ASTRO_585_Lab_4_R_Morehead.ipynb

{
 "metadata": {
  "language": "Julia",
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Lab 4 Feb 7, 2014 \n",
      "#Robert Morehead"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##1a.\n",
      "Let's use Eric's code and the crummy code written by the clearly untalented student. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "include(\"CLASS_REPO/Astro585/lab4/HW4_leapfrog.jl\")\n",
      "include(\"CLASS_REPO/Astro585/lab4/HW4_leapfrog_student.jl\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "test_leapfrog_student (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##1b.\n",
      "I suspect the memory re-allocation for the log array due to the vcat() calls each loop is what made this so terrible. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##1c."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Profile.clear()\n",
      "for i in 0:50\n",
      "    @profile orbit = integrate_leapfrog!([1.0,0.0,00.0,1.0],2pi/200,6pi);\n",
      "    #println(\"X:\",orbit[1][end],\" Y:\",orbit[2][end],\" Vx:\",orbit[3][end],\" Vy:\",orbit[4][end])\n",
      "end\n",
      "Profile.print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: the profile data buffer is full; profiling probably terminated\n",
        "before your program finished. To profile for longer runs, call Profile.init()\n",
        "with a larger buffer and/or larger delay."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1     ...rc/execute_request.jl; execute_request_0x535c5df2; line: 132\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  1 loading.jl; include_string; line: 83\n",
        "      1 no file; anonymous; line: 14\n",
        "       1 ...lab4/HW4_leapfrog.jl; integrate_leapfrog!; line: 95\n",
        "        1 deepcopy.jl; deepcopy_internal; line: 45\n",
        "24    .../lab4/HW4_leapfrog.jl; advance_leapfrog!; line: 46\n",
        "45    .../lab4/HW4_leapfrog.jl; update_derivs_pos!; line: 6\n",
        "60    .../lab4/HW4_leapfrog.jl; update_derivs_vel!; line: 18\n",
        "21    abstractarray.jl; checkbounds; line: 63\n",
        "27    abstractarray.jl; checkbounds; line: 74\n",
        "12    abstractarray.jl; checkbounds; line: 95\n",
        "226   abstractarray.jl; trailingsize; line: 54\n",
        "9     array.jl; copy!; line: 48\n",
        "26    array.jl; getindex; line: 342\n",
        "13    array.jl; setindex!; line: 453\n",
        "25    array.jl; unsafe_copy!; line: 31\n",
        "11    array.jl; unsafe_copy!; line: 38\n",
        "24    deepcopy.jl; _deepcopy_array_t; line: 52\n",
        "68    deepcopy.jl; deepcopy_internal; line: 45\n",
        "16    int.jl; <; line: 228\n",
        "12    operators.jl; >; line: 19\n",
        "21    range.jl; Range1; line: 27\n",
        "131   range.jl; colon; line: 38\n",
        "12    range.jl; maximum; line: 101\n",
        "5     range.jl; minimum; line: 100\n",
        "7     reflection.jl; isbits; line: 36\n",
        "    43235 multi.jl; anonymous; line: 1308\n",
        "      43235 ...Julia/src/IJulia.jl; eventloop; line: 92\n",
        "       43235 ...Julia/src/IJulia.jl; eventloop; line: 68\n",
        "          43235 ...xecute_request.jl; execute_request_0x535c5df2; line: 132\n",
        "            43235 loading.jl; include_string; line: 83\n",
        "                6     no file; anonymous; line: 10\n",
        "                43229 no file; anonymous; line: 14\n",
        "                 5     ...HW4_leapfrog.jl; integrate_leapfrog!; line: 67\n",
        "                 8     ...HW4_leapfrog.jl; integrate_leapfrog!; line: 70\n",
        "                 12    ...HW4_leapfrog.jl; integrate_leapfrog!; line: 73\n",
        "                 1     ...HW4_leapfrog.jl; integrate_leapfrog!; line: 74\n",
        "                  1 .../HW4_leapfrog.jl; update_derivs!; line: 36\n",
        "                 75    ...HW4_leapfrog.jl; integrate_leapfrog!; line: 78\n",
        "                  4  deepcopy.jl; deepcopy_internal; line: 46\n",
        "                   2 deepcopy.jl; _deepcopy_array_t; line: 52\n",
        "                   2 deepcopy.jl; _deepcopy_array_t; line: 53\n",
        "                    2 array.jl; copy!; line: 51\n",
        "                     2 array.jl; unsafe_copy!; line: 38\n",
        "                      2 array.jl; unsafe_copy!; line: 31\n",
        "                    27 array.jl; setindex!; line: 465\n",
        "                 8     ...HW4_leapfrog.jl; integrate_leapfrog!; line: 82\n",
        "                 17    ...HW4_leapfrog.jl; integrate_leapfrog!; line: 84\n",
        "                 21591 ...HW4_leapfrog.jl; integrate_leapfrog!; line: 87\n",
        "                       183  ...4_leapfrog.jl; advance_leapfrog!; line: 46\n",
        "                       58   ...4_leapfrog.jl; advance_leapfrog!; line: 49\n",
        "                       3987 ...4_leapfrog.jl; advance_leapfrog!; line: 51\n",
        "                        132  range.jl; colon; line: 38\n",
        "                         61 range.jl; Range1; line: 27\n",
        "                         50 range.jl; Range1; line: 28\n",
        "                       877  ...4_leapfrog.jl; advance_leapfrog!; line: 52\n",
        "                        119 ...4_leapfrog.jl; update_derivs_vel!; line: 18\n",
        "                        11  ...4_leapfrog.jl; update_derivs_vel!; line: 19\n",
        "                        99  ...4_leapfrog.jl; update_derivs_vel!; line: 21\n",
        "                        3   ...4_leapfrog.jl; update_derivs_vel!; line: 22\n",
        "                        19  ...4_leapfrog.jl; update_derivs_vel!; line: 23\n",
        "                        111 ...4_leapfrog.jl; update_derivs_vel!; line: 24\n",
        "                        79  ...4_leapfrog.jl; update_derivs_vel!; line: 25\n",
        "                        105 ...4_leapfrog.jl; update_derivs_vel!; line: 26\n",
        "                        77  ...4_leapfrog.jl; update_derivs_vel!; line: 27\n",
        "                        65  ...4_leapfrog.jl; update_derivs_vel!; line: 28\n",
        "                        60  ...4_leapfrog.jl; update_derivs_vel!; line: 29\n",
        "                        1   ...4_leapfrog.jl; update_derivs_vel!; line: 30\n",
        "                       3181 ...4_leapfrog.jl; advance_leapfrog!; line: 53\n",
        "                        43   range.jl; colon; line: 38\n",
        "                         37 range.jl; Range1; line: 27\n",
        "                       313  ...4_leapfrog.jl; advance_leapfrog!; line: 54\n",
        "                        202 ...4_leapfrog.jl; update_derivs_pos!; line: 6\n",
        "                        1   ...4_leapfrog.jl; update_derivs_pos!; line: 7\n",
        "                        101 ...4_leapfrog.jl; update_derivs_pos!; line: 8\n",
        "                        3   ...4_leapfrog.jl; update_derivs_pos!; line: 11\n",
        "                       2825 ...4_leapfrog.jl; advance_leapfrog!; line: 55\n",
        "                        22   range.jl; colon; line: 38\n",
        "                         15 range.jl; Range1; line: 27\n",
        "                       6    range.jl; colon; line: 38\n",
        "                 20    ...HW4_leapfrog.jl; integrate_leapfrog!; line: 88\n",
        "                 103   ...HW4_leapfrog.jl; integrate_leapfrog!; line: 91\n",
        "                 1     ...HW4_leapfrog.jl; integrate_leapfrog!; line: 93\n",
        "                 3880  ...HW4_leapfrog.jl; integrate_leapfrog!; line: 94\n",
        "                  250  abstractarray.jl; trailingsize; line: 54\n",
        "                  3594 array.jl; getindex; line: 342\n",
        "                  1    range.jl; Range1; line: 28\n",
        "                  12   range.jl; colon; line: 38\n",
        "                   5 range.jl; Range1; line: 27\n",
        "                   4 range.jl; Range1; line: 28\n",
        "                 17419 ...HW4_leapfrog.jl; integrate_leapfrog!; line: 95\n",
        "                  127  abstractarray.jl; trailingsize; line: 54\n",
        "                  2344 deepcopy.jl; deepcopy_internal; line: 45\n",
        "                  4422 deepcopy.jl; deepcopy_internal; line: 46\n",
        "                   2870 deepcopy.jl; _deepcopy_array_t; line: 52\n",
        "                      160 reflection.jl; isbits; line: 36\n",
        "                   330  deepcopy.jl; _deepcopy_array_t; line: 53\n",
        "                    92  array.jl; copy!; line: 48\n",
        "                    207 array.jl; copy!; line: 51\n",
        "                     199 array.jl; unsafe_copy!; line: 38\n",
        "                      77 array.jl; unsafe_copy!; line: 31\n",
        "                      61 array.jl; unsafe_copy!; line: 33\n",
        "                     3   array.jl; unsafe_copy!; line: 44\n",
        "                   1060 deepcopy.jl; _deepcopy_array_t; line: 55\n",
        "                   51   deepcopy.jl; _deepcopy_array_t; line: 62\n",
        "                  36   deepcopy.jl; deepcopy_internal; line: 48\n",
        "                  43   range.jl; colon; line: 38\n",
        "                   36 range.jl; Range1; line: 27\n",
        "                   1  range.jl; Range1; line: 28\n",
        "                    26   array.jl; setindex!; line: 453\n",
        "                    4923 array.jl; setindex!; line: 454\n",
        "                     9    abstractarray.jl; checkbounds; line: 63\n",
        "                     10   abstractarray.jl; checkbounds; line: 75\n",
        "                     192  abstractarray.jl; checkbounds; line: 95\n",
        "                      95 abstractarray.jl; checkbounds; line: 63\n",
        "                     4648 abstractarray.jl; checkbounds; line: 96\n",
        "                      4615 abstractarray.jl; checkbounds; line: 74\n",
        "                       184  range.jl; maximum; line: 101\n",
        "                       136  range.jl; minimum; line: 100\n",
        "                        1    int.jl; <; line: 228\n",
        "                         48 int.jl; <; line: 228\n",
        "                         51 operators.jl; >; line: 19\n",
        "                      10   abstractarray.jl; checkbounds; line: 75\n",
        "                      5    range.jl; maximum; line: 101\n",
        "                      3    range.jl; minimum; line: 100\n",
        "                    29   array.jl; setindex!; line: 462\n",
        "                    17   array.jl; setindex!; line: 464\n",
        "                    1180 array.jl; setindex!; line: 465\n",
        "                    24   array.jl; setindex!; line: 469\n",
        "                 4     deepcopy.jl; deepcopy_internal; line: 46\n",
        "                 11    range.jl; colon; line: 38\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Profile.clear()\n",
      "for i in 0:50\n",
      "    @profile orbit = integrate_leapfrog_student([1.0,0.0,0.0,1.0],2pi/200,6pi);\n",
      "    #println(\"X:\",orbit[1][end],\" Y:\",orbit[2][end],\" Vx:\",orbit[3][end],\" Vy:\",orbit[4][end])\n",
      "end\n",
      "Profile.print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "the profile data buffer is full; profiling probably terminated\n",
        "before your program finished. To profile for longer runs, call Profile.init()\n",
        "with a larger buffer and/or larger delay.\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    6466 multi.jl; anonymous; line: 1308\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "      6466 ...Julia/src/IJulia.jl; eventloop; line: 92\n",
        "       6466 ...Julia/src/IJulia.jl; eventloop; line: 68\n",
        "          6466 ...xecute_request.jl; execute_request_0x535c5df2; line: 132\n",
        "            6466 loading.jl; include_string; line: 83\n",
        "                6466 no file; anonymous; line: 14\n",
        "                 6384 ...frog_student.jl; integrate_leapfrog_student; line: 31\n",
        "                  1    ...frog_student.jl; leapfrog_update_pos; line: 11\n",
        "                  6383 ...frog_student.jl; leapfrog_update_pos; line: 13\n",
        "                   4    abstractarray.jl; vcat; line: 706\n",
        "                 17   ...frog_student.jl; integrate_leapfrog_student; line: 32\n",
        "                  2  ...pfrog_student.jl; derrivatives; line: 4\n",
        "                  15 ...pfrog_student.jl; derrivatives; line: 7\n",
        "                   2  abstractarray.jl; vcat; line: 706\n",
        "                 2    ...frog_student.jl; integrate_leapfrog_student; line: 33\n",
        "                  2 ...pfrog_student.jl; leapfrog_update_both; line: 20\n",
        "                   1 abstractarray.jl; vcat; line: 706\n",
        "                 22   ...frog_student.jl; integrate_leapfrog_student; line: 36\n",
        "                  1  abstractarray.jl; vcat; line: 706\n",
        "                   4  abstractarray.jl; vcat; line: 925\n",
        "                     1 abstractarray.jl; cat_t; line: 875\n",
        "                     1 abstractarray.jl; cat_t; line: 893\n",
        "                        1 base.jl; Array; line: 149\n",
        "                     1 abstractarray.jl; cat_t; line: 918\n",
        "                     1 abstractarray.jl; cat_t; line: 919\n",
        "                        1 base.jl; append_any; line: 110\n",
        "                   16 array.jl; vcat; line: 1164\n",
        "                 15   ...frog_student.jl; integrate_leapfrog_student; line: 37\n",
        "                  1  abstractarray.jl; vcat; line: 706\n",
        "                   6 abstractarray.jl; vcat; line: 925\n",
        "                     6 abstractarray.jl; cat_t; line: 912\n",
        "                   5 array.jl; vcat; line: 1164\n",
        "                   3 array.jl; vcat; line: 1172\n",
        "                 15   ...frog_student.jl; integrate_leapfrog_student; line: 38\n",
        "                  2  abstractarray.jl; vcat; line: 706\n",
        "                   6 array.jl; vcat; line: 1164\n",
        "                 11   ...frog_student.jl; integrate_leapfrog_student; line: 39\n",
        "                  2 abstractarray.jl; vcat; line: 706\n",
        "                   4 array.jl; vcat; line: 1164\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##1d.\n",
      "Yep it was the vcat calls, interesting how the increase by ~an order of magnitude in each successive line. Your code spends most of it's time on the deepcopy at line 95\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##1e.\n",
      "Pre-allocating the log array might help, changing a value should be a much cheaper process. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#2 \n",
      "---"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2a."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function f(x::Vector{Float64})\n",
      "  return exp(-0.5.*x.^2)/sqrt(2pi)\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "f (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-3,3,1000)\n",
      "y = f(x)\n",
      "using PyPlot\n",
      "plot(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "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",
       "svg": [
        "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
        "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
        "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
        "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
        "<svg height=\"377pt\" version=\"1.1\" viewBox=\"0 0 492 377\" width=\"492pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
        " <defs>\n",
        "  <style type=\"text/css\">\n",
        "*{stroke-linecap:square;stroke-linejoin:round;}\n",
        "  </style>\n",
        " </defs>\n",
        " <g id=\"figure_1\">\n",
        "  <g id=\"patch_1\">\n",
        "   <path d=\"\n",
        "M0 377.615\n",
        "L492.81 377.615\n",
        "L492.81 0\n",
        "L0 0\n",
        "z\n",
        "\" style=\"fill:#ffffff;\"/>\n",
        "  </g>\n",
        "  <g id=\"axes_1\">\n",
        "   <g id=\"patch_2\">\n",
        "    <path d=\"\n",
        "M36.3306 357.338\n",
        "L482.731 357.338\n",
        "L482.731 11.7384\n",
        "L36.3306 11.7384\n",
        "z\n",
        "\" style=\"fill:#ffffff;\"/>\n",
        "   </g>\n",
        "   <g id=\"line2d_1\">\n",
        "    <path clip-path=\"url(#p57b995488c)\" d=\"\n",
        "M36.3306 353.509\n",
        "L42.5865 352.428\n",
        "L48.3955 351.191\n",
        "L53.7577 349.816\n",
        "L58.673 348.327\n",
        "L63.1414 346.76\n",
        "L67.6099 344.965\n",
        "L72.0784 342.918\n",
        "L76.1 340.838\n",
        "L80.1216 338.514\n",
        "L84.1432 335.924\n",
        "L88.1649 333.049\n",
        "L92.1865 329.869\n",
        "L95.7613 326.769\n",
        "L99.336 323.398\n",
        "L102.911 319.742\n",
        "L106.486 315.789\n",
        "L110.06 311.525\n",
        "L113.635 306.94\n",
        "L117.21 302.025\n",
        "L121.232 296.089\n",
        "L125.253 289.714\n",
        "L129.275 282.893\n",
        "L133.296 275.623\n",
        "L137.318 267.905\n",
        "L141.786 258.809\n",
        "L146.255 249.18\n",
        "L150.723 239.037\n",
        "L155.639 227.32\n",
        "L161.001 213.927\n",
        "L166.81 198.789\n",
        "L173.513 180.668\n",
        "L182.45 155.806\n",
        "L197.642 113.462\n",
        "L203.898 96.7165\n",
        "L209.26 82.9992\n",
        "L213.729 72.1521\n",
        "L217.75 62.9328\n",
        "L221.325 55.23\n",
        "L224.9 48.0404\n",
        "L228.028 42.2068\n",
        "L231.156 36.8301\n",
        "L234.284 31.9373\n",
        "L236.965 28.1475\n",
        "L239.646 24.7458\n",
        "L242.327 21.745\n",
        "L244.561 19.559\n",
        "L246.795 17.6651\n",
        "L249.03 16.0685\n",
        "L251.264 14.7734\n",
        "L253.498 13.7835\n",
        "L255.286 13.2129\n",
        "L257.073 12.8403\n",
        "L258.86 12.6663\n",
        "L260.648 12.6912\n",
        "L262.435 12.9149\n",
        "L264.223 13.337\n",
        "L266.01 13.9569\n",
        "L267.797 14.7734\n",
        "L270.032 16.0685\n",
        "L272.266 17.6651\n",
        "L274.5 19.559\n",
        "L276.734 21.745\n",
        "L278.968 24.2175\n",
        "L281.65 27.5533\n",
        "L284.331 31.2793\n",
        "L287.012 35.3816\n",
        "L290.14 40.6227\n",
        "L293.268 46.3287\n",
        "L296.395 52.4712\n",
        "L299.97 59.9871\n",
        "L303.992 69.0179\n",
        "L308.014 78.5901\n",
        "L312.482 89.7721\n",
        "L317.844 103.81\n",
        "L324.547 122.051\n",
        "L334.824 150.787\n",
        "L346.442 183.117\n",
        "L353.592 202.334\n",
        "L359.401 217.331\n",
        "L364.763 230.572\n",
        "L369.678 242.132\n",
        "L374.147 252.124\n",
        "L378.615 261.595\n",
        "L383.084 270.527\n",
        "L387.105 278.096\n",
        "L391.127 285.216\n",
        "L395.149 291.888\n",
        "L399.17 298.116\n",
        "L403.192 303.908\n",
        "L407.214 309.274\n",
        "L410.788 313.696\n",
        "L414.363 317.803\n",
        "L417.938 321.607\n",
        "L421.513 325.119\n",
        "L425.087 328.352\n",
        "L429.109 331.675\n",
        "L433.131 334.683\n",
        "L437.152 337.396\n",
        "L441.174 339.836\n",
        "L445.195 342.023\n",
        "L449.217 343.975\n",
        "L453.686 345.893\n",
        "L458.154 347.571\n",
        "L463.069 349.168\n",
        "L467.985 350.534\n",
        "L473.347 351.793\n",
        "L479.156 352.921\n",
        "L482.731 353.509\n",
        "L482.731 353.509\" style=\"fill:none;stroke:#0000ff;\"/>\n",
        "   </g>\n",
        "   <g id=\"matplotlib.axis_1\">\n",
        "    <g id=\"xtick_1\">\n",
        "     <g id=\"line2d_2\">\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M0 0\n",
        "L0 -4\" id=\"mcb557df647\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
        "      </defs>\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_3\">\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M0 0\n",
        "L0 4\" id=\"mdad270ee8e\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
        "      </defs>\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_1\">\n",
        "      <!-- \u22123 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M10.5938 35.5\n",
        "L73.1875 35.5\n",
        "L73.1875 27.2031\n",
        "L10.5938 27.2031\n",
        "z\n",
        "\" id=\"BitstreamVeraSans-Roman-2212\"/>\n",
        "       <path d=\"\n",
        "M40.5781 39.3125\n",
        "Q47.6562 37.7969 51.625 33\n",
        "Q55.6094 28.2188 55.6094 21.1875\n",
        "Q55.6094 10.4062 48.1875 4.48438\n",
        "Q40.7656 -1.42188 27.0938 -1.42188\n",
        "Q22.5156 -1.42188 17.6562 -0.515625\n",
        "Q12.7969 0.390625 7.625 2.20312\n",
        "L7.625 11.7188\n",
        "Q11.7188 9.32812 16.5938 8.10938\n",
        "Q21.4844 6.89062 26.8125 6.89062\n",
        "Q36.0781 6.89062 40.9375 10.5469\n",
        "Q45.7969 14.2031 45.7969 21.1875\n",
        "Q45.7969 27.6406 41.2812 31.2656\n",
        "Q36.7656 34.9062 28.7188 34.9062\n",
        "L20.2188 34.9062\n",
        "L20.2188 43.0156\n",
        "L29.1094 43.0156\n",
        "Q36.375 43.0156 40.2344 45.9219\n",
        "Q44.0938 48.8281 44.0938 54.2969\n",
        "Q44.0938 59.9062 40.1094 62.9062\n",
        "Q36.1406 65.9219 28.7188 65.9219\n",
        "Q24.6562 65.9219 20.0156 65.0312\n",
        "Q15.375 64.1562 9.8125 62.3125\n",
        "L9.8125 71.0938\n",
        "Q15.4375 72.6562 20.3438 73.4375\n",
        "Q25.25 74.2188 29.5938 74.2188\n",
        "Q40.8281 74.2188 47.3594 69.1094\n",
        "Q53.9062 64.0156 53.9062 55.3281\n",
        "Q53.9062 49.2656 50.4375 45.0938\n",
        "Q46.9688 40.9219 40.5781 39.3125\" id=\"BitstreamVeraSans-Roman-33\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(28.601875 370.2446875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
        "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_2\">\n",
        "     <g id=\"line2d_4\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"110.730625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_5\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"110.730625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_2\">\n",
        "      <!-- \u22122 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M19.1875 8.29688\n",
        "L53.6094 8.29688\n",
        "L53.6094 0\n",
        "L7.32812 0\n",
        "L7.32812 8.29688\n",
        "Q12.9375 14.1094 22.625 23.8906\n",
        "Q32.3281 33.6875 34.8125 36.5312\n",
        "Q39.5469 41.8438 41.4219 45.5312\n",
        "Q43.3125 49.2188 43.3125 52.7812\n",
        "Q43.3125 58.5938 39.2344 62.25\n",
        "Q35.1562 65.9219 28.6094 65.9219\n",
        "Q23.9688 65.9219 18.8125 64.3125\n",
        "Q13.6719 62.7031 7.8125 59.4219\n",
        "L7.8125 69.3906\n",
        "Q13.7656 71.7812 18.9375 73\n",
        "Q24.125 74.2188 28.4219 74.2188\n",
        "Q39.75 74.2188 46.4844 68.5469\n",
        "Q53.2188 62.8906 53.2188 53.4219\n",
        "Q53.2188 48.9219 51.5312 44.8906\n",
        "Q49.8594 40.875 45.4062 35.4062\n",
        "Q44.1875 33.9844 37.6406 27.2188\n",
        "Q31.1094 20.4531 19.1875 8.29688\" id=\"BitstreamVeraSans-Roman-32\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(103.121875 370.2446875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
        "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_3\">\n",
        "     <g id=\"line2d_6\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"185.130625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_7\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"185.130625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_3\">\n",
        "      <!-- \u22121 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M12.4062 8.29688\n",
        "L28.5156 8.29688\n",
        "L28.5156 63.9219\n",
        "L10.9844 60.4062\n",
        "L10.9844 69.3906\n",
        "L28.4219 72.9062\n",
        "L38.2812 72.9062\n",
        "L38.2812 8.29688\n",
        "L54.3906 8.29688\n",
        "L54.3906 0\n",
        "L12.4062 0\n",
        "z\n",
        "\" id=\"BitstreamVeraSans-Roman-31\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(177.475 370.0871875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
        "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_4\">\n",
        "     <g id=\"line2d_8\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"259.530625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_9\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"259.530625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_4\">\n",
        "      <!-- 0 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M31.7812 66.4062\n",
        "Q24.1719 66.4062 20.3281 58.9062\n",
        "Q16.5 51.4219 16.5 36.375\n",
        "Q16.5 21.3906 20.3281 13.8906\n",
        "Q24.1719 6.39062 31.7812 6.39062\n",
        "Q39.4531 6.39062 43.2812 13.8906\n",
        "Q47.125 21.3906 47.125 36.375\n",
        "Q47.125 51.4219 43.2812 58.9062\n",
        "Q39.4531 66.4062 31.7812 66.4062\n",
        "M31.7812 74.2188\n",
        "Q44.0469 74.2188 50.5156 64.5156\n",
        "Q56.9844 54.8281 56.9844 36.375\n",
        "Q56.9844 17.9688 50.5156 8.26562\n",
        "Q44.0469 -1.42188 31.7812 -1.42188\n",
        "Q19.5312 -1.42188 13.0625 8.26562\n",
        "Q6.59375 17.9688 6.59375 36.375\n",
        "Q6.59375 54.8281 13.0625 64.5156\n",
        "Q19.5312 74.2188 31.7812 74.2188\" id=\"BitstreamVeraSans-Roman-30\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(256.5071875 370.2446875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_5\">\n",
        "     <g id=\"line2d_10\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"333.930625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_11\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"333.930625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_5\">\n",
        "      <!-- 1 -->\n",
        "      <g transform=\"translate(331.32625 370.0871875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_6\">\n",
        "     <g id=\"line2d_12\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"408.330625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_13\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"408.330625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_6\">\n",
        "      <!-- 2 -->\n",
        "      <g transform=\"translate(405.55375 370.2446875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"xtick_7\">\n",
        "     <g id=\"line2d_14\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#mcb557df647\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_15\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#mdad270ee8e\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_7\">\n",
        "      <!-- 3 -->\n",
        "      <g transform=\"translate(479.8515625 370.2446875)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"matplotlib.axis_2\">\n",
        "    <g id=\"ytick_1\">\n",
        "     <g id=\"line2d_16\">\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M0 0\n",
        "L4 0\" id=\"mc8fcea1516\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
        "      </defs>\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_17\">\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M0 0\n",
        "L-4 0\" id=\"m0d5b0a6425\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
        "      </defs>\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"357.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_8\">\n",
        "      <!-- 0.00 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M10.6875 12.4062\n",
        "L21 12.4062\n",
        "L21 0\n",
        "L10.6875 0\n",
        "z\n",
        "\" id=\"BitstreamVeraSans-Roman-2e\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(7.2 361.70625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_2\">\n",
        "     <g id=\"line2d_18\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"314.1384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_19\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"314.1384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_9\">\n",
        "      <!-- 0.05 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M10.7969 72.9062\n",
        "L49.5156 72.9062\n",
        "L49.5156 64.5938\n",
        "L19.8281 64.5938\n",
        "L19.8281 46.7344\n",
        "Q21.9688 47.4688 24.1094 47.8281\n",
        "Q26.2656 48.1875 28.4219 48.1875\n",
        "Q40.625 48.1875 47.75 41.5\n",
        "Q54.8906 34.8125 54.8906 23.3906\n",
        "Q54.8906 11.625 47.5625 5.09375\n",
        "Q40.2344 -1.42188 26.9062 -1.42188\n",
        "Q22.3125 -1.42188 17.5469 -0.640625\n",
        "Q12.7969 0.140625 7.71875 1.70312\n",
        "L7.71875 11.625\n",
        "Q12.1094 9.23438 16.7969 8.0625\n",
        "Q21.4844 6.89062 26.7031 6.89062\n",
        "Q35.1562 6.89062 40.0781 11.3281\n",
        "Q45.0156 15.7656 45.0156 23.3906\n",
        "Q45.0156 31 40.0781 35.4375\n",
        "Q35.1562 39.8906 26.7031 39.8906\n",
        "Q22.75 39.8906 18.8125 39.0156\n",
        "Q14.8906 38.1406 10.7969 36.2812\n",
        "z\n",
        "\" id=\"BitstreamVeraSans-Roman-35\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(7.45125 318.50625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_3\">\n",
        "     <g id=\"line2d_20\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"270.9384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_21\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"270.9384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_10\">\n",
        "      <!-- 0.10 -->\n",
        "      <g transform=\"translate(7.2 275.30625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_4\">\n",
        "     <g id=\"line2d_22\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"227.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_23\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"227.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_11\">\n",
        "      <!-- 0.15 -->\n",
        "      <g transform=\"translate(7.45125 232.10625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_5\">\n",
        "     <g id=\"line2d_24\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"184.5384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_25\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"184.5384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_12\">\n",
        "      <!-- 0.20 -->\n",
        "      <g transform=\"translate(7.2 188.90625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_6\">\n",
        "     <g id=\"line2d_26\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"141.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_27\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"141.3384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_13\">\n",
        "      <!-- 0.25 -->\n",
        "      <g transform=\"translate(7.45125 145.70625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_7\">\n",
        "     <g id=\"line2d_28\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"98.1384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_29\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"98.1384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_14\">\n",
        "      <!-- 0.30 -->\n",
        "      <g transform=\"translate(7.2 102.50625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_8\">\n",
        "     <g id=\"line2d_30\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"54.9384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_31\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"54.9384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_15\">\n",
        "      <!-- 0.35 -->\n",
        "      <g transform=\"translate(7.45125 59.30625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "    <g id=\"ytick_9\">\n",
        "     <g id=\"line2d_32\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"36.330625\" xlink:href=\"#mc8fcea1516\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"line2d_33\">\n",
        "      <g>\n",
        "       <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"482.730625\" xlink:href=\"#m0d5b0a6425\" y=\"11.7384375\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "     <g id=\"text_16\">\n",
        "      <!-- 0.40 -->\n",
        "      <defs>\n",
        "       <path d=\"\n",
        "M37.7969 64.3125\n",
        "L12.8906 25.3906\n",
        "L37.7969 25.3906\n",
        "z\n",
        "\n",
        "M35.2031 72.9062\n",
        "L47.6094 72.9062\n",
        "L47.6094 25.3906\n",
        "L58.0156 25.3906\n",
        "L58.0156 17.1875\n",
        "L47.6094 17.1875\n",
        "L47.6094 0\n",
        "L37.7969 0\n",
        "L37.7969 17.1875\n",
        "L4.89062 17.1875\n",
        "L4.89062 26.7031\n",
        "z\n",
        "\" id=\"BitstreamVeraSans-Roman-34\"/>\n",
        "      </defs>\n",
        "      <g transform=\"translate(7.2 16.10625)scale(0.12 -0.12)\">\n",
        "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
        "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
        "       <use x=\"159.033203125\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
        "      </g>\n",
        "     </g>\n",
        "    </g>\n",
        "   </g>\n",
        "   <g id=\"patch_3\">\n",
        "    <path d=\"\n",
        "M36.3306 11.7384\n",
        "L482.731 11.7384\" style=\"fill:none;stroke:#000000;\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_4\">\n",
        "    <path d=\"\n",
        "M482.731 357.338\n",
        "L482.731 11.7384\" style=\"fill:none;stroke:#000000;\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_5\">\n",
        "    <path d=\"\n",
        "M36.3306 357.338\n",
        "L482.731 357.338\" style=\"fill:none;stroke:#000000;\"/>\n",
        "   </g>\n",
        "   <g id=\"patch_6\">\n",
        "    <path d=\"\n",
        "M36.3306 357.338\n",
        "L36.3306 11.7384\" style=\"fill:none;stroke:#000000;\"/>\n",
        "   </g>\n",
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
        "  <clipPath id=\"p57b995488c\">\n",
        "   <rect height=\"345.6\" width=\"446.4\" x=\"36.330625\" y=\"11.7384375\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
        "</svg>\n"
       ],
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x110a55850>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "1-element Array{Any,1}:\n",
        " PyObject <matplotlib.lines.Line2D object at 0x110d90e10>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Looks normal to me! "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2b. -loop"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function loop_interate(f, a::Float64, b::Float64, integration_number::Int=1000)\n",
      "\n",
      "  @assert a < b\n",
      "  interval_bounds = linspace(a,b,integration_number+1)\n",
      "  value_array = zeros(Float64,integration_number) \n",
      "\n",
      "  for i = 2:integration_number\n",
      "    #trapizoid rule, cause that is enough for a homework \n",
      "    value_array[i] = (interval_bounds[i] - interval_bounds[i-1]) *.5*(f(interval_bounds[i-1] )+f(interval_bounds[i] ) ) \n",
      "  end\n",
      " \n",
      "  return sum(value_array)\n",
      "\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "loop_interate (generic function with 3 methods)"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Does it obey the 68\u201395\u201399.7 rule?\n",
      "println(loop_interate(f,-1.0,1.0))\n",
      "println(loop_interate(f,-2.0,2.0))\n",
      "println(loop_interate(f,-3.0,3.0))\n",
      "println(loop_interate(f,-100.0,100.0))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.6822049054334063"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.9542826178365158\n",
        "0.9972732918302741\n",
        "1.0000000000000004\n"
       ]
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2c. -vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function vector_interate(f, a::Float64, b::Float64, integration_number::Int=1000)\n",
      "\n",
      "  @assert a < b\n",
      "  bounds = linspace(a,b,integration_number+1)\n",
      "  lower_bounds = bounds[1:integration_number]\n",
      "  upper_bounds = bounds[2:end]\n",
      "\n",
      "  value_array = (upper_bounds .- lower_bounds) *.5.*(f(lower_bounds ).+f(upper_bounds)) \n",
      "\n",
      "  return sum(value_array)\n",
      "\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 108,
       "text": [
        "vector_interate (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Does it obey the 68\u201395\u201399.7 rule?\n",
      "println(vector_interate(f,-1.0,1.0))\n",
      "println(vector_interate(f,-2.0,2.0))\n",
      "println(vector_interate(f,-3.0,3.0))\n",
      "println(vector_interate(f,-100.0,100.0))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.682689330823248"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.9544994481518971\n",
        "0.9973001241637558\n",
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 120
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2d. -map + reduce"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function trapazoid_rule(a::Float64,b::Float64)\n",
      "  #If f is not alrady complied you are out of luck here. \n",
      "  return (b - a) * .5 * (f(a) + f(b))\n",
      "  \n",
      "end\n",
      "\n",
      "function map_plus_reduce_interate(f, a::Float64, b::Float64, integration_number::Int=1000)\n",
      "\n",
      "  #Don't actually call f anymore\n",
      "  @assert a < b\n",
      "  bounds = linspace(a,b,integration_number+1)\n",
      "  lower_bounds = bounds[1:integration_number]\n",
      "  upper_bounds = bounds[2:end]\n",
      "\n",
      "  value_array = map(trapazoid_rule,lower_bounds,upper_bounds)\n",
      "\n",
      "  return reduce(+,value_array)\n",
      "\n",
      "end\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 143,
       "text": [
        "map_plus_reduce_interate (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 143
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Does it obey the 68\u201395\u201399.7 rule?\n",
      "println(map_plus_reduce_interate(f,-1.0,1.0))\n",
      "println(map_plus_reduce_interate(f,-2.0,2.0))\n",
      "println(map_plus_reduce_interate(f,-3.0,3.0))\n",
      "println(map_plus_reduce_interate(f,-100.0,100.0))\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.682689330823248"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.9544994481518971\n",
        "0.9973001241637558\n",
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 144
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2e. -mapreduce"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#mapreduce can't handle multiple itr, so just tweaking map_plus_reduce wont do it. errgh, tired and grumpy, \n",
      "#don't want to code no more today\n",
      "\n",
      "function trapazoid_rule(bounds)\n",
      "  #If f is not alrady complied you are out of luck here. \n",
      "  return (b - a) * .5 * (f(a) + f(b))\n",
      "  \n",
      "end\n",
      "\n",
      "function mapreduce_interate(f, a::Float64, b::Float64, integration_number::Int=1000)\n",
      "\n",
      "  #Don't actually call f anymore \n",
      "  @assert a < b\n",
      "  bounds = linspace(a,b,integration_number+1)\n",
      "  #lower_bounds = bounds[1:integration_number]\n",
      "  #upper_bounds = bounds[2:end]\n",
      "\n",
      "  return mapreduce(trapazoid_rule,+,bounds)\n",
      "\n",
      "\n",
      "end\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 159,
       "text": [
        "mapreduce_interate (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 159
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Does it obey the 68\u201395\u201399.7 rule?\n",
      "println(mapreduce_interate(f,-1.0,1.0))\n",
      "println(mapreduce_interate(f,-2.0,2.0))\n",
      "println(mapreduce_interate(f,-3.0,3.0))\n",
      "println(mapreduce_interate(f,-100.0,100.0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "LoadError",
       "evalue": "no method trapazoid_rule(Float64,)\nat In[149]:2",
       "output_type": "pyerr",
       "traceback": [
        "no method trapazoid_rule(Float64,)\nat In[149]:2",
        " in mr_pairwise at reduce.jl:135",
        " in mr_pairwise at reduce.jl:153 (repeats 3 times)",
        " in mapreduce at reduce.jl:162",
        " in mapreduce_interate at In[148]:15",
        " in mapreduce_interate at In[148]:10"
       ]
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2f. -devectorize"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#blah! looks interesting...loops faster than vectors? Strange."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 151
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2g."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "println(\"Loop: \",@elapsed loop_interate(f,-1.0,1.0,1000000))\n",
      "println(\"Vector: \",@elapsed vector_interate(f,-1.0,1.0,1000000))\n",
      "println(\"Map+Reduce: \",@elapsed map_plus_reduce_interate(f,-1.0,1.0,1000000))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loop: 0."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "440510142\n",
        "Vector: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.188881352\n",
        "Map+Reduce: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.216344906\n"
       ]
      }
     ],
     "prompt_number": 160
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##2h. \n",
      "Since I only made three versions, let's profile all of them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Profile.clear()\n",
      "@profile loop_interate(f,-1.0,1.0,1000000)\n",
      "Profile.print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1   array.jl; setindex!; line: 412\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    372 multi.jl; anonymous; line: 1308\n",
        "      372 ...IJulia/src/IJulia.jl; eventloop; line: 92\n",
        "       372 ...Julia/src/IJulia.jl; eventloop; line: 68\n",
        "          372 ...execute_request.jl; execute_request_0x535c5df2; line: 132\n",
        "            372 loading.jl; include_string; line: 83\n",
        "                371 profile.jl; anonymous; line: 14\n",
        "                 14  In[83]; loop_interate; line: 4\n",
        "                  14 array.jl; linspace; line: 238\n",
        "                 2   In[83]; loop_interate; line: 5\n",
        "                  2 array.jl; fill!; line: 187\n",
        "                 1   In[83]; loop_interate; line: 8\n",
        "                 353 In[83]; loop_interate; line: 10\n",
        "                    53 In[17]; f; line: 2\n",
        "                    1  array.jl; setindex!; line: 412\n",
        "                    3  float.jl; *; line: 136\n",
        "                    2  float.jl; +; line: 132\n",
        "                 1   In[83]; loop_interate; line: 13\n",
        "                  1 abstractarray.jl; sum; line: 1487\n",
        "                   1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                    1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                     1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                      1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                       1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                        1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                         1 ...ractarray.jl; sum_pairwise; line: 1481\n",
        "                          1 ...ractarray.jl; sum_pairwise; line: 1481\n",
        "                           1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                            1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                             1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                              1 ...ctarray.jl; sum_pairwise; line: 1481\n",
        "                               1 ...ctarray.jl; sum_pairwise; line: 1481\n",
        "                                1 ...ctarray.jl; sum_pairwise; line: 135\n"
       ]
      }
     ],
     "prompt_number": 161
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Profile.clear()\n",
      "@profile vector_interate(f,-1.0,1.0,1000000)\n",
      "Profile.print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    160 multi.jl; anonymous; line: 1308\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "      160 ...IJulia/src/IJulia.jl; eventloop; line: 92\n",
        "       160 ...Julia/src/IJulia.jl; eventloop; line: 68\n",
        "          160 ...execute_request.jl; execute_request_0x535c5df2; line: 132\n",
        "            160 loading.jl; include_string; line: 83\n",
        "                160 profile.jl; anonymous; line: 14\n",
        "                 15  In[108]; vector_interate; line: 4\n",
        "                  15 array.jl; linspace; line: 238\n",
        "                 22  In[108]; vector_interate; line: 6\n",
        "                  22 array.jl; getindex; line: 294\n",
        "                 122 In[108]; vector_interate; line: 13\n",
        "                  3   array.jl; .*; line: 135\n",
        "                  3   broadcast.jl; ##broadcast_T_-#215; line: 189\n",
        "                      3 broadcast.jl; ##-_inner!#217; line: 166\n",
        "                   92 In[29]; f; line: 2\n",
        "                    4  array.jl; .*; line: 135\n",
        "                    14 array.jl; ./; line: 135\n",
        "                    46 array.jl; .^; line: 920\n",
        "                    28 operators.jl; exp; line: 236\n",
        "                   20 broadcast.jl; .*; line: 277\n",
        "                    20 broadcast.jl; ##broadcast_T_*#221; line: 189\n",
        "                      17 broadcast.jl; broadcast_args; line: 87\n",
        "                       17 broadcast.jl; calc_loop_strides; line: 63\n",
        "                        1 broadcast.jl; ##*_inner!#223; line: 136\n",
        "                        2 broadcast.jl; ##*_inner!#223; line: 166\n",
        "                   4  broadcast.jl; .+; line: 276\n",
        "                    4 broadcast.jl; ##broadcast_T_+#209; line: 189\n",
        "                        1 broadcast.jl; ##+_inner!#211; line: 136\n",
        "                        3 broadcast.jl; ##+_inner!#211; line: 166\n",
        "                 1   In[108]; vector_interate; line: 15\n",
        "                    1 abstractarray.jl; sum; line: 1487\n",
        "                     1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                      1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                       1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                        1 abstractarray.jl; sum_pairwise; line: 1481\n",
        "                         1 ...ractarray.jl; sum_pairwise; line: 1481\n",
        "                          1 ...ractarray.jl; sum_pairwise; line: 1481\n",
        "                           1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                            1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                             1 ...actarray.jl; sum_pairwise; line: 1481\n",
        "                              1 ...ctarray.jl; sum_pairwise; line: 1481\n",
        "                               1 ...ctarray.jl; sum_pairwise; line: 1481\n",
        "                                1 ...tarray.jl; sum_pairwise; line: 1481\n",
        "                                 1 ...tarray.jl; sum_pairwise; line: 1481\n",
        "                                  1 ...tarray.jl; sum_pairwise; line: 135\n"
       ]
      }
     ],
     "prompt_number": 162
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Profile.clear()\n",
      "@profile map_plus_reduce_interate(f,-1.0,1.0,1000000) \n",
      "Profile.print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    263 multi.jl; anonymous; line: 1308\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "      263 ...IJulia/src/IJulia.jl; eventloop; line: 92\n",
        "       263 ...Julia/src/IJulia.jl; eventloop; line: 68\n",
        "          263 ...execute_request.jl; execute_request_0x535c5df2; line: 132\n",
        "            263 loading.jl; include_string; line: 83\n",
        "                262 profile.jl; anonymous; line: 14\n",
        "                 14  In[143]; map_plus_reduce_interate; line: 11\n",
        "                  14 array.jl; linspace; line: 238\n",
        "                 189 In[143]; map_plus_reduce_interate; line: 15\n",
        "                  19  abstractarray.jl; map; line: 1696\n",
        "                  170 abstractarray.jl; map; line: 1702\n",
        "                     170 abstractarray.jl; map_to!; line: 1690\n",
        "                        52 In[148]; trapazoid_rule; line: 3\n",
        "                         49 In[17]; f; line: 2\n",
        "                        1  array.jl; setindex!; line: 412\n",
        "                 59  In[143]; map_plus_reduce_interate; line: 17\n",
        "                   59 reduce.jl; reduce; line: 179\n",
        "                    59 reduce.jl; r_pairwise; line: 174\n",
        "                     59 reduce.jl; r_pairwise; line: 174\n",
        "                      59 reduce.jl; r_pairwise; line: 174\n",
        "                       59 reduce.jl; r_pairwise; line: 174\n",
        "                        59 reduce.jl; r_pairwise; line: 174\n",
        "                         59 reduce.jl; r_pairwise; line: 174\n",
        "                          59 reduce.jl; r_pairwise; line: 174\n",
        "                           59 reduce.jl; r_pairwise; line: 174\n",
        "                            59 reduce.jl; r_pairwise; line: 174\n",
        "                             59 reduce.jl; r_pairwise; line: 174\n",
        "                              59 reduce.jl; r_pairwise; line: 174\n",
        "                               59 reduce.jl; r_pairwise; line: 174\n",
        "                                59 reduce.jl; r_pairwise; line: 174\n",
        "                                 59 reduce.jl; r_pairwise; line: 135\n"
       ]
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}