{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Elasticity in 3D\n",
    "\n",
    "## Introduction\n",
    "\n",
    "This example provides a demonstration of using PyMKS to compute the linear strain field for a two-phase composite material in 3D, and presents a comparison of the computational efficiency of MKS, when compared with the finite element method. The example first provides information on the boundary conditions, used in MKS. Next, delta microstructures are used to calibrate the first-order influence coefficients. The influence coefficients are then used to compute the strain field for a random microstructure. Lastly, the calibrated influence coefficients are scaled up and are used to compute the strain field for a larger microstructure and compared with results computed using finite element analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elastostatics Equations and Boundary Conditions\n",
    "\n",
    "A review of the governing field equations for elastostatics can be found in the [Linear Elasticity in 2D](elasticity_2D.html) example. The same equations are used in the example with the exception that the second lame parameter (shear modulus) $\\mu$ is defined differently in 3D.\n",
    "\n",
    "$$ \\mu = \\frac{E}{2(1+\\nu)} $$\n",
    "\n",
    "\n",
    "In general, generating the calibration data for the MKS requires boundary conditions that are both periodic and displaced, which are quite unusual boundary conditions. The ideal boundary conditions are given by:\n",
    "\n",
    "$$ u(L, y, z) = u(0, y, z) + L\\bar{\\varepsilon}_{xx} $$\n",
    "$$ u(0, L, L) = u(0, 0, L) = u(0, L, 0) = u(0, 0, 0) = 0  $$\n",
    "$$ u(x, 0, z) = u(x, L, z) $$\n",
    "$$ u(x, y, 0) = u(x, y, L) $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "import pymks\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import timeit as tm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling with MKS\n",
    "\n",
    "### Calibration Data and Delta Microstructures\n",
    "\n",
    "The first-order MKS influence coefficients are all that is needed to compute a strain field of a random microstructure, as long as the ratio between the elastic moduli (also known as the contrast) is less than 1.5. If this condition is met, we can expect a mean absolute error of 2% or less, when comparing the MKS results with those computed using finite element methods [1]. \n",
    "\n",
    "Because we are using distinct phases and the contrast is low enough to only need the first order coefficients, delta microstructures and their strain fields are all that we need to calibrate the first-order influence coefficients [2]. \n",
    "\n",
    "The `make_delta_microstructure` function from `pymks.datasets` can be used to create the two delta microstructures needed to calibrate the first-order influence coefficients for a two phase microstructure. This function uses the Python module [SfePy](http://sfepy.org/doc-devel/index.html) to compute the strain fields using finite element methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6085a52710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.tools import draw_microstructures\n",
    "from pymks.datasets import make_delta_microstructures\n",
    "\n",
    "\n",
    "n = 9\n",
    "center = (n - 1) / 2\n",
    "X_delta = make_delta_microstructures(n_phases=2, size=(n, n, n))\n",
    "draw_microstructures(X_delta[:, center])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using delta microstructures for the calibration of the first-order influence coefficients is essentially the same as using a unit [impulse response](http://en.wikipedia.org/wiki/Impulse_response) to find the kernel of a system in signal processing. Delta microstructures are composed of only two phases. One phase is located only at the center cell of the microstructure, and the rest made up of the other phase. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating Calibration Data\n",
    "\n",
    "The `make_elasticFEstrain_delta` function from `pymks.datasets` provides an easy interface to generate delta microstructures and their strain fields, which can then be used for calibration of the influence coefficients. The function calls the `ElasticFESimulation` class to compute the strain fields with the boundary conditions given above.\n",
    "\n",
    "In this example, lets look at a two-phase microstructure with elastic moduli values of 80 and 120 and Poisson's ratio values of 0.3 and 0.3 respectively. Let's also set the macroscopic imposed strain equal to 0.02. All of these parameters used in the simulation must be passed into the `make_elasticFEstrain_delta` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed Time 118.738605976 Seconds\n"
     ]
    }
   ],
   "source": [
    "from pymks.datasets import make_elastic_FE_strain_delta\n",
    "from pymks.tools import draw_microstructure_strain\n",
    "\n",
    "\n",
    "elastic_modulus = (80, 120)\n",
    "poissons_ratio = (0.3, 0.3)\n",
    "macro_strain = 0.02 \n",
    "size = (n, n, n)\n",
    "\n",
    "t = tm.time.time()\n",
    "X_delta, strains_delta = make_elastic_FE_strain_delta(elastic_modulus=elastic_modulus,\n",
    "                                                      poissons_ratio=poissons_ratio,\n",
    "                                                      size=size, macro_strain=macro_strain)\n",
    "print 'Elapsed Time',tm.time.time() - t, 'Seconds'\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at one of the delta microstructures and the $\\varepsilon_{xx}$ strain field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nlixZoqamJi1dutRqy8zMVDAYVEZGhiKRyIDq4IXXJ54PfFdddZUikciQ/drh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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6085a52f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_microstructure_strain(X_delta[0, center, :, :], strains_delta[0, center, :, :])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calibrating First Order Influence Coefficients\n",
    "\n",
    "Now that we have the delta microstructures and their strain fields, we can calibrate the influence coefficients by creating an instance of a bases and the `MKSLocalizationModel` class. Because we have 2 discrete phases we will create an instance of the `PrimitiveBasis` with `n_states` equal to 2, and then pass the basis in to create an instance of the `MKSLocalizationModel`. The delta microstructures and their strain fields are then passed to the `fit` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymks import MKSLocalizationModel\n",
    "from pymks.bases import PrimitiveBasis\n",
    "\n",
    "\n",
    "p_basis = PrimitiveBasis(n_states=2)\n",
    "model = MKSLocalizationModel(basis=p_basis)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, pass the delta microstructures and their strain fields into the `fit` method to calibrate the first order influence coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model.fit(X_delta, strains_delta)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it, the influence coefficient have been calibrated. Let's take a look at them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mzJkzZp1bb71VkrR//351dXXJ7/fL6/Vq69atSk1NDQbJOXPmqL29Xd3d3RoeHtaOHTtU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\n8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6085b08d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.tools import draw_coeff\n",
    "\n",
    "\n",
    "coeff = model.coef_\n",
    "draw_coeff(coeff[center])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The influence coefficients for $l=0$ have a Gaussian-like shape, while the influence coefficients for $l=1$ are constant-valued. The constant-valued influence coefficients may seem superfluous, but are equally as important. They are equivalent to the constant term in multiple linear regression with [categorical variables](http://en.wikipedia.org/wiki/Dummy_variable_%28statistics%29)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict of the Strain Field for a Random Microstructure\n",
    "\n",
    "Let's now use our instance of the `MKSLocalizationModel` class with calibrated influence coefficients to compute the strain field for a random two-phase microstructure and compare it with the results from a finite element simulation. \n",
    "\n",
    "The `make_elasticFEstrain_random` function from `pymks.datasets` is an easy way to generate a random microstructure and its strain field results from finite element analysis.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed Time 53.8849179745 Seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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FRERIkpYvX65Zs2bp+PHjkiR/f3/deeedWrhwoXx9xx7zCIQAAMByJlogbG1t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\nk9z/A9n8E43SAjSxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6076fbb410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.datasets import make_elastic_FE_strain_random\n",
    "\n",
    "\n",
    "np.random.seed(99)\n",
    "t = tm.time.time()\n",
    "X, strain = make_elastic_FE_strain_random(n_samples=1, elastic_modulus=elastic_modulus,\n",
    "                                          poissons_ratio=poissons_ratio, size=size, macro_strain=macro_strain)\n",
    "print 'Elapsed Time',(tm.time.time() - t), 'Seconds'\n",
    "draw_microstructure_strain(X[0, center] , strain[0, center])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the calibrated influence coefficients can only be used to reproduce the simulation with the same boundary conditions that they were calibrated with.**\n",
    "\n",
    "Now to get the strain field from the `MKSLocalizationModel` just pass the same microstructure to the `predict` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed Time 0.00195503234863 Seconds\n"
     ]
    }
   ],
   "source": [
    "t = tm.time.time()\n",
    "strain_pred = model.predict(X)\n",
    "print 'Elapsed Time',tm.time.time() - t,'Seconds'\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally let's compare the results from finite element simulation and the MKS model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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o0aMoKytDeno61q9f73WfXV1d2L59O+bNm4dNmzYFdAwj/J6SnqyNvqodfleH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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6079bd8350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.tools import draw_strains_compare\n",
    "\n",
    "\n",
    "draw_strains_compare(strain[0, center], strain_pred[0, center])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the difference between the two plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6ampqYDabYbVasWPHDmkJw1ud5ORkmM1mNDQ0wOl0orKyEjExMdKbivv27cMHH3yAl156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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60b46e04d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.tools import draw_differences\n",
    "\n",
    "\n",
    "draw_differences([strain[0, center] - strain_pred[0, center]], ['Finite Element - MKS'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MKS model is able to capture the strain field for the random microstructure after being calibrated with delta microstructures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Resizing the Coefficeints to use on Larger Microstructures \n",
    "\n",
    "The influence coefficients that were calibrated on a smaller microstructure can be used to predict the strain field on a larger microstructure though spectral interpolation [3], but accuracy of the MKS model drops slightly. To demonstrate how this is done, let's generate a new larger $m$ by $m$ random microstructure and its strain field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m = 3 * n\n",
    "center = (m - 1) / 2\n",
    "t = tm.time.time()\n",
    "X = np.random.randint(2, size=(1, m, m, m))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The influence coefficients that have already been calibrated need to be resized to match the shape of the new larger microstructure that we want to compute the strain field for. This can be done by passing the shape of the new larger microstructure into the 'resize_coeff' method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model.resize_coeff(X[0].shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the coefficients have been resized, they will no longer work for our original $n$ by $n$ sized microstructures they were calibrated on, but they can now be used on the $m$ by $m$ microstructures. Just like before, just pass the microstructure as the argument of the `predict` method to get the strain field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed Time 0.00978684425354 Seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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HUFNTg9WrVw+KTU1NRWFhIVJSUhAWFobS0lKkpaU59m/cuBGtra144YUXEHhJ\nR5+BJW3Gjx+P3t5evPXWWwgJCVFcdoYzhERERKQ6vvYdQgBYunQpCgsLkZubi9DQUOTl5SE2NhZG\noxHLly/HmjVrEBERgcTERGRkZCA/Px9WqxUGgwHZ2dkAAKPRiB07dkCj0SAvLw/AhQm3vLw8pKSk\noLu7G5s3b0ZnZyeCgoJw00034ec///mgwvFSLAiJiIhIdXyxIAwJCcGKFSsGbY+MjERxcbHTtvT0\ndKSnp7uM3bJly2WPYTAYHJeaPcGCkIiIiFTHFwtCX8aCkIiIiFTHDhaEnmBBSERERKpjF3YQoQtY\nEBIREZHq+Npdxr6OBSERERGpDr9D6BkWhERERKQ6LAg9o1gQShaTllJaFBGQL9w7HLy9gLWENxcy\n9mYuwLsLjXvznHnzPSvl7XMrIT23w3E+PGU7b3W7v7SiXJRHf2uUchAAS4P7hbABwHjmtCjXnbNv\nF8V1dJ5SjAkK1IhyjYyNEMVNHjdJMWbtGwWiXJkP/D+iuA9rdoniTn2jfH77u2SLZk+Ikn2u+vr7\nFWPqjx8W5QqbIVuAu9ei/BxGj1LuMwsA7/25TBQ34+5bFWMa2ppEuVpPtoniEKj8e0YfdoMsl5ew\nIPQMZwiJiIhIdVgQeubyze+IiIiI6LrAGUIiIiJSHd5l7BkWhERERKQ6vGTsGRaEREREpDosCD3D\ngpCIiIhUh51KPMOCkIiIiFSHM4SeYUFIREREqsOC0DMsCImIiEh1bGBB6AmvdCrxZpcGaVcFX+7g\nIcknzeXNzhbjx48XxbW0tHjtmNcLf3/Zkp7D0dFE+pkaztfdL8D9GPuMPaI8U2fdLIo70LBHMabu\n4FeiXPFxU0VxWz94WzFmWtwUUa4zhztEcdY+9x1gAGDlD/9fUS5dsFYUFzsmRhS37o+FojiJ8VHK\nXbAAWUeQL7+uE+UytX0jivv6+FHFmIbWRlEuP51sDmf/R7WKMRmLHhbl+uKA8mcFAM5/0qoYYx6t\nE+XyFs4QeoYzhERERKQ6vlgQmkwmFBYWoq6uDqGhocjJyUFKSorL2PLycpSVlcFiscBgMCA3NxeB\ngYHo6+tDUVER9u3bB5PJhKioKOTk5CAxMREAcPjwYWzZsgUNDQ0ICAjA9OnT8eSTTyIsLMzt2Nip\nhIiIiFTHbrcP2Y9UUVERNBoNNm3ahGXLlqGoqMjl1Zna2lqUlZVh1apV2LBhAzo6OlBSUgIA6O/v\nR2RkJPJ7pELlAAAgAElEQVTz81FcXIxFixZh7dq1MBqNAIDz58/jnnvuwYYNG7B+/XpotVps2LBB\ncWwsCImIiEh1fK0gNJvNqK6uxuLFixEUFIT4+HgkJSWhqqpqUGxVVRUWLFiAmJgY6PV6ZGZmoqKi\nAgAQHByMrKwsREZe+ArEnDlzMGbMGDQ0NAAAEhMTYTAYoNVqERQUhO9+97s4dOiQ4vhYEBIREZHq\n2Oz2IfuRaGtrQ0BAAKKiohzb4uLiXM4QNjc3Y8KECU5xXV1dMJlMg2LPnDmDtrY2xMa6/i7tgQMH\nRN9LZ0FIREREquNrM4S9vb3Q6/VO23Q6HXp6Bt80d2msTqdzbL9Yf38/CgoKkJaWhrFjxw7K09TU\nhO3bt+Pxxx9XHB9vKiEiIiLVGepOJQPf8QOAhIQEJCQkOO3XarXo7u522tbd3e0o9i6NvbhQHHic\nVvuPu/3tdjsKCgqg0WiwZMmSQTna29vx61//GkuWLMG0adMUx8+CkIiIiFRnqO8yXrhwodv90dHR\nsNlsaG9vd1w2bmpqcnmpd9y4cWhsbITBYAAANDY2IiwsDCEhIY6YwsJCnDt3DitXrhy09NmpU6ew\nevVqZGVlXfYu5kvxkjERERGpjq9dMg4ODkZycjJKSkpgNptRX1+PmpoapKamDopNTU3Fzp070dLS\nApPJhNLSUqSlpTn2b9y4Ea2trXj++ecRGOg8t9fZ2Ylf/epXuP/++3HPPfeIzxdnCImIiEh1fHEd\nwqVLl6KwsBC5ubkIDQ1FXl4eYmNjYTQasXz5cqxZswYRERFITExERkYG8vPzYbVaYTAYkJ2dDQAw\nGo3YsWMHNBoN8vLyAFxoQJCXl4eUlBR8+OGHOHnyJLZu3YqtW7fCbrfDz88PxcXFbsfmZ1c4Y5Iu\nB97uLiJxubtproS0Q4M3j+nLvPl6Dsc5O3HihChO+stCEuftLjA2m/J3X6TdTLz5/r5Wv2B/+NH/\n53b/xLET3O4fsHb9/xHF2fuUz+/t9wz+q92Vw83KnSgAoLP1lGLM/fd8V5Rr7xFZF5WVT/xUMeZ/\nKv8qynW6q1MUJ+1Ucvb8WcWYj2s/FeWKGBUhinvywUcUY8wWiyjXf/x8tSiu/4xZMUY7eZQoV9KC\n20Rxu0t2KMYEjgwW5fqnx9xfBh3wl/8tV4wZOSZclOvgMtl7UslD7/zEK3kk3nnotSE71rXCGUIi\nIiJSHV+cIfRlLAiJiIhIdVgQeoYFIREREamOHSwIPcGCkIiIiFSHM4SeYUFIREREqmMb4oWpv+1Y\nEBIREZHqcIbQMywIiYiISHVYEHqGBSERERGpDgtCz3ilIPTmSR+OhYylCzFLF/iVnA/posJSkrFJ\nXyfp2CRx0nMmJXkO0veQdKF0yaLT0lzefg3Uwth12u1+s1V5cV9AtuA0ACx+NEcx5kjLMVGuAP8A\nUVz/WeUFj//6V9mCvNYTJlHcR4mfKcaMDAkV5ao9vE8UV/dVnShu7py5ijELku8U5Xpv619Eca+c\nEiweLPz3IHiqbJFlW2evYkzC/ERRrk/++HdRHPqVPweTv3urKNUZU5coru8b5c9ocKxsMWxvYUHo\nGc4QEhERkerYWBB6hAUhERERqQ5nCD3DgpCIiIhUhwWhZ1gQEhERkeqwIPQMC0IiIiJSHRaEnmFB\nSERERKpjZ6cSj7AgJCIiItWxgTOEnmBBSERERKrji5eMTSYTCgsLUVdXh9DQUOTk5CAlJcVlbHl5\nOcrKymCxWGAwGJCbm4vAwED09fWhqKgI+/btg8lkQlRUFHJycpCYeGE9y76+Pqxbtw5Hjx6F0WjE\nqlWrMH36dMWx+Xv1mRIRERH5ALvdPmQ/UkVFRdBoNNi0aROWLVuGoqIilw0camtrUVZWhlWrVmHD\nhg3o6OhASUkJAKC/vx+RkZHIz89HcXExFi1ahLVr18JoNDoeHx8fj+eeew5hYWHisXllhlDajULS\nEUTa8cGbnRy83dliOLpMDEeHF2/+9SU9Z5LXQDoub54zb47f27zdieda0AXr3O7/dN8Xojz9XbKO\nJtvef1sx5uHvZIhyTY+bJoobuUC5I8jrW98Q5Yq6SfbeDRR0UdldXyvKlX77vaK4EN0IUdy5buVu\nK3HRyl2CAODvH8g6eIyNHqsY07TnsChX1C0TRHF3Peh69udi42+UvZ6tp9pFcSe2KXeLCQyU/fM/\ndnS0KA425d+7bV81ynJ5ia/NEJrNZlRXV2PNmjUICgpCfHw8kpKSUFVVhUceecQptqqqCgsWLEBM\nTAwAIDMzE+vWrcMjjzyC4OBgZGVlOWLnzJmDMWPGoKGhAZGRkQgMDMQDDzwAAPD3l8/7cYaQiIiI\nVMfXZgjb2toQEBCAqKgox7a4uDiXf4w3NzdjwoQJTnFdXV0wmQb/IXXmzBm0tbVd9SQHv0NIRERE\nquNrret6e3uh1+udtul0OvT09CjG6nQ6x/aQkBDH9v7+fhQUFCAtLQ1jxyrPgLvDgpCIiIhUZ6gv\nGQ98xw8AEhISkJCQ4LRfq9Wiu7vbaVt3d7ej2Ls09uJCceBxWq3Wsc1ut6OgoAAajQZLliy56vGz\nICQiIiLVGeqCcOHChW73R0dHw2azob293XHZuKmpyeWl3nHjxqGxsREGgwEA0NjYiLCwMKfZwcLC\nQpw7dw4rV6706LuCl8PvEBIREZHq2O22IfuRCA4ORnJyMkpKSmA2m1FfX4+amhqkpqYOik1NTcXO\nnTvR0tICk8mE0tJSpKWlOfZv3LgRra2teP75513eINTX1weLxeL4b6vVqjg+zhASERGR6vjaXcYA\nsHTpUhQWFiI3NxehoaHIy8tDbGwsjEYjli9fjjVr1iAiIgKJiYnIyMhAfn4+rFYrDAYDsrOzAQBG\noxE7duyARqNBXl4egAurSeTl5TnWNPzJT37iWIbmpZdeAgCsX78ekZGRlx0bC0IiIiJSHV8sCENC\nQrBixYpB2yMjI1FcXOy0LT09Henp6S5jt2zZ4vY469ev93hsLAiJiIhIdXztLmNfx4KQiIiIVMcX\nZwh9mVcKQuliiN7sVCIlySftMvFt6PjgDdIPkeS8Sc/t8ePHvXZM6fn35vOUvm+9+R7ydkeW4Xzf\ndpm63O5/MOU+UZ73AneI4k4eVH69Tp05Lcp14NghUZzZotxFxdJ8VpTr+Jcdorg/fK38PK3tyh1D\nAODrd78UxUH2Fhd9FgwLF4hyzZ2XLIr74ssaxZgp8xIUYwDgUOVeUdyf9zYqxgRNHCnKZT78jSgO\ngnscDvyvrPvPkUOyzi23f/dOxZhdb70vyuUtLAg9wxlCIiIiUh07WBB6ggUhERERqQ5nCD3DgpCI\niIhUhzeVeIYFIREREakOZwg9w4KQiIiIVEfaQYQuYEFIREREqsMZQs+wICQiIiLVYUHoGRaERERE\npDosCD3jZ1c4YydOnPDawSQvjnQhYynJ+G022fcMxo8fL4rz5mLY0gWPJYsPe3thbcnr6c3Fn71N\nej4ki2Z7e/ySsUlfJ+n7W/IcrtUv2LCMyW73++tlf7v6+cte0zGGSYoxY8dEi3LVvv2xKM5uUz53\nQZNkCxT37jeK4m7/gfKC3rvf/ECU6+4l3xPFNbXLfmc1H2lSjLEely3UHXzTKFHcrFmzFGO+bj4q\nytXbdV4UN3XqVMWYw8eOiHLdOmOOKO7EyVbFmLaONlGu3vpOUVxASJByTIRWlKvtpU9FcUomrfmO\nV/JINPzs70N2rGuFM4RERESkOpwh9AwLQiIiIlIdFoSeYUFIREREqsOC0DMsCImIiEh1WBB6hgUh\nERERqY4dLAg9wYKQiIiI1McH60GTyYTCwkLU1dUhNDQUOTk5SElJcRlbXl6OsrIyWCwWGAwG5Obm\nIjAwEH19fSgqKsK+fftgMpkQFRWFnJwcJCYmOh67b98+vPHGGzAajZgyZQqeeeYZREZGuh2bv1ef\nKREREZEvsNuH7keoqKgIGo0GmzZtwrJly1BUVORyCbHa2lqUlZVh1apV2LBhAzo6OlBSUgIA6O/v\nR2RkJPLz81FcXIxFixZh7dq1MBovLEd17tw5vPrqq1i8eDE2b96MSZMmYe3atYpjY0FIREREdI2Z\nzWZUV1dj8eLFCAoKQnx8PJKSklBVVTUotqqqCgsWLEBMTAz0ej0yMzNRUVEBAAgODkZWVpZjxm/O\nnDkYM2YMGhoaAACfffYZxo0bh3nz5iEwMBDZ2dloampCa6v79SlZEBIREZHq+NoEYVtbGwICAhAV\nFeXYFhcX53KGsLm5GRMmTHCK6+rqgslkGhR75swZtLa2OpoLtLS0OD02ODgYUVFRis0MFL9DKOle\nIO2Y4M3uC9K7h2JiYhRjvNmxApB1DRkO3r7jSnrevEny/vB2dxRvPk9p5xlvdg2RdtiRfvauBd0M\n999tsTTLOlZYGmVxbV31ijGnx8m6NC167vuiuMCAAMWYt6v+Jso1Oft2UVxwULBiTNDYEFGuqeNv\nEsXpdXpRXPOhY4oxduFnr+erU6K4WusexRjz0TOiXH6BsvkUv2nKz8Ha0S3KdfODyl1PAODTv+9S\njHkw6yFRrr+0vi2K00SNUIwJDtGJcnmNj91l3NvbC73e+fOh0+nQ09OjGKvT6RzbQ0L+8Znt7+9H\nQUEB7rrrLkRHRztiQkNDRce5GG8qISIiIrpKA9/xA4CEhAQkJCQ47ddqtejudi7+u7u7HcXepbEX\nF3ADj9Nq/9H+z263o6CgABqNBkuWLLnsY90d52IsCImIiEh9hniCcOHChW73R0dHw2azob293XHZ\nuKmpyeVVxXHjxqGxsREGgwEA0NjYiLCwMKfZwcLCQpw7dw4rV66Ev/8/ZqxjY2NRWVnp+P/e3l50\ndHQoXr3kdwiJiIhIfXzsS4TBwcFITk5GSUkJzGYz6uvrUVNTg9TU1EGxqamp2LlzJ1paWmAymVBa\nWoq0tDTH/o0bN6K1tRXPP/88AgOd5/aSk5PR0tKC6upqWK1WbNu2DXFxcRg7dqzb8XGGkIiIiGgI\nLF26FIWFhcjNzUVoaCjy8vIQGxsLo9GI5cuXY82aNYiIiEBiYiIyMjKQn58Pq9UKg8GA7OxsAIDR\naMSOHTug0WiQl5cH4MJ33fPy8pCSkoLQ0FAsX74cmzZtQkFBASZPnox//ud/VhwbC0IiIiJSH9+6\npwQAEBISghUrVgzaHhkZieLiYqdt6enpSE9Pdxm7ZcsWt8eZMWOGaO3Bi7EgJCIiItVhL2PP8DuE\nRERERNc5zhASERGR+nCC0CMsCImIiEh9WBB6RLEglHTnkHbmkHRpkHaPkHZ8kJB2IJF2fPDm85R2\nyfDmMb3Jm+MHZO816TGHozOHN99D3u6II8l3zb6T0+8+7z/l5ojS/O0DWaePMbHRijHHd+wX5Xr/\nsw9FcT2dg1tOXWpu0lxRruaTsi4qTW3Kv9vsNtlr+sbvNoviAsK0ykEAzn/aJsil3GnlAmFHk/2n\nFWMeXv6YKNdZ0zlR3EeVyl1DrCfPi3L1mN13mhjw3E9+ohiz/nevi3LFzpZ1qLn71sFLp1wqYmS4\nKJf3sCL0BGcIiYiISH1YD3qEBSERERGpDwtCj7AgJCIiIhViRegJFoRERESkOlyG0DNch5CIiIjo\nOscZQiIiIlIfzhB6hAUhERERqRArQk+wICQiIiL1YT3oET+7wkqzJ04oL4AqXSBXkstms4lyDcci\ny9cL6YLN3lwYWbqYtGQR8eFY9Nvbi0RLxiZdzFu6mLTkvF2rhanH/tvtbvcnzkoU5fn83Y9EcZqY\nGxRjbr75ZlGunl7ZYsEBAQGKMRl33C/KdbTlmCjO2mdVjOm39YtyST8vB44dEsUdq/laMSYiXnkB\ncQCIDIsQxfX19SnGNB48Isp12x3zZcfsVz6/Bxpl5+zx7y4UxTW1K/9uGB0WKcq1+fUiUZy1Q3lx\n7RGGsaJcLf9SKYpTMvYXt3klj0TrS7uH7FjXCmcIiYiISH04Q+gRFoRERESkPlx3xiMsCImIiEh1\nfLEcNJlMKCwsRF1dHUJDQ5GTk4OUlBSXseXl5SgrK4PFYoHBYEBubi4CAy+Ube+99x4qKytx/Phx\nzJ8/H88884zTY3fs2IF33nkHXV1diI+Pxw9/+EOMGjXK7di4DiERERGpj30If4SKioqg0WiwadMm\nLFu2DEVFRS6/t19bW4uysjKsWrUKGzZsQEdHB0pKShz7w8PDkZmZibvuumvQY/fv34+33noL//Iv\n/4I33ngDo0ePxmuvvaY4NhaEREREpD52+9D9CJjNZlRXV2Px4sUICgpCfHw8kpKSUFVVNSi2qqoK\nCxYsQExMDPR6PTIzM1FRUeHYn5ycjKSkJISEhAx67J49e2AwGBATE4OAgABkZmbi4MGDOHnypNvx\nsSAkIiIiusba2toQEBCAqKgox7a4uDiXM4TNzc2YMGGCU1xXVxdMJpPHxx1YHUJplQ4WhERERKQ+\nPnbJuLe3F3q93mmbTqdDT8/gpasujdXpdI7tShITE/Hpp5/i+PHjsFgs2LZtG/z8/GCxWNw+jjeV\nEBERkfoM8V3GF3/HLyEhAQkJCU77tVoturu7nbZ1d3c7ir1LYy8uFAcep9VqFcdxyy23IDs7G6++\n+ip6enrwwAMPQKfTITw83O3jWBASERERXaWFC90vHB4dHQ2bzYb29nbHZeOmpiaXjQ3GjRuHxsZG\nGAwGAEBjYyPCwsJcfmfQlXvvvRf33nsvgAuXqktLSzF+/Hi3j/G5glC6Gr43STtzeJM3u0d4m/SY\nkk4Z3swFyN4fw/F6epvk/SE9t9LzMZznzdruvsvBTQ/EifJ8btslO2CfckekyJHu/5oe0GJulcV1\nKHdqenXdGlEuP43s2z7mY2cUY255SNbN4cZRo0VxP8v5sSjuyB0NijHr/7hRlMvWL+twdbb1tGKM\nvV/2u/nTzz8TxWlClWd0rF3KlwEB+b+PvRazYszhFuXzDwBjZ08SxZ2oUe7w0vuVUZTLa3xs3Zng\n4GAkJyejpKQETz/9NI4dO4aamhqsXr16UGxqaioKCwuRkpKCsLAwlJaWIi0tzbHfZrOhr68PNpsN\nNpsNVqsVAQEB8Pf3h9VqRXt7O8aNGwej0YiNGzfigQceGHS5+lI+VxASERERXa1r1WrzaixduhSF\nhYXIzc1FaGgo8vLyEBsbC6PRiOXLl2PNmjWIiIhAYmIiMjIykJ+fD6vVCoPBgOzsbEee7du3Y9u2\nbY7/37VrF7Kzs5GVlQWr1Yp169aho6MDOp0Od911FxYtWqQ4NhaEREREREMgJCQEK1asGLQ9MjIS\nxcXFTtvS09ORnp7uMk92drZTgXgxvV6PV155xeOxsSAkIiIi9fG9CUKfxoKQiIiI1IcFoUdYEBIR\nEZEKsSL0BAtCIiIiUh/Wgx5hQUhERETqw4LQIywIiYiISHXsrAg9woKQiIiI1If1oEdYEAIu28a4\nIl0l/tveKWM4uqh4u+uGhPR19yZpRxbJ+ZC+TtLnOZzvW1u31e3+3fs+F+Xx0wl/pQUqd/qYM22W\nKFV46ChR3OhRkYoxvRNkHSt2F70niguaMFIxRhek3EkDAL451yWKqzvylSju5DfKXUNeff4lUa7S\ninJRXHvEScWYujdl3W4CQoJEcbc++h3FmL6+PlGu8z3dykEAGluPK8aMuzFGlGv1Uz8Xxf3tk78r\nxmz97ZuiXF7DgtAjLAiJiIhIhVgReoIFIREREakP60GPsCAkIiIi9WFB6BEWhERERKRCrAg9wYKQ\niIiI1If1oEdYEBIREZHqCBdioP9Lee0FIiIiIlI1zhASERGR+nCK0CNDWhBKFsiVLtzrTd5cLFhK\nusi1N8c2HM9TSjo2yWLMw7HgtJT0dfcm6QLWw8nadt7t/nvn3SXK8zdbvyiu7asmxZiP6z4V5Trc\n3CCK62rvVIz54RN5olx7b60VxfXsVV6IefdvZYtcj5gbLYrbX7dPFLf0kScVY4xdyucMAE6cahPF\nHfrfLxVj/PUaUa6RBtnCzie/MSrG5NybKcq178gBUVzHN6cUY2JGy17Pg41fi+LG36j8e9dukX0+\nvcYHf/WZTCYUFhairq4OoaGhyMnJQUpKisvY8vJylJWVwWKxwGAwIDc3F4GBF8q29957D5WVlTh+\n/Djmz5+PZ555xumxn3zyCbZu3YrOzk5ERkZi8eLFmDt3rtux8ZIxERER0RAoKiqCRqPBpk2bsGzZ\nMhQVFbnsElVbW4uysjKsWrUKGzZsQEdHB0pKShz7w8PDkZmZibvuGvzHcmdnJ37zm9/gBz/4AYqL\ni/Hoo49i3bp1OHv2rNuxsSAkIiIi9bHbh+5HwGw2o7q6GosXL0ZQUBDi4+ORlJSEqqqqQbFVVVVY\nsGABYmJioNfrkZmZiYqKCsf+5ORkJCUlISQkZNBjOzs7MWLECMyadaH95pw5cxAcHIyOjg6342NB\nSEREROpjH8Ifgba2NgQEBCAqKsqxLS4uzuUMYXNzMyZMmOAU19XVBZPJpHicSZMmITY2FjU1NbDZ\nbKiuroZGo3HK5wpvKiEiIiLV8bWvEPb29kKv1ztt0+l06OnpUYzV6XSO7a5mBS/m7++PO+64A6+9\n9hqsVisCAwPxs5/9DEFBQW4fx4KQiIiI1MfHbqjTarXo7u522tbd3e0o9i6NvbhQHHicVqtVPE5d\nXR3efPNN5OfnY+LEiTh69Cj+8z//Ez//+c/dzhKyICQiIiL1GeJ68OKbPhISEpCQkOC0Pzo6Gjab\nDe3t7Y7Lxk1NTS5Xxhg3bhwaGxthMBgAAI2NjQgLC1OcHRzIefPNN2PixIkAgJtuugmTJ0/Gvn37\n3BaE/A4hERER0VVauHCh4+fSYhAAgoODkZycjJKSEpjNZtTX16OmpgapqamDYlNTU7Fz5060tLTA\nZDKhtLQUaWlpjv02mw0WiwU2mw02mw1WqxU2mw3AhQLw0KFDaGxsBAAcO3YM9fX1GD9+vNvxc4aQ\niIiI1MfHLhkDwNKlS1FYWIjc3FyEhoYiLy8PsbGxMBqNWL58OdasWYOIiAgkJiYiIyMD+fn5sFqt\nMBgMyM7OduTZvn07tm3b5vj/Xbt2ITs7G1lZWZg+fTqysrKwZs0adHV1ITQ0FA8//DBmzpzpdmws\nCImIiEh9fK8eREhICFasWDFoe2RkJIqLi522paenIz093WWe7OxspwLxUvfddx/uu+8+j8amWBBK\nOit4swOGtJODq9u0XZF0afB2Zw5vdmRRmuL1JJ8vdyAZju4iw9G5RZrLm6+n9LMynGznLG73b/pt\nkSiPJuYGUZz/KPd32wHAJ2UVslzCzhahk0crxvhB9vvvycVPiOKKTMrnzV8rmxfo7zKL4sKnyTpg\n9Jp7FWPeqXpXlOvIp/tFcRPvGnwZ71KzpswQ5bphhOy9tvVv2xVjPqmrFuUadUOYKG563FTFmKr3\ndopydXQqdz0BgINVyt1zLE3uF0am4cUZQiIiIlIfH5wh9GUsCImIiEh17KwIPcKCkIiIiNSH9aBH\nWBASERGR+rAg9AgLQiIiIlIhVoSeYEFIRERE6sN60CMsCImIiEh9WBB6hAUhERERqRArQk+wICQi\nIiLV8cHOdT5NsSCUdPrwZjcNaceK4egy4c1jerszx3B0IZEYjnH5cmcOyecJAPz9/RVjvP08Y2Ji\nFGOk4/eUNiHS7f6IaWNFeYwHT4jiwqbcqBhzaq+sQ8O0O2eJ4hpbjyvGrFn5a1GutCddt7O61M9+\n8jPFmPKP3xflum/eAlFc2+kOUZyE2SrrjvL9p5aI4iRjqzsi63rSclT59QQAa5tJMaYmdK8oV2ba\n90Rx53u7FWMCIoJFuQ5VfyWKs/f2KcaEpA3xvwcsCD2i/K8OEREREakaLxkTERGR+vCasUdYEBIR\nEZH6sB70CC8ZExEREV3nOENIRERE6sNLxh5hQUhERETqw3rQIywIiYiISHV8sR40mUwoLCxEXV0d\nQkNDkZOTg5SUFJex5eXlKCsrg8VigcFgQG5uLgIDL5Rt7733HiorK3H8+HHMnz8fzzzzjONxH330\nETZu3Ag/Pz8AgM1mg8Viwcsvv4yJEydedmwsCImIiEh9fPCScVFRETQaDTZt2oSGhga8/PLLiIuL\nG7Q2cW1tLcrKyrBq1SqMGjUKr7zyCkpKSvDII48AAMLDw5GZmYna2lpYLBanx6akpDgVmRUVFSgt\nLXVbDAJeKgili9V6c5Fiby7sLF3gd6DaViJZwFp6Lry5GLa3F/P25sLIw/Ee8uZr4O3XU7JItDff\nj8PNX+f+V1F0ZJQoz9T7JovigjVBijEj57j+q/1SPZZeUdzXnyov8Nt3UnlBYQCorv1cFBcUqFGM\n6Tb3iHI1d8gW/f7kq2pR3Nnz5xRjzK3KMQBwtP6wKA7+yp+ZSVNuEqWyNHWJ4gIidIoxnZXHRLnO\n3Co7ZsUXuxRjJk+eIso1496bRXFvvfqGYsz82+aLcnmNj9WDZrMZ1dXVWLNmDYKCghAfH4+kpCRU\nVVU5Cr0BVVVVWLBggePfgszMTKxbt84Rl5ycDAA4cuQIOjs73R63srISqampiuPjXcZERERE11hb\nWxsCAgIQFfWPP3Dj4uJcTq40NzdjwoQJTnFdXV0wmZQ731zs1KlTqK+vx5133qkYy0vGREREpD4+\ndsm4t7cXer3eaZtOp0NPz+BZ+ktjdTqdY3tISIj4mJWVlYiPj8fo0aMVY1kQEhERkfoMcT1YUlLi\n+O+EhAQkJCQ47ddqtejudv5aSHd3t6PYuzT24kJx4HFardajMe3atQsPP/ywKJYFIREREdFVWrhw\nodv90dHRsNlsaG9vd1w2bmpqcnlPxLhx49DY2AiDwQAAaGxsRFhYmEezg/X19fjmm28wb948UTy/\nQ0hERESqY7cP3Y9EcHAwkpOTUVJSArPZjPr6etTU1Li84SM1NRU7d+5ES0sLTCYTSktLkZaW5tg/\nsN5H5oEAAAkkSURBVJSMzWaDzWaD1WqFzWZzylFZWYl58+aJZxVZEBIREZH6+FpFCGDp0qUwm83I\nzc1FQUEB8vLyEBsbC6PRiO9///s4ffo0ACAxMREZGRnIz8/Hs88+ixtvvBHZ2dmOPNu3b8fjjz+O\nd955B7t27cJjjz2G0tJSx36r1YpPP/3UqYhUwkvGREREREMgJCQEK1asGLQ9MjISxcXFTtvS09OR\nnp7uMk92drZTgXgpjUaDzZs3ezQ2FoRERESkPr51k7HPY0FIRERE6uNjy874um9tQejNrhvSjg/S\nbhrjx49XjPF21xAJybgA+dgk3WKGo5uGt48pyefL3W6kx/Rm5xlP9X/jvtuH9Dmk3/4dUdyeQ3WK\nMVt/+6YoV/DEkaI4P0GXDKWOLQNuvWWOKK7ywwrFmPQHXV+SutSsKTNEcQebvhbFnTqo3PnksR88\nLsr1+cEvRXFf7z2oGBMeOkqUy24TFhuCMGmu//l9iXIQALulXzFmX3WbKJdmkXK3GwAIGKNXjKl8\n+++iXHhQFkbe9a0tCImIiIguixOEHmFBSEREROrDS8YeYUFIREREqsNy0DMsCImIiEh9WBF6hAUh\nERERqQ8vGXuEnUqIiIiIrnOcISQiIiL14QShR1gQEhERkfqwIPQILxkTERERXecUZwglHQKGo+uG\nv7+slvVm94Xh6LrhTcMxLml3F29205AeU/p+lJw3SdcWYHjeQzExMV7LJT23nrKZ3XdWqKv8QpTn\nlpumi+ICAwIUY4ImyTqQmHYpd9wAgKAJocoxU8JEuao2lovitAmRijE3jhotylX+0fuiuLo/7hLF\n6WYojy3AX/l1AoCIkeGiuL7284oxn5TtFOUKHBksirv3ofsVY3Z+XCHKlb5AORcAHDnRoBhTv1+5\nawsAjAxRft8CwI+W/Vgx5r3dH4hyeQ+nCD3BS8ZERESkOrzJ2DMsCImIiEh9WBB6hAUhERERqRAr\nQk+wICQiIiL18cF60GQyobCwEHV1dQgNDUVOTg5SUlJcxpaXl6OsrAwWiwUGgwG5ubkIDLxQtr33\n3nuorKzE8ePHMX/+fDzzzDNOj7VYLPj973+P3bt3w2azYcKECXjxxRfdjo0FIREREamPDxaERUVF\n0Gg02LRpExoaGvDyyy8jLi5u0I2JtbW1KCsrw6pVqzBq1Ci88sorKCkpwSOPPAIACA8PR2ZmJmpr\na2GxWAYd5/XXX4fdbsdrr72GESNGoLGxUXFsXHaGiIiIVMg+hD/KzGYzqqursXjxYgQFBSE+Ph5J\nSUmoqqoaFFtVVYUFCxYgJiYGer0emZmZqKiocOxPTk5GUlISQkJCBj22tbUVe/bswdNPP42QkBD4\n+flh4sSJiuPjDCERERGpj4/NELa1tSEgIABRUVGObXFxcThw4MCg2ObmZsydO9cprqurCyaTyWUR\neLEjR45g9OjR2LJlC6qqqhAeHo6srCzMmzfP7eM4Q0hERER0jfX29kKv1ztt0+l06OnpUYzV6XSO\n7UpOnz6N48ePY8SIEdi4cSOefPJJrF+/Hq2trW4fpzhDKFmI1psLTktJFwIejoWMvbkY9nAsrH2t\nFh/2xjGlr7s3SV536evky89zOPlr3f8q0k0aJcrTZmwXxdlsNsWY5MS5ijEA8FHzOVGcZLYiasYE\nUarWs4dFcZbGLsWY//51gShX3+nB/2i54qeRLSbd943yP2xlu94V5Uqb4/pL+VdicsoM2TFvlR3T\n2mdVjBk/Qfa6b/0/vxfFBcXcoBijiR4hytXf737R+AEjRygf887Z80W5vMXX1iHUarXo7u522tbd\n3e0o9i6NvbhQHHicVqtVPE5QUBACAwORmZkJPz8/TJ8+HQkJCdi7dy/Gjh172cfxkjERERGpzxBX\nhCUlJY7/TkhIQEJCgtP+6Oho2Gw2tLe3Oy4bNzU1uZwAGDduHBobG2EwGAAAjY2NCAsLU7xcDAAT\n/u8fGHa73TERJJkQ4iVjIiIioqu0cOFCx8+lxSAABAcHIzk5GSUlJTCbzaivr0dNTQ1SU1MHxaam\npmLnzp1oaWmByWRCaWkp0tLSHPttNhssFgtsNhtsNhusVqvjysfNN9+MyMhIvP3227DZbKivr8f+\n/fsxa9Yst+PnDCERERGpj49dMgaApUuXorCwELm5uQgNDUVeXh5iY2NhNBqxfPlyrFmzBhEREUhM\nTERGRgby8/NhtVphMBiQnZ3tyLN9+3Zs27bN8f+7du1CdnY2srKyEBAQgBUrVuD111/H22+/jdGj\nR2PZsmVuLxcDLAiJiIhIjXztS4QAQkJCsGLFikHbIyMjUVxc7LQtPT0d6enpLvNkZ2c7FYiXio2N\nxb//+797NDZeMiYiIiK6znGGkIiIiNTH9yYIfRoLQiIiIlKd4VhC7duMl4yJiIiIrnOcISQiIiL1\n4QShRxQLQsliht7spuHtriExMTFXM5wrIjmmtGtIc3OzKE5yPqS5vNklw5vvDSlvnjNP8nnzmBLe\nfp7DKTBK73Z/14eNojw7W86K4vrPKHfJmHlfsijX3Ptk3RdGaN0/RwBoape9phPvHLzGmSttp5Q7\nt/TUnhLl0s4cLYrzg+x32/3p9yvG3BQzUZTr9a1viOL6TRbFGGu/cmcRACj+s6xrSNI85Y43R3bv\nF+WS3jV7+72D17W7Up/s2CWKO93VqRizIMl74xLhJWOP8JIxERER0XWOl4yJiIhIfThB6BEWhERE\nRKQ+LAg9woKQiIiIVIgVoSdYEBIREZHq8J4Sz7AgJCIiIvVhQegRFoRERESkQqwIPcGCkIiIiFTH\n9FnbcA/hW+VbWxDecsstwz2EqyJdmFrKm+fDl8/tt/15Xi/H9NTNN97kdr+lO1KUJ+jGkaK4fr35\n/2/v3lUUCIIogI7uqLM+RkFd32Jg4P//mZFs4CMzrQIx6nPiS/VAM1B0UBVmTuNt7sy6l8o1/SbM\n1G3uRSM7wH/6+A0z//tZqlb9N0rlsraD+E7n3Umq1mWeG2B9O8T1dm1uMH+7zN37cbgOM9fNOVXr\n3sQD1auqqg7DVSqXEf2b7zMn8UKGxU/76efwRZ2n7c8AAEWzqQQAoHAaQgCAwmkIAQAKpyEEACic\nhhAAoHAaQgCAwr0Axu3bKLRDi78AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6079cd9250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymks.tools import draw_strains\n",
    "\n",
    "\n",
    "t = tm.time.time()\n",
    "strain_pred = model.predict(X)\n",
    "print 'Elapsed Time',(tm.time.time() - t), 'Seconds'\n",
    "draw_microstructure_strain(X[0, center], strain_pred[0, center])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## References\n",
    "\n",
    "[1] Binci M., Fullwood D., Kalidindi S.R., *A new spectral framework for establishing localization relationships for elastic behav ior of composites and their calibration to finite-element models*. Acta Materialia, 2008. 56 (10): p. 2272-2282 [doi:10.1016/j.actamat.2008.01.017](http://dx.doi.org/10.1016/j.actamat.2008.01.017).\n",
    "\n",
    "\n",
    "[2] Landi, G., S.R. Niezgoda, S.R. Kalidindi, *Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems*. Acta Materialia, 2009. 58 (7): p. 2716-2725 [doi:10.1016/j.actamat.2010.01.007](http://dx.doi.org/10.1016/j.actamat.2010.01.007).\n",
    "\n",
    "\n",
    "[3] Marko, K., Kalidindi S.R., Fullwood D., *Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals*. International Journal of Plasticity 24 (2008) 1264–1276 [doi;10.1016/j.ijplas.2007.12.002](http://dx.doi.org/10.1016/j.ijplas.2007.12.002).\n",
    "\n",
    "\n",
    "[4] Marko, K. Al-Harbi H. F. , Kalidindi S.R., *Crystal plasticity simulations using discrete Fourier transforms*. Acta Materialia 57 (2009) 1777–1784 [doi:10.1016/j.actamat.2008.12.017](http://dx.doi.org/10.1016/j.actamat.2008.12.017)."
   ]
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