02_multipole_expansion_P2M.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Multipole Expansion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# importing libraries\n",
    "import numpy\n",
    "from treecode_helper import Particle, Point\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": [
    "The direct summation method calculates the gravitational potential by the equation:\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 we evaluate each source particle's effect on each target particle, and the computation complexity is $\\mathcal{O} \\left(N^2 \\right)$. We can use direct summation for a small scale of particles, but when it comes to a larger scale, the computation time grows proportionally to the square of particles number. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of calculating all pair interactions, here we introduce a treecode method, in which the simulation volume is divided up into cubic cells via an octree, so that only particles from **nearby cells** need to be treated individually (as **direct summation**), and particles in **distant cells** can be treated as a single large particle centered at the cell's center of mass (or as a **low-order multipole expansion**). This can dramatically reduce the computational cost.\n",
    "\n",
    "<img src=\"image/quad_tree.png\">\n",
    "\n",
    "The figure above shows a quadtree structure for a 2D particle distribution. When we are calculating the potential at target (red), we loop over each source particles nearby (green) and use multipole expansion to evaluate the effect of the grouped distant sources (blue).\n",
    "\n",
    "First, we introduce multipole expansion at a cell's center. In a word, we want to decouple the interaction term $\\frac{m_j}{r_{ij}}$ for the particles in a distance:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\Phi_i = \\sum_{j=0}^N{\\frac{m_j}{r_{ij}}} = \\sum_{j=0}^N {A_j B_i}\n",
    "\\end{equation}$$\n",
    "\n",
    "where $A_j$ is the term that only depends on source particles (*multipole*), and $B_i$ is the part depends on target particles (*weight*).\n",
    "\n",
    "Recall the second-order taylor expansion in three variables $x$, $y$, $z$:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "f(x,y,z) & \\approx f(a,b,c) + \\left(x-a\\right)f_x(a,b,c) + \\left(y-b\\right)f_y(a,b,c) + \\left(z-c\\right)f_z(a,b,c) \\\\\n",
    "& + \\frac{1}{2!}[\\left(x-a\\right)^2f_{xx}(a,b,c) + \\left(y-b\\right)^2f_{yy}(a,b,c) + \\left(z-c\\right)^2f_{zz}(a,b,c) \\\\\n",
    "& + 2\\left(x-a\\right)\\left(y-b\\right)f_{xy}(a,b,c) + 2\\left(y-b\\right)\\left(z-c\\right)f_{yz}(a,b,c) \\\\ \n",
    "& + 2\\left(z-c\\right)\\left(x-a\\right)f_{zx}(a,b,c)]\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "We assume that: \n",
    "$$f(x_j,y_j,z_j) = \\frac{m_{j}}{r_{ij}} = \\frac{m_{j}}{\\sqrt{(x_i-x_j)^2 + (y_i-y_j)^2 + (z_i-z_j)^2}}$$ \n",
    "\n",
    "<img src=\"image/multipole.png\">\n",
    "\n",
    "Here we expand the interaction term $f(x_j,y_j,z_j)$ around a center point $(x_c, y_c, z_c)$ to the second order: \n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "f(x_j,y_j,z_j) & \\approx f(x_c,y_c,z_c) + (x_j-x_c)\\, f_{x_j}\\rvert_c + (y_j-y_c)\\, f_{y_j}\\rvert_c + (z_j-z_c)\\, f_{z_j}\\rvert_c \\\\\n",
    "& + \\frac{1}{2!}[(x_j-x_c)^2f_{x_jx_j}\\rvert_c + (y_j-y_c)^2f_{y_jy_j}\\rvert_c + (z_j-z_c)^2f_{z_jz_j}\\rvert_c \\\\\n",
    "& + 2(x_j-x_c)(y_j-y_c)f_{x_jy_j}\\rvert_c + 2(y_j-y_c)(z_j-z_c)f_{y_jz_j}\\rvert_c \\\\ \n",
    "& + 2(z_j-z_c)(x_j-x_c)f_{z_jx_j}\\rvert_c]\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "then we calculate each derivative's value at the expansion center $(x_c,y_c,z_c)$:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "& f_{x_j}\\rvert_c = \\frac{x_i-x_c}{R^3} m_j\\\\\n",
    "& f_{x_jx_j}\\rvert_c = \\left(\\frac{3(x_i-x_c)^2}{R^5} - \\frac{1}{R^3}\\right) m_j \\\\\n",
    "& f_{x_jy_j}\\rvert_c = \\frac{3(x_i-x_c)(y_i-y_c)}{R^5} m_j\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "where $R$ is the distance between target particle $i$ and the cell's center $c$. Now let's write out the interaction term again:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "\\frac{m_j}{r_{ij}} & \\approx \\frac{m_j}{R} + m_j(x_c-x_j)\\left(-\\frac{x_i-x_c}{R^3}\\right) + m_j(y_c-y_j)\\left(-\\frac{y_i-y_c}{R^3}\\right) \\\\\n",
    "& + m_j(z_c-z_j)\\left(-\\frac{z_i-z_c}{R^3}\\right) + \\frac{m_j(x_c-x_j)^2}{2}\\left(\\frac{3(x_i-x_c)^2}{R^5} - \\frac{1}{R^3}\\right) \\\\\n",
    "& + \\frac{m_j(y_c-y_j)^2}{2}\\left(\\frac{3(y_i-y_c)^2}{R^5} - \\frac{1}{R^3}\\right) + \\frac{m_j(z_c-z_j)^2}{2}\\left(\\frac{3(z_i-z_c)^2}{R^5} - \\frac{1}{R^3}\\right) \\\\\n",
    "& + \\frac{m_j(x_c-x_j)(y_c-y_j)}{2}\\frac{3(x_i-x_c)(y_i-y_c)}{R^5} \\\\\n",
    "& + \\frac{m_j(y_c-y_j)(z_c-z_j)}{2}\\frac{3(y_i-y_c)(z_i-z_c)}{R^5} \\\\\n",
    "& + \\frac{m_j(z_c-z_j)(x_c-x_j)}{2}\\frac{3(z_i-z_c)(x_i-x_c)}{R^5}\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "Note that for each term, the first part only depends on source particle $j$, that means as long as we know the source particle information in a cell, we can calculate this part independently from targets $i$. There is a total of 10 terms in the expansion; we call the first term $m_j$ as **monopole**, from the second to the fourth $m_j(x_c-x_j)$, $m_j(y_c-y_j)$, $m_j(z_c-z_j)$ we call them **dipole**, and the remaining six terms $\\frac{m_j(x_c-x_j)^2}{2}$, $\\frac{m_j(y_c-y_j)^2}{2}$, $\\frac{m_j(z_c-z_j)^2}{2}$, $\\frac{m_j(x_c-x_j)(y_c-y_j)}{2}$, $\\frac{m_j(y_c-y_j)(z_c-z_j)}{2}$, $\\frac{m_j(z_c-z_j)(x_c-x_j)}{2}$ are called **quadrupole** with a second-order term in $x_j$.\n",
    "That is why we call this a **multipole expansion**. The multipoles have no relationship with target particles, so we can calculate those constants before looping in $i$. The second part in each term only depends on target particles $i$, so we can calculate this part in the loop. From above we can write the interaction term as:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\frac{m_j}{r_{ij}} = \\sum_{k=1}^{10} A_k(j)\\,B_k(i)\n",
    "\\end{equation}$$\n",
    "\n",
    "Remember that what we just considered is only one source particle $j$'s effect on target $i$. In order to evaluate the potential $\\Phi_i$, we need to take all the source particles into account:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "\\Phi_i & = \\sum_{j=0}^N{\\frac{m_j}{r_{ij}}} = \\sum_{j=0}^N \\sum_{k=1}^{10} A_k(j)\\,B_k(i) \\\\\n",
    "& = \\sum_{k=1}^{10} \\left(\\sum_{j=0}^N A_k(j)\\right) B_k(i)\n",
    "\\end{split}\\end{equation}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For different target particle $i$, the coefficient $\\sum_{j=0}^N A_k(j)$ holds the same. Thus, in the multipole code below we first loop in source particles $j$ to calculate the multipoles, then loop over each target particles $i$ to evaluate the potentials.\n",
    "Even though we have a cluster of $n$ targets, they don't interact with each other. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 50     # number of particles\n",
    "m = 1./n    # mass\n",
    "\n",
    "# initialize sources and targets\n",
    "source_coords = numpy.random.random((n, 3)).tolist()\n",
    "target_coords = (-numpy.random.random((n, 3))).tolist()\n",
    "sources = [ Particle(coord, m=m) for coord in source_coords ]\n",
    "targets = [ Particle(coord, m=m) for coord in target_coords ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The multipole expansion converges and provides an accurate solution under two conditions:\n",
    "* The sources are close to the expansion center (cell's center).\n",
    "* The targets are located far enough from the expansion center.\n",
    "\n",
    "Therefore, in this notebook, we assume there are $n$ sources located in the domain: $x_j$, $y_j$, $z_j$ $\\in$ $\\left[ 0, 1 \\right]$, while $n$ targets in the domain: $x_i$, $y_i$, $z_i$ $\\in$ $\\left[ -1, 0 \\right]$, in order to satisfy the convergence condition above. We also assume the sources are in a cubic cell whose center is located at $(0.5, 0.5, 0.5)$. Now let's initialize the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "center = Point([0.5, 0.5, 0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def P2M(sources, center):\n",
    "    \"\"\"Given sources and cell's information, return multipole\n",
    "    \n",
    "    Arguments:\n",
    "        sources: the list of source objects in 'Particle' class\n",
    "        center: the point object of expansion center\n",
    "    \n",
    "    Returns:\n",
    "        multipole: the multipole array of the cell\n",
    "        \n",
    "    \"\"\"\n",
    "    # prepare for array operation\n",
    "    dx = center.x - numpy.array([source.x for source in sources])\n",
    "    dy = center.y - numpy.array([source.y for source in sources])\n",
    "    dz = center.z - numpy.array([source.z for source in sources])\n",
    "    source_m = numpy.array([source.m for source in sources])\n",
    "    \n",
    "    # calculate the contribution of each source (the expression only\n",
    "    # works with 2nd order Taylor series in 3 variables)\n",
    "    multipole = source_m * [numpy.ones(n), dx, dy, dz, dx**2/2, dy**2/2, \n",
    "                            dz**2/2, dx*dy/2, dy*dz/2, dz*dx/2]\n",
    "    \n",
    "    # sum the multipole over sources    \n",
    "    multipole = numpy.sum(multipole[:], axis=1)\n",
    "    return multipole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def distance(array, point):\n",
    "    \"\"\"Return the distance array between each element in the array and\n",
    "    the point.\n",
    "    \n",
    "    Arguments:\n",
    "        array: an array of n points' xyz coordinates with a shape of (3, n)\n",
    "        point: a xyz-coordinate triplet of the point \n",
    "        \n",
    "    Returns:\n",
    "        the distance array\n",
    "        \n",
    "    \"\"\"\n",
    "    return numpy.sqrt((array[0]-point.x)**2 + (array[1]-point.y)**2\n",
    "                                            + (array[2]-point.z)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "multipole = P2M(sources, center)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def eval_potential(targets, multipole, center):\n",
    "    \"\"\"Given targets list, multipole and expansion center, return\n",
    "    the array of target's potentials.\n",
    "    \n",
    "    Arguments:\n",
    "        targets: the list of target objects in 'Particle' class\n",
    "        multipole: the multipole array of the cell\n",
    "        center: the point object of expansion center\n",
    "    \n",
    "    Returns:\n",
    "        phi: the potential array of targets\n",
    "        \n",
    "    \"\"\"\n",
    "    # prepare for array operation\n",
    "    target_x = numpy.array([target.x for target in targets])\n",
    "    target_y = numpy.array([target.y for target in targets])\n",
    "    target_z = numpy.array([target.z for target in targets])\n",
    "    target_array = [target_x, target_y, target_z]\n",
    "    \n",
    "    # calculate the distance between each target and center\n",
    "    r = distance(target_array, center)\n",
    "    \n",
    "    # prearrange some constants for weight\n",
    "    dx, dy, dz = target_x-center.x, target_y-center.y, target_z-center.z\n",
    "    r3 = r**3\n",
    "    r5 = r3*r**2\n",
    "    \n",
    "    # calculate the weight for each multipole\n",
    "    weight = [1/r, -dx/r3, -dy/r3, -dz/r3, 3*dx**2/r5 - 1/r3, \\\n",
    "              3*dy**2/r5 - 1/r3, 3*dz**2/r5 - 1/r3, 3*dx*dy/r5, \\\n",
    "              3*dy*dz/r5, 3*dz*dx/r5]\n",
    "    \n",
    "    # evaluate potential\n",
    "    phi = numpy.dot(multipole, weight)\n",
    "    return phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "phi_multi = eval_potential(targets, multipole, center)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the spatial distribution of target (red) and source (blue) particles. The center of the cell is marked with a green dot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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msxlRUVH46quvxCkkCYniIDf04DMAr+enTAFS2YRSBxHBZDIhIyMDCoVC9Ezp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97Zg4yMDHbs2M1ff51GrVbToUMcbdu29qr7b9++fTzyyLPY7R+g03VCEAS0WhuHDi1iwIBRbNz4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa98695c8d0>"
      ]
     },
     "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([target.x for target in targets], \n",
    "           [target.y for target in targets], \n",
    "           [target.z for target in targets], s=30, c='b')\n",
    "ax.scatter([source.x for source in sources], \n",
    "           [source.y for source in sources], \n",
    "           [source.z for source in sources], s=30, c='r')\n",
    "\n",
    "ax.scatter(center.x, center.y, center.z, s=30, c='g')\n",
    "\n",
    "ax.set_xlim3d(-1,1)\n",
    "ax.set_ylim3d(-1,1)\n",
    "ax.set_zlim3d(-1,1)\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 = 100   # scale for dot size in scatter plot\n",
    "ax.scatter([target.x for target in targets], \n",
    "           [target.y for target in targets], \n",
    "           [target.z for target in targets],\n",
    "           s=phi_multi*scale, c='b')\n",
    "ax.set_xlim3d(-1,0)\n",
    "ax.set_ylim3d(-1,0)\n",
    "ax.set_zlim3d(-1,0)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_zlabel('$z$')\n",
    "ax.set_title('Target Distribution (radius implies potential)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall in the previous notebook, we use the same list of source particles and target particles, while since here we have separate list of sources and targets, we have to modify the direct summation module as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def direct_sum(sources, targets):\n",
    "    \"\"\"Calculate the gravitational potential (target.phi) at each target \n",
    "    particle using direct summation method.\n",
    "\n",
    "    Arguments:\n",
    "        sources: the list of source objects in 'Particle' class\n",
    "        targets: the list of target objects in 'Particle' class\n",
    "\n",
    "    \"\"\"\n",
    "    for target in targets:\n",
    "        for source in sources:\n",
    "            r = target.distance(source)\n",
    "            target.phi += source.m/r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "direct_sum(sources, targets)\n",
    "phi_direct = numpy.array([target.phi for target in targets])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run the direct summation code and multipole expansion code respectively, and get a rough estimation about the time elapsed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 8.76 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit direct_sum(sources, targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 221 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "multipole = P2M(sources, center)\n",
    "eval_potential(targets, multipole, center)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We found the multipole expansion consumes much less time than the 'brute-force' method, because we decouple the interaction term $\\frac{m_j}{r_{ij}}$ into $A_k(j)\\,B_k(i)$. Therefore, we can calculate the $A_k(j)$ outside the loop in targets $i$, saving us from double loop! If you increase the number of particles $n$, the speedup will be greater.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's verify the accuracy of multipole expansion according the exact solution given by direct summation. We use $L^2$ relative error norm to assess the error:\n",
    "\n",
    "$$\\begin{equation}\n",
    "err_{L^2} = \\sqrt \\frac{\\sum \\left(\\Phi_{direct}-\\Phi_{multi}\\right)^2}{\\sum \\Phi_{direct}^2}\n",
    "\\end{equation}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 Norm error: 0.0032885580660324877\n"
     ]
    }
   ],
   "source": [
    "err = numpy.sqrt(sum((phi_direct-phi_multi)**2)/sum(phi_direct**2))\n",
    "print('L2 Norm error: {}'.format(err))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa97826e5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the relative error band\n",
    "err_rel = abs((phi_multi - phi_direct) / phi_direct)\n",
    "pyplot.figure(figsize=(10,4))\n",
    "ax = pyplot.gca()\n",
    "pyplot.plot(range(n), err_rel, 'bo', alpha=0.5)\n",
    "pyplot.xlim(0,n-1)\n",
    "pyplot.ylim(1e-6, 1e-1)\n",
    "ax.yaxis.grid()\n",
    "pyplot.xlabel('target particle index')\n",
    "pyplot.ylabel('$e_{\\phi rel}$', fontsize=22)\n",
    "ax.set_yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case where sources are close to the expansion center, and targets in a distance, we find this accelerated algorithm gives a very accurate estimation of the potentials at targets. Remember in the multipole expansion code, we first go over each source particles $j$ to evaluate the multipole the cell. That is why we refer this module as **Particle-to-Multipole** or **P2M** in the treecode."
   ]
  },
  {
   "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": 16,
   "metadata": {
    "code_folding": [
     1
    ],
    "collapsed": false
   },
   "outputs": [
    {
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       "}\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": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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
}