Class ID 22542 _ 1352659.ipynb

gistfile1.txt

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Load package\n",
    "import numpy as np\n",
    "\n",
    "# Define A\n",
    "A = np.array([[5,1,20,0,5],\n",
    "              [1,2,1,0,0],\n",
    "              [5,1,5,0,5],\n",
    "              [0,0,5,10,10],\n",
    "              [10,0,0,15,30]], dtype=np.float32)\n",
    "\n",
    "# Normalize A\n",
    "for i in range(A.shape[1]):\n",
    "    A[:, i] = A[:, i] / A[:, i].sum() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.23809524 0.25       0.6451613  0.         0.1       ]\n",
      " [0.04761905 0.5        0.03225806 0.         0.        ]\n",
      " [0.23809524 0.25       0.16129032 0.         0.1       ]\n",
      " [0.         0.         0.16129032 0.4        0.2       ]\n",
      " [0.47619048 0.         0.         0.6        0.6       ]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of eigenvalues:\n",
      "[ 1.         -0.13700466  0.05162274  0.3724222   0.6123453 ]\n",
      "\n",
      "List of eigenvectors (shown in columns):\n",
      "[[-0.29666978 -0.62488663 -0.36838657  0.7118548  -0.49538493]\n",
      " [-0.04115295  0.03421432  0.04167876 -0.34398633 -0.28943142]\n",
      " [-0.19992964  0.24681665 -0.03551326  0.30960253 -0.2767215 ]\n",
      " [-0.34294128 -0.3221922  -0.44963944 -0.496214    0.4066375 ]\n",
      " [-0.86759025  0.6660479   0.81186044 -0.18125694  0.65490025]]\n",
      "\n",
      "Normalized eigenvector with eigenvalue = 1:\n",
      "[0.169692   0.02353906 0.11435765 0.19615881 0.4962525 ]\n"
     ]
    }
   ],
   "source": [
    "# Get eigenvalues and eigenvectors\n",
    "from numpy import linalg as LA\n",
    "values, vectors = LA.eig(A)\n",
    "print(\"List of eigenvalues:\")\n",
    "print(values)\n",
    "print(\"\\nList of eigenvectors (shown in columns):\")\n",
    "print(vectors)\n",
    "\n",
    "# Normalize eigenvector that corresponds to lambda = 1\n",
    "print(\"\\nNormalized eigenvector with eigenvalue = 1:\")\n",
    "print(vectors[:, 0] / vectors[:, 0].sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Initial Distribution \\#1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.20034178 0.03621352 0.10356759 0.22225807 0.43761906]\n",
      " [0.16733351 0.03098773 0.11722016 0.19313149 0.49132714]\n",
      " [0.17234687 0.02724342 0.11562744 0.1944245  0.49035782]\n",
      " [0.17147995 0.02555862 0.11553119 0.19449095 0.49293935]\n",
      " [0.1710484  0.02467184 0.11514621 0.19501832 0.49411532]\n",
      " [0.17059318 0.02419547 0.11487727 0.19540236 0.49493182]\n",
      " [0.17027384 0.02392694 0.11468807 0.1956759  0.49543537]\n",
      " [0.17005896 0.02377136 0.11456474 0.19585551 0.49574956]\n",
      " [0.16992076 0.02367936 0.11448621 0.1959703  0.49594352]\n",
      " [0.16983359 0.02362425 0.11443703 0.19604234 0.49606296]]\n"
     ]
    }
   ],
   "source": [
    "# Define column vector with distribution\n",
    "v1 = np.array([[0.1, 0.05, 0.2, 0.3, 0.35]]).T\n",
    "v2 = np.array([[0, 1, 0, 0, 0]]).T\n",
    "v3 = np.array([[0.2, 0.2, 0.2, 0.2, 0.2]]).T\n",
    "show_convergence(v3)\n",
    "\n",
    "def show_convergence(v, niter = 10) :\n",
    "    '''Receive distribuition and save every step for niter (default : 10) steps.'''\n",
    "    steps = []\n",
    "    for i in range(niter):        # For 10 steps\n",
    "        v = A@v                   # Move one step forward\n",
    "        steps.append(v.T[0])      # Save the state\n",
    "    print(np.array(steps))        # Print after done\n",
    "    \n",
    "show_convergence(v1)\n",
    "show_convergence(v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Initial Distribution \\#2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.25       0.5        0.25       0.         0.        ]\n",
      " [0.34581413 0.26996928 0.22484639 0.04032258 0.11904762]\n",
      " [0.30679596 0.15870509 0.19799932 0.0762041  0.26029552]\n",
      " [0.26649398 0.10034895 0.17068786 0.11447612 0.34799309]\n",
      " [0.23345869 0.06837072 0.15086779 0.14291937 0.40438343]\n",
      " [0.21045048 0.05016915 0.13744994 0.16237795 0.4395525 ]\n",
      " [0.19528217 0.03953989 0.12877414 0.17503103 0.4613728 ]\n",
      " [0.1855981  0.0332231  0.12328803 0.183057   0.47483382]\n",
      " [0.17951985 0.02942659 0.11986435 0.18807473 0.48311455]\n",
      " [0.17574276 0.02712845 0.11774388 0.19118576 0.48819923]]\n"
     ]
    }
   ],
   "source": [
    "v2 = np.array([[0, 1, 0, 0, 0]]).T\n",
    "show_convergence(v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Initial Distribution \\#3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.2466513  0.11597542 0.14987711 0.15225807 0.33523811]\n",
      " [0.21793908 0.07456776 0.14541789 0.15212458 0.40995072]\n",
      " [0.20534526 0.05235283 0.13498177 0.16629447 0.4410257 ]\n",
      " [0.19316751 0.04030901 0.12785376 0.17649418 0.46217558]\n",
      " [0.18477337 0.03347727 0.12290865 0.18365436 0.4751864 ]\n",
      " [0.17917752 0.02950216 0.11970559 0.188323   0.4832918 ]\n",
      " [0.17559545 0.02714482 0.11767339 0.19129492 0.48829152]\n",
      " [0.17334211 0.02573001 0.11640338 0.19315585 0.49136876]\n",
      " [0.17194026 0.02487434 0.11561605 0.19431083 0.49325865]\n",
      " [0.1710736  0.02435435 0.11513036 0.19502381 0.49441802]]\n"
     ]
    }
   ],
   "source": [
    "v3 = np.array([[0.2, 0.2, 0.2, 0.2, 0.2]]).T\n",
    "show_convergence(v3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (Anaconda 5)",
   "env": {
    "LD_LIBRARY_PATH": "/ext/anaconda5/lib",
    "PROJ_LIB": "/ext/anaconda-2019.03/share/proj",
    "PYTHONHOME": "/ext/anaconda5/lib/python3.5",
    "PYTHONPATH": "/ext/anaconda5/lib/python3.5:/ext/anaconda5/lib/python3.5/site-packages"
   },
   "language": "python",
   "metadata": {
    "cocalc": {
     "description": "Python/R distribution for data science",
     "priority": -1,
     "url": "https://www.anaconda.com/distribution/"
    }
   },
   "name": "anaconda5"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}