Block Diagonal Stuff

BlockDiagonal.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "N = 3\n",
      "M = 2\n",
      "\n",
      "mats = [np.random.random((N, N)) for i in range(M)]\n",
      "\n",
      "X = np.zeros((N * M, N * M))\n",
      "for i in range(M):\n",
      "    X[i * N: (i + 1) * N, i * N: (i + 1) * N] = mats[i]\n",
      "    \n",
      "print(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.72861009  0.61886456  0.868937    0.          0.          0.        ]\n",
        " [ 0.58373219  0.05713773  0.54441987  0.          0.          0.        ]\n",
        " [ 0.92424286  0.52670066  0.41588838  0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.82193237  0.26313266  0.78248449]\n",
        " [ 0.          0.          0.          0.76988054  0.41347041  0.54500163]\n",
        " [ 0.          0.          0.          0.25286906  0.17003135  0.33396628]]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U, S, V = np.linalg.svd(X)\n",
      "print(U)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-0.68911493  0.         -0.42665971 -0.5857321   0.          0.        ]\n",
        " [-0.40573348  0.         -0.44254771  0.79970737  0.          0.        ]\n",
        " [-0.60041731  0.          0.78874141  0.1318561   0.          0.        ]\n",
        " [ 0.         -0.72157809  0.          0.         -0.61288965  0.3220114 ]\n",
        " [ 0.         -0.63518218  0.          0.          0.77109167  0.04428589]\n",
        " [ 0.         -0.27544267  0.          0.         -0.17258017 -0.94569943]]\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U[0, 1] == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for u,s,v in [np.linalg.svd(m) for m in mats]:\n",
      "    print u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-0.68911493 -0.42665971 -0.5857321 ]\n",
        " [-0.40573348 -0.44254771  0.79970737]\n",
        " [-0.60041731  0.78874141  0.1318561 ]]\n",
        "[[-0.72157809 -0.61288965  0.3220114 ]\n",
        " [-0.63518218  0.77109167  0.04428589]\n",
        " [-0.27544267 -0.17258017 -0.94569943]]\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
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   "metadata": {}
  }
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