03_shift_the_expansion_M2M.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Multi-level Multipole Expansion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall in the previous notebook, we grouped all the sources in the same cell. However, when the number of particles becomes very large, instead of grouping all the sources in a single cell, we need to build a hierachical structure to group the particles. The picture below shows a quadtree structure for a 2D particle distribution, where each parent cell (grey) can be split into 4 child cells (orange). From the previous lesson we know that the multipole of a cell only depends on the sources in that cell and the center of the cell, namely, the multipole is a \"property\" of a cell. \n",
    "\n",
    "<img src=\"image/m2m.png\">\n",
    "\n",
    "Now that multipole is a property of a cell, we should be able to evaluate the multipole of a parent cell given the multipole values of its child cells. That is our goal for this notebook! Here we use an octree to subdivide a parent cell into 8 child cells in 3D.\n",
    "\n",
    "First, let's review the terms in the multipole of a child cell $c$. Notice we are only showing some terms, the remaining ones can be deducted by similarity:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "M_c &= \\sum_{j=0}^{N_c} m_j\\\\\n",
    "D_{c_x} &= \\sum_{j=0}^{N_c} m_j\\,( x_c - x_j)\\\\\n",
    "Q_{c_{xx}} &= \\sum_{j=0}^{N_c} \\frac{1}{2}m_j\\, ( x_c - x_j)^2 \\\\\n",
    "Q_{c_{xy}} &= \\sum_{j=0}^{N_c} \\frac{1}{2}m_j\\, (x_c-x_j)(y_c-y_j) \\\\\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "where $N_c$ is the number of sources in the child cell, $x_c$ is the cell's center, $M$, $D$, $Q$ are respectively monopole, dipole and quadrupole. When we expand the particles from a smaller group (*child*) to a larger group (*parent*), we also need to shift the center of expansion from ($x_c$, $y_c$, $z_c$) to ($x_p$, $y_p$, $z_p$). Now we expand them in a parent cell $p$ with 8 child cells:\n",
    "\n",
    "$$\\begin{equation}\\begin{split}\n",
    "M_p &= \\sum_{j=0}^N m_j = \\sum_{c=0}^7 M_c\\\\\n",
    "D_{p_x} &= \\sum_{j=0}^N m_j\\,( x_p - x_j) = \\sum_{c=0}^7 \\left[\\sum_{j=0}^{N_c} m_j\\,(x_c-x_j) + ( x_p-x_c)\\sum_{j=0}^{N_c} m_j\\right]\\\\\n",
    "&= \\sum_{c=0}^{7} \\left[D_{c_x} + (x_p-x_c)\\,M_c\\right] \\\\\n",
    "Q_{p_{xx}} &= \\sum_{j=0}^N \\frac{1}{2}m_j \\,(x_p - x_j)^2 = \\sum_{c=0}^7 \\left[\\sum_{j=0}^N \\frac{1}{2}m_j\\left[(x_c-x_j)+(x_p-x_c)\\right]^2 \\right]\\\\\n",
    "&= \\sum_{c=0}^7 \\left[\\sum_{j=0}^N \\frac{1}{2}m_j (x_c - x_j)^2 + (x_p-x_c) \\sum_{j=0}^N m_j(x_c-x_j) + \\frac{(x_p-x_c)^2}{2} \\sum_{j=0}^N m_j \\right]\\\\\n",
    "&= \\sum_{c=0}^7 \\left[Q_{c_{xx}} + (x_p-x_c)D_{c_{x}} + \\frac{(x_p-x_c)^2}{2}M_c \\right]\\\\\n",
    "Q_{p_{xy}} &= \\sum_{j=0}^{N} \\frac{1}{2}m_j\\, (x_p-x_j)(y_p-y_j) \\\\\n",
    "&= \\sum_{c=0}^7 \\left[\\sum_{j=0}^{N} \\frac{1}{2}m_j(x_c-x_j)(y_c-y_j) + \\frac{(x_p-x_c)}{2}\\sum_{j=0}^{N}m_j(y_c-y_j) \\right.\\\\\n",
    "&+\\left. \\frac{(y_p-y_c)}{2}\\sum_{j=0}^{N}m_j(x_c-x_j) + \\frac{(x_p-x_c)(y_p-y_c)}{2}\\sum_{j=0}^{N}m_j\\right]\\\\\n",
    "&= \\sum_{c=0}^7 \\left[ Q_{c_{xy}} +\\frac{(x_p-x_c)}{2}D_{c_y} +\\frac{(y_p-y_c)}{2}D_{c_x} + \\frac{(x_p-x_c)(y_p-y_c)}{2}M_c \\right]\n",
    "\\end{split}\\end{equation}$$\n",
    "\n",
    "Each multipole term $M_p$, $D_p$, $Q_p$ in parent cell can be expressed by a summation of its child's multipole terms $M_c$, $D_c$, $Q_c$. Therefore, we refer this expansion shifting process as **Multipole-to-Multipole** or **M2M**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the same spatial distribution of sources and targets as the previous lesson, and they are well separated. 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: $x_i$, $y_i$, $z_i$ $\\in$ $\\left[ -1, 0 \\right]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we assign all the sources in the **parent** cell centered at $(0.5, 0.5, 0.5)$ with a side length of $1$. Then we subdivide the unit cube into 8 **child** cells to form an octree. The child's side length should be $0.5$. We index the $8$ child cells from $0$ to $7$, and calculate the coordinates of child's center based on the index (octant)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# importing libraries\n",
    "import numpy\n",
    "from treecode_helper import Particle, distance, l2_err, plot_err\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'] = 16\n",
    "rcParams['font.family'] = 'StixGeneral'"
   ]
  },
  {
   "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": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Cell():\n",
    "    \"\"\"The class for a cell.\n",
    "    \n",
    "    Attributes:\n",
    "        x, y, z: xyz coordinates of the cell's center\n",
    "        multipole: the array of the cell's multipoles\n",
    "    \n",
    "    \"\"\"\n",
    "    def __init__(self, x=None, y=None, z=None):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.z = z\n",
    "        self.multipole = numpy.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create parent cell\n",
    "parent = Cell(0.5, 0.5, 0.5)\n",
    "# create an array of 8 child cells\n",
    "octant = numpy.arange(8)\n",
    "# use \"//\" as integer division and \"/\" as floating-point division\n",
    "x = (octant % 2) * parent.x + parent.x/2\n",
    "y = ((octant//2) % 2) * parent.y + parent.y/2\n",
    "z = ((octant//4) % 2) * parent.z + parent.z/2\n",
    "children = [Cell(x[i], y[i], z[i]) for i in range(8)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we create the octree, we need to loop over sources to distribute them into child cells. Then perform a P2M to calculate the multipoles for each child. The two steps both require loop in source $j$, therefore, we can merge them into one function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def P2M(sources, parent, children):\n",
    "    \"\"\"Calculate the multipoles for child cells.\n",
    "    \n",
    "    Arguments:\n",
    "        sources: the list of source objects in 'Particle' class\n",
    "        parent: parent cell object\n",
    "        children: the list of child cell objects\n",
    "        \n",
    "    \"\"\"\n",
    "    for source in sources:\n",
    "        octant = (source.x > parent.x) + ((source.y > parent.y) << 1) \\\n",
    "                                       + ((source.z > parent.z) << 2)\n",
    "        dx, dy, dz = children[octant].x-source.x,\\\n",
    "                     children[octant].y-source.y,\\\n",
    "                     children[octant].z-source.z\n",
    "        \n",
    "        children[octant].multipole += source.m*numpy.array((1, dx, dy, dz,\\\n",
    "                                                dx**2/2, dy**2/2, dz**2/2,\\\n",
    "                                                dx*dy/2, dy*dz/2, dz*dx/2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"two less than\" sign $<<$ is a bit shift operator, if you are not familiarized with this you can find go to the [Bitwise Operators](https://wiki.python.org/moin/BitwiseOperators) wiki from python. The first line inside the loop is how we find the octant of a source particle. The RHS of the expression returns a integer from $0$ to $7$, representing one of the eight octants. Think about how this line of code works like a charm. It is in accordance with the way we generate the coordinates of the child cell's centers. In addition, since we have $8$ cells, the multipole array becomes a 2d array, the first argument refers to one of the eight octants, and the second is one of the ten multipole terms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P2M(sources, parent, children)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the multipoles of the child cells, we can write the M2M kernel following the equations we just derived above. We also call this part \"upward translation\" since we shift the expansion center from child cell to parent cell.\n",
    "\n",
    "The M2M kernel do not explicitly include the information of the sources as an input, instead it loops over each child cell and multipoles of child cells contain the information of sources $x_j$, $y_j$, $z_j$, $m_j$ in each octant. M2M returns the 10 multipole terms of the parent cell, which contains the information of all the sources in the domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def M2M(parent, children):\n",
    "    \"\"\"Given the child cells' multipoles, calculate the parent's multipoles.\n",
    "    \n",
    "    Arguments:\n",
    "        parent: parent cell object\n",
    "        children: the list of child cell objects\n",
    "        \n",
    "    \"\"\"\n",
    "    for child in children:\n",
    "        dx, dy, dz = parent.x-child.x, parent.y-child.y, parent.z-child.z\n",
    "        parent.multipole += child.multipole\n",
    "        parent.multipole[1:4] += child.multipole[0] * numpy.array((dx, dy, dz))\n",
    "        parent.multipole[4:7] += child.multipole[1:4] * numpy.array((dx, dy, dz))\\\n",
    "                                + 0.5*child.multipole[0] * numpy.array((dx**2, dy**2, dz**2))\n",
    "        parent.multipole[7:] += 0.5*numpy.array((child.multipole[2], child.multipole[3], child.multipole[1])) * numpy.array((dx, dy, dz))\\\n",
    "                                + 0.5*child.multipole[1:4] * numpy.array((dy, dz, dx))\\\n",
    "                                + 0.5*child.multipole[0] * numpy.array((dx*dy, dy*dz, dz*dx)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "M2M(parent, children)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have the multipole array of the parent cell, so we can loop in targets in order to evaluate the potential at each target by an multipole expansion. (Recall multipole expansion in the previous notebook)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "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": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "phi_multi = eval_potential(targets, parent.multipole, parent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How should the domain looks like?\n",
    "\n",
    "The black dot shows the parent's center, while the greens are the centers of child cells.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LZPvWMEaTJgPIBqA1OV6CSb3uMDoPqwv28ykAhcn3NRo2bEhVqlShTz75xOqJ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\nik+fU1Ao95RzDTNlmdHW+gWKhpV7/h+SzrgFl+IV2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcfc8abd128>"
      ]
     },
     "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(x, y, z, s=50, c='g') #center of child cells\n",
    "\n",
    "ax.scatter(parent.x, parent.y, parent.z, s=30, c='k') #center of parent cell\n",
    "\n",
    "ax.set_xlim3d(-1,1)\n",
    "ax.set_ylim3d(-1,1)\n",
    "ax.set_zlim3d(-1,1)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_zlabel('$z$')\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": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "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": 13,
   "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": [
    "Then we use direct summation method to calculate the potentials.\n",
    "\n",
    "Compare the two results and calculate $L^2$ relative error norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 Norm error: 0.0017548017922207433\n"
     ]
    }
   ],
   "source": [
    "l2_err(phi_direct, phi_multi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcfc8aae5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_err(phi_direct, phi_multi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 11.3 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit direct_sum(sources, targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 1.48 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "P2M(sources, parent, children)\n",
    "M2M(parent, children)\n",
    "eval_potential(targets, parent.multipole, parent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results show a good match between multi-level multipole expansion and direct summation. We first perform a P2M for each child cell to calculate the multipoles of child cell (expansion at the child's cell center). Then we use M2M kernel to calculate the multipole of parent cell (shift the expansion to the parent's cell center). Finally, we evaluate the potential by multipole expansion. Here we only have one parent cell and its eight child cells, however, when there are millions of particles, we need to build a more complex hierarchical tree to store the particles. Child cells may still have their child cells, and evaluation of the potentials may require a traverse of the tree. So in the next notebook, we will discuss how to 'construct' this tree of cells."
   ]
  },
  {
   "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": 18,
   "metadata": {
    "code_folding": [
     1
    ],
    "collapsed": false
   },
   "outputs": [
    {
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       "    font-size: 30pt;\n",
       "    line-height: 100%;\n",
       "    color: rgb(0,51,102);\n",
       "    margin-bottom: 0.1em;\n",
       "    margin-top: 0.3em;\n",
       "    display: block;\n",
       "}\t\n",
       "\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Nixie One', serif;\n",
       "    margin-top:16px;\n",
       "\tfont-size: 22pt;\n",
       "    font-weight: 600;\n",
       "    margin-bottom: 3px;\n",
       "    font-style: regular;\n",
       "    color: rgb(102,102,0);\n",
       "}\n",
       "\n",
       ".text_cell_render h4 {    /*Use this for captions*/\n",
       "    font-family: 'Nixie One', serif;\n",
       "    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": 18,
     "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
}