{ "metadata": { "name": "", "signature": "sha256:54ac9afff786095c83ff8ef7561dba5546bd53301469aac7e243ca6f7f668b28" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Random walk modelling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During this seminar we will immulate the random walk on knight's network, which you should build in the first place." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider $n \\times n$ chessboard with a single knight on it. \n", "\n", "1. Construct a network with all knight's possible moves. In this network each node represents chessboard locations and an edge between two locations appears if knight is admitted to move from one to another.\n", "2. Implement simulation of knight random walk on chessboard\n", "\n", " * Calculate average probability to visit chessboard locations\n", " * Calculate average recurrence time of a node" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from numpy.random import choice, rand \n", "import networkx as nx\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Knight's Network" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def GenKnightNetwork(boardSize):\n", " G = nx.Graph()\n", " pos = {}\n", " for row in xrange(boardSize):\n", " for col in xrange(boardSize):\n", " nodeId = row + col*boardSize\n", " pos[nodeId] = np.array([1.0*row/boardSize, 1.0*col/boardSize])\n", " newPos = GetLegalMoves(row, col, boardSize)\n", " for e in newPos:\n", " nid = e[0] + e[1]*boardSize\n", " G.add_edge(nodeId, nid)\n", " return G, pos\n", "\n", "def GetLegalMoves(x,y,boardSize):\n", " newMoves = []\n", " moveOffsets = [(-1,-2),(-1,2),(-2,-1),(-2,1),\n", " ( 1,-2),( 1,2),( 2,-1),( 2,1)]\n", " for i in moveOffsets:\n", " newX = x + i[0]\n", " newY = y + i[1]\n", " if isLegalCoord(newX,boardSize) and \\\n", " isLegalCoord(newY,boardSize):\n", " newMoves.append((newX,newY))\n", " return newMoves\n", "\n", "def isLegalCoord(x,boardSize):\n", " if x >= 0 and x < boardSize:\n", " return True\n", " else:\n", " return False" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "boardSize = 8\n", "(G,pos) = GenKnightNetwork(boardSize)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "nx.draw(G, pos)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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KMJ9P2rCya0/aywmQB0BmY2UqBrOdN4A0YWU7j7H/jR9kwoQJcdVfjWe2EbfO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\nAADH/g/oq2esC2gGBgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Random Walk Process" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def RandomWalk(G, xi, n, till_first_return = False):\n", " nodeSeq = []\n", " nodeSeq.append(xi)\n", " if till_first_return:\n", " xInit = xi\n", " while True:\n", " neig = np.array(G.neighbors(xi))\n", " xi = choice(G.neighbors(xi),1)[0] \n", " nodeSeq.append(xi)\n", " if xi == xInit:\n", " return nodeSeq\n", " else:\n", " for i in xrange(n):\n", " neig = np.array(G.neighbors(xi))\n", " xi = choice(G.neighbors(xi),1)[0] \n", " nodeSeq.append(xi)\n", " return nodeSeq\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "nodeSeq = RandomWalk(G, 0, 100)\n", "edgeSeq = [(nodeSeq[i-1], nodeSeq[i]) for i in xrange(1,len(nodeSeq))]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "nodeSeq = RandomWalk(G, 0, 100, True)\n", "edgeSeq = [(nodeSeq[i-1], nodeSeq[i]) for i in xrange(1,len(nodeSeq))]\n", "nx.draw(G, pos)\n", "nx.draw(G, pos, edgelist = edgeSeq, edge_color='blue', width=2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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/PH++fbOOWCwxzE4b1n/3uw2WfZvN+hInw85tbeTmzeSFF7aaBuKhQ1vYr1+D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\nS2zHrF9leujQIeEdfyRz8Hwj0f6cDDvrmYcPb3C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KSZCwkpDbb/8xM8lkMpd3JmtNZiXP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\n2SwrO0iga/3n/hrnVDnbYVf/ORVx7qtI8s1gvK42/dZtNk4C06atotG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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "nodeSeq = []\n", "for xi in xrange(G.number_of_nodes()):\n", " nodeSeq.append(RandomWalk(G, xi, 1000))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "h = plt.hist(nodeSeq, bins = G.number_of_nodes())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.bar(range(0,64), G.degree().values())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 27, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "returnTime = []\n", "for i in xrange(1000):\n", " returnTime.append(len(RandomWalk(G, 27, 0, True)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.boxplot(returnTime)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "{'boxes': [],\n", " 'caps': [,\n", " ],\n", " 'fliers': [,\n", " ],\n", " 'medians': [],\n", " 'whiskers': [,\n", " ]}" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 36 } ], "metadata": {} } ] }