01_direct_summation_P2P.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Direct Summation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "from matplotlib import pyplot, rcParams\n",
    "%matplotlib inline\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# customizing plot parameters\n",
    "rcParams['figure.dpi'] = 100\n",
    "rcParams['font.size'] = 14\n",
    "rcParams['font.family'] = 'StixGeneral'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many physical problems require the evaluation of all pairwise interactions of a large number of particles, and we usually call them N-body problems. Some typical examples are molecular dynamics, astrodynamics and electromagnetics. Their pairwise interactions can be expressed as:\n",
    "\n",
    "$$\\begin{equation}\n",
    "f_i = \\sum_{j=1}^n{P \\left(\\boldsymbol{x}_i, \\boldsymbol{x}_j \\right)w_j} \\tag*{for $i=1,2,...,n$ }\n",
    "\\end{equation}$$\n",
    "\n",
    "where subscript $i$,  $j$ respectively denotes *target* and *source*, $f_i$ can be a *potential* (or *force*) at target point $i$, $w_j$ is the *source weight*, $\\boldsymbol{x}_i, \\boldsymbol{x}_j$ are the *spatial positions* of particles, and $P \\left(\\boldsymbol{x}_i, \\boldsymbol{x}_j \\right)$ is the *interaction kernel*. In order to evalute the potential $f_i$ at a target point $i$, we have to loop over each source particle $j$. Since there are $n$ target points $i$, this 'brute-force' approach costs $\\mathcal{O} \\left(n^2 \\right)$ operations. \n",
    "\n",
    "Through this tutorial, a treecode algorithm is demonstated step by step to reduce the computation cost to $\\mathcal{O} \\left( n\\log n \\right)$ on a **gravitational N-body problem**.\n",
    "In the first IPython Notebook, we will use the most straightforward way to calculate the gravitational potential at each target point. \n",
    "\n",
    "Assuming there are $n$ point mass particles in the 'galaxy', each can be treated as a target and a source to other particles. To begin with, let's generate a random location for each particle in the domain $x$, $y$, $z$ $\\in$ $\\left[ 0, 1 \\right]$. Here we also assume that every particle has the same mass with a summation of 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Point():\n",
    "    \"\"\"The class for a point.\n",
    "    \n",
    "    Arguments:\n",
    "        coords: a three-element list, containing the 3d coordinates of the point\n",
    "        domain: the domain of random generated coordinates x,y,z, default=1.0\n",
    "    \n",
    "    Attributes:\n",
    "        x, y, z: coordinates of the point\n",
    "    \"\"\"\n",
    "    def __init__(self, coords=[], domain=1.0):\n",
    "        if coords:\n",
    "            assert len(coords) == 3, \"the size of coords should be 3.\"\n",
    "            self.x = coords[0]\n",
    "            self.y = coords[1]\n",
    "            self.z = coords[2]\n",
    "        else:\n",
    "            self.x = domain * numpy.random.random()\n",
    "            self.y = domain * numpy.random.random()\n",
    "            self.z = domain * numpy.random.random()\n",
    "            \n",
    "    # overload distance function\n",
    "    def distance(self, other):\n",
    "        return numpy.sqrt((self.x-other.x)**2 + (self.y-other.y)**2\n",
    "                                          + (self.z-other.z)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Particle(Point):\n",
    "    \"\"\"The derived class for a particle, inheriting the base class \"Point\".\n",
    "    \n",
    "    Attributes:\n",
    "        m: mass of the particle\n",
    "        phi: the gravitational potential of the particle\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, coords=[], domain=1.0, m=1.0):\n",
    "        Point.__init__(self, coords, domain)\n",
    "        self.m = m\n",
    "        self.phi = 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The class `Particle` is a subclass of `Point` and we can check it by using the function `issubclass()`. Let's try it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issubclass(Particle,Point)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create our particles using our `Particle` class, and we store them in a list. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 50\n",
    "particles = [ Particle(m=1.0/n) for i in range(n) ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Direction summation is the closest implementation to a physical problem, where each particle can \"feel\" the gravitational force due to others in the system. Therefore, the number of interactions scales as $\\mathcal{O} \\left(n^2 \\right)$. The potential $\\Phi_i$ at a target point $i$ in the gravitational field can be expressed as:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\Phi_i = \\sum_{\\substack{j=0\\\\ j \\neq i}}^n{\\frac{m_j}{r_{ij}}}\n",
    "\\end{equation}$$\n",
    "\n",
    "where $m_j$ denotes the mass of source point $j$, and $r_{ij}$ is the distance between target point $i$ and source point $j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def direct_sum(particles):\n",
    "    \"\"\"Calculate the gravitational potential at each particle\n",
    "    using direct summation method.\n",
    "\n",
    "    Arguments:\n",
    "        particles: the list of particles\n",
    "\n",
    "    \"\"\"\n",
    "    for i, target in enumerate(particles):\n",
    "        for source in (particles[:i] + particles[i+1:]):\n",
    "            r = target.distance(source)\n",
    "            target.phi += source.m/r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "direct_sum(particles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is an array of the gravitational potential at each target point. Later we will use the direct summation result as the accurate solution when compared to the result of using multipole expansion and the final treecode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [
    {
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plUqX3ztf++zZs3Hx4kW88cYb4HkehBBBPu/ZswcPPfSQ9xfkBZGRkXjxxRcxZ84cbN++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\nBGEybndfHnnkPEaPHklhYWFYvVzDgao/+MknX7NqVSmyXIwgaFCUjXT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oLnS6uor1siyz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\nmjTB5s2LsGvXfhw6NBUajQ4NG4Zh+PDejJg0l2dKYjN53c/PD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fba4f83e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot spatial particle distribution\n",
    "fig = pyplot.figure(figsize=(10,4.5))\n",
    "# left plot\n",
    "ax = fig.add_subplot(1,2,1, projection='3d')\n",
    "ax.scatter([particle.x for particle in particles], \n",
    "           [particle.y for particle in particles], \n",
    "           [particle.z for particle in particles], s=30, c='b')\n",
    "ax.set_xlim3d(0,1)\n",
    "ax.set_ylim3d(0,1)\n",
    "ax.set_zlim3d(0,1)\n",
    "ax.set_xlabel(r'$x$')\n",
    "ax.set_ylabel(r'$y$')\n",
    "ax.set_zlabel(r'$z$')\n",
    "ax.set_title('Particle Distribution')\n",
    "# right plot\n",
    "ax = fig.add_subplot(1,2,2, projection='3d')\n",
    "scale = 50   # scale for dot size in scatter plot\n",
    "ax.scatter([particle.x for particle in particles], \n",
    "           [particle.y for particle in particles], \n",
    "           [particle.z for particle in particles],\n",
    "           s=numpy.array([particle.phi for particle in particles])*scale, c='b')\n",
    "ax.set_xlim3d(0,1)\n",
    "ax.set_ylim3d(0,1)\n",
    "ax.set_zlim3d(0,1)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_zlabel('$z$')\n",
    "ax.set_title('Particle Distribution (radius implies potential)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try a magic function [**%timeit**](https://docs.python.org/2/library/timeit.html) to evaluate the computation time of direct summation method. (Try **%lsmagic** to see a list of line magics and cell magics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 7.59 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit direct_sum(particles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output shows the average time taken by the best 3 loop run by `timeit` . When we dive into treecode, we will use this magic funtion to achieve the benchmarks. In the code, we use double loops to evaluate the interaction of each pair. We usually refer the direct summation function as the **Particle-to-Particle** or **P2P** kernal. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. R. Yokota, 12 Steps to a Fast Multipole Method on GPUs, Pan-American Advanced Studies Institute, Valparaiso, Chile, 3-14 January, 2011.\n",
    "2. Raykar, V. C., \"[A short primer on the fast multipole method: FMM tutorial](http://www.umiacs.umd.edu/labs/cvl/pirl/vikas/publications/FMM_tutorial.pdf),\", University of Maryland, College Park, Apr. 8, 2006."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": false
   },
   "outputs": [
    {
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       "    font-size: 14pt;\n",
       "    text-align: center;\n",
       "    margin-top: 0em;\n",
       "    margin-bottom: 2em;\n",
       "    font-style: regular;\n",
       "}\n",
       "\n",
       ".text_cell_render h5 {  /*Use this for small titles*/\n",
       "    font-family: 'Nixie One', sans-serif;\n",
       "    font-weight: 400;\n",
       "    font-size: 16pt;\n",
       "    color: rgb(163,0,0);\n",
       "    font-style: italic;\n",
       "    margin-bottom: .1em;\n",
       "    margin-top: 0.8em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h6 { /*use this for copyright note*/\n",
       "    font-family: 'PT Mono', sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 9pt;\n",
       "    line-height: 100%;\n",
       "    color: grey;\n",
       "    margin-bottom: 1px;\n",
       "    margin-top: 1px;\n",
       "}\n",
       "\n",
       ".CodeMirror{\n",
       "        font-family: \"PT Mono\";\n",
       "        font-size: 90%;\n",
       "}\n",
       "\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"],\n",
       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# loading style sheet\n",
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open('./style/fmmstyle.css', 'r').read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}