poly_stats.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:3532d8829b9210fcd270ee646bd548c8859a0f50f8140f4917fc7e0f3cd892a3"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 400
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy as sp\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.colors as colors\n",
      "import matplotlib.cm as cm\n",
      "\n",
      "import mpmath as mp\n",
      "mp.mp.dps = 100\n",
      "import polyhedra as poly\n",
      "import bga_4_0 as bga\n",
      "\n",
      "bga = reload(bga)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 401
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#poly_name = \"rhombicuboctahedron\"\n",
      "#poly_name = \"truncated_octahedron\"\n",
      "#poly_name = \"truncated_cuboctahedron\"\n",
      "#poly_name = \"rhombic_triacontahedron\"\n",
      "#poly_name = \"rhombic_dodecahedron\"\n",
      "\n",
      "#poly_name, PolyName = \"tetrahedron\", \"Tetrahedron\"\n",
      "#poly_name, PolyName = \"cube\", \"Cube\"\n",
      "#poly_name, PolyName = \"octahedron\", \"Octahedron\"\n",
      "#poly_name, PolyName = \"dodecahedron\", \"Dodecahedron\"\n",
      "#poly_name, PolyName = \"icosahedron\", \"Icosahedron\"\n",
      "\n",
      "#poly_name, PolyName = \"truncated_tetrahedron\", \"Truncated Tetrahedron\"\n",
      "#poly_name, PolyName = \"cuboctahedron\", \"Cuboctahedron\"\n",
      "#poly_name, PolyName = \"truncated_cube\", \"Truncated Cube\"\n",
      "#poly_name, PolyName = \"truncated_octahedron\", \"Truncated Octahedron\"\n",
      "\n",
      "#poly_name, PolyName = \"triakis_tetrahedron\", \"Triakis Tetrahedron\"\n",
      "#ERR#poly_name, PolyName = \"rhombic_dodecahedron\", \"Rhombic Dodecahedron\"\n",
      "#ERR#poly_name, PolyName = \"triakis_octahedron\", \"Triakis Octahedron\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 402
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "verts, face_inds, cents = getattr(poly, poly_name)()\n",
      "V, E, F, S, species, f_types, adj_list, dual = bga.get_poly(poly_name)\n",
      "ints, ids, paths, shell_int, shell_paths, edges, shell_edge, degens = bga.get_bg_ss(poly_name, get_degens=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 403
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import rc\n",
      "rc('font', **{'family':'serif','serif':['Palatino']})\n",
      "rc('text', usetex=True)\n",
      "\n",
      "fig_width = 10\n",
      "fig_height = 10\n",
      "fig_dpi = 200"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 404
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Rs = bga.generate_rotations(adj_list)\n",
      "print len(Rs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "24\n"
       ]
      }
     ],
     "prompt_number": 405
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#rs = bga.get_rs(ints, adj_list, Rs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 406
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Ss, Ts = bga.get_degeneracies(ints, edges, adj_list, Rs=Rs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 407
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#edge_adj, edge_adj_inds = bga.edge_adj_list(edges, inds=True)   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 408
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#shellings = bga.get_shellings(edges,ints,degens,shell_int,adj_list)\n",
      "#print shellings[-5:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 409
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#shellings[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 410
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def int_hist(data):\n",
      "    counts = np.zeros(int(data.max()) - int(data.min()) + 1)\n",
      "    for x in data:\n",
      "        counts[int(round(x))] += 1\n",
      "    return counts, data.min(), data.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 411
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dofs = np.zeros(len(ints))\n",
      "for k, int_num in enumerate(range(len(ints))):\n",
      "    dofs[k] = bga.DoF(ints[int_num], verts, face_inds)[0]\n",
      "\n",
      "dof_max = int(dofs.max())\n",
      "counts, dmin, dmax = int_hist(dofs)\n",
      "N = dmax - dmin + 1\n",
      "\n",
      "ind = np.arange(N)  # the x locations for the groups\n",
      "width = 0.65       # the width of the bars\n",
      "\n",
      "fig, ax = plt.subplots()\n",
      "rects1 = ax.bar(ind, counts, width)\n",
      "\n",
      "ax.set_ylabel('Number of Intermediates')\n",
      "ax.set_xlabel('Degrees of Freedom')\n",
      "ax.set_title(PolyName+' Degrees of Freedom Histogram')\n",
      "ax.set_xticks(ind+width*0.5)\n",
      "ax.set_xticklabels(range(dof_max+1))\n",
      "ax.set_xlim(dmin - 0.25, dmax+1)\n",
      "ax.set_ylim(0,1.2*counts.max())\n",
      "\n",
      "plt.savefig(poly_name+\"_dof_hist.eps\", dpi=fig_dpi, format='eps')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hVjKur+nie6lmWpqeUedrrzytrqNNvu4W871VhPXKU9ifr0cIefJWZb6Yr9Vt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\nWwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f495db9cc90>"
       ]
      }
     ],
     "prompt_number": 412
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = int(round(max(dofs)))\n",
      "N = len(ints[0,:])\n",
      "w = 0.8\n",
      "\n",
      "inds = np.arange(N+1)\n",
      "df_dist = np.zeros((M+1,N+1))\n",
      "\n",
      "for k,d in enumerate(dofs):\n",
      "    t = sum([1 for x in ints[k,:] if x != 0])\n",
      "    df_dist[d,t] += 1.0\n",
      "\n",
      "for j in range(N+1):\n",
      "    df_dist[:,j] /= sum(df_dist[:,j])\n",
      "\n",
      "fig = plt.figure(202)\n",
      "plt.clf()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "rects_total = np.zeros((N+1))\n",
      "for i in range(M+1):\n",
      "    colour = colors.rgb2hex(sp.rand(3))\n",
      "    rects = ax.bar(inds,df_dist[i,:],width=w,color=colour,bottom=rects_total)\n",
      "    rects_total += df_dist[i,:]\n",
      "\n",
      "ax.set_xlabel('Number of faces of intermediate')\n",
      "ax.set_ylabel('Distribution of degrees of freedom')\n",
      "ax.set_title('Degrees of freedom distribution by size of intermediate for the '+PolyName)\n",
      "ax.set_xticks(inds+w*.5)\n",
      "ax.set_xticklabels(inds)\n",
      "ax.set_xlim(-0.5*w,N+1.5*w)\n",
      "ax.set_ylim(0.0,1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 413,
       "text": [
        "(0.0, 1.0)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WYppGN2MKw093NHYi0pdcvI6Gk8FTxE+faWBj6PlC/6+ZfZha4B5MR5dd/vZR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f495cb276d0>"
       ]
      }
     ],
     "prompt_number": 413
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "M = int(round(max(dofs)))\n",
      "N = len(ints[0,:])\n",
      "w = 0.8\n",
      "\n",
      "inds = np.arange(N+1)\n",
      "df_dist = np.zeros((M+1,N+1))\n",
      "\n",
      "for k,d in enumerate(dofs):\n",
      "    t = sum([1 for x in ints[k,:] if x != 0])\n",
      "    df_dist[d,t] += 1.0\n",
      "\n",
      "for j in range(N+1):\n",
      "    df_dist[:,j] /= sum(df_dist[:,j])\n",
      "\n",
      "fig = plt.figure(202)\n",
      "plt.clf()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "for i in range(M+1):\n",
      "    colour = colors.rgb2hex(sp.rand(3))\n",
      "    rects = ax.plot(inds,df_dist[i,:],color=colour)\n",
      "\n",
      "ax.set_xlabel('Number of faces of intermediate')\n",
      "ax.set_ylabel('Proportion of intermediates')\n",
      "ax.set_title('Degrees of freedom distribution by size of intermediate for the '+poly_name)\n",
      "ax.set_xticks(inds)\n",
      "ax.set_xticklabels(inds)\n",
      "#ax.legend()\n",
      "#ax.set_xlim(-0.5*w,N+1.5*w)\n",
      "#ax.set_ylim(0.0,1.0)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = int(round(max(dofs)))\n",
      "N = len(ints[0,:])\n",
      "w = 0.8\n",
      "\n",
      "inds = np.arange(N+1)\n",
      "df_dist = np.zeros((M+1,N+1))\n",
      "\n",
      "for k,d in enumerate(dofs):\n",
      "    t = sum([1 for x in ints[k,:] if x != 0])\n",
      "    df_dist[d,t] += 1.0\n",
      "\n",
      "for j in range(N+1):\n",
      "    df_dist[:,j] /= sum(df_dist[:,j])\n",
      "\n",
      "amp = 1.0\n",
      "fig = plt.figure(num=None, figsize=(amp*fig_width, 0.4*fig_height), dpi=fig_dpi, facecolor='w', edgecolor='k')\n",
      "plt.clf()\n",
      "ax = fig.add_subplot(111)\n",
      "\n",
      "plt.tick_params(\n",
      "    axis='both',          # changes apply to the x-axis\n",
      "    which='both',      # both major and minor ticks are affected\n",
      "    bottom='off',      # ticks along the bottom edge are off\n",
      "    top='off',         # ticks along the top edge are off\n",
      "    left='off',\n",
      "    right='off')\n",
      "\n",
      "#grd = ax.imshow(df_dist, cmap=cm.gist_earth, interpolation='nearest')\n",
      "grd = ax.imshow(df_dist, cmap=cm.bone_r, interpolation='nearest')\n",
      "plt.colorbar(grd)\n",
      "ax.set_xlabel('Faces in Intermediate')\n",
      "ax.set_ylabel('Degrees of Freedom Proportion')\n",
      "ax.set_title(PolyName + ' Degrees of Freedom Histograms by Face Count')\n",
      "ax.set_xticks(inds)\n",
      "ax.set_xticklabels(inds)\n",
      "#ax.set_xlim(-0.5*w,N+1.5*w)\n",
      "#ax.set_ylim(0.0,1.0)\n",
      "\n",
      "\n",
      "plt.savefig(poly_name+\"_dof_hist_facecount.eps\", dpi=fig_dpi, format='eps')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lRDB326dYLMLj8WBhYQFTU1Nt3ZCCIKBSqaDRaODmzZtD9+uWArgNgsGgdn9q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\nPUF94NajAE4I6QkK4NajAE6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       "text": [
        "<matplotlib.figure.Figure at 0x7f495cc25490>"
       ]
      }
     ],
     "prompt_number": 414
    }
   ],
   "metadata": {}
  }
 ]
}