n-body-thread.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:49c2416115ad54471a8ec4a97f0c8096d4754acf776b494783a213e92e7a4c44"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "def remove_i(x, i):\n",
      "    \"\"\"Drops the ith element of an array.\"\"\"\n",
      "    shape = (x.shape[0]-1,) + x.shape[1:]\n",
      "    y = np.empty(shape, dtype=float)\n",
      "    y[:i] = x[:i]\n",
      "    y[i:] = x[i+1:]\n",
      "    return y\n",
      "\n",
      "def a(i, x, G, m):\n",
      "    \"\"\"The acelleration of the ith mass.\"\"\"\n",
      "    x_i = x[i]\n",
      "    x_j = remove_i(x, i)\n",
      "    m_j = remove_i(m, i)\n",
      "    diff = x_j - x_i\n",
      "    mag3 = np.sum(diff**2, axis=1)**1.5\n",
      "    result = G * np.sum(diff * (m_j / mag3)[:,np.newaxis], axis=0)\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from threading import Thread\n",
      "\n",
      "class Worker(Thread):\n",
      "    \"\"\"Computes x, v, and a of the ith body.\"\"\"\n",
      "    def __init__(self, *args, **kwargs):\n",
      "        super(Worker, self).__init__(*args, **kwargs)\n",
      "        self.inputs = []\n",
      "        self.results = []\n",
      "        self.running = True\n",
      "        self.daemon = True\n",
      "        self.start()\n",
      "        \n",
      "    def run(self):\n",
      "        while self.running:\n",
      "            if len(self.inputs) == 0:\n",
      "                continue\n",
      "            i, x0, v0, G, m, dt = self.inputs[0]\n",
      "            a_i0 = a(i, x0, G, m)\n",
      "            v_i1 = a_i0 * dt + v0[i]\n",
      "            x_i1 = a_i0 * dt**2 + v0[i] * dt + x0[i]\n",
      "            result = (i, x_i1, v_i1)\n",
      "            self.results.append(result)\n",
      "            del self.inputs[0]\n",
      "            \n",
      "class Pool(object):\n",
      "    \"\"\"A collection of P worker threads that disrtibutes tasks \n",
      "    evenly across them.\n",
      "    \"\"\"\n",
      "    def __init__(self, size):\n",
      "        self.size = size\n",
      "        self.workers = [Worker() for p in range(size)]\n",
      "        \n",
      "    def do(self, tasks):\n",
      "        for p in range(self.size):\n",
      "            self.workers[p].inputs += tasks[p::self.size]\n",
      "        while any([len(worker.inputs) != 0 for worker in self.workers]):\n",
      "            pass\n",
      "        results = []\n",
      "        for worker in self.workers:\n",
      "            results += worker.results\n",
      "            worker.results.clear()\n",
      "        return results\n",
      "    \n",
      "    def __del__(self):\n",
      "        for worker in self.workers:\n",
      "            worker.running = False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def timestep(x0, v0, G, m, dt, pool):\n",
      "    \"\"\"Computes the next position and velocity for all masses given \n",
      "    a initial conditions and a time step size.\n",
      "    \"\"\"\n",
      "    N = len(x0)\n",
      "    tasks = [(i, x0, v0, G, m, dt) for i in range(N)]\n",
      "    results = pool.do(tasks)\n",
      "    x1 = np.empty(x0.shape, dtype=float)\n",
      "    v1 = np.empty(v0.shape, dtype=float)\n",
      "    for i, x_i1, v_i1 in results:\n",
      "        x1[i] = x_i1\n",
      "        v1[i] = v_i1\n",
      "    return x1, v1\n",
      "\n",
      "def initial_cond(N, D):\n",
      "    \"\"\"Generates initial conditions for N unity masses at rest \n",
      "    starting at random positions in D-dimensional space.\n",
      "    \"\"\"\n",
      "    x0 = np.random.rand(N, D)\n",
      "    v0 = np.zeros((N, D), dtype=float)\n",
      "    m = np.ones(N, dtype=float)\n",
      "    return x0, v0, m    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def makefig(x, v, t):\n",
      "    plt.plot(x[:,0], x[:,1], 'ro')\n",
      "    if not np.all(v == 0.0):\n",
      "        plt.quiver(x[:,0], x[:,1], v[:,0], v[:,1])\n",
      "    plt.xlabel('x')\n",
      "    plt.ylabel('y')\n",
      "    plt.title('Time t = {0}'.format(t))\n",
      "    plt.savefig('n-body-t{0}.svg'.format(t))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "x0, v0, m = initial_cond(10, 2)\n",
      "pool = Pool(4)\n",
      "x1, v1 = timestep(x0, v0, 1.0, m, 1.0e-3, pool)\n",
      "del pool"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 374 ms, sys: 7.13 ms, total: 382 ms\n",
        "Wall time: 403 ms\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "makefig(x0, v0, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEYCAYAAAC3LjroAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f524c23bef0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "makefig(x1, v1, 1e-3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEYCAYAAAC3LjroAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f524c1a2c50>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import animation\n",
      "from JSAnimation import IPython_display\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = plt.axes(xlim=(0, 1.0), ylim=(0, 1.0))\n",
      "viewport = [0.0, 1.0, 0.0, 1.0]\n",
      "\n",
      "N = 10\n",
      "x0, v0, m = initial_cond(N, 2)\n",
      "pool = Pool(4)\n",
      "\n",
      "def init():\n",
      "    ax.clear()\n",
      "    ax.plot(x0[:,0], x0[:,1], 'ro')\n",
      "    ax.quiver(x0[:,0], x0[:,1], v0[:,0], v0[:,1])\n",
      "    ax.axis(viewport)\n",
      "    return ax\n",
      "\n",
      "def animate(i):\n",
      "    global x0, v0, pool\n",
      "    x, v = timestep(x0, v0, 1.0, m, 1.0e-3, pool)\n",
      "    ax.clear()\n",
      "    ax.plot(x[:,0], x[:,1], 'ro')\n",
      "    ax.quiver(x[:,0], x[:,1], v[:,0], v[:,1])\n",
      "    ax.axis(viewport)\n",
      "    x0, v0 = x, v\n",
      "    return ax\n",
      "\n",
      "animation.FuncAnimation(fig, animate, frames=3, init_func=init, interval=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
        "     this.frames[i] = new Image();\n",
        "     this.frames[i].src = frames[i];\n",
        "    }\n",
        "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
        "    this.set_frame(this.current_frame);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.get_loop_state = function(){\n",
        "    var button_group = document[this.loop_select_id].state;\n",
        "    for (var i = 0; i < button_group.length; i++) {\n",
        "        var button = button_group[i];\n",
        "        if (button.checked) {\n",
        "            return button.value;\n",
        "        }\n",
        "    }\n",
        "    return undefined;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.set_frame = function(frame){\n",
        "    this.current_frame = frame;\n",
        "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.next_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.previous_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.first_frame = function()\n",
        "  {\n",
        "    this.set_frame(0);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.last_frame = function()\n",
        "  {\n",
        "    this.set_frame(this.frames.length - 1);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.slower = function()\n",
        "  {\n",
        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.faster = function()\n",
        "  {\n",
        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
        "  {\n",
        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_reverse = function()\n",
        "  {\n",
        "    this.current_frame -= 1;\n",
        "    if(this.current_frame >= 0){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.pause_animation = function()\n",
        "  {\n",
        "    this.direction = 0;\n",
        "    if (this.timer){\n",
        "      clearInterval(this.timer);\n",
        "      this.timer = null;\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.play_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.reverse_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = -1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
        "  }\n",
        "</script>\n",
        "\n",
        "<div class=\"animation\" align=\"center\">\n",
        "    <img id=\"_anim_imgCAPMNFKXYMKCSJRG\">\n",
        "    <br>\n",
        "    <input id=\"_anim_sliderCAPMNFKXYMKCSJRG\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animCAPMNFKXYMKCSJRG.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAgyTCyQ6wAAANRJREFUKM9jYBjO4AiUfgzFGGAp4+yayUvX6jMwMDCsYmBgOCS4OAOrSYmMgcc8/pd5Q3irC+Neh/1AlmeBMVgZmP8yMLD8/c/cqv9r90whzv/MX7Eq/MfAwMDIwCuZdfSV8U8WDgZGRmYGrAoZGRgY/jO8b3sj/J2F6T8j4z80pzEhmIwMjAxsSbqqlkeZGP//Z8SlkJnhPwMjwx/Guoe1NhmRwk+YGH5jV8jOwMPHzcDBysAwh8FrxQwtPU99HrwBXsnAwMDAsJiBgYGBoZ1xmKYqALHhMpn1o7igAAAAAElFTkSuQmCC\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkR91DQ2AAAAKtJREFUKM9jYCANTEVib2K4jcRbzQihGWEC00JuNjN8Z2Q0Zo3VYWA4lL005venH9+c3ZK5IfIsMIXMBtc12Bj+MMgxMDAwMPzWe2TBzPCf4SLcZCYY4/9/RgZGBiaYFf8gljFhKiQERhUOeoX/Gf8y/GX4y/APmlj+Mfxj+MfwH64Qnnq0zr9fyfLrPzP3eQYGBobvk5x4GX4xMIij23gdib0cRWYHiVmAAQDK5ircshCbHQAAAABJRU5ErkJggg==\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkd/uac8wAAAMhJREFUKM9jYBie4DEUQ8B+fEq3+3UrMzAwMFxjYGBgYJizYubaOUxYFUaXh/6vWfRfEMIL/+//P5gZJoei4/f/7wxnY1PeNUXdE2RgYGZgYoCrY2BBVsjKwMDAwvCS4f3SG/dXxm5gYESSQ1HIwvCPgZmB8f8Pxv+Kxxb/YfiPJIdi9T8GJgaG/38ZFd4Fx0xUYsZt4h8GBgb2D2bLy7KnMTAwMEIxFoVCXIYr1IoDnkF4XAysqNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAknOOpFQQAAAS9JREFUKM/dkrEvQ3EQxz/33mtoQxiYpANbLU26NAabSCcSUouGBVNDjYQaOiDpIEiKjURIw2Kx04hEYmkHEpGoJpSISaXq9Wd4P03/ht5y98197/u9XA4aK4rAWw3lgWddZ3S+/G9mEovtAB8AHE4pgTQAx8PbJweRmsq6GimmNpxaNYXVzMNNCI6A2figimwCGACK786zuWgh3qcsKf/w0pM4X0m/doNVFVzVGlEQsdRj193VxEWpH0RsdRu+zi3tVMqCAsDShoiYqiSV4OouVDFEqS9Pbiyg7vV62lpQ2BJ4Gg0meg0MbNpkYG/e+540NNFyrE1a8qHk5BaAjfnrzUaHfAWImVrLIXbgnx4/9X06s35cweWsVACa3a24PVp0X+rPv1aHFnSONdiL8Qci0lzwpOM5sQAAAABJRU5ErkJggg==\"></button>\n",
        "    <button onclick=\"animCAPMNFKXYMKCSJRG.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectCAPMNFKXYMKCSJRG\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgCAPMNFKXYMKCSJRG\";\n",
        "    var slider_id = \"_anim_sliderCAPMNFKXYMKCSJRG\";\n",
        "    var loop_select_id = \"_anim_loop_selectCAPMNFKXYMKCSJRG\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAHsdJREFUeJzt3X9UVVX+//HX9WLgQDbkgDgrYQwU0G6ohfmphQEWNuGM0sKpqSab1rhmFoWms8x+TKH5RT6T9rHQPo1rHNP6To7ZON9pAgsi0X7RtaQxTcwwtZYpOC5UIEDhfP9ovHpHNDS45+zL87EWa92z7+b2vjvcr7vPOfccl2VZlgAAMEwfuwsAAOBCEGAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACM5MsC2bNmilJSUsz5fWloqj8ejpKQkFRUVBbAyAIBTOC7Afvvb3yorK0uWZXX6fFNTk/Ly8lRRUaHt27dr/fr1qq6uDnCVAAC7OS7AnnzySX344YdnDTCv16vRo0crOjpabrdbubm5Ki0tDXCVAAC7OS7AJJ01vCRp//79io6O9m1HRUXpwIEDgSgLAOAgjgywc3G5XHK73X5tbW1tNlUDALBLiN0FnK+YmBjV19f7tuvq6jRo0KAz+iUkJKi2tjaQpQGA8eLj4/XZZ5/ZXUaXGLECO3r0qPbt2ydJGjNmjDZv3qz6+nqdOHFCf/3rXzV+/Pgzfqe2tlaWZfFjWSooKLC9Bqf8MBaMBWNx7h+TPvg7LsAKCgo0adIk1dbWasyYMdq0aZP+9re/aerUqZKkiIgILV26VBkZGRoxYoSysrKUlpZmc9UAgEBz3C7EefPmad68eX5t48aN8wWYJGVnZys7OzvQpQEAHMRxKzB0v/T0dLtLcAzG4hTG4hTGwkwuy7LOfs66wVwul4L0rQFAjzFp7mQFBgAwEgEGADASAQYAMBIBBgAwkuNOo8d3s6mkRGXFxQppbdWJ0FBde889uvnWW+0uCwC6HQEWRDaVlOj1GTNUeNo36X/59tsKDw/X9RMn2lgZAHQ/diEGkbLiYr/wkqTnmpu1eu5cewoCgB5EgAWRkNbWTtu/rKlRR0dHgKsBgJ5FgAWRE6GhnbYfbGrSmjVrAlwNAPQsAiyIeKZM0Z19+/q1/UxSjaTf/e533DcNQFAhwILIrb/6lW5/4QX9bMgQZbpcSpW0XlKjpN27d2v58uU2VwgA3YdrIQapL774QgUFBVq5cqVvHAYOHKja2lqFh4fbXB0ApzJp7mQFFqQGDx6sFStWaOvWrb5bzxw8eFBPPfWUzZUBQPdgBdZLVFZW6oEHHtDOnTu1e/duDRgwwO6SADiQSXMnAdaLWJaltWvX6vDhw/rNb35jdzkAHMikuZMA64Usy5LL5bK7DAAOZNLcyTGwXojwAhAMCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEcF2ClpaXyeDxKSkpSUVFRp31WrVolj8ejxMRETZkyRU1NTQGuEgBgN0cFWFNTk/Ly8lRRUaHt27dr/fr1qq6u9utz8OBBPf7446qqqtLOnTsVHR2tJUuW2FQxAMAujgowr9er0aNHKzo6Wm63W7m5uSotLfXr09bWpqamJh07dkySFBMTo9DQUDvKBQDYKMTuAk63f/9+RUdH+7ajoqK0a9cuvz6DBw/WzJkzlZycrNzcXB08eFBr164NdKkAAJs5agXmcrnkdrv92tra2vy2jxw5oldeeUVVVVWaMGGCdu/erYqKikCWCQBwAEetwGJiYlRfX+/brqur06BBg/z6lJeXKzk5WYmJiUpMTFRERISeeeYZ3XzzzWe83ty5c32P09PTlZ6e3lOlA4CRKisrVVlZaXcZF8RlWZZldxEnNTY2yuPxyOv1KjIyUpmZmSosLFRKSooaGhoUGxur6upq3XbbbaqqqlJkZKTmz5+vY8eO6YknnvB7LZfLJQe9NQAwgklzp6N2IUZERGjp0qXKyMjQiBEjlJWVpbS0NK1bt05Tp06VJI0aNUr33Xefxo4dq+HDh6umpkYFBQU2Vw4ACDRHrcC6k0mfInB2m0pKVFZcrJDWVp0IDVXW9Okal51td1lA0DJp7nTUMTDgdJtKSvT6jBkqrK31tT3y78eEGABH7UIETldWXOwXXpJUWFurcr64DkAEGBwspLW10/avDx0KcCUAnIgAg2OdOMsVVvr94AcBrgSAExFgcKys6dP1SHy8X9vD8fG6MT/fpooAOAlnIcLRNpWUqHzJErlbWtQeFqYb8/M5gQPoQSbNnQQYAMDHpLmTXYgAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACNxNXogyHFLGgQrAgwIYtySBsGMK3EAQWzayJH64z//eUb7oxMmaP5rr9lQEZzOpLmTY2BAEHM1N3fa7m5pCXAlQPcjwIAg1ta3b6ft7WFhAa4E6H4EGBDEfjh+vG79jzZuSYNgwUkcQBCLT0nREkn3jhmjqH791B4Wppu4JQ2CBAEGBDGXy6Wp996rpUuX2l0K0O0IMCCIDRkyRFOmTLG7DKBHcBo9AMDHpLmTkzgAAEYiwAAARiLAAABGIsAAAEYiwAAARiLAAABG4ntgABDkgvWecAQYAASxYL4nHLsQASCIvfb0037hJUmFtbUqX7LEpoq6DwEGAEGmvb3d97j+88877RMM94QjwAAgyMyePVvNzc2qr6/Xtj17Ou0TDPeE4xgYAASR9vZ2rVixQiEhIWpoaNC2Eyd0q6Q1p/V5OD5eNwXBPeEcdzHf0tJSzZkzR8ePH9fUqVP10EMPndGnublZs2fPVllZmdra2rR161Zdcsklfn1MuiAlAHSX6upqjR49Wn369JFlWbIsS2kjR2rcwIEKaWlRe1iYbjzHPeFMmjsdtQJrampSXl6evF6vBgwYoIyMDN10000aNWqUX7/8/HwNHjxYu3btsqlSAHCmjRs3SpI6Ojp8bYOHD9cPUlM1dOhQZRt+5uHpHHUMzOv1avTo0YqOjpbb7VZubq5KS0v9+hw4cEDvv/++CgoKbKoSAJzrZICd7sUXX9SiRYs0ZMgQGyrqOY4KsP379ys6Otq3HRUVpQMHDvj12bZtm1wulzIzM5WUlKQ777xTzc3NgS4VAByno6NDmzZtOqN96NCheueddzR8+HAbquo5jgowl8slt9vt19bW1ua3XVdXp2HDhqmsrEyffPKJBg4cqHnz5gWyTABwpE8++USHDx/2axs5cqTeeustxcXF2VRVz3HUMbCYmBjV19f7tuvq6jRo0CC/PpdeeqnCw8PVt29fSdKkSZO0aNGiTl9v7ty5vsfp6elKT0/v9poBwCn+c/dhWlqa/vGPf5xxktvpKisrVVlZ2cOV9QxHnYXY2Ngoj8cjr9eryMhIZWZmqrCwUCkpKWpoaFBsbKyOHj2qK6+8Uhs3blRcXJweeughXXzxxXr44Yf9XsukM2kAoDv87Gc/09q1ayVJEydO1EsvvaR+/fqd12uYNHc6ahdiRESEli5dqoyMDI0YMUJZWVlKS0vTunXrNHXqVElS//799ac//UmTJk3SiBEjdOjQIc2ePdvmygHAXpZl+VZgd955p9atW3fe4WUaR63AupNJnyIA4LuqqalRcnKy8vPz9dRTT6lPnwtbn5g0dxJgABAEli1bpoMHD+rRRx+Vy+W64Ncxae4kwAAgCNTW1io+Pv47v45JcycBBgDwMWnudNRJHAAAdBUBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADBSiN0FAAC+mxMnTsjr9eqNN95QY2OjnnjiCbtLCgiXZVmW3UX0BJfLpSB9awB6Ocuy9Omnn6q8vFzl5eWqrKzU0aNHFSHpF6mpiv7e93QiNFRZ06drXHb2eb22SXMnKzAAMEBdXZ0qKipUXl6uN954Q1988YXf8xGSfup26383b/a1PVJbK0nnHWKmYAUGAA5WW1ur+++/X6+++uo5+10taXMn7Y9OmKD5r73W5f+eSXMnJ3EAgIPFx8fr73//u9555x3df//9uuyyyzrtF36W33e3tPRccTYjwADA4fr06aNrr71Wixcv1t69e/Xuu+9q5syZGjx4sK9P01l+tz0sLDBF2oBdiABgqI6ODnm9Xr300kv6fy+8oNRDh7TmtOcfjo/XTU8/fV7HwEyaOwkwAAgCHR0d+uPixdry5z9rUP/+ag8L0435+UF9FiIBBgDwMWnudNwxsNLSUnk8HiUlJamoqOicfRcuXCiPxxOgygAATuKoAGtqalJeXp4qKiq0fft2rV+/XtXV1Z32feedd7R69Wq5XK4AVwkAcAJHBZjX69Xo0aMVHR0tt9ut3NxclZaWntHv0KFDmjVrlpYtW2bMUhcA0L0cFWD79+9XdHS0bzsqKkoHDhzw62NZlu6++24tXLjQry8AoHdxVIC5XC653W6/tra2Nr/txYsX69prr9W4ceNYfQFAL+aoayHGxMSovr7et11XV6dBgwb59dmzZ4/Kysr0wgsv6Pjx4/ryyy91/fXXa+PGjWe83ty5c32P09PTlZ6e3lOlA4CRKisrVVlZaXcZF8RRp9E3NjbK4/HI6/UqMjJSmZmZKiwsVEpKihoaGhQbG+vXf+/evZo4caI+/vjjM17LpFNBAcApTJo7HbULMSIiQkuXLlVGRoZGjBihrKwspaWlad26dZo6deoZ/S3L4ixEAOilHLUC604mfYoAAKcwae501AoMAICuIsAAAEYiwAAARiLAAABGIsAAAEZy1BeZAfQ+m0pKVFZcrJDWVp0IDVXW9OnnfQ8r9E4EGADbbCop0eszZqiwttbX9si/HxNi+DbsQgRgm7LiYr/wkqTC2lqVL1liU0UwCQEGwBaWZenQ3r2dPuduaQlwNTARAQYg4J599lmlpqbqw507O32+PSwswBXBRBwDAxBQL7/8sh566CEdOXJEEZJulbTmtOcfiIvTxPx8m6qDSbgWIoCAOHz4sO677z6tXr3arz1CUpKkcElNkmokRQ4erNTUVI0ZM0ZjxozRVVddpf79+we+6F7IpLmTAANwwaeyW5alpqYm1dfXq66uzu/n9Lba2lrt2bNHHR0d51VXWFiYpkyZol//+te67rrrLvTt4TyYNHeyCxHo5To7lf2BnTv12Wef6YeJid8aTl9//XW313TllVdq2rRpuuOOOxQZGdntr4/gwAoM6OV+N2GC/k9Z2RntqZI++A6v27dvX3V0dKi9vV2SFBISoszMTI0fP14DBw7U9u3btXDhQl//8PBw/fznP9e0adOUmprKvf5sYtLcyQoM6OVCWls7bQ//j223263o6GhFRUUpOjra93P6dlRUlPr3769nn31WzzzzjO93x40bp5UrV2rIkCG+tpycHElSamqqpk2bpttuu00XX3xxt78/BC8CDOjlToSGdto+dORIzS8u9gXU97//ffXpc+qbN5ZlqbGx0S90Nm/erNzcXNXU1EiSQkNDVVRUpBkzZvj97pEjRxQXF6ePPvpIKSkpPfTOEOzYhQj0cp0dA3s4Pl43Pf30OU/kKC4u1oABA3THHXeora1N8+fPV1FRkW+XYWpqqlatWqXk5OQefw/oPibNnQQYAG0qKVH5kiVyt7SoPSxMN+bnnzO83nzzTWVlZemxxx5TTk6Opk6dqurqaknfHOsqKCjQgw8+qJAQdvKYxqS5kwADcF4+//xzXX311Tp8+LAuv/xyffnll2pra5MkXXHFFXr++ec1atQom6vEhTJp7uRSUgC6rKmpSZMnT9bhw4clSbt371ZbW5v69OmjOXPm6IMPPiC8EDCs7wF0iWVZuvvuu7V169Yznlu0aJFmzpxpQ1XozViBAeiSBQsW6OWXX+70uVmzZum2227T/v37A1wVejOOgQH4Vq+++qp++tOfdvpvKjExUTk5OcrJydHVV1/td7q8qfbt26dFixbppptuUmZmpsJ60dXxTZo72YUI4Jx27Nih22+/3W9Su+qqq5STk6NbbrklKE+Tj42N1TXXXKPs7GxFRETo5ptv1uTJk3XzzTfrkksusbs8/BsrMABn1dDQoDFjxqi2tlbjxo1TTk6OJk+erNjYWLtLC4gHHnjA73JXffv21fjx4zV58mRNmjRJMTExNlbXM0yaOwkwAJ2yLEvLli3TRRddpJ/85CeKioqyu6SAa29v18SJE/Xaa6+d8ZzL5dLYsWN9oT506FAbKux+Js2dBBgAnMPJVeiuXbs6fT4pKUkLFy7UxIkTA1xZzzBp7iTAAOBb1NTU6JprrtHRo0f92uPi4uT1ehUdHW1TZd3PpLnT/NOFAKCHJSUl6cUXXzzjFi979+7VyJEjVVpaalNlvRsBBgBdkJ2drQULFvi2/+u//kuS9NVXXyk7O1vTpk07Y4WGnkWAAUAXzZkzR7feeqvcbrc2btyo5cuXKyIiQpK0fPlyeTwevfnmmzZX2XtwDAxAj9m3b59iYmJ00UUX2V1Kt2lubtZdd93luyrJnj17dM8992jDhg2+Pvn5+coeN05v/fGPCmlt1YnQUGVNn37OK/w7hUlzJwEGoMcsWLBA119/va677jq7S+lWLS0tflfn6Ojo0DPPPKM5c+bo66+/VoSkSSEh+r8nTvj6PBIfrwnfco81JzBp7mQXIoAes3r1ar+VSbD4z0tL9enTR/n5+froo480duxYJUl+4SVJhbW1Kl+yJIBVBj/HBVhpaak8Ho+SkpJUVFR0xvOtra264YYblJCQoMTExE77ALDftm3btG3btl51TGjYsGF6++235RkypNPn3S0tAa4ouDkqwJqampSXl6eKigpt375d69ev993l9XSPPPKIPvvsM23dulVr1qzRP//5TxuqBXAuf/nLXyRJ7777rlp60cTtdrv1w7NclaO9F10UOBAcFWBer1ejR49WdHS03G63cnNzz/h+RWhoqDIyMnyPExISVFdXZ0e5gE97e7sxxw0CwbIsrV69WtI3e02qqqpsriiwsqZP1yPx8X5tD8fH68b8fJsqCk6Ouhr9/v37/b7RHhUVddbLt0jSwYMHVVVVpRUrVgSiPECNjY369NNPVVNT4/vZuXOnpk2bpvvuu8/u8hzjgw8+0O7du33bGzZsUHp6un0FBdjJEzUeXbJE7pYWtYeF6ab8fMefwGEaRwWYy+WS2+32a2tra+u0b0tLi6ZMmaIFCxaof//+gSgPvchXX32lHTt2+AVVTU2NvvjiC79+brdbK1as0F133WVTpc50cvV10oYNGzRv3jybqrHHuOxsAquHOSrAYmJiVF9f79uuq6vToEGDzujX2tqq3NxcZWdnn3PimDt3ru9xenp6r/oEiO/m448/1u23365//etfZ+3Tr18/rV27VtlMUn7a29u1Zs0av7aqqio1Nzfre9/7nk1V4WwqKytVWVlpdxkXxFHfA2tsbJTH45HX61VkZKQyMzNVWFiolJQUNTQ0KDY2Vs3NzcrJydH48eP1wAMPnPW1TPouA5xp165dGjNmjBoaGs54LjIyUiUlJb7LCeGUyspK33Hq05WVlenGG2+0oSKcD5PmTketwCIiIrR06VJlZGTo+PHj+sUvfqG0tDStXLlSq1at0oYNG+T1erVx40bt27dPzz33nCTplltuUWFhoc3Vw1SbSkpUVlzsu2JC2rRp+uSLL7Ro0aJOw+uyyy7T66+/ruHDh9tQrfOdPPvwP23YsIEAQ7dy1AqsO5n0KQL22VRSotdnzFBhba2v7fY+ffSPjg41dtI/OTlZr7/+ugYPHhy4Ig1y/PhxDRo0SBdffLGOHj2qw4cP69JLL9WxY8d01VVX6b333rO7RHwLk+ZOR51GDwRaWXGxX3hJ0osdHUqSlJCQoOXLl+uXv/ylJGns2LF66623CK9z2Lt3r/7whz9o165dvjOK09PTtWPHDl1++eVqbOzsYwFwYRy1CxEItJDW1k7bU5OTVbx1q0JCQvTee+/pxz/+sdauXavw8PAAV2iWhIQEJSQkSPrmwgSSFB4ervj4eP35z3825pM9zECAoVc7ERraafuA2FiFhHzzzyMnJ0dZWVnq27dvIEsz3ukBdtJ/3hAS+C7YhYherStXTMjOzia8LkBnAQZ0J1Zg6NW4YkLPaG9vV+u/d88SYOgpBBh6Pa6Y0P2am5t9j/nyMnoKuxABdLuTuw8lVmDoOQQYgG5HgCEQCDAA3Y4AQyBwDAxAt3uvrExXSwqXVPHf/62Y8HCOM6LbEWAAutWmkhLV/M//aPPJhupqPTJjhiQRYuhW7EIE0K3Kiou1+Kuv/NoKa2tVvmSJTRUhWBFgALrV2S7P5W5pCXAlCHYEGIBudbbLc7WHhQW4EgQ7AgxAt+rK5bmA7sD9wAB0u00lJSo/7fJcN3J5LmOYNHcSYAAAH5PmTnYhAgCMRIABAIxEgAEAjESAAQCMRIABAIxEgAEAjESAAQCMRIABAIxEgAEAjESAAQCMRIABAIxEgAEAjESAAQCMRIABAIxEgAEAjESAAQCMRIABAIxEgAEAjESAAQCM5LgAKy0tlcfjUVJSkoqKii64DwAguDkqwJqampSXl6eKigpt375d69evV3V19Xn3gb/Kykq7S3AMxuIUxuIUxsJMjgowr9er0aNHKzo6Wm63W7m5uSotLT3vPvDHP85TGItTGItTGAszOSrA9u/fr+joaN92VFSUDhw4cN59AADBz1EB5nK55Ha7/dra2trOuw8AIPiF2F3A6WJiYlRfX+/brqur06BBg867jyTFx8fL5XL1XLGGmTdvnt0lOAZjcQpjcQpj8Y34+Hi7S+gyl2VZlt1FnNTY2CiPxyOv16vIyEhlZmaqsLBQKSkpamhoUGxs7Fn7pKWl2V0+ACCAHLULMSIiQkuXLlVGRoZGjBihrKwspaWlad26dZo6deo5+wAAehdHrcAAAOgqR63Azhdfej7l295na2urbrjhBiUkJCgxMbFXj8XpFi5cKI/HE6DKAq8rY9Hc3Kx7771XQ4cOVVxcnI4cORLgKgOjK2OxatUqeTweJSYmasqUKWpqagpwlYGzZcsWpaSknPV5I+ZOy1CNjY1WXFycdfDgQevEiRNWWlqatWXLlvPuEwy68j5bWlqsN9980/c4JSXF+uijj+wot0edz//zt99+2xo1apTl8XgCXGVgdHUs7rnnHqugoCDwBQZQV8biwIED1uWXX241NjZalmVZeXl5VlFRkR3l9rhZs2ZZAwYMOOvfvilzp7ErML70fEpX3mdoaKgyMjJ8jxMSElRXV2dHuT2qq//PDx06pFmzZmnZsmWygnQvelfG4sCBA3r//fdVUFBgU5WB0ZWxaGtrU1NTk44dOybpmzOeQ0ND7Si3xz355JP68MMPz/q3b8rcaWyA8aXnU873fR48eFBVVVW65pprAlFeQHVlLCzL0t13362FCxf69Q02XRmLbdu2yeVyKTMzU0lJSbrzzjvV3Nwc6FJ7XFfGYvDgwZo5c6aSk5M1bdo0bd68WXl5eYEuNWDO9cHNlLnT2ADjS8+nnM/7bGlp0ZQpU7RgwQL1798/EOUFVFfGYvHixbr22ms1bty4oF19SV0bi7q6Og0bNkxlZWX65JNPNHDgwKD8PlRXxuLIkSN65ZVXVFVVpQkTJmj37t2qqKgIZJmOYcrcaWyAdeeXnk3X1ffZ2tqq3NxcZWdn66677gpkiQHTlbHYs2ePnn/+eSUnJ+uGG27Qrl27dP311we61B7XlbG49NJLFR4err59+6pPnz6aNGmSduzYEehSe1xXxqK8vFzJyclKTExUbm6uFi1apGeffTbQpTqCMXOnrUfgvoNjx45ZP/rRj6y6ujrr+PHjVlpamrVp0ybryJEj1t69e8/ZJ9h0ZSyampqsrKws6/e//73N1fasrozF6fbs2WNdccUVNlTa87oyFkeOHLHi4uKsPXv2WJZlWQ8++KBVWFhoZ9k9oitjsWXLFmvYsGHW4cOHLcuyrMcff9yaPXu2nWX3qM8//9zvb9/EudPYALMsy3r11VetESNGWMOGDbPmz59vWZZlPffcc1Z6evo5+wSjbxuLDRs2WKGhoVZSUpLv5+GHH7az5B7Tlb+Lkz7//POgPQvRsro2Fm+88YaVkpJiDR8+3PrVr35ltbW12VVuj+rKWBQXF1vDhg2zkpOTrdtvv913RmKweeyxx6wrr7zS6tevn5Wammpt3LjRWrlypXFzJ19kBgAYydhjYACA3o0AAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAYiQADABiJAAMAGIkAAwAY6f8DLVjG17Feb8oAAAAASUVORK5CYII=\"\n",
        "  frames[1] = \"data:image/png;base64,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\"\n",
        "  frames[2] = \"data:image/png;base64,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\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
        "        animCAPMNFKXYMKCSJRG = new Animation(frames, img_id, slider_id, 100, loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.animation.FuncAnimation at 0x7f524c159978>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "del pool"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simulate(P, N, D, S, G, dt):\n",
      "    x0, v0, m = initial_cond(N, D)\n",
      "    pool = Pool(P)\n",
      "    for s in range(S):\n",
      "        x1, v1 = timestep(x0, v0, G, m, dt, pool)\n",
      "        x0, v0 = x1, v1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "import time\n",
      "Ps = [1, 2, 4, 8]\n",
      "runtimes = []\n",
      "for P in Ps:\n",
      "    print(\"running\", P)\n",
      "    start = time.time()\n",
      "    simulate(P, 64, 3, 300, 1.0, 1e-3)\n",
      "    stop = time.time()\n",
      "    runtimes.append(stop - start)\n",
      "print(runtimes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "running 1\n",
        "running"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2\n",
        "running"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 4\n",
        "running"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 8\n",
        "[56.02754735946655, 145.93722319602966, 391.36282658576965, 748.9838373661041]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "CPU times: user 22min 17s, sys: 57.7 s, total: 23min 15s\n",
        "Wall time: 22min 22s\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rts = runtimes[0] / np.array(runtimes) \n",
      "plt.plot(Ps, rts, 'ko-')\n",
      "plt.xlabel('Number of Threads, $P$')\n",
      "plt.ylabel('speedup, $t_1/t_P$')\n",
      "plt.savefig('n-body-thread-speedup.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAETCAYAAAAs4pGmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f524c0eb438>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(Ps, rts / Ps, 'ko-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f5246d64eb8>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAEACAYAAABBDJb9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f524c1a4358>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rts"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "array([ 1.        ,  0.3839154 ,  0.14316012,  0.07480475])"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rts[1:] / rts[:-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([ 0.3839154 ,  0.37289495,  0.52252506])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(Ps[1:], rts[1:] / rts[:-1], 'ko-')\n",
      "plt.xlabel('Number of Threads, $P$')\n",
      "plt.ylabel('Relative Double Speedup, $t_P/t_{\\\\frac{P}{2}}$')\n",
      "plt.savefig('n-body-thread-double-speedup.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEOCAYAAABIESrBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEwgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f524c02bb70>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "runtimes[0]/1.9455578327178955"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "28.79767767231955"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}