dfroger/metis0.ipynb

## metis0.ipynb
{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Partitionnig a mesh using Metis"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook presents a function of Metis to partition a mesh, its input and output data structure."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We use standard scientific Python tool [NumPy](http://www.numpy.org/) and [Matplotlib](http://matplotlib.org/)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also use [pymetis](http://mathema.tician.de/software/pymetis/), a Python binding form [metis](http://mathema.tician.de/software/pymetis/), which we will use to partition the mesh."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymetis import part_graph"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are options for our futur plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def scale():\n",
      "    grid()\n",
      "    axis('scaled')\n",
      "    xlim(-0.5,3.5)\n",
      "    ylim(-0.5,2.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create $nx \\times ny$ regualary spaced nodes, and a function to plot them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nx, ny = 4,3\n",
      "x2d, y2d = meshgrid(range(nx),range(ny))\n",
      "x1d = x2d.flatten()\n",
      "y1d = y2d.flatten()\n",
      "def plot_nodes(marker=True, index=True):\n",
      "    if marker:\n",
      "       plot(x1d, y1d, 'ko')\n",
      "    if index:\n",
      "        for ipoint,(x,y) in enumerate(zip(x1d,y1d)):\n",
      "            text(x+0.1,y+0.1,'%i'%ipoint)\n",
      "plot_nodes()\n",
      "scale()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x45482d0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We connect nodes with triangles, and for each triangle store its 3 nodes indexes. In order to plot trianges with their indexes at centre, so compute triangle center.\n",
      "We plot the triangles and as an example, the nodes of the 7-th triangle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Store nodes of each triangles.\n",
      "triangle1 = ((0,4,1),(1,5,2),(2,6,3),(4,8,5),(5,9,6),(6,10,7))\n",
      "triangle2 = ((1,4,5),(2,5,6),(3,6,7),(5,8,9),(6,9,10),(7,10,11))\n",
      "triangle = array(triangle1 + triangle2)\n",
      "ntri = len(triangle)\n",
      "\n",
      "# Compute center of triangles.\n",
      "xcenter = empty( (ntri) )\n",
      "ycenter = empty( (ntri) )\n",
      "for itri,tri in enumerate(triangle):\n",
      "    xcenter[itri] = sum(x1d[tri]) / 3.\n",
      "    ycenter[itri] = sum(y1d[tri]) / 3.\n",
      "    \n",
      "# Plot all triangles.\n",
      "def plot_triangles(lines=True,index=True):\n",
      "    if lines:\n",
      "        triplot(x1d, y1d, triangle)\n",
      "    if index:\n",
      "        for itri,(x,y) in enumerate(zip(xcenter,ycenter)):\n",
      "            text(x,y,itri,color='red')\n",
      "\n",
      "# Plot one triangle nodes.\n",
      "def plot_triangle_nodes(itri):\n",
      "    for i in triangle[itri]:\n",
      "        plot(x1d[i], y1d[i], 'ko')\n",
      "\n",
      "plot_triangles()\n",
      "plot_nodes(marker=False,index=True)\n",
      "plot_triangle_nodes(7)\n",
      "scale()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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StDBav2t16hSQlgbcdZc7flq4EKip8fu6clAmSwSM4R1tTIw7V2xqch8fPuz+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\nyGQJgiB0hEyWIAhCR/4fuCFu0/kbyVkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x454e450>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For each triangle, we store the triangle(s) which share a segment with it. For example, triangle $7$ has triangles $1$, $2$ and $4$ as neighbours"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "adj1 = {0:[6],1:[6,7],2:[7,8],3:[6,9],4:[7,9,10],5:[8,10,11]}\n",
      "adj2 = {6:[0,1,3], 7:[1,2,4], 8:[2,5], 9:[3,4], 10:[4,5], 11:[5]}\n",
      "adj = dict( adj1.items() + adj2.items() )\n",
      "for tri, neighbours in adj.iteritems():\n",
      "    print \"tri %i has neighbours: %r\" % (tri,neighbours)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "tri 0 has neighbours: [6]\n",
        "tri 1 has neighbours: [6, 7]\n",
        "tri 2 has neighbours: [7, 8]\n",
        "tri 3 has neighbours: [6, 9]\n",
        "tri 4 has neighbours: [7, 9, 10]\n",
        "tri 5 has neighbours: [8, 10, 11]\n",
        "tri 6 has neighbours: [0, 1, 3]\n",
        "tri 7 has neighbours: [1, 2, 4]\n",
        "tri 8 has neighbours: [2, 5]\n",
        "tri 9 has neighbours: [3, 4]\n",
        "tri 10 has neighbours: [4, 5]\n",
        "tri 11 has neighbours: [5]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, we call the Metis functions that partion our mesh. It takes as first argument the number of partition we want, $3$ in our case, and as second argument the adjacency map we define above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "npart = 3\n",
      "cuts, part = part_graph(npart,adj)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It returns cuts and part.\n",
      "\n",
      "part is an array telling on which partition a triangle belong. For exemple, part[4] == 2, so triangle $4$ belongs to partition $2$.\n",
      "\n",
      "cuts is the number of connection beetween triangles (on segment) that are cutted by the partitions.\n",
      "\n",
      "Finally, we convert part from list to array."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print part\n",
      "print part[4]\n",
      "print cuts\n",
      "part = array(part)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0]\n",
        "2\n",
        "4\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We plot the triangles, and give them as color the partition number they belong to.\n",
      "\n",
      "We also print the triangle that belong to partition 0, 1 and 2."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tripcolor(x1d, y1d, triangle, facecolors=array(part), edgecolors='k', cmap=cm.Pastel1)\n",
      "plot_triangles(index=True)\n",
      "for ipart in range(npart):\n",
      "    print \"triangles of partition %i:\"%ipart, where(part==ipart)\n",
      "scale()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "triangles of partition 0: (array([ 2,  5,  8, 11]),)\n",
        "triangles of partition 1: (array([0, 1, 6, 7]),)\n",
        "triangles of partition 2: (array([ 3,  4,  9, 10]),)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LRivbP4bJ0MkqdbfHSPmPYVZ3sko97N3w/L2zpfvHMHayF0VFRWHDhg2YNGkS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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x49149d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that informations contained in the adjaceny map can also be stored in two arrays, in the CSR format. In this format, the 'adjncy' array contains in series the neighbours of triange $0$, then the neighbours of triange $1$, etc. The array 'xadj' is used to index the 'adjncy' array: use the i-th value of xadj to extract from adjncy the first neighbour of triangle i."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xadj = [0,1,3,5,7,10,13,16,19,21,23,25,26]\n",
      "adjncy = [6,6,7,7,8,6,9,7,9,10,8,10,11,0,1,3,1,2,4,2,5,3,4,4,5,5]\n",
      "\n",
      "itri = 7\n",
      "\n",
      "# Get neighbours from map.\n",
      "print adj[itri]\n",
      "\n",
      "# Get neighbours from CSR arrays.\n",
      "i0 = xadj[itri]\n",
      "i1 = xadj[itri+1]\n",
      "print adjncy[i0:i1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 2, 4]\n",
        "[1, 2, 4]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Instead of the map, the part_graph function can take these arrays as input:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cuts2, part2 = part_graph(npart, xadj=xadj, adjncy=adjncy)\n",
      "cuts2 == cuts\n",
      "all(part2 == part)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}