQgsJOJjuW9UiX1MaR+W4sB+WJ9l8snYGSkMw/K8d\nnspsf6ikXxSvUMqyoofQooAkSqvhfBjr5CQ0YQY7m+TcBMC35+fAJXZieTp+uwl4B6rY8w1kHeGy\n+L4VIzg94xnsN8EOWDIup7MWJ5pooqW0vrMWDx8anYvAcQgsMFhiCVDsAGgdfzEYKf4JyQ5A/kL2\niVBnNrKREuVp/9gYhQ2iio1Cuc8s416SoXdjuWITEEjPr2MPlDEk5zDKX012Z1+DEufAuO4Pf+fm\n2qBI3uVraxl59sEjgyZL2xYIia+FDEM+d7FGa49nwDI6X/OCkCY1yWPcqNxpAb1jKhRLErVIsO86\ns1SSzmSfjT1KxiTvOSJDCFMMxN1CrKab0fZoDdMAgERxRTZGoVzzfRsOjcv1jli34dBY3BXfBNYy\niHOSkAzXc73GJGq0Nszg8qtvBIDqYiC/gfHCUHMYqsUiZHUfxzFkWUvNc6orLwZMeuKP8QymKQbi\nziY+a5HHgbeT2sWAw5HXVOSez8KFLgZCVuXIlpNsJyGLwY48a5GNc7zDKOW3pPU0CJwPf6QAvTB4\ndgbK6GiBh6T8Vvpcenfex3zKs313OjdhdxCDhnxeYc2IyIYVA5IunwE7SWPPVijDUkc0YlLatQqY\nyPmzYZIXoVk4iWW09hiIgHYMCqHIaCW2m5bf2EmIYx6UNNofgdNIuRG+3XeM2nFKrptQ7NMV5xB0\nPkxyf7fJ0HutXJGtRUVoOepaDMFZE3D2waMjoyHGBKyjkuQjvgLWl8bOWfZZ4LqdPnE4T34ef4xF\nyJ/1rajRpE2YaKKJAOwQzIDJO5uAZX1LbIsgxCl5pa35IyQuIV3z+Y2MT/D9QOVZbcjkm7D7yDs3\nwdvtgcRuV49PY+9FR2Swhm41U2PPPsCeryhk03jHvXG5OxIz8ChGYE7qFZ7gnoEQQMAegXe8eMwM\nqs/WghoI0uVI2rwg2YHhGDiJS7Xcn3wTdgfxAsCkD0jxEXvPmanvY44ytBAoJLUfA5GcvwrD7kzh\nEIq2QmkuKO25HvCd8jXtCMzgYi93t8nQU7mr07rOWtyKcteqTRDDn7yKBcN2D/+ZjbfKu4L2a+2D\nx0lI0JGIMZjiuUtLXlIXLw1zA1wfFiUm2tnkmRSzr0GM2pW4ZmfAxMg/I/zMxnsiA2szWHPBHMO+\nWch2BpwHH/EWqTrWBqLaD8uTbD4xZgDYOHJl8gnZycmLRE6zQnprXOTFSLA2DZwPl8Vle/pfpsnO\nYGeTYAb28NRaHEPPJoCPUt83qx+r7tkocLk1B7rRBuTkGaNelGzMBGDrYiBONNFEFxGt79yE4cxD\njl3IxCy92BSIXQGfXyB/vFPbE3BKngUzkMARHEcxAOo362olr2J4VHwWRIfL+QRKv5dk6N1YrsQo\ntBuyjLN9M21/IN87+QgcLaz84IPQx3LGgbjLi3jhj3VdphAHYo00XoESz0A4Dw54AhSDJfG5WIXW\n75vQx+xTIJPIEmsWakepa/a+vCsfQ/KXBUbqIHl6LtLKjZpEjD4i+0rUVIvWn2KinUtsgSikLPaa\n5ZohVusBGjNgrQSz7kWLAXXPK6rmWzDSVuRydf6rxNZYO2bAPgK1iVUD42oxDAJ8cAaUjwUcly0G\nvV0MqM6c3vOnmDCDnU3/5MMJM7AxDIRsnEGmZfYHdjHwsuHJutHFgOvq4Ro2/x1tZyDstRCj8UxR\nL9QAihsykOwJ+J1lTku1ZZA1Fz38U5WZU4mUFRtK2TpPtPOJDX5iME5wlQHDjkTKY3B4l+0ALMjo\nOSTFpcwAACAASURBVBix52TN/sBqB4IZm1L/GnBZo7VhBnLm4eg8QxRHI8YD2JY7Ulr2a2ARIOdp\nZC22M2AcgklkwtpZi6B6js975JgKqW67TYbea+Wyrz/HzeDnQlqOj3j0U0eH8xb8vHmHFo5S8AbB\nlET9KBwI+0pwHfgsBsEM9OYTq/EY+ICXGk3ahIkmmgjADsAMbAwAT2fPcrkWBfyY9N5uL/eZJMUo\nSoxj61BbU2OEy4JxnSfMYGcTn7VotU9CfN+LMyjaqfJuednzNbDXbnBeY0NQsydYFsGIfR8W2Rks\nxAzatn0tgF8F8Mmu694x3HMPV1310FUhL9gpUHwTAD1ZM4sT9IfhUFHlnvZxYJKffSxyXS3QySog\nJosTqyxIE+08shGq0v96wBG+Zt8BZexG73IaLx9G/hkPqBkv1c4akbxsPjYGSI2WiQmXAPgX8qNt\n2wbmcNXa/WWHrk6+CVO5F0O5F9O5CQsXg67rDgL4c7o1Oly1bduXevex4NBVAC7YZ9kdScNgnLBL\nIRRU3+bVhAI4svESk5g+S958X8iCmKpuA/jDK16qX8zs5ipBKCfaWcTnIIjhEAAF9nEaIat6lHfZ\nAInJpmeDJSHhWIXhkDkQ1Dgr9eF8pAxWbS6jjaoWvxX+4aqhct89dBUoh5YGGOOI4flo8g3/A4sJ\npo0qtoED7zahHN7KDkZWVGG3aGU/zuXRtafGnIVSHzngc7tpKnc1YvWdLN46/Fn5vix/z2M5THUU\n14AmJB+o4tm/WKOjLGqaAc4qSjkklmluhnxWkcetCXv2ZwCeB+DnAfzCcP2VBferxOz6vYcPbej3\nfYcPqWPSNvr++fy+kPJu/+QnFAs7/d5Zv888cESx3Rv9ffoC3/fyO72B5176Re/XaCn/0Lbt6wH8\nra7r3tG27QzA7QBuG979WNd1r6ndr+V58ODB+OlHn867tBcQlbmEWqAQ3tEZBLQNlDebEHDPXXfg\nVbfcqoyFpAxAgzO1OnC5NQ0FL8RPnTq2lt3y9k9+Yip3BRILRBtc1CNG9WdNwKkTR7D/mpur3obJ\nBqZcL4toZCMXcVk8ps48UMqVqlqPSw/QXHQK80LOoG3bdyKBhG9s2/Zfd103h3O4au3+IupJnha5\nyDotMWaQG0l5iIiRA03me1Dp5b6duGzcwTEQpA7jg1PEL0HHTOD6sNOI55Qy0c4lDi6qVYxhxOID\nhf3u+/HE84LkWuMlMRCSTVBUjGVc6nfZ2CljZoShcbmzIaqSiLeMPdRoLSP14MGD8ZIr01mLHMMA\nWL7j2h0dzn3bkd67EWXRsHEUPOszdVhFqKgZ6V1WLU4xEHc2CWfAtgLMAdiJ7qkfrV+At6PbxYHV\ngN7BrrX0stEAmnuwXItn+nzedgbbQTbwKU9Kxa4zkOewcjwRG+hAEIw3Ks6ismDwgGC7gRqxKFGL\n1TjRziW2A9DapPTf2iGUTQQKKMym6jRebYARz3gpvQ/KR9Jr8dg7E0Gf0qRBQy846iJamzny/UcO\nZRWgiAMBJU5AhGbXhf0RuSujvgNLNdI+CLtH90II+YxHgMWKop7ROIL2a+B8mFiU4DxFlNhLevfd\nWC6z2cW3RH97FvlYDSjAnI5bUMZH0wQV20DKsh6OtdgDLJ548QxYCg0hlLr1RQxZlSbfhIkmmgjA\nGjGDS69KmIGNM8hykRCz91am9w5JBaWpxS7keANW1s/orFl1hayrshBjEiwyTL4JO5vYN0GIWXRG\n/jmIifUp8EKiL5IWa5iBd3YDX1tQmrUVLNp42o0dHc/ATlYPtAHKh+oJ+RMRQogBPiEbAEUtGJI3\n6EMGHQmXFyHOn1k3Jl5UJtRg95F2/S3fWLhtPjeB7f85CnITgJ7y4PHoBVBdtQ5MWcNFGBovTlZ1\nuQpN5yZsA+02GXoqd3W6mHwT1sYZZKAw+oEkGjohgVF9/9DzMQrL9zlvL6BJQOEGegJpBNCUfFjr\n4akrmXtI9VjaDRPtAFKIPX2zos3SbL9813Nz7R/QE78uadg0WfIq13Dvc1lsmmzdpZkbSe0AGEo/\nN7AnLIYsorVhBmJnwCw3T9Kxv/c4H77Fba0Z+uij0/x0NXfPmorS4hBeeRNmsLPp5z70EID6JsIs\nN4+zmvWf9QPwzkRogn+uQQ2rsOXW7AzypmbmjKR/07PrmMGkTZhoookArHExuO/IobxyZVNMes46\nfl7h+LwCy/jkGIlRm4Oy6TDbGUi5nJ7f7+kvrdhsHJL+7IrtmSnvJRl6t5erXeWLjt8bKyGEHAOR\nTYFD8O0GrEET2xzw2M1phjL54FehUyeOUB6h2BiEAoLLfTZ3XkRrwwze88EHcdm9M+0eOmuU9Z+Q\nGISU3yTHNwU9nc97Nw37ej996iFcdv8+lXY2a3L+1pJMW4aN2UjxQ5A6eyzbkw8fw2W/95R6zxKz\nmTXHLO6XWogtrufXTx/HJR9+MrdR2mw1NfyT8y/srU7LtvjWQq7vI54+dRxX/P7Tbnm2T4X4G9Tq\nVitXxs3Tp1J7a2HFPdXfbNbgb3z31SVP+vbaZV1E2ZLPrNE+NsValcKh0RbH5s4ySYGxilKuZ7RV\nszggbZHw7KzRYAVF7qKmHrCVaW2cwWVXXrdnyt1Lbd1r5e6/5uZtL3Oryl27nUENeOHVm1c13kFm\ntHT2fVS/tbFGuec5lsznvdLPMnfCnIdXz6rrasP5RDd/zpfrb1lFppIGKs2y+nOedjevcQPcV1ye\nNqrx7efHTjYFci19X/Kp9emiHS2z8MTlcV1rXAgAt6/5O7IdgHUN9mz+2f4gBI3km0rnS21nMP4+\n53oef1rLwIZP9tsA4/4c1cOhtXEGT586DsBjcQte4BF/+Pm8V+fkzec95vM+o7w8EGSAff30iawG\nYvdTKZc/vAz63nQ4E2MJMvh4IgHA10+foPRFxrM27FL/UqcwEh84jVd/9rN45swJVZ8sQ84aitOv\n+ye7vZpFusjAIS9cLNalfk5/T508bvqotDnGqNqgZXAWs0jFG0oeXFdO0zSpvTIWyrcYsKChvrII\ncP/lbxD43AsdQoxJbP6bAHXWIpfLYc9YXpd3a+L7TH1v7SIteYYQMmag+wcKM5D00dShRpM2YaKJ\nJgKwRjFB5Lv5vC9mnCMDCtD9wn7KM7tqa5beZ5Uvv0rkSg38FdFD14HZZq9czY75zy678jrFvvF1\nTSRhllBzK2X9LgCdrptcX3qgyNDMzve93oF5t/TYcwvuWbHItu3yq67LaLzkJa8wR2Q5EI/d5XxA\nrulWfOr7iEv2XzsCShlw9EREwLc34XE2rk+6d24eceW1SXZndp1DnKd6DHWMxluRymOthddGBjeb\nALzoFTdlDonNjrlb2Gx6Fe/FtWMGLNOzXKQ1C7E6gHQ+Y/mTJ4qWu+oDWijlVwaTl6Y2mMeTvjxj\nUYepJt9ynrLICbsv+XmaDjuJa/3maWGS2OLXI02skl7jB+P09W+gv0dpgg4a4vWHxTp4fHhWfjGi\niinx+QW8ILOYwvnx4sQ4AfsIsJ8Cp2HNA+fL2gevXMCPS8AaBGuwxNjGrsAM9kK5e6mte63cyTdh\nE4iBHW/lZzYtPR/vPnpH6NXOxzsCkwXCOG15119FvV2P2UZ+l3c9flcj5XrX9ljxmmkrcxsWaCwi\n0piVtmXxuwK4DbkqtF6j775GZJEtBvdDAf0akNSj+o7bxvX3tBVW28H3heuxHEY9n3G/2GPOfI5B\na3GECeHPV+NqARNeb3inptGQ8sZjpG5KXztFmmntmIHFAERmt0gxk48ZBFcE0JMy4NID1w3vj404\n5F3/w/uDKb1X6jxXHy/dv+LF16u6l/rZSbm43NpA4vozXX7VK9VzFiuWLSpazIEa6CwyyT2pX99H\nXHrgWrUwMIaTFmHkemhRp9SdJyu3rYgneuGKsZTr+QJwH9n6eCKoGPQAQAxQ34C/zYEBM7AYA38O\nqQLHQ7TIPhssMX5Qw5oEqxCtBwAVfZk3KV6cFtGkTZhoookArHExEH0/wPpZ1jvr9J5e2OrFre5e\nqOjUI545cyKnFQ0Bl2VtFIpNQLku+nldzmzW5DQCRjVNwJMPH1P2Csz1aD17Kcurf0pfgC5ur/Qh\n1/mpk8eyTl84JOEQJB+uM+fPfS5su+w2lu2X+sl3kD72vh3bE1g7CybpE4/jkXJtH9lyuV/YzsIa\ndbFunseY2BtYuxCOhyiye4wgOwCqF/Wd5hZ0PcUOINcljNNwW08ePzxKz9wGA4ZNswm+CZVTmD8A\n4DuRFpK3dF33heH+hk5hFmIEt64FCDTQSzqLdksaZt2thkIPcF9u9sQEPfg0q1jaouvjWf1xeqsF\nsP4Stk+sTM+sq+27ZeS1i9/jfrAIvZXFy/thtOiVND4GMlcquHHFa2KSZZubplELmrSnaEdKnk2j\ntSwccoy/PavsGBdh9L4ZFoY+aq0Bv+uFSWMcQh3ZZr63pGka7c4sixOrDO0x7bXFpEYbOoUZALqu\ne1vXdd+LdGiKLBAbPoV5L9mv76W27rVyD1xEvgkbPYWZ6XEA3xiuN3wKsy8aRGLpS1o2W2XTWDYx\nteg2s4eS3ur3WXzwRAC+z+n1DqrNXz2yIkDN5NeCWbJ7WRaddyn7xyw9s/Dl/cKRyE7OfcttZ7GC\nxRB+34K13M6aOW9NnNPi01hTY0VFFnWKKTr3CwyngnxPj7/x95boQN4Oy33HLsbcR0xigixcjuUg\neXePtOsvA4xHhlex/NXSLKILwQzeCuD9w3U+nXk4iVlOYa6SyNF6MBU2kwcTT3yW9T0cQagMpqCu\nv376uPvBWKYVkokvdWE8wLNzT22wSLfgI2Vx4ne5LB4otYHFE78shFDX8u4zZ7RPhF0gvD+7KFsR\npGAOKZ1MQvY1eOrkMfV9uD01nMBTC5ffZXLwOLD1e/rUcbUg6c1FT9Yyzvzxx6w49/vMfCfBDHhx\n1P4FemMSvCGEgj0we88b5EikIrlf4igIRmHbZVWMqxz1d16LQdu2bwTwma7rPj3c2vApzN/48hfy\n9dOnjiuDkYvt9zNf+sKOqs9W//7Gl3dXey/01OTzOUX5Qk9x/vIXP7Xw+aJTmWu0FGHgU5iH3zcC\n+LGu695OaTZ8CvPf//DXSyVCAfsY/NEmqVTpSq09oxpLHuBnjXB4V/eAPMu6erudRaxr5Vs228uz\nBqBxmVKccAySxgMuF9V/Wd1k9+RXPBDUakX4uy5rQ63NngbB5rNoDHnfuGkC/uZrXpzfrwUckXft\nSUhMXJaqZxinb4IGHKXOnD+fCm3TCzEAbzUK3KZVzlrc0CnMw+0OwE1t2368bdtfA87vFOaaPLlM\npcTEbJ3Nky0NOb01ZpI0jD1o/GDsYsssMLPTgC+jMgvJrCu3l9ValmVm8cS2n/P18vFwDhadrL2+\nFovGcnWRt33sguvNrLgnK+t+h6mHthLV/YHRtxFapIrkvtJq2TF7bymLJCSXM94yLo/D7pWFQNSA\nXE3BKFjrMDfjoCfxj+u8bxZc1WIN51hEC1WLXdf9SwD/0tx7SSXtR5EWgpXo6VPH14L+rqPcdbb1\n0gPXrqXcZ139yuUJt6Dc7W7vmQeOrCXa0VaUuzZzZEadWXeujWvi6FrSJRrvNABGXngshshOxDp+\nZonZBdZZ8EfpgcUiREmf7rELMiPGY9PcwmnwfU9cYlafOQsB9VK5uizuK68tlqMas/zR/NY7uuzE\ncp/z98sr+bDIwNyBFv82pkdn8Uk4nJRn0USdU67dfE1iY6P9BYRjsmORxQ0haxfgsfdK5HQ4CKmP\n/J0jBZkVI5nTWIXWthhcsv9a0hqMUXlAy+vMhrMczA40bFxUJrS2kbd285In+0QIsZhRk/slnVBm\nDanOV7z4elrYfFt7LkMvEjG3xQZu5Uko6VmceNbVr1T17/tiKKSNmXz5nCeGlfl9DCddXHbldaqP\nWa617y4jEUlKnXgBL+XGmHwT7MLlYS/cVj0+6nK/194mAFe/8pZ8f07fhp2NFFZA41iK4AVi1kDt\nKJ4IAgAvesXNo35lXGHVg1OYJt+EiSaaCMBafROKvt8DAa3NgZDWifu6bItSC83nfVYpsVENg1Fs\n/MP511Zorr+OyVjKFb0777CpvlpHzHXWNgelP7h/5F0GBJmeOnlc5aNtEcYAmv0WNXC2lIuhL9ko\nSr6ttV2wZsJePmNw19MgsH0Bc1NizyEk4iVza5b7ZBCQwV1OO6MyxXgohLTzPnzscN6NPV1+Hwto\naMHoGlAoRkr8bfgPAB556CjERDmLDPMCADNXsMy+QGiN8Qy0rAnU1T8sN9roPYw38KDyZGjWpGp1\nHLF+C9R3ZYJrRyrGA6wFnUeeupKJRQBme9PgHLeRWWl5ZvPRecLN37LYjN/UcBFeJOXSUz164n0I\n2irULtySxsMx+Hepv/7eFnvg781lMlbh4RN9ZBFuXD4wDnvGJ3Z7KkGmGKMbDs3iDbqvh81rNKbH\n4uyq0sJ0bsJFWuZU7vbQdG7CJhDvRnNiiQRsH+vbx8ARp+HVXvsq+ECQXaVru7iHfLPeXu/u2rvN\nM0AKwd+5x8DXuF7cLs0JgO5rQM+KGrbOzCX0fa+4FuaEuCzOwxrw8O4rgKWtq5Atj9NwP7I2xQtu\n0jSN8qLk9ljuQfLUoGS63wQgOpwRczoaWPWDodg2a5uSUn9ur7JDcAyNatoTXTdjAEfJV4iHuv4Y\niKI682319cAACvstSCrLgHK/FnC0aYJ7XkP6vVh2Z5mYsQE2zhHcQM5ukGsbm8+T1+3CZ2Vb6SsP\ne2BjIe6Hp08dVzK21EfekcHDcrWksX3LfaKNhbRzmWAGtm2e2MT9WxM9uC9sX2u/g5DPp2AsRa49\nLZHtd7E6tCo8rpucqyiLpZgBs0ESv9sb3MLDQmwd8veOvvFcE4DTJw47/ab7kH0ZFomtOd/Fjyea\naKK9QmsTEyQ+n0V7hZj95Bh8DCBa+4PCTmqUmcEfsTNgwFF2XFuucB9yLWTrwOQBkEnvjpwPg5Ul\nH21EpFlU5hpqddbPgWRnUNhnfaQYA4te/mwEJb8lH+4jtumQ9lyy/1oFZlmRievNopcWaUo79I43\n7udU/3ImhmcrwKKUtEPue6w1f1Zurz0A9YUvvymz6tmQq2eAWYsGHmhsjZo8s2L1zQJw4Npb8v1s\nMNeUeltwswZeMq01OjIwRmcZS2B5X6PiYzmYO3qMXvuyFrNunlzLKDpPOJahNYKrFwJ9FmQxHGIj\nIo7A47FxWtbvcxmMH/CCkSaYiElj0UPqrCdDufbqYMUuNpySxUHKgBOZmcvmwWutLm27yzXcdvIC\ntYwF1jiBn7gXPSDGiyQHLOVFjserLCQ1+ZytFzlPdkiyi1AtH89ikRcq3si4boto7ZjBXih3L7V1\nr5U7nZuwCcSgkBCzWsDYxwAY69e9NJI/oJF/+S0AjmfKbEny9EyOuRzvPU/na3XFTPp3rY3pP4c7\nt7YIvPN6Whj9rtaweHp2q8WoaXGsRoBapnZQRvK9PmJuqyYm2ZOz+14O3B1HkLLvMsfH3JsWbVK9\nJf9ltgJ9H7MmIoSQQ5Mzy2/Ng7MGwdgHcJ5eeX0s/chprJm5XK9ymhKwxsVAvNrsx2Z1lLUPT6Qd\nboSsfFsbcOITIeg6YOXPUhKz0DX10rj+YxHmL7zoGjWZPDyAWXc7qbx+WMV2nj0Ha2z0Ivaa+5nZ\neSv+6LqEjAd5GAh/D564vKBxGSwCsIjl1fVZV79S9WnNEpXR/Lp44ncM+xo0AbjquiS780RvzBjy\nYiDwBmQnPC/OjJGwwk3OWpQ6SR38OWOPf/dp0iZMNNFEANa4GEgMRNYdi5ggu4QAWvwHQOnLJb3o\n9j3dOeuU+bwGIdnpeScTgLGma5f6cDxAS3L/6VPHXVsKTlMry2OjuU0sMqU+K+lZhrb5cH9y+eyD\n4NkljOz26QwGLldEDmsDwnW1u5jXfi67JhJK3Z98+Jiyp5AymBNjIDMDyKHs5ny/jLuYg49Ytv/U\niSPjiEfmt/gazHv9jUsMQ/tXxiJ/V8mnj8DZB48WDiguNjnuzfiu0drjGTDbaJH5mpzuaQeseo2T\ne2JFjWqqQlblJdY1DnlqVr/mklw7Z4BJW/9JWVZrsLje3A81lak+4dpXX9m2WxVgDZnXRlo+LlHS\njrVJkseiiV/u63el7SySaNFu3HmzWTOKTyDX+RsEHW8gf0KjbfBchhkHY7GI8xzXs1xzeiGJxiw4\nEGsxPMxn2SIgNPkmXKRlTuVuD02+CZtMtd1Ss2uM/pb7vHuV90rezDpb+wNrlCL3vJ3SItQ1hJvz\ntmy9lMPor4dei1GU5O1pTxhYG9mkO0h/Qp5L/TU3VtJ4u4hng8EilefPoHcmbfvgcSgiVtj7dqf0\noj554oa9z9wJj5X5vM8An9L39zpSELebAcScjwWS87cB5LuqKEkzPc6E9s04GEpUZch9a2fAAU20\nnQJfL2cP1m5nYNnGch3VNduhC9Vs21O+4/MDY4yDj78tS8vNzOpaed7DObhMVl1Kei6T8Qbta6Db\nJX9crkx6vVhpjERYbPGJkPxrIlKxnisTZvw3Zn+5L6xK7+lTxxWGY99nnKe0DarN3M7ynm6zVa99\n/fRx5XfAbZD3ZXEVDKcZJui5eRyp4PjwE8Yecj/3kXwEgsIedP8M35tkd4sfSCyEc/NyfqJMdMEJ\n5H4q90geQzwOuc+1wdryIMOTNmGiiSYCsFbfhGJHziuukD0yTciKALzaMQtZ07eKXKlt4X1WOEbN\nAnM9PSMoFiu47ik2HyjNGOSxbDXXzemGqv8C209csp/LdbtjlKev8Ri/74lYwqHJt7XPhQpSPo5k\nJPl4YhL3L/cL+0RYgLHUDeZ+zG2WtrAunsttgn7G4oPEImS/AC2y1nX/PJ7YqMkHFktcxRh17EWh\nRcFQVgERN3wK83D/EgCfBfDLXde9b7i3oVOYtTw5lvFYrgX0h7cstaT3fNpTGfmKBkFdRCnvaS2A\nd835a9S8bhXIbWT53jPMsdqEjC6TU8NsVvrQWh1yfXgR8mTIGmpv+5LL9hZs2wZ7LkKt/faZ5M/9\nqxdkndbLh+vA6mivPmPLxZTIRiDW2ofh21B+tYNWRtjOcHmu11oDNkzy0vfRj3hsv58/B+q04VOY\nB3obgHvkx/mcwryX7Nf3Ulv3WrkXk2/Chk9hbtv2cgDfD+CDdHvDpzALyWpv7aoXAWqLgC1+fxGw\naMEyBmH09TgYKYNdnsZA8mAQiYOGSJ5ssKOByHEf8S4oXBBfM4jHQBmT18/Wdt/aCWhzaX2MmwVc\n0/3C5fAZFeW7lDZIv5Y8FoszlgMofecDfFxvMXEWMcjrU3vNY8UDsGvjdd4XA6EYCyAoY5a5iT5q\nILyPeuzmMRQKoNnQ2NV9ocUED+ReROeDGfwMgN8A8O10L5/CPPyWU5g/V8vkihdfD0CLA8y+8cBL\nsmyRIXnAcHohO9h5UghmYLGGGtLKMrcnrzJuMZ/7bP+lB4oMPR7Qi8UBNjRi0YP7YCwWpUSXX3Wd\nus/pmfSC4Mvn7HZtVa5s3NL36fwC68NQ2uwbLFnVaPld3yQsybf18B9up154bZSpcX34O1lR5cC1\nSd/PPgvWAKlfMm5C0P4FHM1Y8mG/gz4il6vFS2scVsradNVi27bPBXBr13V/ACgzwA2fwryTTuGd\nfu/t35txCvPpCzxV2b6/6BTnC/1do6XLBZ/C3LbtDwL4WQBfBvAdSJzFjwP4DDZ4CvN//v4juOzK\n69Rux2Ai7yBjboDZuHH+Y7a7/Hjq5DFcduV1o93XQ3wtAMM7lAf22ROPpNyvnz7uciQW8PHqwCDm\novZqFjnd5zMeLRjl9Y9NYyMYyTX3r+WwxL6BT5HiMrTrcf27ev1ivwfr0Lm9NWCYRQeu19/47qvz\nNYs73vFk9j6fecg7uqd9EFsBm2ctWAlAIKM5lo3L5TQ8Drwj3hadwrxMm/BOAD8A4AVt2z6n67qf\nBPCR4dlPAHhW13UPDb9/CekUZmCFU5g9oxLLqjNLzNes7mOrtZr9P7PfNeOLZSo+mPj0QjxYF/kU\nCNnYAJ6YwPdrxkJ2weNBXPpKH0GmfTR4QpZ3OSKTtpqsLyTcfpHLuS/SYlvaz3X2FgAma6XIC4DF\nWaQtou3QGhE/uvB83qsoRso/glR8Qk0TFjoFST6NszCEUDQTLBrYo9eViEHfidvC16zt8PpzFREB\nWIEz2Ao6ePBg/C9/75lSCUcOtjsCp+HB56mOFi0GTJ4pc13fr1VzQlY9xlyOhwHU8qxdW06itkB6\n1zXVpd2dS5/7XA6THVf2e3gLo21/eTdW+1rIgna8GNTKWhbrkdvQ9xFvfF06WJyby3naxYDrz8SL\nChNjAyzHr7IYePiKvW85JnnOqkihH37O2fPjDLaD7IqtddP+ElyLgOTF4LfBN3hQLme/o2vIZMUK\nD7Thci3777HMnJ4XOQsElTw0eMpt4XI8zonJtqV22hNPDKvp8RYNNhzSYoaeEHqR5PdL/fSkLIl4\n8Zd2z2a2r8d9AeiF3WPR2c4/hLEfgk3f99pwSIN36ZrFAXuas64zjVeZ0NAiDOfZq36L+b9wFZaL\nqtGOOGsxDbDCDdjOYbWTsIrCnhb2sPjf82CVHU4GvfgJaFUh51/UVByrQAa01U4ApT6lfmVwx5hk\nWRZRWFSR/G09WaUpxO+y6kgWlbLzpeunTh5T9fT6luvJbWR1l96ZiwhRYz9TPAP/HEnJQ76Z/Olx\noL+9Nw5Y3Sz99OTDxzK3ISpo7rOS3q22IsslcEwCrg+fm8DtlVgFQPE7sGsmp5d+ZvdkJv5sTRNw\n9sEj2UDJU4eqd2k8LaLJN2GiiSYCsEYxgX3PGeRidpJZP0/XzKyllQmZFffK5fTMQjNYpmVuLX/r\nlXjcPs6fz02w9ReyZsSlb6z8XNJ78iuLDBwDscb2M3EdageiWlbdtjnG5IvBZTLIyBiDAH6SZsum\nJAAAAyBJREFUtob2szjE7S99k9699MC1I86N+5RFJsuVSj4eQKnFM82uC6I/0sQ4dgbKYCmiulPz\nmG5IE8FtOUCaBPlSI/CRsIpVQMS1nsIMjGVFfi7Ith0cDBZJI63hjRUV5B7LkJ4szsg3D1aW05hY\nPuS8NKBZYjDotvN7Wqa1ZUjdmLxJEqMfMYnL0vWtA6ZeP9v3029fhq5RzchMztzkBYMXPf4GGrsI\nLtahv5deOPkZg3csx7PKbp8zKdmmqsdY/WrrYLGxmkpX8u2j77QUgj1opaQv+WsfCc+XwdLa4xns\nhXL3Ulv3WrmnVzDm2Qq6qM5NELLmrB6XkHavcaQcqwb09f3j/BnoA8boeB3AKvXxRQljYuqcFlQz\nlbbAlrd7WqMm3hktd2Ova+JG32vNTE1LYvvA12drcNe+Y6mmoRHwz1IIvuZG7i9CzXlscd6suuyh\n/RvEzsfaFuT+HYGxyO9635LL5nHJgVYZaLSGQyzONAMoCYw5Asmzz994hx+vJvKsVq9Z1sdjFf0Q\nX+ndMkA9S7++j/msRWvkU/t4WsQodfA+akrLAzrmtrJ867O9vl7btpHrXLNJl3wuu/I615Yi1aUs\nJGzUYyd76RPQ+8jttH3U9zGfTaHJH41a7i/t5YWX+7dZwMuKZSl/p5otSaSJImTVrDz5uL4cJu0F\nf+0mZScAjH0TPDGyCciLicUXuO95kWCR4YUvvyn7MUjRfKai7f7agsw0aRMmmmgiAGtcDJ46eUzt\nSCGMLfvkvkVChUW2qHHR95f4b6wvDyHgmTMn8m7O6UveYzHA+5O6sQluzUiKZdkaqsv14fZwHTQY\nVfqhr+xCXz99XNleiJ7damY8+wPW4/NvFtFkhy1llPba98u3LKKatd3g71SuS19YGw1b32fOnFB1\nk/6wn4VtSYBiB8B9OhvVv4yVeR+zF+HZB4/k9ySN9Tvgb5bbEq2oN6aarwNQzk0QkNEGZB1bLPoA\nuEqz+PHW0MGDBz8B4HXrKHuiifY4ffK22257/borMdFEE0000UQTTTTRRBNNNNFEE0000UQTTTTR\nRBPtRvr/AUYvkw1vDCfkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111dbfa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x111de8b90>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ElbM1bjs/J939nDtV6bb7h8fdz+uvn4i77u4bRXffKH788nG33d03ioy0FGSk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\nPXbs2FGB36uhoaGh8TOF/w9tJ/w6E38PhgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11184dd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11184ded0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df3dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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i7TSivuWVoEXcSSPaAJbnEny8qWXOJAqIxWYc6Bis+jiv6D7g9AQW8QcAJx9+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\nh32xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121189d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(generate_dataset(option='g', noise=1.0, noise_background=False), cmap=plt.cm.Blues)\n",
    "plt.title(\"Original Data\")\n",
    "plt.show()\n",
    "\n",
    "data = generate_dataset(option='g', noise=1.0, noise_background=False, shuffle=False)\n",
    "X = data\n",
    "\n",
    "U, S, V = nmtf(X,5,5,num_iter=1)\n",
    "\n",
    "plt.matshow(U, cmap=plt.cm.Blues)\n",
    "plt.matshow(S, cmap=plt.cm.Blues)\n",
    "plt.matshow(V, cmap=plt.cm.Blues)\n",
    "\n",
    "plt.matshow(U.dot(S).dot(V), cmap=plt.cm.Blues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}