Test DPP.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from math import pi, cos, sin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 100\n",
    "angles = np.linspace(0, 2*pi, N)\n",
    "x = np.array([20*cos(th) for th in angles])\n",
    "y = np.array([20*sin(th) for th in angles])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11582bd68>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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idxGWuetoI09t7cRLZrbW3U8HKc2XB92gpZhZhUaw/5S7PxAczt11ALj7lJl9\nEfhhGmnl4aCX35e/q1z28NsxsytC3+4AvhY8fhj4maBa5+3At0NDwkwJbQ7/k754c/hbzGyVmW0k\nv5vD5+k6/h64IqioWAncQqP9efUwcFvw+DbgoQG2ZUnW2Cz748DT7v7R0FO5uQ4zW9OstDOzKvBj\nNOYivgj8VPCy/lzDoGewU5gRPwicAL4C/CVQ9wsz5b9HI3f2JKGqkax90ZjEfB44Hnx9LPTcXcE1\nnAR+fNBtXeI6bqSRmzwHvAQczul1vJtGdcgzwF2Dbk8X7b4POA3MBL+H9wP/GvgC8HXgEeCSQbdz\niWt4B410zVdC/z+8O0/XAfwgcCy4hhPAh4Ljb6XR0TkF/DmwKu226E5bEZGSKFxKR0REoingi4iU\nhAK+iEhJKOCLiJSEAr6ISEko4IuIlIQCvohISSjgi4iUxP8HfE59GwC7DecAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1156f9a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.column_stack((x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics.pairwise import linear_kernel, rbf_kernel\n",
    "K_lin = linear_kernel(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(K_lin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_rbf = rbf_kernel(X)\n",
    "np.linalg.matrix_rank(K_rbf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def sample(K):\n",
    "    N, _ = K.shape\n",
    "    lam, v = map(np.real, np.linalg.eig(K))\n",
    "    V = v[:, [random.random() < lam[i] / (lam[i] + 1) for i in range(N)]]\n",
    "    _, nb = V.shape\n",
    "    selected = []\n",
    "    while nb:\n",
    "        V, _ = np.linalg.qr(V)\n",
    "        proba = ((V ** 2) / nb).sum(axis=1)\n",
    "        k = np.random.choice(N, p=proba)\n",
    "        selected.append(k)\n",
    "        removed_index = np.where(V[k, :] != 0)[0][0]\n",
    "        remover = V[:, removed_index] / V[k, removed_index]\n",
    "        V = V - np.outer(remover, V[k, :])\n",
    "        V = np.delete(V, removed_index, axis=1)\n",
    "        nb -= 1\n",
    "    return selected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[13, 37]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x117118e80>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/H3KfkqQhpKrGXcOLJNkF/HhW01HAfJeLLnUe29K1nI/PY1t6Xl5VfY2TH5DBP1eSqaqa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117059d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "selected = sample(K_lin)\n",
    "print(selected)\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.scatter(x[selected], y[selected])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35 points [0, 6, 7, 10, 12, 16, 18, 21, 30, 32, 34, 38, 40, 41, 46, 50, 52, 53, 60, 61, 62, 63, 64, 66, 67, 69, 71, 75, 79, 80, 82, 83, 86, 94, 97]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x117019c18>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116f602e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "selected = sample(K_rbf)\n",
    "print(len(selected), 'points', sorted(selected))\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.scatter(x[selected], y[selected])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Django Shell-Plus",
   "language": "python",
   "name": "django_extensions"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}