docs/examples/parallel/rmt/rmt.ipynb

{
    "nbformat": 2, 
    "metadata": {
        "name": "rmt"
    }, 
    "worksheets": [
        {
            "cells": [
                {
                    "source": "# Eigenvalue distribution of Gaussian orthogonal random matrices", 
                    "cell_type": "markdown"
                }, 
                {
                    "source": "The eigenvalues of random matrices obey certain statistical laws. Here we construct random matrices \nfrom the Gaussian Orthogonal Ensemble (GOE), find their eigenvalues and then investigate the nearest\nneighbor eigenvalue distribution $\\rho(s)$.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": false, 
                    "prompt_number": 1, 
                    "input": "from rmtkernel import ensemble_diffs, normalize_diffs, GOE\nimport numpy as np\nfrom IPython.parallel import Client"
                }, 
                {
                    "source": "## Wigner's nearest neighbor eigenvalue distribution", 
                    "cell_type": "markdown"
                }, 
                {
                    "source": "The Wigner distribution gives the theoretical result for the nearest neighbor eigenvalue distribution\nfor the GOE:\n\n$$\\rho(s) = \\frac{\\pi s}{2} \\exp(-\\pi s^2/4)$$", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 2, 
                    "input": "def wigner_dist(s):\n    \"\"\"Returns (s, rho(s)) for the Wigner GOE distribution.\"\"\"\n    return (np.pi*s/2.0) * np.exp(-np.pi*s**2/4.)"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 3, 
                    "input": "def generate_wigner_data():\n    s = np.linspace(0.0,4.0,400)\n    rhos = wigner_dist(s)\n    return s, rhos"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": false, 
                    "prompt_number": 4, 
                    "input": "s, rhos = generate_wigner_data()"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 17, 
                            "text": "<matplotlib.text.Text at 0x3828790>"
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": 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oUeqcDCkYQljOrILx8ssvs2DBAlq1asWMGTOIc/Kps1Iwai83N5gxQ33KcIGH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\nSUVORK5CYII=\n"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 17, 
                    "input": "plot(s, rhos)\nxlabel('Normalized level spacing s')\nylabel('Probability $\\rho(s)$')"
                }, 
                {
                    "source": "## Serial calculation of nearest neighbor eigenvalue distribution", 
                    "cell_type": "markdown"
                }, 
                {
                    "source": "In this section we numerically construct and diagonalize a large number of GOE random matrices\nand compute the nerest neighbor eigenvalue distribution. This comptation is done on a single core.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 6, 
                    "input": "def serial_diffs(num, N):\n    \"\"\"Compute the nearest neighbor distribution for num NxX matrices.\"\"\"\n    diffs = ensemble_diffs(num, N)\n    normalized_diffs = normalize_diffs(diffs)\n    return normalized_diffs"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 7, 
                    "input": "serial_nmats = 1000\nserial_matsize = 50"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "stream", 
                            "text": "1 loops, best of 1: 1.19 s per loop"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 8, 
                    "input": "%timeit -r1 -n1 serial_diffs(serial_nmats, serial_matsize)"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": false, 
                    "prompt_number": 9, 
                    "input": "serial_diffs = serial_diffs(serial_nmats, serial_matsize)"
                }, 
                {
                    "source": "The numerical computation agrees with the predictions of Wigner, but it would be nice to get more\nstatistics. For that we will do a parallel computation.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 10, 
                            "text": "<matplotlib.text.Text at 0x3475bd0>"
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": 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CWKxqWTAyczM5EH8Af2d/raMIU0lpDXtfhSeeB12+1mmEsEjVsmDsu7SPjk06\n0uCBBlpHEaZ04GWokQFdV2qdRAiLVC0LhoxfVFPKFn74AvzngcMZrdMIYXGqZcGQ8YtqLKk9RL4B\nT00omPRWCGGwalcwku4kcSb5DL4P+WodRWglegbk14DuWgcRwrJUu4KxO243vVr1oqZtTa2jCK0o\nG9j8OfSCEwkntE4jhMWodgUj8mIk/q39tY4htHbTBX6xocM/O6Cz1aHTFX/Y2ztonVIIs1LtCkbE\nxQj6tO6jdQxhDg7mQ2Z/6Pl/FNzBr+gjLe2mpvGEMDfVqmAkZyRz4eYFOjfvrHUUYS42fwrdFhfc\n2lUIcV/VqmDsvbSXbg91w87WTusowlyktoSd78Ow8WCbrXUaIcxatSoYERcj8Gvtp3UMYW6OToCU\nltDnba2TCGHWqlXBiLwYKeMXogQ62PIxdFkNrSO1DiOE2ao2BSM1K5WTCSfxedBH6yjCHN1uDj98\nDsPHQt0bWqcRwixVm4Kx//J+Hm3xKLVq1NI6ijBXZwcVHJ4a/j+gy9M6jRBmp9oUjIiLEfg5+2Fv\n71DiOff3PkQ1tnt+wWy2fm9pnUQIs6NJwYiMjMTNzY127dqxbNmyYsvXrl2Lp6cnnp6ejB07ltOn\nT1d8mxcj6dOqz91z64ufc1/0IaotZQub1kHnT+BhrcMIYV40KRgzZ84kJCSEsLAwVqxYQWJiYpHl\nLi4uREZG8uuvvxIQEMDbb1fs7JU7OXf49fqvdG8pkwcJA9xuBt+thacgPjVe6zRCmA2TF4yUlBQA\n+vTpQ+vWrRkwYADR0dFF2nTv3p0GDQruVREYGEhERESFthkVH0Wnpp2oY1enQusR1UicP8TY0HJW\ny1KnDpHpQ0R1Y/KCERsbi6urq/65u7s7UVFRpbb/+OOPGTp0aIW2WTh+IYRR9uZD1iDoG0xphy9l\n+hBRndTQOsD9hIWFsWbNGvbv319qm3nz5ul/9vf3x9/fv1ibyIuRzO4xuwoSCqumgO++gqDOcKkX\n/PGk1omEKJfw8HDCw8MrvB6dUsqko7wpKSn4+/tz5MgRAKZPn87AgQMJDAws0u63337j6aefZtu2\nbbRt27bEdel0OsqKn5WbheMHjlx5+Qr2tezvngVV1kcuq01lrMOctmNOWczwMz8YDWOHwn92wg3P\nYm1M/CckRIUZ8t1ZEpMfkiocm4iMjCQuLo6dO3fi61v0ZkaXLl1i+PDhrF27ttRiYaiYKzG4Orpi\nX8u+QusbXyY1AAAWJ0lEQVQR1dgVX/hpeUHRqH9F6zRCaEaTQ1KLFy8mKCiInJwcZsyYgaOjIyEh\nIQAEBQXx1ltvkZyczNSpUwGws7MjJiamXNuS6UBEpTg+Ehqdh7FD4PNIyK6vdSIhTM7kh6QqkyG7\nVQO+GsA0n2k80f4J/Xss57CJGR6esZrtlCeLgqEvQP2r8M3mgtu8yiEpYYEs5pCUKeXk5RAVH0Wv\nVr20jiKsgg62rgSbXBg4E7nIU1Q3Vl0wDl87TJtGbXCoLefKi0qSbwcbNxTMatt9kdZphDApsz6t\ntqJk/EJUiawGsG4rTO4BchmGqEaseg9DbpgkqkxKK/h6MwyFA5cPaJ1GCJOw2oKRl5/Hvsv76N2q\nt9ZRhLW61gW+hye/eZLo+Oiy2wth4ay2YPx24zea1WtG03pNtY4irNlZ+PzJzxn69VBirpTv1G8h\nLIXVFgwZvxCmEvhIIJ89+RlDvx5K7JVYreMIUWWstmDI+IUwpSGPDOHTJz5lyNdDpGgIq2VVF+7Z\n2zv8d/bQfwAhQGpJ77SUi8vM+SI2S99O5WW597/BLX9sYfKPk9k6ditdH+xaxnuF0IZcuAf/vZue\n0zHIcoFUuZueMK2h7YfyyROfMOTrIRy8elDrOEJUKuu8DqN1JFyU8QuhjSfaP4FSisB1gWx8ZqOM\npQmrYVV7GHrOEXBRxi+Edp50fZI1w9YwYsMI1vy2Rus4QlQKKywYClpHQJwUDKGt/g/3Z/f43by5\n+03mhc+TSQqFxbO+guFwtmAW0VvOWicRgg5NOhA1OYqfz/7MuB/GkZWbpXUkIcrNqs6S0ul00Hk1\nOIfDd6UdBrCkM3ks74why9lO5WUp60/I3t6BtMybMAyoC3wDZPx3ef36jUhNTS5jO0JUHjlLqpAM\neAszk5Z2E3IUbMyDy6/C822h8R8UnrmnPxVcCDNnhQVDxi+EmVI2EPYu7HsVJvWCDhu0TiSEUazr\ntNoGQI0sSHpE6yRClO7w83DdC4aPhbbb4GetAwlhGOvaw3Dm7uEoncZBRPVRA51Od99Hia4+CiGH\nQekgCLnIT1gE6yoYrZHxC2FiuRSfTcDA2QWy68GPn8IvMHjtYN7f9z75Kr/qIwtRTtZXMGT8Qlia\n4xA7JZYtp7cw4KsBXEm9onUiIUpkNQXjatpVqA0kdNA6ihBGa92wNbvH78avtR+eH3ny7/3/Jicv\nR+tYQhRhNQUj8mIkXKLgTBQhLFANmxq86fcm+yfvJ+x8GJ4febLr/C6tYwmhZzXfrpEXI+Gi1imE\nqLhHGj/Cz//zMwv6LmDyj5MZuXEkl1Muax1LCOspGBEXIyBO6xRCVA6dTsdTrk9x4sUTuDm54RXi\nxYI9C8jIySj7zUJUEasoGAnpCcSnxsMNrZMIUbnq2NVhvv98YqfEEns1loeXPszC/QtJz07XOpqo\nhqyiYOy5tIeeLXuCnJEorJRLIxe+H/U9P/3PT0RdicJlqQsL9iwgNavEW0oKUSWsomDI/buFZSv7\n4j97ewcAvJp5sfGZjewev5uTiSdxWeLC3PC5JGfI5IWi6llFwYi8GCl3NRMWrOyL//46QaG7kztf\nDfuKqOejuJJ6hYeXPsykzZPYd2mf3HdDVBmLn948+U4yrRa3Iml2ErVq1MKcpr22nO2YUxb5zKW1\nud+f6vXb1/nPr//h0yOfYqOzYZLXJMZ5jqNpvaZlrFdUR9V2evN9l/fh+6AvNW1rah1FCM00q9eM\n2T1nc+rFU6weupoTiSdov7w9w9YPI/R0KLn5uVpHFFbA4vcwgncEY1/Tnjf93rw70Zv5/IvQcrZj\nTlnkM5fWxtg/1bSsNNYfX8+nRz7lTNIZAtoGENgukIFtB+JQ28GodQnrUt49DIsvGD6rfXi/3/v4\nOftJwbCKLPKZS2tTkT/V+NR4fjrzE1vPbCU8LpxOTTsR2C6QwHaBeDTxKH1WXWGVqm3BqPtOXRJn\nJ/JAjQekYFhFFvnMJbOjYHC8dIbe6jUzN5PwuHC2ntnK1tNbyVN5DGw7kO4Pdcf3QV/aO7bHRmfx\nR6vFfVTbgtH7s95ETozUPzefP3BL2o45ZZHPXJE2xv45K6U4lXiKHed2EH0lmpgrMSTeSeTRFo/i\n86APPg/64PugL83rNzdqvcK8lbdgWPwd9/yc/bSOIITF0ul0uDm54ebkpn8t8U4isVdiib4SzceH\nPub5H5+ntl1tfB70wc3RjbYObWnn0I52jdvhVMdJDmdVI5rsYURGRhIUFERubi4zZsxg+vTpxdq8\n9tprrF+/nkaNGrF27VpcXV2LtdHpdOw4u4P+D/fXPzfPfxGGA/4m2E5F2+ym5JymzGItexjh/Lcv\nzXcPIzw8HH9///u2UUpx/uZ5Yq/G8kfiH5y9eZYzSWc4m3yWnPwc2jq0/W8RcWinf+5U16nSDm0Z\nktMcWEpOi9rDmDlzJiEhIbRu3ZqAgADGjBmDo6OjfnlMTAx79uzh4MGDbN++neDgYEJDQ0tcV4+W\nPUwVuwLCKf2L2JyEYxk5LUE4ltCXhnzB6XQ6HnZ4mIcdHi627GbGTc4kFxSPM0lnCLsQxqqDqzh3\n8xy3Mm/RuHZjmtRtQpO6TWhar2nBz3Xu+blwWd2m1LarXaGc5sBScpaXyQtGSkoKAH36FFyZPWDA\nAKKjowkMDNS3iY6OZsSIETg4ODBmzBjeeOONUtdXt2bdqg0shMWoYcDhITug6I2Z5s+ff9/lhqzj\nr+rXb8Sdm3dIvJPIn+l/6h830m/wZ/qfnEk+o//5z/Q/uXH7Bjqdjno161HXri51a9bV/1yvZj0u\nnLzAlS1X9M8L/3/2rDlkpt6B7LuRcimYU+6eR93a9hz77Vdq2NQo9WGrs5VDawYwecGIjY0tcnjJ\n3d2dqKioIgUjJiaG5557Tv/cycmJc+fO8fDDxf+FI4QoVDjFyP389dDWvLuP0pYbso7i0tJ02Nna\n0bx+c4MGzJVSZORmkJ6dTnpOOrezb5Oefff/c9L5z57/4NPCR78sNTuVq7evktnkDjw4EmreLnjY\nZoNNbpFHus0pHvvyMXLycsjNzy3xkafysNXZFikidrZ2pRaYwkNtOgqKjE6nQ4eOa4euseXjLfpl\nhUXor+0Kf9ayXXmY5aC3UqrY8bXSPmTx1w3pjMpoY+w65hvQpjK2U5E28yk9pymzmPIzV2WW+Qa0\nqYztVLTNX3/nlbOdyv4X+6ZVm0pZsqHM98YZcLOcvLv/yyLLuGB/cT30eoXeb85MXjC6du3KP/7x\nD/3z48ePM3DgwCJtfH19OXHiBAEBAQAkJCTg4uJSbF0WfEawEEJYHJNfndOgQQOg4EypuLg4du7c\nia+vb5E2vr6+bNq0iaSkJNatW4ebm1tJqxJCCGFCmhySWrx4MUFBQeTk5DBjxgwcHR0JCQkBICgo\nCB8fH3r16sWjjz6Kg4MDa9as0SKmEEKIeykzFxERoVxdXVXbtm3V0qVLS2wzZ84c1aZNG9W5c2d1\n8uRJEycsUFbO3bt3K3t7e+Xl5aW8vLzU22+/bfKMEydOVE2aNFEeHh6ltjGHviwrpzn0pVJKXbp0\nSfn7+yt3d3fl5+en1q5dW2I7rfvUkJxa92lGRoby8fFRnp6eytfXV3344YclttO6Lw3JqXVf3is3\nN1d5eXmpIUOGlLjc2P40+4Lh5eWlIiIiVFxcnGrfvr1KSEgosjw6Olr17NlTJSUlqXXr1qnAwECz\nzLl79241dOhQTbIVioyMVIcPHy71i9hc+rKsnObQl0opde3aNXXkyBGllFIJCQmqTZs2KjU1tUgb\nc+hTQ3KaQ5+mp6crpZTKzMxUHTp0UGfOnCmy3Bz6Uqmyc5pDXxZauHChGjt2bIl5ytOfZj3D2L3X\nbLRu3Vp/zca9/nrNxsmTJ80yJ2g/SN+7d28aNWpU6nJz6EsoOydo35cAzZo1w8vLCwBHR0c6dOjA\nwYMHi7Qxhz41JCdo36d16tQB4Pbt2+Tm5lKrVq0iy82hL6HsnKB9XwLEx8fz008/8fzzz5eYpzz9\nadYFo7RrNu4VExODu7u7/nnhNRumZEhOnU7H/v378fLy4uWXXzZ5RkOYQ18awhz78uzZsxw/fhwf\nH58ir5tbn5aW0xz6ND8/H09PT5o2bcq0adNo2bJlkeXm0pdl5TSHvgSYNWsWH3zwATY2JX/Nl6c/\nzbpgGEIZcc2Gljp37szly5eJjY3F3d2dmTNnah2pGOnL8klLS2PUqFEsWrSIunWLzjxgTn16v5zm\n0Kc2Njb8+uuvnD17lpUrV3LkyJEiy82lL8vKaQ59GRoaSpMmTfD29i51b6c8/WnWBaNr166cOnVK\n//z48eN069atSJvCazYKlXbNRlUyJGf9+vWpU6cOdnZ2TJ48mdjYWLKyKnaBUGUzh740hDn1ZU5O\nDsOHD+e5557jySefLLbcXPq0rJzm1KfOzs4MHjy42GFdc+nLQqXlNIe+3L9/Pz/++CNt2rRhzJgx\n/PLLL4wbN65Im/L0p1kXDEu5ZsOQnDdu3NBX8y1bttCpU6cSj31qyRz60hDm0pdKKSZPnoyHhwcv\nvfRSiW3MoU8Nyal1nyYmJnLr1i0AkpKS2LFjR7HCZg59aUhOrfsSYMGCBVy+fJkLFy7wzTff8Pjj\nj/Of//ynSJvy9KdZTg1yL0u5ZqOsnN9++y2rVq2iRo0adOrUiYULF5o845gxY4iIiCAxMZGWLVsy\nf/58cnJy9BnNpS/LymkOfQmwb98+1qxZQ6dOnfD29gYK/lAvXbqkz2oOfWpITq379Nq1a4wfP568\nvDyaNWtGcHAwzZs3N7u/dUNyat2XJSk81FTR/rToO+4JIYQwHbM+JCWEEMJ8SMEQQghhECkYQggh\nDCIFQwghhEGkYIhKZWNjQ3BwsP75v//977/cArTq+fv7c/jwYQACAwNJTU2t0PrCw8MZOnSowa9X\nxbaq0tWrV3nmmWdMuk1hmaRgiEpVs2ZNvv/+e5KSkgDjr8TNy8urcIZ7t7l161bs7e0rvE5r1qJF\nCzZu3Kh1DGEBpGCISmVnZ8cLL7zAokWLii27evUqM2fOxNPTk1mzZnHjxg0AJkyYwMsvv4yvry+v\nvvoqEydO5JVXXsHHx4f27dtz5MgRXnjhBTp06MC8efP06/v73/9O165d6dGjB6tXry4xj7OzM0lJ\nSXz00Ud4e3vj7e1NmzZtePzxx4GCecDGjRuHr68vc+bM0V+RGxsbS9++ffH29mb79u1lfu6MjAw+\n/PBD/Pz8CAwMJDw8HIDu3bsXuZq2cO8nMzOzxPaluXz5MoMGDcLLywtPT0/OnTtHXFwc7u7uTJ48\nGTc3N+bPn6/P//bbb+Pj40PXrl1ZsGBBkfW88soreHt706VLFy5cuEBcXBwdO3YE4IsvvmD06NEM\nHjwYDw8Pli5dqn/vtm3b6N69Oz4+Prz00ktMnz69WM6jR4/St29fvLy86Ny5M7dv3y6z74QFqcjU\nuUL8Vb169VRqaqpydnZWKSkp6t///reaN2+eUkqpWbNmqffff18ppdSCBQvU7NmzlVJKjR8/Xvn5\n+emn3J4wYYIaNGiQysrKUl988YWqV6+eCg8PV1lZWcrNzU0/dXxycrJSSqmsrCzl6+urbt++rZRS\nyt/fXx06dEgppZSzs7NKSkrS58vJyVG9e/dWoaGh+ra3bt1SSik1e/Zs9c033yillOrUqZOKjo5W\nt2/fVgMHDixxeujdu3fr7zPw+eefqyVLliillLp+/bry8fFRSim1aNEiNXfuXKWUUlevXlXt27e/\nb/t713mvuXPnqk8++UT/GTIyMtSFCxeUTqdT3333ncrMzFRPP/20+vbbb4v0TW5urho6dKg6deqU\nvq9XrFih77c7d+6oCxcu6KeS//zzz1WTJk3U1atXVWpqqnrooYdUdna2ysnJUc7OzurChQsqKSlJ\nde7cWU2fPr1YzvHjx6uwsDClVME04Lm5ucXaCMslexii0tWvX59x48YV+dcpwM8//8ykSZMAmDx5\nMlu2bAEKDiGNGDGC+vXr69uOGDGCmjVr0r17dxo2bIifnx81a9bE29tbPxPwzp07CQwMxNvbm/Pn\nz/PLL7+UmW3GjBn07duXwMBADh06xLFjx/D398fb25vQ0FAiIyO5cuUKSil8fHyoW7cuo0aNKnO6\n6k2bNrF69Wq8vb0ZOHAgN27c4MKFC4wcOZJvv/0WgA0bNujHCkpqf/78+VLX37VrVxYvXsx7771H\ncnIyDzzwAFAwLc2wYcOoVasWY8aMYdu2bQAcPHiQ4cOH06lTJw4fPsyOHTvIzs5m9+7dTJkyBSg4\nfFi7du1i2xowYADNmzenfv36uLu7c/jwYaKioujYsSPOzs44ODjwxBNPlNgn3bt3Z86cOSxfvpzc\n3FxsbW3L/J0Iy2H2U4MIy/TSSy/RuXNnJk6cWOT10r54mzdvXuR54fxcNWvWpGHDhvrXa9asSXZ2\nNmlpacyZM4c9e/bw4IMPMmzYMG7evHnfTF988QWXL19m5cqVQME01R4eHuzevbtIu/j4eMM+5D3y\n8/NZsWIFffr0KbascePG/P7772zYsEE/NUNp7Qun6/irwMBAunTpwpo1a+jZsycbN24s0i+FCsdv\npk+fzrfffouHhwezZs3i5s2b6HS6Emco/au/9ndmZiY1atQoMjZU2jqCgoLo37+/fiqS6OhomjZt\net/tCcshexiiSjRq1IiRI0fy6aef6r9oBg8ezJdffkl+fj6fffYZTzzxRLnWrZTi1q1b2NnZ0axZ\nM06fPs2uXbvu+55Dhw6xcOFCvvrqK/1rXbt25caNG/o9lvT0dM6cOcNDDz2Era0tsbGxpKens2HD\nhjIzjR07lpCQENLS0gCKTHk9atQo3nvvPVJTU/Hw8CizfUkuXLign7uob9+++nGRlJQUfvjhB7Ky\nsli/fj0DBw4kMzOTtLQ0nJ2duXLlCps3bwYKxpcee+wxVq9ejVKKrKwsMjIyyvxsOp2Obt268fvv\nvxMXF0dycjKhoaElntBw7tw5XFxc+N///V9cXV3N4l4lovJIwRCV6t4vkVdeeYXExET98+DgYC5d\nuoS3tzc3btzg5ZdfLvF9f31e0rKWLVsyfPhwPDw8mDZtWqmnohb+q3rFihXcvHmTxx57DG9vb154\n4QUAvvrqK1atWkWnTp3o0aMHf/zxBwAff/wxr732Gr169cLT07PEL0edTqd/fcSIEfj4+BAQEICH\nhwdz587VtxsxYgTr169n5MiRRV4rqf2967zXhg0b8PDwoGvXrty5c0e/LldXV3788Ue8vLzw8PAg\nMDCQBx54gDlz5uDj48OoUaMYPHiwfj3vvPMOZ8+exdPTk549e+pPPCjcZmnbt7W1Zfny5YwaNYqB\nAwfSsWNH2rRpU6zdkiVL6NixIz4+Pri6utKjR48Sfy/CMsnkg0JYqLi4OIYOHcrvv/9uku2lp6dT\nt25dUlJSGDJkCJ988gnt27c3ybaFeZAxDCEsmCnvODdv3jzCwsKws7Pj2WeflWJRDckehhBCCIPI\nGIYQQgiDSMEQQghhECkYQgghDCIFQwghhEGkYAghhDCIFAwhhBAG+X8LAxP1Be5fBAAAAABJRU5E\nrkJggg==\n"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 10, 
                    "input": "hist_data = hist(serial_diffs, bins=30, normed=True)\nplot(s, rhos)\nxlabel('Normalized level spacing s')\nylabel('Probability $P(s)$')"
                }, 
                {
                    "source": "## Parallel calculation of nearest neighbor eigenvalue distribution", 
                    "cell_type": "markdown"
                }, 
                {
                    "source": "Here we perform a parallel computation, where each process constructs and diagonalizes a subset of\nthe overall set of random matrices.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 11, 
                    "input": "def parallel_diffs(rc, num, N):\n    nengines = len(rc.targets)\n    num_per_engine = num/nengines\n    print \"Running with\", num_per_engine, \"per engine.\"\n    ar = rc.apply_async(ensemble_diffs, num_per_engine, N)\n    diffs = np.array(ar.get()).flatten()\n    normalized_diffs = normalize_diffs(diffs)\n    return normalized_diffs"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 12, 
                    "input": "client = Client()\nview = client[:]\nview.run('rmtkernel.py')\nview.block = False"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 13, 
                    "input": "parallel_nmats = 40*serial_nmats\nparallel_matsize = 50"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "stream", 
                            "text": "Running with 10000 per engine.\n1 loops, best of 1: 14 s per loop"
                        }, 
                        {
                            "output_type": "stream"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 14, 
                    "input": "%timeit -r1 -n1 parallel_diffs(view, parallel_nmats, parallel_matsize)"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "stream", 
                            "text": "Running with 10000 per engine."
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 15, 
                    "input": "pdiffs = parallel_diffs(view, parallel_nmats, parallel_matsize)"
                }, 
                {
                    "source": "Again, the agreement with the Wigner distribution is excellent, but now we have better\nstatistics.", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 16, 
                            "text": "<matplotlib.text.Text at 0x376c950>"
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": 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EVW18Ex4dCOqcsCeEU7BoD+Py5cu0bdvW+LxNmzZcvnzZ6qFszXDKIFd3O7oL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\nYgzjDehT9fgt8mPlwZWy+q2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P8+bNGTZsWJnbJDw8nJkzZ/Lee+9RUFBAnTp1Kv2ZCMdh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\n"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 16, 
                    "input": "hist_data = hist(pdiffs, bins=30, normed=True)\nplot(s, rhos)\nxlabel('Normalized level spacing s')\nylabel('Probability $P(s)$')"
                }
            ]
        }
    ]
}