expansion-filters.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functional Expansions\n",
    "OpenMC's general tally system accommodates a wide range of tally *filters*. While most filters are meant to identify regions of phase space that contribute to a tally, there are a special set of functional expansion filters that will multiply the tally by a set of orthogonal functions, e.g. Legendre polynomials, so that continuous functions of space or angle can be reconstructed from the tallied moments.\n",
    "\n",
    "In this example, we will determine the spatial dependence of the flux along the $z$ axis by making a Legendre polynomial expansion. Let us represent the flux along the z axis, $\\phi(z)$, by the function\n",
    "\n",
    "$$ \\phi(z') = \\sum\\limits_{n=0}^N a_n P_n(z') $$\n",
    "\n",
    "where $z'$ is the position normalized to the range [-1, 1]. Since $P_n(z')$ are known functions, our only task is to determine the expansion coefficients, $a_n$. By the orthogonality properties of the Legendre polynomials, one can deduce that the coefficients, $a_n$, are given by\n",
    "\n",
    "$$ a_n = \\frac{2n + 1}{2} \\int_{-1}^1 dz' P_n(z') \\phi(z').$$\n",
    "\n",
    "Thus, the problem reduces to finding the integral of the flux times each Legendre polynomial -- a problem which can be solved by using a Monte Carlo tally. By using a Legendre polynomial filter, we obtain stochastic estimates of these integrals for each polynomial order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import openmc\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To begin, let us first create a simple model. The model will be a slab of fuel material with reflective boundaries conditions in the x- and y-directions and vacuum boundaries in the z-direction. However, to make the distribution slightly more interesting, we'll put some B<sub>4</sub>C in the middle of the slab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define fuel and B4C materials\n",
    "fuel = openmc.Material()\n",
    "fuel.add_element('U', 1.0, enrichment=4.5)\n",
    "fuel.add_nuclide('O16', 2.0)\n",
    "fuel.set_density('g/cm3', 10.0)\n",
    "\n",
    "b4c = openmc.Material()\n",
    "b4c.add_element('B', 4.0)\n",
    "b4c.add_element('C', 1.0)\n",
    "b4c.set_density('g/cm3', 2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define surfaces used to construct regions\n",
    "zmin, zmax = -10., 10.\n",
    "box = openmc.model.RectangularPrism(10., 10., boundary_type='reflective')\n",
    "bottom = openmc.ZPlane(z0=zmin, boundary_type='vacuum')\n",
    "boron_lower = openmc.ZPlane(z0=-0.5)\n",
    "boron_upper = openmc.ZPlane(z0=0.5)\n",
    "top = openmc.ZPlane(z0=zmax, boundary_type='vacuum')\n",
    "\n",
    "# Create three cells and add them to geometry\n",
    "fuel1 = openmc.Cell(fill=fuel, region=-box & +bottom & -boron_lower)\n",
    "absorber = openmc.Cell(fill=b4c, region=-box & +boron_lower & -boron_upper)\n",
    "fuel2 = openmc.Cell(fill=fuel, region=-box & +boron_upper & -top)\n",
    "geom = openmc.Geometry([fuel1, absorber, fuel2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the starting source, we'll use a uniform distribution over the entire box geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "settings = openmc.Settings()\n",
    "spatial_dist = openmc.stats.Box(*geom.bounding_box)\n",
    "settings.source = openmc.IndependentSource(space=spatial_dist)\n",
    "settings.batches = 210\n",
    "settings.inactive = 10\n",
    "settings.particles = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the tally is relatively straightforward. One simply needs to list 'flux' as a score and then add an expansion filter. For this case, we will want to use the `SpatialLegendreFilter` class which multiplies tally scores by Legendre polynomials evaluated on normalized spatial positions along an axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a flux tally\n",
    "flux_tally = openmc.Tally()\n",
    "flux_tally.scores = ['flux']\n",
    "\n",
    "# Create a Legendre polynomial expansion filter and add to tally\n",
    "order = 8\n",
    "expand_filter = openmc.SpatialLegendreFilter(order, 'z', zmin, zmax)\n",
    "flux_tally.filters.append(expand_filter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last thing we need to do is create a `Tallies` collection and export the entire model, which we'll do using the `Model` convenience class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "tallies = openmc.Tallies([flux_tally])\n",
    "model = openmc.model.Model(geometry=geom, settings=settings, tallies=tallies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running a simulation is now as simple as calling the `run()` method of `Model`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp_file = model.run(output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the run is finished, we need to load the results from the statepoint file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "with openmc.StatePoint(sp_file) as sp:\n",
    "    df = sp.tallies[flux_tally.id].get_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've used the `get_pandas_dataframe()` method that returns tally data as a Pandas dataframe. Let's see what the raw data looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>spatiallegendre</th>\n",
       "      <th>nuclide</th>\n",
       "      <th>score</th>\n",
       "      <th>mean</th>\n",
       "      <th>std. dev.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>P0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>36.538951</td>\n",
       "      <td>0.078499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>P1</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.012072</td>\n",
       "      <td>0.043053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>P2</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-4.419424</td>\n",
       "      <td>0.025499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>P3</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.005595</td>\n",
       "      <td>0.021585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>P4</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.277076</td>\n",
       "      <td>0.013788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>P5</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.001362</td>\n",
       "      <td>0.011802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>P6</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.124089</td>\n",
       "      <td>0.009633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>P7</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.004958</td>\n",
       "      <td>0.008716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>P8</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.102922</td>\n",
       "      <td>0.007807</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  spatiallegendre nuclide score      mean  std. dev.\n",
       "0              P0   total  flux  3.65e+01   7.85e-02\n",
       "1              P1   total  flux -1.21e-02   4.31e-02\n",
       "2              P2   total  flux -4.42e+00   2.55e-02\n",
       "3              P3   total  flux -5.60e-03   2.16e-02\n",
       "4              P4   total  flux -2.77e-01   1.38e-02\n",
       "5              P5   total  flux  1.36e-03   1.18e-02\n",
       "6              P6   total  flux  1.24e-01   9.63e-03\n",
       "7              P7   total  flux  4.96e-03   8.72e-03\n",
       "8              P8   total  flux -1.03e-01   7.81e-03"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the expansion coefficients are given as\n",
    "\n",
    "$$ a_n = \\frac{2n + 1}{2} \\int_{-1}^1 dz' P_n(z') \\phi(z')$$\n",
    "\n",
    "we just need to multiply the Legendre moments by $(2n + 1)/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = np.arange(order + 1)\n",
    "a_n = (2*n + 1)/2 * df['mean']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the flux distribution, we can use the `numpy.polynomial.Legendre` class which represents a truncated Legendre polynomial series. Since we really want to plot $\\phi(z)$ and not $\\phi(z')$ we first need to perform a change of variables. Since\n",
    "\n",
    "$$ \\lvert \\phi(z) dz \\rvert = \\lvert \\phi(z') dz' \\rvert $$\n",
    "\n",
    "and, for this case, $z = 10z'$, it follows that\n",
    "\n",
    "$$ \\phi(z) = \\frac{\\phi(z')}{10} = \\sum_{n=0}^N \\frac{a_n}{10} P_n(z'). $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = np.polynomial.Legendre(a_n/10, domain=(zmin, zmax))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot it and see how our flux looks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Flux [n/src]')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wr/i413FaDCsQUep/523laGUNv7x0sA3GZ1qEn100CJ8P/jx3q9dRWgwrEFFo64FS/rF8F988oyf97Ipp00J079CKb52VxZtf7GF9frHXcVoEKxBR6PdzNtE6MY7vT7Irpk3L8r2JfUlJjud3czbZaa9hYAUiyny67SAfbynkzol96dA6wes4xoRVSnI8d0/qx+LcQyzYUuh1nIhnBSKK1PiU387ZREb7ZKaNy/I6jjGuuGlsT3p1as1v52yi2iYWOiVWIKLIW1/ks2lfCfdeOMBOazUtVkJcDD+9cCA5BWW8umK313EimhWIKHG8sob//WALIzJTuHR4N6/jGOOqC4Z04fSsVP4ybytlFdVex4lYViCixKzP8thXXM7PLhpkEwGZFk9E+PnFgzlYVsmTC3O9jhOxXCsQIjJLRApEZH0d638iIqud23oRqRGRDs66HSKyzlm3wq2M0aKwtILHPs5hyuAujO3d0es4xjSJ07q355LhXXnqkzwKSyu8jhOR3GxBPAtcWNdKVf2Tqp6mqqcB9wMLVbUoYJOJzvpsFzNGhYfnb6Wi2sd9Uwd6HcWYJnXPlAFU1vj460c2Z8TJcK1AqOoioKjBDf1uAF5xK0s0yzt4lFeW7+bGsT3ondbG6zjGNKlenVpzXXZ3Xl6+i91Fx7yOE3E874MQkVb4WxpvBCxW4AMRWSki0xt4/nQRWSEiKwoL7bzn2h6at5WE2BibRtRErbsn9SNGhL/MsyE4GsvzAgFcCnxW6/DS2ao6CpgK3CEi4+t6sqrOVNVsVc1OS7PZ0AJt2FvMv9bs5dtnZ5HWNtHrOMZ4Ij0liVvGZfHW6ny27C/1Ok5EaQ4F4npqHV5S1Xzn3wLgLWCMB7ki3p/nbiElOZ7p4/t4HcUYT3333D60SYzjzx9s8TpKRPG0QIhICjABeCdgWWsRaXviPjAFCHomlKnb5zuK+HhLITMm9CElOd7rOMZ4qn2rBG4f35t5Gw+wcudhr+NEDDdPc30FWAIMEJE9InKriMwQkRkBm10JfKCqRwOWdQE+FZE1wHLgPVV9362cLZGq8sf3N9O5bSK32JAaxgDwrbN60alNIn98f7MN5BeiOLdeWFVvCGGbZ/GfDhu4bDswwp1U0WHBlkI+33GYB64YSnKCDalhDEDrxDjuOq8vv5y9gUXbDjKhv/VZNqQ59EGYMPL5lD/O3UKPDq34RnZ3r+MY06zcMKYHmanJ/GmutSJCYQWihXl33T427SvhR+f3JyHOfr3GBEqIi+EHk/uzPr+EeRsPeB2n2bO/IC1IVY2Phz7YwsD0tlw2wgbkMyaYK07rRq9OrXlo3lZ8PmtF1McKRAvy2oo97Dh0jB9PGWAD8hlTh7jYGO6e1I/N+0t5f8N+r+M0a/V2UovIj0J4jaOq+mSY8piTVF5Vw8PztzKqR3smDersdRxjmrVLR3Tjrx/n8Jd5W7lgSDqx9oUqqIZaED8B2gBt67nd42ZAE5oXl+7kQEkFP7lgICL2YTemPrExwg8m92NbQRnvrdvndZxmq6HTXF9Q1d/Ut4FzMZvx0LHKap5YmMtZfTtyZh8bztuYUFw0tCsDuuTwfx9u5aKh6cTF2hH32up9R1T13oZeIJRtjLteWLKTg2WV/HByf6+jGBMxYmKEH57fj+2FR5m9Zq/XcZqlkEqmiPxORNoHPE4VkQddS2VCVlbhbz2M759GdlYHr+MYE1GmDE5ncNd2PDx/G9U1Pq/jNDuhtqmmquqREw9U9TBwkSuJTKM8t3gHh49V8cPJNpy3MY3lb0X0Z+ehY7z5Rb7XcZqdUAtErIh8OV60iCQDNn60x0rLq5i5aDvnDezMyB6pXscxJiJNHtSZYRkpPDJ/G5XV1ooIFGqBeAmY7wy4dyswD3jOvVgmFM98toPi41XW92DMKRARfnR+f/YcPs7rK/d4HadZabBAiP+cyZeBB4FBzu0BVf2jy9lMPYqPV/H3T7Zz/uAuDMtM8TqOMRHt3AFpjOzRnr9+tI2K6hqv4zQbDRYI9Y9oNUdV31fVHzu3uU2QzdRj1qd5lJZX8wPrezDmlIkIP5zcn73F5by2wloRJ4R6iGmViJzuahITsiPHKpn1aR5Th6YzpJu1HowJh3P6dWJkj/Y8viDX+iIcoRaIscASEckVkbUisk5E1roZzNTtqU/yKKus5gfW92BM2IgId0/qR/6R47yxyloREPqEQRe4msKErOhoJc98lsfFw7oyIL2t13GMaVEm9E9jRGYKf/s4h2tGZxIf5VdXh/rTxwH7VXUn0Au4HCh2LZWp08xF2zlWVWN9D8a4QES4e3I/9hw+zlur7LqIUAvEG0CNiPQFZgLd8Z/ZZJrQwbIKnlu8g8tHdKNvZ2s9GOOGiQP810X89eOcqL+6OtQC4VPVauAq4FFV/QnQ1b1YJpgnF+ZSUV3D9ydZ68EYt4gI35/Uj11Fx3h7dXSP0RRqgagSkRuAm4F3nWXx9T1BRGaJSIGIrK9j/bkiUiwiq53bLwLWXSgiW0QkR0TuCzFji1ZQUs7zS3Zy5chMeqe18TqOMS3a5EGdGdS1HX+L8lZEqAXiW8CZwG9VNU9EegEvNPCcZ4ELG9jmE1U9zbn9BkBEYoG/AVOBwcANIjI4xJwt1uMLc6n2Kd+f1NfrKMa0eP4zmvqSd/Ao766N3vki6i0QIjJTRK4Edqvq91X1FQBVzVPVP9T3XFVdBBSdRKYxQI6qblfVSuAf+DvFo9b+4nJeWraLa0Zl0rOjTb9hTFOYMjidgelteeSjbdRE6dzVDbUgngZGAHNEZL6I/FRERoRx/2eKyBoR+beIDHGWZQC7A7bZ4ywLSkSmi8gKEVlRWFgYxmjNx+MLcvD5lDvPs9aDMU0lJka46zz/fBHROutcQxMGLVPVX6nqOcB1wC7gHqfPYJaIXHcK+14F9FTVEcCjwNsn8yKqOlNVs1U1Oy0t7RTiNE8HSsp55fPdXDM6k+4dWnkdx5ioMnVoOv06t+HR+dvwRWErIuSrQFT1kKq+oqo3q+pp+PsJTvp0GlUtUdUy5/4cIF5EOgH5+E+jPSHTWRaVHl+Qi8+n3DHRWg/GNLWYGOGuSf65q/+9fr/XcZpcSFdSO3NBXA1kBT6nofmqG3jNdOCAqqqIjMFfrA4BR4B+Tkd4PnA9cOPJ7ieSFZSU88ryXVw1KsNaD8Z45OJhXXn4w608+tE2pg5NJyZGvI7UZEJtQbyDv6O4GjgacKuTiLwCLAEGiMgeZy6JGSIyw9nkGmC9iKwBHgGuV79q4E5gLrAJ+KeqbmjsD9YSPLFwO9U+5c6Jdt2DMV6JdfoiNu8v5YON0dWKCHUspkxVbeiU1a9Q1RsaWP9X4K91rJsDzGnM/lqagtJyXlq2kytHZtCjo7UejPHSJcO78vD8bTw8P4cLhqTjnyan5Qu1BbFYRIa5msR8xcyF26mq8VnfgzHNQFxsDHdO7MumfSV8uKnA6zhNJtQCcTaw0rm62Yb7dllhaQUvLtvJFadl0KuTXfdgTHNw+Wnd6NmxFQ/P34p/HrWWL9RDTFNdTWG+4u+fbKey2mfXPRjTjMTFxnDHxL7c+/paPt5SwHkDu3gdyXUhtSBUdWewm9vhotHBsgpeWLKTy0Z0szGXjGlmrhyZQWZqMo9+lBMVrYiGhtpY1dALhLKNCd3fP9lOeXUNd55nZy4Z09zEx8Zw+4Q+fLHrCEtyD3kdx3UNHWIa1EBfgwA2KXKYFB2t5IUlO7l0eDf6drbWgzHN0bWjM3l0/jb++nEO4/p28jqOqxoqEANDeI2acAQx/tbD8aoaG7HVmGYsKT6W6eN78+B7m1i58zCje6Z6Hck1DY3FFLTvodbNZvcOg8NHK3l+8Q4uHtbVZoszppm7cWwPUlvF87ePc7yO4qronpG7GXnqU/9c0zZbnDHNX6uEOG49uxcfbS5gfX6x13FcYwWiGThyrJLnFu/koqFd6d/FWg/GRIKbx2XRNimOxxa03FZESAUi2IxuInJuuMNEq6c/zaOsopq7rO/BmIjRLimeaWdm8e/1+8kpKPU6jitCbUH805ksSEQkWUQeBX7vZrBoUXysimc/28HUoekMTG/ndRxjTCN8++xeJMXF8tjHuV5HcUWoBWIs/jkaFgOfA3uBs9wKFU2e/iyP0opq63swJgJ1aJ3ATWN78M6avew6dMzrOGEXaoGoAo4DyUASkKeqPtdSRYmS8iqe+SyPC4Z0YVBXaz0YE4m+M743sTHC4wtbXisi1ALxOf4CcTpwDnCDiLzmWqoo8cKSnZSWV9t8D8ZEsC7tkrguO5PXV+5mX/Fxr+OEVagF4lZV/YWqVqnqPlW9HJjtZrCW7lhlNU9/mse5A9IYlmkXoxsTyW4f3wefwsxF272OElahFogCEekReAMWuhmspXtl+W6KjlZyp833YEzE696hFVeOzOCV5bs4WFbhdZywCbVAvAe86/w7H9gO/NutUC1dRXUNMxflMrZXB7KzOngdxxgTBt89tw8V1T6e/jTP6yhhE+pw38NUdbjzbz9gDP75ps1JeH3lHg6UVHCXjdhqTIvRJ60NFw/rygtLdlJ8rMrrOGFxUldSq+oq/Ke+mkaqrvHxxMJcRnRvz1l9O3odxxgTRndM7EtZRTXPLt7hdZSwCGlGORH5UcDDGGAU/msh6nvOLOASoEBVhwZZfxPwU/xDhpcC31XVNc66Hc6yGqBaVbNDyRkJZq/Zy+6i4/zikiFRM/G5MdFiUNd2TB7UhWcW53HrOb1okxjqpJ3NU6gtiLYBt0T8fRGXN/CcZ4EL61mfB0xQ1WHAA8DMWusnquppLak4+HzK3z7OYWB6WyYN7Ox1HGOMC+48ry9HjlXx8rLIn3QzpPKmqr9u7Aur6iIRyapn/eKAh0uBzMbuI9K8v2E/uYVHefSGkcTEWOvBmJbotO7tGdenI09/mse0cVkkxsV6Hemk1VsgRORfQJ0Tr6rqZWHKcStfPStKgQ9ERIEnVbV26yIw43RgOkCPHj3CFCf8VP2th96dWnPRsK5exzHGuGjGhD7cPGs576zey3XZ3b2Oc9IaakH82e0AIjIRf4E4O2Dx2aqaLyKdgXkisllVFwV7vlM8ZgJkZ2c321nEF2wpZMPeEv50zXBirfVgTIt2Tr9ODO7ajicX5nLNqMyIPWLQUIHIU9Vdbu1cRIYDTwFTVfXLGcBVNd/5t0BE3sJ/Wm3QAhEpHluQQ0b7ZK4YmeF1FGOMy0SE2yf05u5/rGb+5gLOH9zF60gnpaFO6rdP3BGRN8K5Y+dq7DeBb6rq1oDlrUWk7Yn7wBRgfTj33dRW7izi8x2H+c45vYiPtTmajIkGFw/rSkb7ZJ6I4EH8GvprFdgu6t2YFxaRV/BfTDdARPaIyK0iMkNEZjib/ALoCDwmIqtFZIWzvAvwqYisAZYD76nq+43Zd3Pz5MLttG8Vz3WnR+6xSGNM48TFxvCdc3qxcudhVuwo8jrOSWnoEJPWcb9BqnpDA+tvA24Lsnw7MKIx+2rOcgrKmLfpAHdN7EurhMg+J9oY0zjXnd6dh+dv44mFuTwVgcPqNNSCGCEiJSJSCgx37peISKmIlDRFwEj31CfbSYiN4eZxWV5HMcY0sVYJcdx8ZhYfbipg24HIm5a03gKhqrGq2k5V26pqnHP/xGOb4aYBBSXlvLkqn2uzM+nUJtHrOMYYD0wbl0VSfAxPRuBQ4NZj6qJnFu+g2ufjtrMb1X1jjGlBOrRO4BvZ3XlndX7ETShkBcIlZRXVvLh0J1OHdiWrU2uv4xhjPHTbOb3xKcyKsKHArUC45B/Ld1FaXs308dZ6MCbade/QiouHdeXlZbsoKY+cocCtQLigqsY/acgZvTswont7r+MYY5qB287pxdHKGl5bscfrKCGzAuGC99fvZ19xufU9GGO+NDyzPdk9U3l2cR41vmY7KtBXWIFwwTOf5dGzYyvOsyG9jTEBvn12L3YXHefDTQe8jhISKxBhtmb3EVbtOsK0M7MidoAuY4w7pgzuQkb75IjprLYCEWbPLt5Bm8Q4rs1u8dNbGGMaKS42hmnjerIsr4gNe4u9jtMgKxBhVFBSzrtr93LN6EzaJsV7HccY0wx9I7sHrRJieeazHV5HaZAViDB6cdkuqn3KLTashjGmDimt4rlmdCazV++lsLTC6zj1sgIRJhXVNby8bCfnDehsF8YZY+p1y7gsKmt8vNTM5622AhEm767Zx8GySr51Vi+voxhjmrneaW04b2BnXly6i8pqn9dx6mQFIkyeX7qTvp3bcFbfjl5HMcZEgG+e2ZODZRV8sHG/11HqZAUiDDbsLWbN7iPcOKYHInZqqzGmYRP6pZGZmsxLS12b1fmUWYEIg5eX7SIxLoarR9mprcaY0MTECDeO7cGS7YfIKSjzOk5QViBO0dGKat5ZvZeLh3clpZWd2mqMCd112d2JjxVeXtY8WxFWIE7R7DV7Kauo5qaxPbyOYoyJMJ3aJHLh0K68vnI35VU1Xsf5GisQp+jlZbsY0KUto3qkeh3FGBOBbhrbg5Lyat5du8/rKF/jaoEQkVkiUiAi6+tYLyLyiIjkiMhaERkVsG6aiGxzbtPczHmy1u0pZl1+MTeOtc5pY8zJGdurA307t+HFpc3vmgi3WxDPAhfWs34q0M+5TQceBxCRDsAvgbHAGOCXItLsvqK/vHwXSfExXDEyw+soxpgIJSLcNLYHq3cfaXbjM7laIFR1EVBUzyaXA8+r31KgvYh0BS4A5qlqkaoeBuZRf6FpcuVVNby7Zi8XDe1KSrJ1ThtjTt5VIzNJiItpdpMJed0HkQHsDni8x1lW1/KvEZHpIrJCRFYUFha6FrS2eRsPUFpRzdWj7dRWY8ypSWkVz5TBXXh7dT4V1c2ns9rrAnHKVHWmqmaranZaWlqT7feNVXvolpLEmb3tymljzKm7ZnQmR45V8dGmAq+jfMnrApEPdA94nOksq2t5s1BQUs6irYVcOSrDJgUyxoTFOf3SSG+XxGsrm89hJq8LxGzgZudspjOAYlXdB8wFpohIqtM5PcVZ1iy8vTofn8JVduW0MSZMYmOEq0ZlsHBrIQUl5V7HAdw/zfUVYAkwQET2iMitIjJDRGY4m8wBtgM5wN+B7wGoahHwAPC5c/uNs8xzqsobK/MZ2aM9fdLaeB3HGNOCXDM6kxqf8tYXzeOASZybL66qNzSwXoE76lg3C5jlRq5TsWFvCVsOlPLgFUO9jmKMaWF6p7VhdM9UXlu5h+nje3t+fZXXh5gizjur84mPFS4d3s3rKMaYFujqUZnkFJSxYW+J11GsQDSGz6e8t3Yf4/ul2cB8xhhXTB2aTlyM8K81e72OYgWiMVbtOsze4nIuGdHV6yjGmBYqtXUC4/un8a81e/H51NMsViAa4d21+0iIi2HyoC5eRzHGtGCXjejG3uJyVu467GkOKxAhqvEp763bx8QBabRNssNLxhj3TB7chcS4GGav9vYwkxWIEC3PK6KwtIJLrHPaGOOyNolxTB7UhTnr9lFd4/MshxWIEL27di/J8bFMGtTZ6yjGmChw6YhuHDpayeLcQ55lsAIRghqfMnfDfs4b2JlWCa5eOmKMMQCcOyCNtolxzPbwbCYrECFYvfswB8sqmTLEOqeNMU0jKT6W8wd3Yd7GA1R5dJjJCkQIPth4gLgY4dwBdnjJGNN0pgxJp/h4FcvzvBlpyApECOZtPMAZvTvaxEDGmCY1oX8aSfExzN2w35P9W4FoQG5hGdsLj3L+YDu8ZIxpWskJsYzvl8YHGw7gH7quaVmBaMC8jQcA/3nJxhjT1KYMSWd/STlr9zT9fNVWIBowb+MBhma0I6N9stdRjDFRaPKgzsTGiCeHmaxA1KOwtIJVuw5z/qB0r6MYY6JU+1YJjO3VgQ+coxlNyQpEPRZuLUQVuzjOGOOpKYO7kFNQRm5hWZPu1wpEPRZuLSStbSJDurXzOooxJopNcgYI/XhzQZPu1wpEHWp8yqfbCjmnXyfPZ3UyxkS37h1a0SetNQu3Fjbpfq1A1GFdfjGHj1UxoX+a11GMMYaJAzqzbHsRxyqrm2yfViDqsGhrISJwdt9OXkcxxhjOHdCZyhofS5pw8D5XC4SIXCgiW0QkR0TuC7L+LyKy2rltFZEjAetqAtbNdjNnMIu2FjIsI4WObRKbetfGGPM1p/dKpVVCLAu2NN1hJteGJhWRWOBvwPnAHuBzEZmtqhtPbKOqPwzY/i5gZMBLHFfV09zKV5/i41V8sfsI353Qx4vdG2PM1yTGxTKuT0c+3lKAqjZJ36ibLYgxQI6qblfVSuAfwOX1bH8D8IqLeUK2OOcgNT5lvPU/GGOakQkDOrPn8HFyC482yf7cLBAZwO6Ax3ucZV8jIj2BXsBHAYuTRGSFiCwVkSvq2omITHe2W1FYGJ6m16JthbRNjGNkj/ZheT1jjAmHc50vrQu2NM3prs2lk/p64HVVrQlY1lNVs4Ebgf8TkaDHe1R1pqpmq2p2Wlp4vvEvzj3E2N4diY9tLm+PMcb853TXRdsONsn+3PwLmA90D3ic6SwL5npqHV5S1Xzn3+3AAr7aP+GavUeOs/PQMc7s07EpdmeMMY1yVt9OrNhRRGW1+5MIuVkgPgf6iUgvEUnAXwS+djaSiAwEUoElActSRSTRud8JOAvYWPu5bliW5z+F7IzeHZpid8YY0yjj+nTkWGUNa/cccX1frhUIVa0G7gTmApuAf6rqBhH5jYhcFrDp9cA/9KuDnQ8CVojIGuBj4H8Cz35y09LcIlKS4xmUbsNrGGOan7G9OiLiPxTuNtdOcwVQ1TnAnFrLflHr8a+CPG8xMMzNbHVZsv0QY3p1ICbGhtcwxjQ/qa0TGNy1HYtzD/L9Sf1c3Zf1wgbIP3KcXUXHOKO39T8YY5qvcX06smrnEcqrahre+BRYgQiwbLv1Pxhjmr9xfTpRWeNj5c7Dru7HCkSApdsPWf+DMabZO71XB2JjhMW57p7uagUiwPK8Iut/MMY0e20S4xiRmeL6wH1WIBwHyyrYcegY2T1TvY5ijDENOr1XB9blF7vaD2EFwrHKOZY32gqEMSYCnN6zA1U1yto9xa7twwqEY+Wuw8THCkMzUryOYowxDTrxZfbzHUWu7cMKhOOLnUcY0i2FpPhYr6MYY0yDUlsn0LdzG1ZYgXBXZbWPNXuO2OElY0xEye6Zysqdh/H5tOGNT4IVCGDTvhIqqn1WIIwxESU7qwMl5dVsKyhz5fWtQMCXF5uM6mEFwhgTOU6cdblipzuHmaxAAKt2HSajfTLpKUleRzHGmJD17NiKTm0SWbHDnSuqrUDgP8V1lB1eMsZEGBHh9KxU11oQro7mGgkqqms4q28nzu7XyesoxhjTaNeMzmR0z1R8Pg37KBBRXyAS42L507UjvI5hjDEnZdKgLq69th1iMsYYE5QVCGOMMUFZgTDGGBOUFQhjjDFBWYEwxhgTlBUIY4wxQVmBMMYYE5QVCGOMMUGJqjvDxHpBRAqBnSf59E6AuzOAnxzL1TiWq3EsV+O0xFw9VTUt2IoWVSBOhYisUNVsr3PUZrkax3I1juVqnGjLZYeYjDHGBGUFwhhjTFBWIP5jptcB6mC5GsdyNY7lapyoymV9EMYYY4KyFoQxxpigrEAYY4wJKqoKhIhcKyIbRMQnItm11t0vIjkiskVELqjj+b1EZJmz3asikuBCxldFZLVz2yEiq+vYboeIrHO2WxHuHEH29ysRyQ/IdlEd213ovIc5InJfE+T6k4hsFpG1IvKWiLSvY7smeb8a+vlFJNH5Hec4n6Ust7IE7LO7iHwsIhudz//dQbY5V0SKA36/v3A7l7Pfen8v4veI836tFZFRTZBpQMD7sFpESkTkB7W2aZL3S0RmiUiBiKwPWNZBROaJyDbn36DzJYvINGebbSIy7aQCqGrU3IBBwABgAZAdsHwwsAZIBHoBuUBskOf/E7jeuf8E8F2X8/4v8Is61u0AOjXhe/cr4McNbBPrvHe9gQTnPR3scq4pQJxz/w/AH7x6v0L5+YHvAU84968HXm2C311XYJRzvy2wNUiuc4F3m+rzFOrvBbgI+DcgwBnAsibOFwvsx38xWZO/X8B4YBSwPmDZH4H7nPv3BfvMAx2A7c6/qc791MbuP6paEKq6SVW3BFl1OfAPVa1Q1TwgBxgTuIGICHAe8Lqz6DngCreyOvu7DnjFrX24YAyQo6rbVbUS+Af+99Y1qvqBqlY7D5cCmW7urwGh/PyX4//sgP+zNMn5XbtGVfep6irnfimwCchwc59hdDnwvPotBdqLSNcm3P8kIFdVT3aEhlOiqouAolqLAz9Ddf0dugCYp6pFqnoYmAdc2Nj9R1WBqEcGsDvg8R6+/h+oI3Ak4I9RsG3C6RzggKpuq2O9Ah+IyEoRme5ijkB3Os38WXU0a0N5H930bfzfNoNpivcrlJ//y22cz1Ix/s9Wk3AOaY0ElgVZfaaIrBGRf4vIkCaK1NDvxevP1PXU/SXNi/cLoIuq7nPu7weCTUodlvctrvHZmjcR+RBID7Lq56r6TlPnCSbEjDdQf+vhbFXNF5HOwDwR2ex823AlF/A48AD+/9AP4D/89e1T2V84cp14v0Tk50A18FIdLxP29yvSiEgb4A3gB6paUmv1KvyHUcqc/qW3gX5NEKvZ/l6cPsbLgPuDrPbq/foKVVURce1ahRZXIFR18kk8LR/oHvA401kW6BD+5m2c880v2DZhySgiccBVwOh6XiPf+bdARN7Cf3jjlP5jhfreicjfgXeDrArlfQx7LhG5BbgEmKTOAdggrxH29yuIUH7+E9vscX7PKfg/W64SkXj8xeElVX2z9vrAgqGqc0TkMRHppKquDkwXwu/Flc9UiKYCq1T1QO0VXr1fjgMi0lVV9zmH2wqCbJOPv5/khEz8fa+NYoeY/GYD1ztnmPTC/01geeAGzh+ej4FrnEXTALdaJJOBzaq6J9hKEWktIm1P3MffUbs+2LbhUuu475V17O9zoJ/4z/ZKwN88n+1yrguBe4HLVPVYHds01fsVys8/G/9nB/yfpY/qKmrh4vRxPA1sUtWH6tgm/URfiIiMwf+3wdXCFeLvZTZws3M20xlAccDhFbfV2Yr34v0KEPgZquvv0FxgioikOoeDpzjLGsftXvjmdMP/h20PUAEcAOYGrPs5/jNQtgBTA5bPAbo593vjLxw5wGtAoks5nwVm1FrWDZgTkGONc9uA/1CL2+/dC8A6YK3zAe1aO5fz+CL8Z8nkNlGuHPzHWlc7tydq52rK9yvYzw/8Bn8BA0hyPjs5zmepdxO8R2fjPzS4NuB9ugiYceJzBtzpvDdr8Hf2j2uCXEF/L7VyCfA35/1cR8DZhy5na43/D35KwLImf7/wF6h9QJXzt+tW/H1W84FtwIdAB2fbbOCpgOd+2/mc5QDfOpn921AbxhhjgrJDTMYYY4KyAmGMMSYoKxDGGGOCsgJhjDEmKCsQxhhjgrICYVoUEbmy1kicq8U/eu9Ul/Y3Q0Rudu7fIiLdAtY9JSKDw7CPEyPp/iYMr3WO+Ed1dfW6GdMy2GmupkVzxve5CZioqj6X97UA/4i3YR1OXER+BZSp6p/D9HpZ+EciHRqO1zMtl7UgTIslIv2BXwDfrF0cRCRL/PNIvCQim0TkdRFp5aybJCJfiH+eglkikugs/x/n2/daEfmzs+xXIvJjEbkG/4VKLzmtlmQRWSDOvCMicoPzeutF5A8BOcpE5LfOoG9LRSTYwGu1f642IvKM83prReTqgNf6k/jnfPhQRMY4GbaLyGXheVdNNLECYVokZ+yhl4F7VHVXHZsNAB5T1UFACfA9EUnCfyX7N1R1GP7xyr4rIh3xX4k/RFWHAw8GvpCqvg6sAG5S1dNU9XhAlm7456o4DzgNOF1ErnBWtwaWquoI/GMQfSeEH++/8Q85MczJ8lHAa32kqkOAUifj+U7uUz48ZaKPFQjTUj0AbFDVV+vZZreqfubcfxH/kBQDgDxV3eosfw7/pC3FQDnwtIhcBQQd96kOpwMLVLVQ/QM9vuS8JkAl/xn4cCWQFcLrTcY//AQA6h/v/8Rrve/cXwcsVNUq534or2vMV1iBMC2OiJwLXI1/vJz61O6Aq7NDzvnDPgb/JD+X8J8/xKeqSv/TEVjDqY2wHPhaPvxjjuEcXmtxIzcb91mBMC2KM3LlM8DN6p89rT49RORM5/6NwKf4B2vMEpG+zvJvAgvFP5dCiqrOAX4IjAjyeqX4p/SsbTkwQUQ6iUgs/lFCFzbm56plHnDHiQdSx5zExpwqKxCmpZkBdAYer3Wq6zeCbLsFuENENuGft/dxVS0HvgW8JiLr8H8TfwL/H/53RWQt/kLyoyCv9yzwxIlO6hML1T889X34h4tfA6zUU5u86kEg1enwXgNMPIXXMqZOdpqriUqRdKqnneZqvGItCGOavzJgergulAP+BTTFzGcmwlkLwhhjTFDWgjDGGBOUFQhjjDFBWYEwxhgTlBUIY4wxQVmBMMYYE9T/B7+Wx21sac+1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = np.linspace(zmin, zmax, 1000)\n",
    "plt.plot(z, phi(z))\n",
    "plt.xlabel('Z position [cm]')\n",
    "plt.ylabel('Flux [n/src]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you might expect, we get a rough cosine shape but with a flux depression in the middle due to the boron slab that we introduced. To get a more accurate distribution, we'd likely need to use a higher order expansion.\n",
    "\n",
    "One more thing we can do is confirm that integrating the distribution gives us the same value as the first moment (since $P_0(z') = 1$). This can easily be done by numerically integrating using the trapezoidal rule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36.53891107688235"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trapz(phi(z), z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to being able to tally Legendre moments, there are also functional expansion filters available for spherical harmonics (`SphericalHarmonicsFilter`) and Zernike polynomials over a unit disk (`ZernikeFilter`). A separate `LegendreFilter` class can also be used for determining Legendre scattering moments (i.e., an expansion of the scattering cosine, $\\mu$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zernike polynomials\n",
    "\n",
    "Now let's look at an example of functional expansion tallies using Zernike polynomials as the basis functions.\n",
    "\n",
    "In this example, we will determine the spatial dependence of the flux along the radial direction $r'$ and $/$ or azimuthal angle $\\theta$ by making a Zernike polynomial expansion. Let us represent the flux along the radial and azimuthal direction, $\\phi(r', \\theta)$, by the function\n",
    "\n",
    "$$ \\phi(r', \\theta) = \\sum\\limits_{n=0}^N \\sum\\limits_{m=-n}^n a_n^m Z_n^m(r', \n",
    "\\theta) $$\n",
    "\n",
    "where $r'$ is the position normalized to the range [0, r] (r is the radius of cylindrical geometry), and the azimuthal lies within the range [0, $ 2\\pi$]. \n",
    "\n",
    "Since $Z_n^m(r', \\theta)$ are known functions, we need to determine the expansion coefficients, $a_n^m$. By the orthogonality properties of the Zernike polynomials, one can deduce that the coefficients, $a_n^m$, are given by\n",
    "\n",
    "$$ a_n^m = k_n^m \\int_{0}^r dr' \\int_{0}^{2\\pi} d\\theta Z_n^m(r',\\theta) \\phi(r', \\theta).$$\n",
    "$$ k_n^m = \\frac{2n + 2}{\\pi}, m \\ne 0. $$\n",
    "$$ k_n^m = \\frac{n+1}{\\pi}, m = 0.$$\n",
    "\n",
    "Similarly, the problem reduces to finding the integral of the flux times each Zernike polynomial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To begin with, let us first create a simple model. The model will be a pin-cell fuel material with vacuum boundary condition in both radial direction and axial direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define fuel \n",
    "fuel = openmc.Material()\n",
    "fuel.add_element('U', 1.0, enrichment=5.0)\n",
    "fuel.add_nuclide('O16', 2.0)\n",
    "fuel.set_density('g/cm3', 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define surfaces used to construct regions\n",
    "zmin, zmax, radius = -1., 1., 0.5 \n",
    "pin = openmc.ZCylinder(x0=0.0, y0=0.0, r=radius, boundary_type='vacuum')\n",
    "bottom = openmc.ZPlane(z0=zmin, boundary_type='vacuum')\n",
    "top = openmc.ZPlane(z0=zmax, boundary_type='vacuum')\n",
    "\n",
    "# Create three cells and add them to geometry\n",
    "fuel = openmc.Cell(fill=fuel, region= -pin & +bottom & -top)\n",
    "geom = openmc.Geometry([fuel])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the starting source, we'll use a uniform distribution over the entire box geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "settings = openmc.Settings()\n",
    "spatial_dist = openmc.stats.Box(*geom.bounding_box)\n",
    "settings.source = openmc.IndependentSource(space=spatial_dist)\n",
    "settings.batches = 100\n",
    "settings.inactive = 20\n",
    "settings.particles = 100000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the tally is relatively straightforward. One simply needs to list 'flux' as a score and then add an expansion filter. For this case, we will want to use the `SpatialLegendreFilter`, `ZernikeFilter`, `ZernikeRadialFilter` classes which multiplies tally scores by Legendre, azimuthal Zernike and  radial-only Zernike polynomials evaluated on normalized spatial positions along radial and axial directions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a flux tally\n",
    "flux_tally_legendre = openmc.Tally()\n",
    "flux_tally_legendre.scores = ['flux']\n",
    "\n",
    "# Create a Legendre polynomial expansion filter and add to tally\n",
    "order = 10\n",
    "cell_filter = openmc.CellFilter(fuel)\n",
    "legendre_filter = openmc.SpatialLegendreFilter(order, 'z', zmin, zmax)\n",
    "flux_tally_legendre.filters = [cell_filter, legendre_filter]\n",
    "\n",
    "# Create a Zernike azimuthal polynomial expansion filter and add to tally \n",
    "flux_tally_zernike = openmc.Tally()\n",
    "flux_tally_zernike.scores = ['flux']\n",
    "zernike_filter = openmc.ZernikeFilter(order=order, x=0.0, y=0.0, r=radius)\n",
    "flux_tally_zernike.filters = [cell_filter, zernike_filter]\n",
    "\n",
    "# Create a Zernike radial polynomial expansion filter and add to tally \n",
    "flux_tally_zernike1d = openmc.Tally()\n",
    "flux_tally_zernike1d.scores = ['flux']\n",
    "zernike1d_filter = openmc.ZernikeRadialFilter(order=order, x=0.0, y=0.0, r=radius)\n",
    "flux_tally_zernike1d.filters = [cell_filter, zernike1d_filter]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last thing we need to do is create a `Tallies` collection and export the entire model, which we'll do using the `Model` convenience class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "tallies = openmc.Tallies([flux_tally_legendre, flux_tally_zernike, flux_tally_zernike1d])\n",
    "model = openmc.model.Model(geometry=geom, settings=settings, tallies=tallies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running a simulation is now as simple as calling the `run()` method of `Model`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp_file = model.run(output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the run is finished, we need to load the results from the statepoint file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "with openmc.StatePoint(sp_file) as sp:\n",
    "    df1 = sp.tallies[flux_tally_legendre.id].get_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've used the `get_pandas_dataframe()` method that returns tally data as a Pandas dataframe. Let's see what the raw data looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cell</th>\n",
       "      <th>spatiallegendre</th>\n",
       "      <th>nuclide</th>\n",
       "      <th>score</th>\n",
       "      <th>mean</th>\n",
       "      <th>std. dev.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>P0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.542523</td>\n",
       "      <td>0.000576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>P1</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000616</td>\n",
       "      <td>0.000493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>P2</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.055513</td>\n",
       "      <td>0.000316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>P3</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000066</td>\n",
       "      <td>0.000227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>P4</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.001267</td>\n",
       "      <td>0.000214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>P5</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000476</td>\n",
       "      <td>0.000163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4</td>\n",
       "      <td>P6</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000051</td>\n",
       "      <td>0.000140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4</td>\n",
       "      <td>P7</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000396</td>\n",
       "      <td>0.000141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4</td>\n",
       "      <td>P8</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000190</td>\n",
       "      <td>0.000137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4</td>\n",
       "      <td>P9</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>0.000106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4</td>\n",
       "      <td>P10</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000153</td>\n",
       "      <td>0.000114</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    cell spatiallegendre nuclide score      mean  std. dev.\n",
       "0      4              P0   total  flux  5.43e-01   5.76e-04\n",
       "1      4              P1   total  flux  6.16e-04   4.93e-04\n",
       "2      4              P2   total  flux -5.55e-02   3.16e-04\n",
       "3      4              P3   total  flux -6.56e-05   2.27e-04\n",
       "4      4              P4   total  flux -1.27e-03   2.14e-04\n",
       "5      4              P5   total  flux -4.76e-04   1.63e-04\n",
       "6      4              P6   total  flux -5.08e-05   1.40e-04\n",
       "7      4              P7   total  flux  3.96e-04   1.41e-04\n",
       "8      4              P8   total  flux -1.90e-04   1.37e-04\n",
       "9      4              P9   total  flux  4.04e-05   1.06e-04\n",
       "10     4             P10   total  flux -1.53e-04   1.14e-04"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the scaling factors for expansion coefficients will be provided by the Python API, thus, we do not need to multiply the moments by scaling factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_n = df1['mean']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading the coefficients is realized via calling the OpenMC Python API as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = openmc.legendre_from_expcoef(a_n, domain=(zmin, zmax))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot it and see how our flux looks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Flux [n/src]')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = np.linspace(zmin, zmax, 1000)\n",
    "plt.plot(z, phi(z))\n",
    "plt.xlabel('Z position [cm]')\n",
    "plt.ylabel('Flux [n/src]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A rough cosine shape is obtained. \n",
    "One can also numerically integrate the function using the trapezoidal rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.542522648365342"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trapz(phi(z), z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cases show how to reconstruct the flux distribution Zernike polynomials tallied results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "with openmc.StatePoint(sp_file) as sp:\n",
    "    df2 = sp.tallies[flux_tally_zernike.id].get_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cell</th>\n",
       "      <th>zernike</th>\n",
       "      <th>nuclide</th>\n",
       "      <th>score</th>\n",
       "      <th>mean</th>\n",
       "      <th>std. dev.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>Z0,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.542523</td>\n",
       "      <td>0.000576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>Z1,-1</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000462</td>\n",
       "      <td>0.000298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>Z1,1</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000572</td>\n",
       "      <td>0.000323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Z2,-2</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000362</td>\n",
       "      <td>0.000228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>Z2,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.064447</td>\n",
       "      <td>0.000328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,2</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000015</td>\n",
       "      <td>0.000105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,4</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000081</td>\n",
       "      <td>0.000098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,6</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,8</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000055</td>\n",
       "      <td>0.000090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,10</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000091</td>\n",
       "      <td>0.000081</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>66 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    cell zernike nuclide score      mean  std. dev.\n",
       "0      4    Z0,0   total  flux  5.43e-01   5.76e-04\n",
       "1      4   Z1,-1   total  flux  4.62e-04   2.98e-04\n",
       "2      4    Z1,1   total  flux  5.72e-04   3.23e-04\n",
       "3      4   Z2,-2   total  flux  3.62e-04   2.28e-04\n",
       "4      4    Z2,0   total  flux -6.44e-02   3.28e-04\n",
       "..   ...     ...     ...   ...       ...        ...\n",
       "61     4   Z10,2   total  flux -1.50e-05   1.05e-04\n",
       "62     4   Z10,4   total  flux  8.10e-05   9.77e-05\n",
       "63     4   Z10,6   total  flux  1.94e-04   9.42e-05\n",
       "64     4   Z10,8   total  flux -5.53e-05   9.02e-05\n",
       "65     4  Z10,10   total  flux  9.11e-05   8.06e-05\n",
       "\n",
       "[66 rows x 6 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the flux in radial direction with specific azimuthal angle ($\\theta = 0.0$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Flux')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_n = df2['mean'] \n",
    "zz = openmc.Zernike(z_n, radius)\n",
    "rr = np.linspace(0, radius, 100)\n",
    "plt.plot(rr, zz(rr, 0.0)) \n",
    "plt.xlabel('Radial position [cm]')\n",
    "plt.ylabel('Flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A polar figure with all azimuthal can be plotted like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_n = df2['mean']\n",
    "zz = openmc.Zernike(z_n, radius=radius) \n",
    "#\n",
    "# Using linspace so that the endpoint of 360 is included...\n",
    "azimuths = np.radians(np.linspace(0, 360, 50))\n",
    "zeniths = np.linspace(0, radius, 100)\n",
    "r, theta = np.meshgrid(zeniths, azimuths)\n",
    "values = zz(zeniths, azimuths)\n",
    "fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))\n",
    "ax.contourf(theta, r, values, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes, we just need the radial-only Zernike polynomial tallied flux distribution. \n",
    "Let us extract the tallied coefficients first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "with openmc.StatePoint(sp_file) as sp:\n",
    "    df3 = sp.tallies[flux_tally_zernike1d.id].get_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cell</th>\n",
       "      <th>zernikeradial</th>\n",
       "      <th>nuclide</th>\n",
       "      <th>score</th>\n",
       "      <th>mean</th>\n",
       "      <th>std. dev.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>Z0,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.542523</td>\n",
       "      <td>0.000576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>Z2,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.064447</td>\n",
       "      <td>0.000328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>Z4,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>0.000327</td>\n",
       "      <td>0.000264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Z6,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000730</td>\n",
       "      <td>0.000182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>Z8,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>0.000145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>Z10,0</td>\n",
       "      <td>total</td>\n",
       "      <td>flux</td>\n",
       "      <td>-0.000176</td>\n",
       "      <td>0.000155</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cell zernikeradial nuclide score      mean  std. dev.\n",
       "0     4          Z0,0   total  flux  5.43e-01   5.76e-04\n",
       "1     4          Z2,0   total  flux -6.44e-02   3.28e-04\n",
       "2     4          Z4,0   total  flux  3.27e-04   2.64e-04\n",
       "3     4          Z6,0   total  flux -7.30e-04   1.82e-04\n",
       "4     4          Z8,0   total  flux -7.25e-05   1.45e-04\n",
       "5     4         Z10,0   total  flux -1.76e-04   1.55e-04"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A plot along with r-axis is also done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Flux')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_n = df3['mean']  \n",
    "zz = openmc.ZernikeRadial(z_n, radius=radius)\n",
    "rr = np.linspace(0, radius, 50)\n",
    "plt.plot(rr, zz(rr)) \n",
    "plt.xlabel('Radial position [cm]')\n",
    "plt.ylabel('Flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can also re-construct the polar figure based on radial-only Zernike polinomial coefficients. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_n = df3['mean']  \n",
    "zz = openmc.ZernikeRadial(z_n, radius=radius)\n",
    "azimuths = np.radians(np.linspace(0, 360, 50))\n",
    "zeniths = np.linspace(0, radius, 100)\n",
    "r, theta = np.meshgrid(zeniths, azimuths)\n",
    "values = [[i for i in zz(zeniths)] for j in range(len(azimuths))]\n",
    "fig, ax = plt.subplots(subplot_kw=dict(projection='polar'), figsize=(6,6))\n",
    "ax.contourf(theta, r, values, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on Legendre polynomial coefficients and the azimuthal or radial-only Zernike coefficient, it's possible to reconstruct the flux both on radial and axial directions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f92f6e3f8b0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reconstruct 3-D flux based on radial only Zernike and Legendre polynomials\n",
    "z_n = df3['mean']  \n",
    "zz = openmc.ZernikeRadial(z_n, radius=radius)\n",
    "azimuths = np.radians(np.linspace(0, 360, 100)) # azimuthal mesh \n",
    "zeniths = np.linspace(0, radius, 100) # radial mesh \n",
    "zmin, zmax = -1.0, 1.0 \n",
    "z = np.linspace(zmin, zmax, 100) # axial mesh \n",
    "# \n",
    "# flux = np.matmul(np.matrix(phi(z)).transpose(), np.matrix(zz(zeniths))) \n",
    "# flux = np.array(flux) # change np.matrix to np.array\n",
    "# np.matrix is not recommended for use anymore\n",
    "flux = np.array([phi(z)]).T @ np.array([zz(zeniths)])\n",
    "#\n",
    "plt.figure(figsize=(5,10))\n",
    "plt.title('Flux distribution')\n",
    "plt.xlabel('Radial Position [cm]')\n",
    "plt.ylabel('Axial Height [cm]')\n",
    "plt.pcolor(zeniths, z, flux, cmap='jet')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can also reconstruct the 3D flux distribution based on Legendre and Zernike polynomial tallied coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define needed function first \n",
    "def cart2pol(x, y):\n",
    "    rho = np.sqrt(x**2 + y**2)\n",
    "    phi = np.arctan2(y, x)\n",
    "    return(rho, phi)\n",
    "\n",
    "# Reconstruct 3-D flux based on azimuthal Zernike and Legendre polynomials\n",
    "z_n = df2['mean']\n",
    "zz = openmc.Zernike(z_n, radius=radius) \n",
    "#\n",
    "xstep = 2.0*radius/20\n",
    "hstep = (zmax - zmin)/20\n",
    "x = np.linspace(-radius, radius, 50)\n",
    "x = np.array(x)\n",
    "[X,Y] = np.meshgrid(x,x)\n",
    "h = np.linspace(zmin, zmax, 50)\n",
    "h = np.array(h)\n",
    "[r, theta] = cart2pol(X,Y)\n",
    "flux3d = np.zeros((len(x), len(x), len(h)))\n",
    "flux3d.fill(np.nan)\n",
    "#\n",
    "for i in range(len(x)):\n",
    "    for j in range(len(x)):\n",
    "        if r[i][j]<=radius:\n",
    "            for k in range(len(h)):\n",
    "                flux3d[i][j][k] = phi(h[k]) * zz(r[i][j], theta[i][j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us print out with VTK format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You'll need to install pyevtk as a prerequisite\n",
    "from pyevtk.hl import gridToVTK\n",
    "import numpy as np\n",
    "#\n",
    "# Dimensions\n",
    "nx, ny, nz = len(x), len(x), len(h)\n",
    "lx, ly, lz = 2.0*radius, 2.0*radius, (zmax-zmin)\n",
    "dx, dy, dz = lx/nx, ly/ny, lz/nz\n",
    "#\n",
    "ncells = nx * ny * nz\n",
    "npoints = (nx + 1) * (ny + 1) * (nz + 1)\n",
    "#\n",
    "# Coordinates\n",
    "x = np.arange(0, lx + 0.1*dx, dx, dtype='float64')\n",
    "y = np.arange(0, ly + 0.1*dy, dy, dtype='float64')\n",
    "z = np.arange(0, lz + 0.1*dz, dz, dtype='float64')\n",
    "# Print out \n",
    "path = gridToVTK(\"./rectilinear\", x, y, z, cellData = {\"flux3d\" : flux3d})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use VisIt or ParaView to plot it as you want. Then, the plot can be loaded and shown as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f92f69934c0>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0RHlAEBHOnBsRRTFV5UNYb0H4XropxH3oZHbxKqXxgv1f6AlWeHc5bDf4kUOAiWrS7ppeuiSJ1jaClRKc6WB93pwt5wV7cQU2loTPkOiQk5EDUDpJ9c+ROq/YL9LlZKzcQpxs0ttm9FiypMNMBszosyZFjKK+mEPc+1vDwarLm+qDQ055IHAn3Ep2hAC/CHxOVf/r1q6PAR8AftZd/2Zr+98XkV/FLsiNgx/8cNEfZPQHQyZjP33YZ0Q4L0H6oIkNm73w+tSzAY0X7PsvtL1go8hQSfoFSVIQS0kk9nW82+uthC0mGy/Yi686uyEjp8+CLksMNeqS1qqN3VDQY0lM4ZqmxeRkrUW6gi5KjyUFMSs6zOmzJiGmJKG0oh5DMUgoktS+T1eQMjY99HDiRiBwR9xKJPxdwH8MfFpE/sxt+z9jxffXReSDwNeAH3P7fgubnnYem6L2k8d5woF7TxwbTp/pMxmPaVamfC1xZJvtHLUbdrB2g7ckvPD6yLiHjYoHIInN91UX8SpCTEWPBduMN6lnfiEOfP+ekiEzeizokG/21S6VQlzknJETU6LOcihIqFwGRMqazD12TcqKDgt6rDeLdOvNcan0mciQWg2FUZeuJjAQxnWHYh6Tqf+iCgTujFvJjvj/8vW/8N97g+MV+Km7PK/ACXPm3ICvfGmKqveAx9j11couxGVYH7gtvLhDS5quaVvu4o9xXnCNIaGgy5ItJmwx2eT1NpGtLbjoYRfquixJXGQLbEQ4c89jxbVGnRdcEmOoSShIWTNkRuUW6VZ0Du23qW0FaxbM6KMIKzr2y8CURElF3Te2Sq+GfJGwNAlZFUQ4cHeEirnA6xARdnc7pFmXfOUlb41tL5lAL7PORErjk7YHag7YRL2HevnWtogjdVkJ2xzYUmJnN7SFt8OKLSb0WJCydgtx3tNQIkp6LOmxIHERc+2KNmqXZdGVxsrwi3Br0o34dliRkVOQsKDHis7GrrB+9Mq9Vk0dG/Iko4oNxFDHwiTqsl0t78+HEnjDEkQ4cEOyTsRolHJ1VdDkkVVA6rxgOTxaqEsjvD4DosYuwimIKGm8ZmDmmwwGbxkc9YJHTJw4N8LrxbHLij5zuqxcQprF9n1XEi1ItSAxxaGCjUojIpf9EEvJgDkVEUvnBXuxTijosyClYEGPMSPWkhFTsY4UErWuzBD2ix5PrfeCLxy4K4IIB26ICJw91+Xqlfaf22OoH4dKQV3nNG9HjGhlP9AIdBfMsCbpFTYybS3C+UW2ATNGTDdRrxdnYLPI5suUfYaE8UeoYrQmrkrSyj6WyDb3qcUgPirWFQOZA7Dc5FJkm9Q1b0esyIgpN9kRXph7LJC4ZjYYUBURLIVx2t1E7oHAnRJEOHBDRITTZzuYaL3JS0BnttuYiwQZ0RTV+QQKaPrv7tAM1BRsv1/XLKJDzpBJq9qtEXsvzn3mDJnRcVHvRpxd1BtXJWm5JqmKJp5u5R+bdU1clqT1GokVUlhLapv2UJGwZiA1PRbkZMwZUBK7Yo/K+cjTzSJhLYaFsyY0hXmWUURR8IUDd0UQ4cDXZTSK6PcN07mriDM5JCswWeMFlzTtJ30GxBBrT0RAJdSRFd6IiiFTdjmg4xbZ2l6wQZ04T1sZEs6SUAAh1pJutSIt10S1Vf1W10t7Pq4pu9S2qbu45A4FTF3T0ZyurChNxIoOS7obn9gWa+CW9azXXGGtDGtnFGhXKOuYPI+ZphnZMohw4M4JIhz4usSJsHs6YTr3w9kUdAzFVhP5ekvCC69x21VtUZ0qHbNiizF9FvRYOOE1h7xg35ynS+7E2dfBeS94SV/npGWB1Io0a3RN28mVuwbEN5j3bS/c1IxYys2Yo1oEI+3UNOtFL+kwZosVnU0JtM1LnlOLUEcjyji2i3Npl9PL+T3/LAJvXIIIB74h5x5P+drFoumdIAeQPGUryPwi3EZ4OWRJmJ6tiOvKkkiaiNd3LeuzYIsxPZdeFlNRtxbqUtYMmDFwUXF7IQ6wzd38nDgfjDZ93u22FZvJyeL7WcT2OyKuKrrVkl68ZCldFvRcalq2KQjxXwU+7S0nw5gaiRXtCAeDHjoORRuBOyeIcODrIiJsb0cksVDgeuyaMQxyMN1WQ3fs7YhmKOdQ0EQ2C2S+RDh1LSnb1XDw+oU637LS5gXXG2HezIGbu+v2mlj7fHz0a9x5pW6bG/ApK4hMRdSp0Eg2dkNMSVdWtp8FBcKQ3IlyTLkpgS46CethxsG0Sy1CpGFxLnBnBBEOfEO6XcNw27B3ULk//QuoZlB0bIaEcjhLwvvDJWhshdMvsu2wv+kBYb1WQ9TKCx4yO9SMXVBUXe5wodbrXdJMUW6XQxdsJim5F22GgLTtCj8/LrORsTrhTqRgZCak5MwYuKdMNguCPRaA/bJYS8qSLuskY5mm5HFMryju1UcQeIMTRDjwDTEGzp5J2JtXjcda74E5baNeP97e0AijK8zIorzl9S5dZ7MYZb0pVR4yc3nBuYs8lVqtX2xUSYqSJC+Q3M2ta+cm11jRXbDxgjdjkvxxeet2QjPRw0fFC5BcSdM19KGQeNNtLXF2iI+Sm8wJW4GXJwXFMGLa79A7CCIcuDOCCAe+ISLCmVMxf/k1W59hG9hMIKuBqKmW8wKcAH2QgS3OENFNVm9FtCm42HItKbusXKKF2eTcZuT06wXJukBKRbzP3I5qvR1xI2Eu3MX3nvdj7b1nvXSPTUA6bDI5VG1E3NOF7U4slYvY440QZ+QMmVMTUZiERdLjoN/j7ME0+MKBOyKIcOCmjAYRna5hUbjGPdUcqiWsB00TH99LwguaWNEt3a+Yn4a8w4EtfNg037HiayvV5gyY0SHHaM1mmLJPh1tgxTen8Xw9JVac/T5DMxnDf0kUwMxt99F73TxWJpBla5JuSU1EvMmOKOiwYsAMEGoi5vRsn4u4ZjwI444Cd04Q4cBNSRPh1E7MYm/tLIkK6jGYvs2S8PNAnRdsK+pselpPFoyYbnpEAFREh3pE+Io5P0UDaNINcqxwtr1gj7r9SzatLQ7t8+PxfETsmrJvMj0KGksjBXogBkynxki96U9sUBv5kpLT2eQQd1hRZAmTnQ5VZIirMO4ocPuYmx8SCMDpnbiJPGMgOmga+Hgx89ZACr1oQVeWZM6srYjcRGSzGU/ko+LNxGQ1tmtbBSxAD4AJjd/ro2K3n31sc7ecZpHOp6bNAf/4duTsmrIzcY+ftc7f+8Qr6BWLzRSPxiMuNtkRIyb0ZUFiCladlFUa4pnAnRF+cwI3RUTYHUXEKZSbCHUMVQHrtKmO62C7q3WgMpHrRWacF6x0WTJwlkPqFuc2F4W4LsiKNSavoQDxVoe3I1ZY0WyLaruLW0HjEwvNSCIvzD6v2I/Jy2giZv+cJUgF0aBCE1vMEVPSd9kRFRErss2MulhKqgymgw6Dpf+2CARunSDCgVui34kY9iP2c5clwQp0DuJEOGsdXEIZ2V8tX+02cv2CQTeLdHa2m5351te57fHQFl6wwjjHRr6+KKNtO7QLNtoLeG3h9oUkR73gqvW8Kbh6ZfsaJZiyphctEYNrAp8cioh9K81pMmRvt89jVydhcS5w29zUjhCRjoj8oYj8uYj8hYj8F277cyLyCRE5LyK/JiKp2565++fd/mfv8XsI3AciA6dGcSOAkQJ77prGe619f4bVoblwNUJJ7KYd1y7LYMrANcihvQjnphozwc4Z9XaD/2314nrgjlnRWCU+sp1j7Qa/v13Rt8ZG1GNeH1m7Yg6mYBY1SVUQU2yKNTrkLpq3k6ATKcjIGW910aDAgTvgVjzhHPheVX0n8C7gB0TkPcA/AX5OVd+M/XX/oDv+g8C+2/5z7rjAQ46IcHY7QXwBBMBqbBfhvKfq/syXVDej5v3AzZqIiJqB64yWuc5oiqFW+2uohdjIdIwV0ar1WtB4vV48fWpuO3XNi6tr4rOZf+dT08bu4oXZi29x+LGyto83VU2iJR1d2YjddXXzi3MptkXnqh9RRWGJJXD73PS3Ri0zd7edcfm9wG+47R8FfsTdfp+7j9v/XjcsNPCQs92L6KSm8VpLF0YarCXhSoMrtVm1vuLM/um+2CxyeSvCesFCWq9JlgWy0CbLQWhsg5wmKj66SOe7prWFud3cpy2uM5rn91Hvyj3vlMN5xzVIbqPhTrHaVPKlLipO3HvyU5qLjmHV8X09A4Fb55a+ukUkckM+rwC/A3wJOFDdTDm8gB1Ahrt+BcDtH2Pn7wYecrJY2OlFzYKYFKATO7bIR5Oln3tsxwPZlpTloUU6P1/O5gVP6egKo4q0fxtLDke1bb8XGnGdtvb77Agf9Xpx9VVzXnx9xHyAjay9leK8YJZsRF9ykMo2jk8oNlOefR/kjpsQIpEyHbWN8UDg1rglEVbVSlXfBTwJfDvwtrt9YRH5kIh8UkQ+medhTtfDwtmtpNU4HVgcNA1zXB+JTGxHNON68RYbL1g36Wk9lodGF2Fo8n6nWHFslyLjXmPV2t/unOYzILy4Lmii4nYGxBwrsN6uaPvEC/d4Xwbd8omzcs1QrRXhm7wnbpZzh5wOSyY7WZixEbhtbsvEUtUD4PeA7wS2RcRnVzwJvOpuvwo8BeD2bwHXb/BcH1HVl1T1pSwLFUcPAyLCqV5E5KvREiA/gKiywpzY7bWajfD6huh95pvxRb5ReqVWzbWURgDbWV7tqHdOYxncKHWtHfW2c4b9Y31E7f1rnx3ho16fT1y2Lq4vhcwgyquND2wjYpsdYW2KFV1ZMR1lYXEucNvcSnbEGRHZdre7wPcBn8OK8Y+6wz4A/Ka7/TF3H7f/d1VDn783Cr00op9Eje9aL4FlEzmWUNXRoVHzGWtn38YbW6LG0CEnLdaYdd3YDYamIMPnBfuotY1fpGsLsz8nH/VOseK6pInUvR2xcPu98Ldzjf0+n/rmhLud9dFtzcNLXC3duieUSVicC9wet5In/DjwURGJsP9Ffl1V/62IfBb4VRH5L4E/BX7RHf+LwL8SkfPAHvD+e3DegRMiNnBmGDOZVS4SrWC6D4PBplQ5iqvNNGRfjOEF2I4Iyt1gzTUiHM648F6vtyPaUa+3K3xur7cb2nm/K5poWEC9zVFj+wgv3PEd/4Zoypt9RkYPG9X7iNi1wYziik4nZ20yYik305sHzFnSZZYNybsx6ToUbQRunZuKsKp+CvjWG2z/MtYfPrp9BfydYzm7wAPJ6V7Ml6c56nv25gcQPeWavrvmPWKzI2o3qCh2E4tT5zfYgg1DLQZT14hv1O6j1nbBhl8sW3DYjrBPdLidpYuINwkSNdQlmNpOkNbI9RGubWXc5vXaBR3tzAnXGlNSoANxXRKbcjOBOSdjRcdO/jAVi2HCcBxEOHDrhIq5wG0hIux2YrJIWHmXaT21zd7XKVqC1kIRJa4t5dot0tVu7Sze5A6LKlFRHbYb2uLrm/ccjXpbPR6ONvZRbEvKyl3Qw3UgqD3VTepbduQ5fQWeJzm8LyorOrH1gpd0nSVRuQW6FfPtCL0Qxh0Fbp0gwoHbJouFrW7Eqiit2qxzWEwhPwUCiRabxudeeO0inf1167g0r1TdqHo/ggiaqLc9vqhtR3jP9ohwqzjxrcB33ITDFnPpMijiEkwEmmIHhnoPue0rR1iB9gt0c1xErJi0JonKzfgl21ttRU8WzLeHqHF9LwKBWyCsIgRuGwHOdl1hggFihZUrYU5sj+B2wYb3gmOX0hVR2Xxh25Sh6cTmxxfdaJFuSdPSsmVXqIKWUOVQrqHdTfJoyrB/aA2bhTj1mRU+c6IdEfsFvHbfigqiynreXVYbIc5Yk1Kw7hqKNPy3Ctw6IRIO3DYiwm4W2/UwHznOD6CuYR1Rpr5U2Q7Q7LEgotpUyZXElBojqlbc2otp7UU6Xw3Xzhk+6gUvnb3Qyr/xFcztdT2/quyt30IhySGKQBJstZ/PnPCv4dPw2uK8giQp6SZLZtLfDP/00TBpzboXka1CKBy4NcJXduCOGKaGvi9hFiBfWFsityZs2vKCawxrUirnORgq23+hKA+XKLcLNnz0eXSRzkfMLrVMtNnXzmprZ6VBo6++IZu3hVG7SKdtm8On23nh9UNCc1tBR2GHl8ZakpHTZWXT7VgTScViFIeijcAtE0Q4cEckIuwmcTNWnhJWByAgRqkkYk2ysSQAFzEWxG6Scm1Mk57mVdIvtMHrMyR8doSzKxTrBXvLoZ0g4fd7YfaJF+0hzQWwqqHyItvqBLd5YDsdrlXIEZUVmdro1+cLx5R0WbLY8QZ3IHBzgggH7phz3hf2qjbb30SPa1LU2RG+25i1fmMqbRq+bxbi2sLb9g7aGRA+O8It0tUlrAto13r40/FJDkcy1w7VY7RTkbW2U5u0oBmZ5Bv6tLMxVu5BBaS6JjlaRSdLViNDHXQ4cIsETzhwR4gIO0lEGglro1YcZ1MoKzsVI1UnvLoR3JKYihhDvRGuzRQMP6MOGvE9WqLsF+m8SLaUt13L4d2EtiXgU3+hqbBO29srSFYcns7sI2I/sSO1t8VFw0lakumaTHIy1q7L2pqyI5SZIVoEXzhwc0IkHLhjupFhK4qaCLVcQjHbhJ0lMTmdQ4M9U3ISCmrEqqFvi+l7QPjo0z9n2yf2ZcROuNua7Xcf7WTZrvM4Omqu3bcnVxsJb1TZp6b5c2ovzvkKuqraNPHxVktCgYlL8kH4rxW4NcJvSuCOEeCUH3Cp2OyIyQFVFW2a+Ch23L2fJgewFvtH/OZxPh2snR3hFbbt17ZKkVUagW3ZxIfSiV1Xi0PN1NrFcO2o2YuyFqDL1mu2vWBvVThLwtQ1kVYk+JzhtfWHpWQ1isLiXOCWCCIcuCvOpDZVbePV7u+hrtmNca0ra4xbjotctZwhoURzaVbRfGc2OOy/tj0Eb0cUdsZoS5eBw2t7Xlxp7fPBbTv5od23JwdKL7jt6cv+Qc4LbkfFcV1umr17i6VDznIU/msFbo3wmxK4Y0SEURTRFdOoYT4HWVOqzQWuiMjJ3MTlerNQF1FRG3NjL7jgsA/c7qrWGuh5tJtlezAGrX1F62n9Ap23KtoJGSW2+AOfsuZf72g07B+4hqgqNxWC1pYoyCRnNYqow4pL4BYIIhy4K1KfquZZr2E6ZV2nVK6fsGBnzoFSuRLmghiNBPXhq1dPv0gX0coj4/DYIxoRbUe2NLs3+zb5wByOer2++pdttxGu2qrdnkGXtx5U2sEiUV07O6Kg44o2UnLKLhSd8N8rcHPCb0ngrjkTx4fTx/b2KI3NgsC5wVZ4E+cT22YPcV1aBfVWhE9P88112sLrCjoUW5p8VGD9+t2aw/1+4HBq2lHx9bnE3pbePGflFuqO7myPQXINfWItjyzOlZioZjU0wRcO3JQgwoG7QkQ4HcUkSBPJzsaoUQpJWLveEb6HREK56aiGcSXDfj5m24etafKF/T4Xjao2RXbCEU+3dW7taHnJYeFtF3K0RdlHxdoW202ITJNS0VJs46Jh3xfDFm4UrEYhWThwc4IIB+6arjEMjGl6Rc4XsLCtHivnK1g/2MatBQmVxDZNrbXYdigtrb0Q5+0KFxW3beKitQsO28teK48WcpStp7xRytoa1xPjqE/Rjoh9VFxZEfaNfPylF+Usn+qyOpNRRxIi4sDX5ZaXDtxkjU8Cr6rqD4vIc8CvYicp/zHwH6vqWkQy4JeAb8POlvtfq+pXj/3MAw8MBjgVxeyrnbYhVYHs71MPdkmkQDeFGtYLLrC9husqItKyEV/XFP6QR+DLol3Y61PTbuQDw2G3wDsZbdvB9233248mQRiaOg1TW9/3dQtzLQGWwuYLR1oRS0UWVewMapLemr205tILZ+CS0Du/YHRhRjbJEQ39hgMNtxMJ/6fY2XKefwL8nKq+GdgHPui2fxDYd9t/zh0XeINzLkpsMx0FUMzVK9SuY1pOumnkblOBy03vCPWLcP4vdy9wcMgL9oZvVR3OfmgPWr5RROxF1ke8R/OF2/pac9iSqMtWA/jXrd6xEWRT1/TSisd31rzl8Rlv2b7Oc9lFnpFXeCK9SPepFVf+xhn+9O98M5/+3reyGISpzIGGWxJhEXkS+F8B/8LdF+B7gd9wh3wU+BF3+33uPm7/e93xgTcoIsKWiehIU8amkxl1UW0sici1Q9tkR0hCFUWHQ0LvKScc9oK9d0DjA/tdR6NeOOz5tvu0t7f7gPZoNNxuJ6ztnQWH/YvSli93BR4bKC+MlrzQv87T0SXehL08wSUe5wrnxF62uhMmb+7zyjvOUnRCp7WA5VbtiP8G+M+Bobt/CjhQVb8OcgF4wt1+AngFQFVLERm7468dxwkHHkwyhB1ilrrGqBLlS+LphOqUwY64N5t8YXsxJKawohZxuIS57RV4jJ0P59tNtDMjfLAMjWa2xVda26ApzPO3vfD6mZ8bn7idVtESYVNDv4atBFIFGduvl3S4oDPI6SSurSXNbGm/OLlOEi696xxrI/yVT7xs/3oIPNLcysj7HwauqOofH+cLi8iHROSTIvLJPF/e/AGBB56zJnFDNgXqGrl+jVwzSmLWZFQYjF2O2/SS2DROP2rSQiPMrYnJ3tdtVzYftSPa+3y03G7o47W1va8+ctmIcUulY4UdgSdrOFtAtg/mKshl4DLIVYj2KobLGafrPc7oNXY4YJsJW0wYMKMvC6JUuPL0KeaD7Bh/+oGHlVuJhL8L+Nsi8kPYQeEj4OeBbRGJXTT8JPCqO/5V4CnggojEwBZ2ge4QqvoR4CMAO7vnQjzwkCMinDIRsYpLQFPq62PqF56ijGzSlk1NE9vgXW0JcxRXjeq1PWAvvjcIbdupae1ByUfFt72PG1y3RVePPGazvYasgpFCfw3RzM2P80nH7Ry30u6LpGIQzSnSmDk9ZvRd43fb+jKp16y0YjLqMJjmYZHuEeemkbCq/oyqPqmqzwLvB35XVf8u8HvAj7rDPgD8prv9MXcft/93VTWI7CNAj4ie2o5pADKdYVaLzVSNiog1KaUzAyo1zW9gjB2s2Y58W/nC6pRXpBHM9lCOo+Lb7oAJhxfkjt4+GgH7X9YUOFfB42sYzSCaWOuBCXAA+NsT7Jy6mbvMwaxrOrom2/Qctj8BoaYyCevekPFW965/5oGHn7vJE/5p4B+KyHms5/uLbvsvAqfc9n8IfPjuTjHwsBADZ0zTDELLCh1PN4tzvmIuokZQ20nN+8ApjSLC4XzhtuHbSu8yr9+12XdUfI9GAXrk0ragO8A2dgGkVijWoHM2ArsZ09Fu8u7zh0uQCqS2z+wzhGuEgtj2WasjWK6YjDpoCIMfeW6rxYiq/j7w++72l4Fvv8ExK+DvHMO5BR5CzhDzFRVXVFFTXzugfHwHFaEg2ZQw55LRZWm9YeMk0q+Y+Xzh1hQNH9r6Te3NPs3Y09a19uLcjWwJfzFADyu+HZoexf57IFJI2ulpbR/Dv0DLSqkj+37XYss4clfQnGtGURpYFcz7KWUckRbtcpLAo0aomAscGyI2QyJVQ63uV+tgjJQFuRsKby0J+we6oFSVOZwd4dPTjoibtHKJ25YCHNbr152Tu75RJAxW7/vYhY6Mw2lvh3KLj/Sw2DQZ8iM6Mqx690AHUKQpc+kxp8uMPnN6TOkzYUA9z0FrVmnC0o+ICjyyBBEOHCuZCNvqE8AEXebUi5wFnY0z6gs3agyViVAvvD5L4mgFXdt34LAPfDQihtcL8lFxFqxuDtzlqBPSXhuM3SXyguvFtotVb/8kI+wS9BbUA8M87jFmyB477LPNhCFjHTEtMsqFK1aJDNNhJ+QLP+IEEQ4cKwKcIUFdOCtVhV4/oNR44wMXrYKNMoobNfX+b4RVRt/Osh0Vm6atBByOcI+2ID6KwernkEZ8vb77gDY9crsLdAxEHRAfMnvBPQXsNhc9BdWuYdbtc93ssC/b7LHDdXa5rGeZLyO4ekBd6sYtPgiLc488QYQDx4ognJYY07IkdO+ASo3rtpu5+cS2hwRGUBGrfD7ybRdseHFujT3y0a+PWA2Ho+OjWRMJVnS3sMFrRuMg+MDWB7c9d8zQXXoGYm8W7wI7wGkaAT4DnAM9B/VZw6zX5zJnuMRZXuUxrnCaS5zlteoM80lNXOROgO0bGY96YXHuESf0/g8cOwMiekTkYqO9ajynzktW3cw17+GQLVFFESYtb6yqCRsvWFyK2tHD4PVRsNBEvT6gpvU4n5DhxbhHI8LeYegkEPWBLZBtrBBvY8X3VHPRHah2IsbZiGvsckW8CD/Oq/o4r5Zn2J/GmDymy+HCpFk/C4tzjzhBhAPHTgxsk/CaGmIRdF2g0zmrbgc90tSnJEaNoE5gN+Pm24Zsa0HMi7B3Ltp67Z2MPs363pHK540AexHOaMTX27x9A0kXGIEMscK74y7eftgGPQ26K+TDlEk85Kqc5iJnucwZLnKOr+rTfKV+knyyJp6ObeTv4mCfS50nMYtuSlqEqtFHlSDCgXvCOU14TYyVHIVqb0Jx5nFKicnJXJN3oRLTKKo3Y72aejFuZyOATVXTwwKcYoX0aAW0O3wj3F6Ak9ZjXFIDvSPer3jv19sQzgfWU/Z+vWWYd3tcM7tclVNcZ5dXeZzX9DEu1me4OB+ST2esipguih19KpteEgBVZJgMOmxNlqFy7hEliHDg2BGEHSIiIlQFESivT6jqN7GO7BS22vUYzkntrDkjSKKN9+uVsp2m4KvmaKJaX1jRXsNrZzrAYQ33T7vxggWSCKKWFyFDNpkOjLAC7IRXt+3t1SDjIBqxJ7tc4gxXOMNlzvCyPslXeZLpXOjtXcbQBTdnD6DGEFE1ZdwijEc9nnpt//g/iMBDQRDhwD2hi2GkCRNj56zpfAWrFct+k6pWkGxyh+OoRBO1+cBtAfaC7CJiiSCpoFPZNbGj7SWOliu3LQgf/UYG4hhMCuL9iD7IAGsit9LNvA+su9Z6KAYJs7TPNdnlspxhj21e4zFe1cd5Tc9yebnFYqasVkLHRb3AJi+6JLaTpjFueU4ZD7rWjgm5ao8kQYQD9wQBTpNwgO0loWVFuT9j1RtQSbTJlFAMpcQkaYGJayu2GWzWr1pRcBxBL7MaGZduDlwNpUuJUGjETCASMAaME3KJQFppEdLBmcBYIfYpFD4NbduKb70lFP2EaWfAgWxxXXa4xDmb+aBnuVCfZX/ZYzWtqPIx4pLbSpJNK8uSiIiagoSu2jdnB57CrJdRxBFZWJx7JAkiHLgnCMIZTTivEbUYlIry2oTiiW3WpKxaxRtrUjrx6nDI2qpGS9Yw6sIggtj3afDzjdS2mASasudWBC3eMG4n/7Zz0rz4Dtnkpuk2sA310LDqZ0zSIWMZckXOcJXTXNVTNv2s3mE6jyima4piCkQYF/EaanJSOqyItCInI2VNJXa/1OoWJIU8S5h3M7Jica8/lsADSBDhwD1jiCFzs+UAqv0pdVGxSjvkzoawlkRi+0e0ijQkgmwAowj6XTA5yBrbMOdoTXGb6AaXdlKwTxLerMYBA1AfAfehGCbMsh6zeMB1drgip7nODpf1LFc4xbVyi8VUKRcldbl2ecmN7wsgKAUJPRZEVGgtGFNTq2l84ToGA5URDoY9diaLsDj3CBJEOHDPSBB2NOGKuBkTeUE1W7Hc7WyKNVZ07PRlIqK0Iuoo/REMu9DJQZYgc5rpnj4Cbo/KaCcLt1fg/HXmrn0E7Co21Ee+HaEaRiw7HaZmwJ5sc51d9mWLK5zmip7mOrtcz/vk8xpdLDHV4UF4XoB9s3pDTalx07ze7gSglJiYklJj658oHIy6TUfuwCNFEOHAPeUMCZecL1zXWF945/TGF/YLc3WSMjxTsX2qolMqTEFyYEET/eYcFmDfCN7Xffo8NJ9r3E4I7thr7YL2hTozlJ2YadxnHvWZMuC67LDPFtfZ5Rq7XNcdruoppuuUerKEZY7RapPn2xZeL8Sbi6qNeiVqfGE9vDjXTuGYdLvUIkSh9fYjRxDhwD1DEE5pjNGYSuywz+LahPK5s6zFZkaQpiT9IUlfMNGMQpeQl6Rba0xZWxH2gzZ9FOz7CldNs/dDeWtehDOs75oIZRpTZYbcZMykz0K6jBmxzzZTGXCdba6xy5gR1/UUBzpgsYyop0uifEGkJdFGfH0qnGteT3uyRysiVqUkQkQxaq2IyFRUGpFIgTsQFBadjHUS0V37sY2BR4UgwoF7ShdDn5iFK1SopivqvCTf3Yahoco6TE2fWhbMmNKVFb3OgoSCHivirRJKpWty6kqggthU1IXBRDW1OlEUoRZBY2GtCRJjrQ6JWdJhQZeF9JjRY8yICUMmDNljm6kOONARszxlen3NcngKFjkmXxBR+lZETnT1deLr/62dQBvXtF5Q1pqSSY6RmnWdklBQ17ZARSq7OAewjiMWnSyI8CPILYmwiHwVO8ClAkpVfUlEdoFfA54Fvgr8mKruu/H2Pw/8EDaO+QlV/ZPjP/XAw4ABzmrKl4isUK4rVl+9zP4Tb6PsnmMp19hjwRYTN4dtRU+WZKzJyImkIk0LDIqJK2JnB5CBYogobR8KsZbHiozSTfBYkbGky5IOU/qbvr4HumVnv+Ux02SHYqXUkwVxvmD9xYtU52rMqNdq/i6b1pumFQvb/X6ftO4p4pJ+yzqmY1YYqVG1ecOq/rlqqtp6KTXCuNtldzIPi3OPGLcTCf8NVW2Prf8w8HFV/VkR+bC7/9PADwIvust3AL/grgOPKKc05rzYGXMRFauvXGF9fc703W/hyptfYJSsGDGjw4qhzDYCHFPawZgURNTWRxWIqKmdKIJvBuRn2CWugXzCSjvM6ZFXEbOyQy4ZizxiFfUx8znrr11l1Skwwz4RJaqQjDqsDybosI+KtCJgaCTW3vYrgu3IuI2IUvneymIfrepsCo0xpqYq1CUyCwf90NbyUeRu7Ij3Ad/jbn8UO/bop932X3LDPf9ARLZF5HFVvXg3Jxp4OBGEERGp6yHsK8WqyYLpv/sM9fl9Lr/0bqLdN3Fq/FWinTeRJtDTBUaUDjkACcVmWrOvOLOlzxEClLVhLSmaFyzjPvUiZ5kMYbUmmoyZffFl4heeZPbFy8gLz5DEisli9OJVdNAHsZaG6XfQa2PX46GJgn3bndptNRtzoqFuCbahRsRaF1UdIcZGx1UdIbVSVfYLiRL7v1Bh3OmFxblHkFsVYQX+F7F/Y/1zN67+XEtYLwHn3O0ngFdaj73gtgURfkTJELY14RoRKgb1cqU19YVLrPf/gPo9f5XqlT1k8Qr5u7+NZKmk5Zz6yefpXL9EMsww169RZR2qndMke1dhewuuXScadikuXMNsC9XeFElXaA3Fakz6+A49BYoCXRVEkVDNluh2l6iXQr6H1nbKRYUSdxKkKqkrRWM5ZEUA2KNkY0aAF9+mm3Ej2Tb9rNZos62uzEaMo7jyTwAKyzihiCKiMvjCjxK3KsJ/TVVfFZGzwO+IyOfbO1VVRW6v8l1EPgR8CKDbG97OQwMPIWc05bLEVBSY1h/ugmIWC+qDCeXuGeLzX6HufIX1029CP/E56lVMUeT0rx1gRFn++09jvuPdrC7uk52t0IMp8XgBCuWlfcyoT3X1gPhNp6mvXKV+7BQ1hnjQoZwtiEY9ivGMamuAiRJMbKhWBdJPrVBGEXFqWK9y6kHn0HuwElu7a9MS4iZfQjcJaVa0RZR1nRBHJRioS0NsSihBE/dzcBkfeRyzSFM6QYQfKW5psoaqvuqurwD/Bjtl+bKIPA7grq+4w18Fnmo9/ElukIauqh9R1ZdU9aUsC17YGxlBOEWM0WjTztFut1JmtITr+9T9ISZLkOvXbYedXhf2x+hgQLU/QwZ9Iq2opzPYGlKNZ8ioTzVZYAY96tkK00mpVwUkMdQ1WlZUEhFvdanGC8ywRz1buvMwRL0MnS8251RhiIZd6smMWs0RO8LGuRXN+2g8YjYC7HOIRWy/zap0kbCxDS5qMVDT+MWu85AiHHSaBcHAo8FNRVhE+iIy9LeB7wc+A3wM+IA77APAb7rbHwP+nljeA4yDHxzoq2GgMdUhIW6qy2RvHzURurWFmU3RdUF9+gx6bY86zSgLqKMYGfTRvSn1YEg1XaLdLtWqoE4S6spVP0SGqqisIC9zuyDYy2CVI0mEqUu0LK3/OurBdIaqsx3EEA07MJkeEmAf3VatLxHL5qvE5QofllAVoa6s6Hrx9UUmWgoSKVRN96GDbu++fB6BB4dbsSPOAf/GZp4RA/+9qv7PIvJHwK+LyAeBrwE/5o7/LWx62nlsitpPHvtZBx46ImBXEyYui8G0BtcLiizm1HlOefos0eXrVOMJ9c425muvUJc1ZbdPnReYMzvopQlEMZUaYsWKd1EhnZR6tcYMuuh0aa2JyZxq2IU4RiKhLipMN6Oer6i2+5h+Fy4cgOomG8J0M0y+T+28YmDj8fovD+sD2/8+ppUvgXtH3o7wSRRlHVO7lm517cS4tMUkVGzCoWnSoUaIQjz8yHBTEVbVLwPvvMH268B7b7BdgZ86lrMLvHEQOK0xX9l0VTOb7FqDImVJvT+h3D5FagSu7lG/7QUiIzCdUY+2qKdjzPYI85VLdmRSt4sucxj0qSdzZDSw1sSoT3l1TPSm0xTXJlQYGw0Pu5TznGirRzWZoVsDGxkbtc/XsRkcxAkmMZTrCrrJIQGuXAl2M/G5qZCriDaRsi9d9m++LgwmrqlNBLnY/3kltqRa2XSEm0epXZyrgi/8qBCmLQfuC3baRkxaR9QatWrK/DJXBdf2qbp9pN+F8ZhaYnQ0gv0DtN+nnK3RXh9jQA8mMBpY8d0eUU5WyKBPNVtBJ6NerZEkgrqmLmvrC4+61LMF0aAHyxUANRHS71LNVm7kks1yiAadxqZwxRVlK82u7RGXLk+5Rg69Z8VFuWCzImoFVSu+BnuNu+0X56KYRZzej48k8IAQRDhw38gQtjR2EWN0aIFOUGQ8BoVq+xTRYgGrnOr0Gbi2h8YxVWHHAcmoj+4dQL9PPV8hWYquC4hjtHLWQGTQosR0UnSZ23ziXgdd5miaoFVNVVmf1mwN7ERotxBnfeEuHEw2AtxeiAM278G+j8Yn9lZE+/1h2PjCm/9xvh9GQTOPqQathYM4+MKPEkGEA/cNAc6S2EhYfYcFi0ExyyWMZ1Q7pzB1AXsH1KNtJF+heUHZ6Vv74dQOjCdgnDjWiiYp9bpEOxnVcg2DPuV0jY6GlJMFhSbWFxbQssKksRVkBNPLkMXCDiR1wiq9DrJY2EUzeF1E7DMkoHG2beVefGjhTkShdtGv75qmWPEVd21ohFiFgzRkSDxKBBEO3DdEhFMSY2pD5f60b6d5SV3B/gHV1i4miZBre2ini6YZ1WRJuXOKcrpEd3eQfE2dl1SDIdXc+sLVdAlDl842GlBNl0i/h85WrsxZiPop9XyJ6XeoJ3MqjdAksaZIWTUinMREEVCUVnz19eILbKJev72dHaEqaN0qea6kEWLfjtiLcMGmaGMqnddZG4E3LkGEA/eVIRG92mzEa1PU4KV4/wCNU7Q/QCZjG0Vu78D1fbTXp56tIMswaYROpjAcUh9Y0a2nc8zIliybToqu1kgSo1qjZU0hKTIaUo2X4ES6JEbFEPVSdL5sUtIkQnoZTOdoKa/LGfYRcdn6MoHDoqy40dDiKudW0vQ8dp0sD00IaYnwyiT3+6MJnBBBhAP3lQjY0djaES1hs8UNNTKeQF5Qbe8iK2tP1Fs7mP09QChrQ12Dbo2or4+pez3KVWHLmdc1dWQX1yoVNIqoihrpdKiWaxvhdjN0vkSyFCkKtKpQMZitPoynm/FDpcSY0QD2JxtxVBUqjSi1EV9Pkx0RbcqVBZf/662ItTRim2MF2e9rLc4VEjE32X39XAInRxDhwH3nnCRQ+cqz9gIdUK5tStrWrm1ws3+ADkZIsYbFiro3ol6sYHcb3R9TaUQlCXUFtfOF6XXR+QozsNkQMuqjznqQOHY9HGpIY3S5piBBB0N0vjyUtSH9DizmG+HU0ub43igi9gt0HsUVafiFNy+47cyzErvfz8xzF1UY0w2+8CNCEOHAfUVE2JGIpLK5wj7ytNFwbXNrr+1TdbfRNIODA3vd7cF4Qr21jU4XsL2FKQtYrtB+H50tYDCw+0ZDqskcRgN0skD6Per5yra7lBjpdylna2Q0QCc2DY00tp50UVGrsxSyro1m1yWUYufBOWo1Nip2C3E3KmtGxVoR/mGlQNW6f3RxzmVIoHBgQobEo0IQ4cB9pyuGbY2o6yaVq91zgf19MJGNgKczWJXoaMemqqUdimVNmfWh20EPpraQY7JAt0YUs5yqP7CTkDs96lWBJjF1rVQlro9ED8ZTzKiPTmdWQCVCOhnMFtS1sUM6jfOFF0t74q6ooi4NVe2Fls3C3dFFu81jvLiCHdHkLYiitc2LcQ3UwkQ7VBr+ez4KhE85cN8R4DQxVGyq2Q6xXMIqR7d2kSKH8QTd2kEmE6jtAE0tK2RnC90/gF6XOi8gS9F1CeIKiVUhMuDyhVnaaFj7PepFTp110KKirIRCEhj0YTzfCKYisDWAybTJ6y0F6sMRsfeIFZvGtqmAa0+E9m88d7cjGhuibUc4gV7WKXmYPnbfiKJGCo0xGPN6aTRGMMYgIoeOv1uCCAfuOyLC2SjBFILWBlVD7QqBbV5tCdcPqIenrYjuH6DdAdQ1zBdod4BO59Q7O5jJBFWo4xQtKzTN0NUa7fWo5jn1YEA5XVGPtignS3LNqBO76FVXWOHOCxuFj/own28i16qOqAdDmC2g9E12aCLiwlBXxgovTUpaXRgrpt4LhqZxz6r1g1i7ay/A0twuNGKuYXHufpCmCe/6lrfzwnNPEUUR7/qWt/Gud76NLEvZ3h4RRcZtfzvv+pa3sbU15Fvf9Y5je/0gwoETYWAMfXUtHTm82AXA/h6adZEsg/EYTAz9EeyN0d6IerpEhyMoS+rpirI7pJysnDUxR0cjyskSRiOqg5nzhd3CmxhM31oPZtiHma2Wqzo9KErIKyhcxNvt2C+Fum4i3ALr7WrrUglauFxgbUYfbY73EbG3IXyecIUVY79A5/ZpBeOySxiycQyoIlWFVCVSlURGSJKYJIkxRiiKkqvX9tjaHlLXNX95/qsI8K3vfDtvf9vzvPtd7+Cxx06zWK7Y2x8TRYbyGHs+BxEOnAgJwq7GtpOYStMi0qvOdGr3DXZshsJqhW5tw8EBZB00L9E0Qbod2DuA4RAdz9BBn3q2tP0nFkvouMg4jlx/YbXWw9bIlioPh3Awg8J2YyNLYbFqIl4xkCQwXzV+rt/no1tvJ9BavDsqtl6XvdD6+z4a9r6wf84KDuqwOHccSFXx3L//Ld76O7/GW3/n1/j2L/4hbzm3w3PPPsFg0Gd7a0i32wGF3Z0t3vUtb+NgPKWua8qyYpWv0VoZDHrs7IxYrwu0Pr5vx2A6BU6M01HM18o1xK7vrhdiUchz20BndAouX7L5uv1tuPAq5CU1KZorsnvGivCTT1LnJZJk1JWgklATY9RQxxlVrtSdHrosIOmQ9XvoaweQprBa2aIQFdga2i+Aft9GuzEwHMB4Blnferm+7BiscMY04YwXUV+AAUciaKzg+rzgksYrjtw+11t4kneoUkMsbWM5cLsIys50n+70AID6T/+IL59+nuXWKbvfZbAsFiviKOL8l16mqipeuXCJ4bDPeDylLCum0xnGGKbTOV/44leP7fyCCAdOBBFhN45JcqGoFI0MtbgQUwW0hvEBevasbcZzcACnzoAxMLGCqAczdHcXuXAZXVeoSdF1BZ0urAro9dD5yqWqzV1K2pR62GtKlWvARLDIgS70BnDxVTiF/d9RC4z6cPUK6Fm7MOe7oEXu0kotO4QX65xGtI27n9IIMTT5w17Aa1iWKXkdE5s1gTtHgBEwcPcrOLQUrKrs708A+9HMfTYMcP36web2dLbY3F6tco6LYEcEToyeMYzUWP+18p6wcXaqwv4YJEM7fZjYDmv0RzA+sGI5mUGvbyPn+cLens5hMLT7RkN0MkdHWzYVrTeA6YK6MqwlQ/t96sUa+gNrSZRAJ7MrdlXLA447sF7DWg/1eNiI7IqmKMPbFF5823aEf75V637OYWvDt7gsoagi5kVYnDsO+sDQXQa8XviGwz5pakvFu52MTuf+/dyDCAdODAOcjZOmkqxyfqrPKphPoChguGMtg4MF9LbhYAwkkNegEdrrw/UxZEPYn0PWp56sqDsDqsWauttHC0VNbMU1r9BakK2BtR62nQWhCmogimCZNwtmUQxxZIW4bS3kNB4xNOLrH+fxpctrmkh35e67CRubtpYtj1krGK/C4tzdIljhHbUu7Uj47Jldnn3mCb7pHW/GGOHpp9/Eu77lrfft/G5JhEVkW0R+Q0Q+LyKfE5HvFJFdEfkdEfmiu95xx4qI/FMROS8inxKRd9/btxB4mDkdxxgvPq5QYZNxUBQwnUFvx0a707GNhFdLK4hRBvkatrfh+h7EKeSlFc1abbWaiaAqIU3ssZ0OLJe2/Lg7gOnSRrqrvIl0fZTdbj056MFs1oipL7jwUewaWHK4TNmLst9maNLQ/EKcofGBi9bruZ/HQR4W5+4WL8I+Et7Z3mb31C67O1tkaUK32+G1165Q14oxhouXrpIkCXEcfeMnPiZuNRL+eeB/VtW3YUcdfQ74MPBxVX0R+Li7D/CDwIvu8iHgF471jANvGESErSSiq6ZJ0WpXl4GtnksHECc2M8J0IEptAUU6gPEURrtWmIsCJLZRbNKxApt24WAOXWc5dIawP0XXQh1ntl9wjY1+V7kV/9EQZtOmD3Au0B3a1yr1sPh6Ub6RHdHOjsDd9v7wmsO2RTtTwtsYlTCZdajq8Afr3TIAtvwlS+l2UrIsxUQR0+mcZ55+HCPCubOneP65p6wvfJ/+ArnpwpyIbAF/HfgJAFVdA2sReR/wPe6wjwK/D/w08D7gl9ysuT9wUfTjYeJy4EYkImxLxLysmywD30cBYLwPTz0PvREcTKCsoL8F1w/gyWdhbw+e2bUiOp5Dpw8HUxvN7k1hewv2r8PZs/DqRXjiCbh6vXn+no2MGQxspNvp2Mh4ubZ2RxzZv127XShyl0InTZpZxOszI3wk3LYp2kLtBbfdW9gLtJ8952yJZZ6SlzFxFBbn7hS/MLft7heXr3Dt1Utc2rJ/eiyXK6azBVVlvzEvX75u/xipqhs82/FzK1+xzwFXgf9ORP5URP6FiPSBcy1hvYSdygzwBPBK6/EX3LZDiMiHROSTIvLJPF8e3R14hDiTJYf/xG//7i+WNkc324ZibSva+tswm1irwZcQDwZ2wa47gNncNvxZLiCzo+5JEyhLZ0/UsK5sa8nuAPanNtI9mLuoNIIkhrxoolsT2+tVeeN8YR/dVke2rzksuD5XeEEj0u3Fvvb8uQqKImK+CItzd0sXuzjXB3q8XviKoqCua5sbXFX3TYC5wbnciBh4N/ALqvqtwJzGegDwE5ZvK3hX1Y+o6kuq+lKWdW/noYE3ECLC6TQmbi9QtZve1JXNjOhtW493/wDiofV350ugA9MVdLdtZZ3EsKrAt5EsFOoIFiVIAvO1jXQnSyuOvb4r6uhYkVdXntwfwGLRZD+UYqPh+fxQ6TK5298W39JtzznsKx9dnGsLdLtyrrVdK9gb98Li3F0gQM/AIGou5gEaXHIrInwBuKCqn3D3fwMrypdF5HEAd33F7X8VeKr1+CfdtkDghvRiw5Co8VDbZb4KHOxB3LP+7njP+sNZFyYTyAZ28W6wZTMolgWYzOb9pl0r1J2e7f/Qd5bD0GVDVGqfq1bXu8HYx+diCzPGE+sBe9EcDGHuvOI1h1PToBHSoxFxQbNoB82infeCfe6wF+YjlXP7k/69+cE/KgjIEMzIXmTEA5UXdtNTUdVLwCsi4nM23gt8FvgY8AG37QPAb7rbHwP+nsuSeA8wDn5w4BsRCZzO4mYxq111BnYRbo1NQVsuYLW2ke9kDEnXCmzatYLqMyhmM2s1TGfQG9rn6AxgMofUiXKOfd44tYt4WQ+mC/vanS7kvpIOa11EPXvcksMi63N/23nB6p57wevT1Xy064/30fTRMma3ODc9yCjLB0g1HkZ62NW5AdaTeIB+nLd6Kv8H4JdF5FPAu4D/C/CzwPeJyBeBv+nuA/wW8GXgPPB/B/6T4zzhwBsPEeFsJ0F8hkQ7S0KxC2LLGfR2bbrZZAadbZhOrN2wUruI1hvZEuaob3OKTQ/GCxsZT3PQxFbSaQSl84VrsSXKM1eqPLPtMl0tNSyKJh84Se1JVVUjvj4ibucL+8h3U4JMI8pLGt/XCzE0kbGPpFtTN1bLhOUyzJy7Y3yOmk+PeMAi4VsqW1bVPwNeusGu997gWAV+6u5OK/CosZVGZCqsCrW/lb61I1jB3D+A7XN20Wy6D489azubLRc2Ql4tYLgNr7xsbYW1qwOusT6viax4xonNMc46Nq0tGdpUt8keDM7A/KIV9UhcZDyH7cyNpRdIMptNoUP7/EdLl32E7PGRr/+C8fjo2fei8DaE946leUy5FmaThNHo+EplHzn6gF/f9FktDwgP0PdB4FEmjYXtNHv94pUX48kBSApJDw72YW0gHlhf2Lgc4HgI68JmQ0Qd2w0t9QUZPWdFuGMTmy/MUsGkNvXNR95rl382GMHCecc5NortDG0EftTzXXF4gc77u0ej5JLD1kXeOqZ0r+Ej4gL72oVwcNAJi3N3imAj4B132eaBUr4H6FQCjzICnO2YRoD9Ip0XtMXUFmOkI1ivbJe17rYt4JDMCq1JIUqsuCauuCIb2LzhrvOFvU/c6dnsB3WvnnXswl6nZ1tn5oD0bL6wX1Srxe7PFza69qlmbY/YC6u3HTxefL1F4aNe3+Td2xN163H+dgXj/QcodHsY6WB9YX95gJTvATqVwKOMiHCqFxH5CLJqXcAK8MEM4l1rQ0wPINmC1cz6xBo3hRzTfWslLJeQdqxlEWdWuKPENm7H+cJ5ZQUzHdrijmRkRTxXmxsMUBYtcezY0uhZ3US+cDgibucQ++i2fWw7SvbHr9xx0GRK+H11bdsrtxf4AreOYOuV257wke80EWndthewI43uNaGVZeCBYZhFDIgYF1UTHni/VYHFPpx62grpeA/6Z6E21reNhtZu6OzCtS/Baay3uwIKA8saygiWlV2gm61tCfRkacuUewPbf2LrDKwvNxF47AZ91qnrHWzs6+cr6PYbP7emaW/p+0O0izA87XS1Q8M9abqq5a3nKAEqVktYroQkDZ7EbeNF2Kud/zm77JvhsM+Lb36G+XzJ+S99jW/+K28BhcVyRZalfP4LX6Yojm+SxlFCJBx4YIgMnO7FTXaAFyEviON9WEcgfZstoUBnBLMDSPvWRugObIHHagVJ30XDfVjObfbEYm4Fd+FS17znK6nLCTZW2JclLAUS5ztX2pxHZwD5vElB8yLso+UljR3Rzozwx0IjsksakfbvG1xam9pzoqAs18ym904I3vAcaqMmmNhsotzdnS1efvk1Op0MYwxf/soFTGTYGg3IspRe794WkwURDjwwiAhnBrFNVWs3wPF+63ppK+XSU7DOnQ+8DbMx1IlNJ6sSuyg3n1hfeD6zC3izGcSu33Dk7huXL7zE5QFnTfOfxdIJbh/Wi6Y0eYH9EpjObdc1H8H6bIe2+HrbYc7h6jlvNfhtbdH2PvMaG8lX/slrFnNBw+rc7SMcaihsnn4zz771Rd76lufY2hpSFAW7u9ukScyg3+Ptb32eg4MpB+Mp4/GU4eDedrILdkTggWKrH5HUwrrQw5aEYj3fxRiyLbt9tg/DM3D9q7BYQxHZ62zLLth1zsH4Cpw9A7MVDFPbh2IQW1/X5wsXlW3U0xvYCLvrKuqyoRX1Qm3Zs0lsvWvSgWplF+dqaSwFg/0f1U5L85rZFmrvefvt3n4Qt1+xr6m+0YRNGs5XFeG/7B3im0YA9fqLfPn8F7gwt+ONptMZZ2vl4qWrGBEuXb5GUZRMpjMG/R5Xru7d01MLn2jggaKbGrY7EVfyshGmtpBNrsPp00DmRPhJayWspjZFbTmD7g7sf9FFo2oX8jA2T1hiu8hnEtsrInb5wuJmLoxfg60dmF6zI4hisVV5+Qo6iYt8Y6gi24fCdBov2IuvLzbxazrtLmrtcuwcGyXX9u1sImKjdmGQGpjhFX2xWBP+y94B3hN2qd2bYhlHXSuXLl/b3B9PZpvbs9ZIo3tFsCMCDxQicHoYN3m07ZzhGiu2CqRbVnAXpW0IcHAA1cBWyOnAeqmzBajLD9a+7ZKmfTu0UwawN7Pi6/OFo9RmWogB1N6usZkTq5m1HxbYc0ucB72p6sPuW/D6XGGfwgaNPzyn8Yd9hOwLS5Y4f7psPckaufcL9W9MvB3hy5aHPFDK9wCdSiDgSph3Eowv4/WLc95nzXPbqrLehqqAfArpNiwntpquqFwryi5M9htfONuyi3PZoLlezWwfiXzRTPWQ1BZ7kNnUtlxsvvB03ni4Krboo5hb28BHsG3xzWm83aP+sLccoFmcq7ACvPY+cA3qRdgayINB+O96x7QX5oaEirlA4Bsx6Bn6xrx+lJDLmWV2AGbLZjFM9qEauUq5JZSpXVyLtmF5AKbrKuBS2/hHU9s/onK+cBG5CLeyAhkNbFFH5PpJVGpT0urCZl140Sxdh7aVNlGuj2hnHF6IK2nEt93I3Yu319kpzrKoaVbzJsCaKKo491joH3FHHO0dscUDpXwP0KkEApYkFk55S+Lo+KAKK651B0wfVmMgtmI7mwAD111ty1bELSqb1raobL6wz6BYFq6hz9pW3C2XtmdwNoD13Ka1reeukMJA5Rb1fHRrYjv3zlsW7ci3bVHM3fa2+C7cdp9xpq4BEdjnVD+CuRk+l2UVvYE5VFQQuA1uNm75BHmATiUQsIgIZ08lTctHb0d4TVpNXTe0kU0fK9YgW7A6sGlo+cpei7H745677kM+swKbz2wOcO76SKxclVye2oKOVQSrGialjVKTISynrUo4AbrWspjRRLRHxffQlweN+PrnyYGF2qi8LqGe0xjGM+yL7zPcEpIkCPAd0Z5vtI2NhIMdEQh8Y3a2I1KVJtvAZxaU2PrdYmYtibKyzX3Ytt7vQqzYLdzfoPOxXbCbTtz1DErXV7gaWK+3cn2EF0AlrqHP2uYbF0vrFUcDJ/jaLMBFQ+sv+0IOH+UuOJwr7MW3PU15jbUffNCr2qpLVhohttUcp8/EYWHuLtCuUPftRfutuuQHgCDCgQeSTscw6IqNTttNfbzYTQ9gtQV1DPmB7aRWqy3o0A4UK7tgN9u3hRyrHEisPyxJk6ZW1XYhT+vG841cvrAZwWpuMyeKzPWZqN0immvyXs0bL3jeOse2z+u9YL8457dtpoKVNIbw4dsiOc+90OGZ57JgRdwhKrCMesyj/uZSP0A/yyDCgQcSY+Ds6bjxg32mhI+I87H1dBnAYmJLjKu+9YvLgR1DVDq7oiztQlxRQhlbIa4SW31XuQW7ylXJzQXqvq2o034zZw5jfeA6b1W5pVaYF9Xhkfc5jZOwaY+J1dY5TSaEVlAvQWc0TzqmGVK3T39Q8U3f0iHLHhzRePgQZgyYyIiJjJgypH6A/IibirCIvFVE/qx1mYjIPxCRXRH5HRH5orvecceLiPxTETkvIp8SkXff+7cReKMhIpw5E2NqV7jQ7jNcAuuZbWlZjmz1WrGy9sTsAMqerZCrO7aoYjyDYgjjlgWhwyZ/eDYG4/pIlGrtiHrtIuTKRsg59nnnsyb7QV2pc71sFuemNClnvtTZ27wVgNqou1jbiSHqV+e8l+GVfA4oW9uGJCFEwXeBIszoM2HkLkOqlvQlScxbXnyWc2dPIQLPPvMEzz7zxC05FqPRgL/xH34H/+F3/1W+469+yx2d363MmPuCqr5LVd8FfBv2N+XfYCcuf1xVXwQ+TjOB+QeBF93lQ8Av3NGZBR55trZjut3SCmOuh/sMV5WNdqvTdv9qH4oRlHOb4lUZa0+YIRRj69+Wc9tHovDXC5uKtp7bPhKFi3qXBtYJTNfWhpiurMcsA7uAt5k7B5SukGPO6/sKz2kK3lSt9ZGXLvL2IbJPR5u4J5gC14A5Tz2T8s3vDJPIj4MZw5YIj6hb0vfYudPM50ueeNM5kiShLEt2d7dIkpunBE4mM65e2+OP/vjT5Pn6psffiNu1I94LfElVvwa8D/io2/5R4Efc7fcBv6SWPwC2/VTmk0BdVnwSx3SylDh+cP4MCXxjktSwe8pAlbvpFtp0VyuAcs9WxJHC4gCKgc37nc9g1bVtKstTNo2tiGFVNdkPy9hW2y0i6/nOjb2euajXDGE9tf5wMXP+bQeqte03sQBmzrpYze0XgbpCiwWHxbdWO25ptbYLiU2neuCAprO7V+6KNDO8+NaEbi+kpd0tijCnx5QhU4aoeSvPP/cW3vZW28BHRKiqalNmHkUR0+mc9frWGjhfvHiVd37zW9nbH9/R+d2uCL8f+BV3+1xrivIl4Jy7/QTwSusxF9y2Q4jIh0TkkyLyyTxfHt19bIy3r7Hsz+n3u7ztrc/z3d/1bffstQLHi4hw9lwKFDZzoFSbneB94eWBswaGUE6sbcAAin3b6ayYuEg4tz5w6fpGVKm9VpcFQWYtDcmgctkQ6rIhahcpL4BZBHlsexH7dDkS5xM7YZ5iiz/U2w6lrfIrKifkfsVuj6ZxhGIffA0TrXnqmYT/4LsHbG1HQYCPAQWmjDhgmwO2uVgvOf/yy3zx/NeYTGZcvnKdU6e2uX79gNOndnjT42cxxmDMzeXx1Klt3v725wHY2hre5Ogbc8vdQEQkBf428DNH96mqioi+/lFfH1X9CPARgJ3dc7f12Ft+DZSDZ66w98Qltn73b3Hm9A5/+MlP34uXCtwjdnYz4jinLAVKA2ps42EAWVvx5DTU16CcgWyDuQTV00BuBbeMoTiwUXMxc8I6swt5ufOJqylUQ1hPIB/YxjyrEhJXWWdcp7VoAOUS6EAhbqEvhXrlonJaRRylE17Xi2JT0dFOFF5grQi78nj2nOHdf7WDMcEHPj6EOX18xUwFFJVSVfZ+nq/5i8+e3xz92sUrt/zMWisXLlxmPJny5BOP3dHZ3U4k/IPAn6jqZXf/srcZ3LU/81eBp1qPe9JtOxH2T13h5b/+efJ3XuVrr7zGchkm1j5M9AcpO6cSNg14q9raATWuDeV1WA1s9FqNbQFHkdsKtDy1Y+11ZFPalq5Be96zrSqLnsuicFkQdc+WPhdYsScGLbDR7sr2HF4Nrb3hCzQqrFesMzZCW81cq8tNI2Rs1sOEJo0ix0bDB0CBMcKZsylve0c3CPAxowhTBkc84eOxJff2x5RVxeOPnaG4RfviKLcjwj9OY0UAfAz4gLv9AeA3W9v/nsuSeA8wbtkW953urM+5155mu3eKp558nLe+5dnwC/4QYYzw+Js62IjRDWWrK5t2VtfWeihSKDr2dp5BmUB9YCPdagbVDtRTILKP1cj2giCyTYBU3HZpnnsBLPswmdnr+dRVu3XczDlnOdS1TX9jDyuyvo2aTwoeY4XW+xelO/Y63gvePRXx7f9Bl+/87gE7u3H4/TxmrB0x3NgRY7YOZUccxwuc2t2+4wKQW7IjRKQPfB/wv2tt/lng10Xkg8DXgB9z238L+CHgPPY38ifv6MyOibf80UvMXj3g+rWcj+d/cJKnErgDRIQzZ0ek2Wus87nb6hrwas0mr7bug+7bvgsyhGIP9Bkor4Kcs6lgRQ5V1127wZ9VxxZy1G7actUFVjabwgzs4zkL9SVrM2CACnTpHIUKSLACvIv9L+WrN3xk5GcZ+fDZWhGjLeG5F2KeejomSUP0e++wdkTh5K5GqTd+/DE8u8ByuWI07N/R429JhFV1Dpw6su06Nlvi6LEK/NQdnc0xIwiiQjrrUPRz4jx0oXoYGW31ePdLz/HpP7/AfDbHjkiosV3X58BrVkRZAROb+8trQGIj3SiCOrN+sAztQpsMQafA0EbL7et66iyGxC7UiUDtZturYkX1MrYRgaHpPJ9zeK6994KXWAG2j+104dnnY154c0yaBfG91ygwY0BM6u4rNddoOijdHVev7jGbLXj++adufvANeCTa9CfzlPljY7p7g5M+lcAdICI8/sQOvX6HT/3pK1y7OqMR4gj7577PgnzN3Z4D+3aBTKegGeCi4/qajY65BrzJXusQu6wxBD2Acsf5wmD/oAMb7fbsMVzDdoLxw+IArmLbdXlRbke+kCTCsy9EPPdCRL8vQXzvGzYSFnzOdX0oT/hu6HYz3vH2N7O7s8WFC5fu6DkeCRE2ZUQdVyiKcGu/+FtbA7RWTGRYLlbkd2i6B44HEWFru8u3f+fz/PmfvMxrr45RzbC/wlexbbIU2MdmRMZYUe1af5gh8GXgLFQ+Q8H3nWy3jvRJyC51jS5WTDtYYY9p+jsc0ES8PffaXZq5RSUgxHHE409EvPBiws5uEN/7jV2YG6J4u6AmwxyLDI9GQ86c3uWVCxeZL+4s1faREGFwQpxURMWtvGWlrpXv/q5vYzye8ok//NQ9P7/AzRERsk7Mt33Hs/Q/e4nzX7hMXfsvxxlWNK9jF77AiuTAXZ+i6UoW42YUYSPZqHW9dNe+G0/lnnPUel6haWjhn2Pu9vvhnIIxcOp0zNu+KePUaYNIsB5Oijl9KjdkTqhIjkmEr1/b5+VXXmM6nbNc3Vnm1SMhwoKQzDOK3ppofPO3nCWfY9B9me1Rwddefpqyqm76mMD9QcRGlu/4pscZDjt8+s9fYZ1PsQt0ghXa61hBvgjsYEW4h41aL2OF8zWsp3wRG8m+ihXf11r7T2P/iyzd87THZdg192ZEsr9eACm7pyLe8vaMs+dioiiI70miroFPwQiwIrx1TClqZVXx2c996a6e45EQYYBknrE8PSUbd7+OJaGIQL+/Ymd0lUHvK3zmsxd49dXsvp9r4OaYyPD0s7sMhhl/8kdfZjq5CJzBivA+toBzzeFIt4cV6KdofOSxe5zLgtg89oAmzcz3pFy6x/vGxq9ixdnQ6Rq2d7ZYLQ3PPNflqacTkjRYDw8CvmJuxTYAhpI3teJgEWF7e8RyuWK1yun3u9S1zWAZDvpcu35AXR9PJsWNeGREOCpiquRGEa1ijDIaLen3c1arhMtX381lnmRdnMb+5ws8iIgIu6f6vOe7XuRTf/oa+3tCp9tlMr6K9XALrFD6LArBiuwZmk7rU6yPO3XHjbFR9IG79jm/l7H/na8BI+I4RcT2G3ju+YRnX0jp9brUlRLFQXwfLIQFPRbYhXlDcWhh7uzZXU7tbtPpZPzpn32OXrfD7u423W5GVVbs7Y+5hxr86IgwCqYyLV9YSZKKrdGCLCuZzTMuXtymrgX7n/XO6sAD9xcRYTDs8NJ7nmG1VLJsi89++gKvvFySZn1WyzGqZ2nyeJfYVicFVlhX2Oi2wApwjRVkGz+JdBkMe1TllG5vwHo9oT+IXGVbCsSHejwYE8T3QUMRJjpkptsAPCYFZ0+dol8ok8mMTpZx+fJ1nnryMUSE5SpH1e7LspSzZ07dVinz7fLIiHDjC+f085rdHZv4P550uX59iN5i1kTgwUNEyLKYzDlH7/y2Z3jm+YJ+P+blr11nMs7odrcoqw5Zeo4vfXFNmvVYr9f0BwOWizW93oDVas1gOKQsKra2t5jNKh5/U8yTT3fQukecGOpqQBQJJgKRzsm+8cCtoVDnEfXK+sBFUVNVai0GVcbjKc8//xRlWXHmzA7T6Zx8vSZLUzqdjEuXr93T03tkRBggnXXY2brIMOpz9dqIdRFBS3x3d7Y4dWqbK1f3OHf2FH/5xa+e2LkG7pwoMpw6bRX5xbee8TUSjg5verKg04nJ85puL6IoapLEUJU1SWpA7YxQVVoZDW4hJw5f1g8l3nUC9tbKlWtjVtf2AVjla/78U1/Y+L6qyssv204Lxhjb5vIe8kiJsCki8svn6C/mbMuc/W6fwoY0AEymc/76X3uJd78r5eO/H0qc3wiICEf/yBlt2cqpNLO+oO8xfbTXdLB13yD4QSUTd7/kdRXLR4XWFv6+fvu94JESYUHIo5SLg4ROWXBmbr2//W6f/nRMXq6ZzV7i6aceZzqd3/T5AoHAQ4DPJvRq5wcDPCA8UiK8QYRVkvJanBDXFecm+/zwv/8trhY5X3nLs/zu5Wt86zvfzh/84Z+f9JkGAoHjYMbGUbpRJHySPJoi7BGhjGL2si4XROiLofp3/47PvrOk2w+zvQKBNwTejvAi7LMOHxAebRF2LLt9fvt7/iMUQbMutSrz+b0buRQIBO4zvokdBBF+IBGh7I9O+iwCgcC9wEfCXnhrgiccCAQC9w2/MOcn0tc8UJHwLTUSEpH/TET+QkQ+IyK/IiIdEXlORD4hIudF5NfcIFBEJHP3z7v9z97TdxAIBAI3w6eoTbCC/DCJsIg8AfwfgZdU9a9g7e33A/8E+DlVfTO2IP+D7iEfBPbd9p9zxwUCgcDJ4CPhSetyxI6IjNnkhRtzf3t/3GpLzRjoikiMbUV1Efhe4Dfc/o8CP+Juv8/dx+1/r4RuJoFA4CTx3U790OtWJLw1GvCud76Nt7/tBQAeO3eG55+7s1FFd8JNRVhVXwX+K+BlrPiOgT8GDlTVD2m6gB1ngLt+xT22dMcfmk8HICIfEpFPisgn8zxkIgQCgXuEYts8T+0lWkJiIuI42rSx/OrLr5EkMcYYJtPZfW3EdCt2xA42un0OO5CrD/zA3b6wqn5EVV9S1ZeyLOTkBgKBe4Qf9+esiGd7wovPPs7zzz3FaNgnz9ecPbNLmiSMRv3mMfeJW8mO+JvAV1T1KoCI/Gvgu4BtEYldtPsktnEr7vop4IKzL7awvQIDgUDgZJizyY740ueVzy4uMMouA7ZnTFGUfG31GqqQ52tevnDxvp3arXjCLwPvEZGe83bfC3wW+D3gR90xHwB+093+mLuP2/+76rthBAKBwP1GsVHwgbv4ttF+tyrX9w5YLFYslyvquibP1zd4onvDTSNhVf2EiPwG8CfYqus/BT4C/E/Ar4rIf+m2/aJ7yC8C/0pEzmMnH77/Xpx4IBAI3DJTrC8MNvR82Io1VPUfA//4yOYvA99+g2NXwN+5+1MLBAKBY0CBpcLc/UEe8UDlCYeKuUAg8AZHYZ1DvrJ3o8J27H9ACCIcCAQeAXyOGjxovSyDCAcCgTc4il2N83kID1ZX9yDCgUDgEWBBI3cPVi/LIMKBQOANjq/W8DxYbdSCCAcCgTc4XoS98FYctSOGgz7roiDP12SZHQR7NFc4y1JEhLIoSbOUxeJ42i0EEQ4EAo8AcxrhPRwJd7sd3v3ud/AXnz1PVVW84+0vEEcRn//Lr7C1NeTq1T3quuabv+lFVBURoaprXrlwiWvX9u/6zIIIBwKBNzhKlu1TFgkAg0HG9naXwTBmuVwRRYb9vTFPPvEY168fcP5LL/PiC8/wre98O0VR8uwzT3D58jXmiyXLVU6+WnP69A7rvDiWswsiHAgE3tBEkfKd3/3aJjV4d2eL7e0MkYyqrIgiA2LLlx9/7AzvePsLvPzKRYqyJMtSrl7b4+rVPV588VkG/R5pmlIUBfn6eEqbgwgHAoE3NCKQpo39MF/sM18cPuYv//KrFGWJiGE8maIKq9WKLE1Z5WtUlT//1OcREYwxxFFEUZQcB0GEA4HAI88qbwbQlWUjrstVvrl9XKJ7FHkQGpyJyBT4wkmfxzFwGrh20idxDLxR3ge8cd5LeB8PFt/ofTyjqmdu9YkelEj4C6r60kmfxN0iIp8M7+PB4o3yXsL7eLA4zvdxqzPmAoFAIHAPCCIcCAQCJ8iDIsIfOekTOCbC+3jweKO8l/A+HiyO7X08EAtzgUAg8KjyoETCgUAg8EgSRDgQCAROkBMXYRH5ARH5goicF5EPn/T5fCNE5CkR+T0R+ayI/IWI/Kdu+66I/I6IfNFd77jtIiL/1L23T4nIu0/2HTSISCQifyoi/9bdf05EPuHO9ddEJHXbM3f/vNv/7Ime+BFEZFtEfkNEPi8inxOR73xIP4//zP1OfUZEfkVEOg/DZyIi/1JErojIZ1rbbvvnLyIfcMd/UUQ+cKPXOoH38X9zv1efEpF/IyLbrX0/497HF0Tkb7W2376eqeqJXbAj974EPA+kwJ8D7zjJc7rJ+T4OvNvdHgJ/CbwD+L8CH3bbPwz8E3f7h4D/FyDAe4BPnPR7aL2Xfwj898C/dfd/HXi/u/3PgP+9u/2fAP/M3X4/8Gsnfe5H3sdHgf+tu50C2w/b5wE8AXwF6LY+i594GD4T4K8D7wY+09p2Wz9/YBc7OHgX2HG3dx6A9/H9QOxu/5PW+3iH06oMeM5pWHSnenbSv3zfCfx26/7PAD9zkud0m+f/m8D3Yav9HnfbHscWnwD8c+DHW8dvjjvh834S+DjwvcC/df8prrV+4TafC/DbwHe627E7Tk76Pbjz2XLiJUe2P2yfxxPAK06EYveZ/K2H5TMBnj0iXrf18wd+HPjnre2Hjjup93Fk338E/LK7fUin/Odxp3p20naE/+XzXHDbHnjcn4DfCnwCOKeqF92uS8A5d/tBfX//DfCf0zRVPQUcqKovjm+f5+Y9uP1jd/yDwHPAVeC/c9bKvxCRPg/Z56GqrwL/FfAycBH7M/5jHs7PBG7/5/9Afi5H+N9go3g45vdx0iL8UCIiA+B/AP6Bqk7a+9R+BT6weX8i8sPAFVX945M+l2Mgxv4J+Quq+q3Yzt2HfLgH/fMAcJ7p+7BfKm8C+sAPnOhJHRMPw8//ZojIP8JOB/3le/H8Jy3CrwJPte4/6bY9sIhIghXgX1bVf+02XxaRx93+x4ErbvuD+P6+C/jbIvJV4FexlsTPA9si4nuJtM9z8x7c/i3g+v084W/ABeCCqn7C3f8NrCg/TJ8HwN8EvqKqV1W1AP419nN6GD8TuP2f/4P6uSAiPwH8MPB33RcKHPP7OGkR/iPgRbcKnGIXGT52wuf0dRERAX4R+Jyq/tetXR8D/IruB7Besd/+99yq8HuAcevPtBNBVX9GVZ9U1WexP+/fVdW/C/we8KPusKPvwb+3H3XHPxCRjapeAl4Rkbe6Te8FPstD9Hk4XgbeIyI99zvm38dD95k4bvfn/9vA94vIjvur4PvdthNFRH4Aa9v9bVVtdyD+GPB+l6XyHPAi8IfcqZ6dlJnfMq9/CJtl8CXgH530+dzkXP8a9k+rTwF/5i4/hPXjPg58Efh/A7vueAH+W/fePg28dNLv4cj7+R6a7Ijn3S/SeeD/CWRue8fdP+/2P3/S533kPbwL+KT7TP5H7Or6Q/d5AP8F8HngM8C/wq68P/CfCfArWB+7wP5l8sE7+fljPdfz7vKTD8j7OI/1eP3/9X/WOv4fuffxBeAHW9tvW89C2XIgEAicICdtRwQCgcAjTRDhQCAQOEGCCAcCgcAJEkQ4EAgETpAgwoFAIHCCBBEOBAKBEySIcCAQCJwg/38gS6x58M6sNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1 = plt.imread('./images/flux3d.png')\n",
    "plt.imshow(f1, cmap='jet')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}