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   "cells": [
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Linear Elasticity in 2D for 3 Phases\n",
      "\n",
      "##Introduction\n",
      "\n",
      "This example provides a demonstration of using PyMKS to compute the linear strain field for a three phase composite material. It demonstrates how to generate data for delta microstructures and then use this data to calibrate the first order MKS influence coefficients. The calibrated influence coefficients are used to predict the strain response for a random microstructure and the results are compared with those from finite element. Finally, the influence coefficients are scaled up and the MKS results are again compared with the finite element data for a large problem.\n",
      "\n",
      "PyMKS uses the finite element tool [SfePy](http://sfepy.org) to generate both the strain fields to fit the MKS model and the verification data to evaluate the MKS model's accuracy."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Elastostatics Equations and Boundary Conditions\n",
      "\n",
      "The governing equations for elasticostaics and the boundary conditions used in this example are the same as those provided in the Linear Elastic in 2D example. \n",
      "\n",
      "Note that an inappropriate boundary condition is used in this example because current version of SfePy is unable to implement a periodic plus displacement boundary condition. This leads to some issues near the edges of the domain and introduces errors into the resizing of the coefficients. We are working to fix this issue, but note that the problem is not with the MKS regression itself, but with the calibration data used. The finite element package ABAQUS includes the displaced periodic boundary condition and can be used to calibrate the MKS regression correctly."
     ]
    },
    {
     "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",
      "Here we use the `make_delta_microstructure` function from `pymks.datasets` to create the two delta microstructures needed to calibrate the first order influence coefficients for a two phase microstructure. The `make_delta_microstructure` function uses SfePy to generate the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = 21\n",
      "n_phases = 3\n",
      "from pymks.tools import draw_microstructures\n",
      "from pymks.datasets import make_delta_microstructures\n",
      "\n",
      "X_delta = make_delta_microstructures(n_phases=n_phases, size=(L, L))\n",
      "draw_microstructures(X_delta[0], X_delta[1], X_delta[2], X_delta[3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x181cf278>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "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. Any given delta microstructure is composed of only two phases with the center cell having an alternative phase from the remainder of the domain. The number of delta microstructures that are needed to calibrated the first order coefficients is $N(N-1)$ where $N$ is the number of phases, therefore in this example we need 6 delta microstructures."
     ]
    },
    {
     "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.\n",
      "\n",
      "In this example, lets look at a three phase microstructure with elastic moduli values of 80, 100 and 120 and Poisson's ratio values all equal to 0.3. 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. The number of Poisson's ratio values and elastic moduli values indicates the number of phases. Note that `make_elasticFEstrain_delta` does not take a number of samples argument as the number of samples to calibrate the MKS is fixed by the number of phases."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymks.datasets import make_elastic_FE_strain_delta\n",
      "from pymks.tools import draw_microstructure_strain\n",
      "\n",
      "elastic_modulus = (80, 100, 120)\n",
      "poissons_ratio = (0.3, 0.3, 0.3)\n",
      "macro_strain = 0.02\n",
      "size = (L, L)\n",
      "\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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "draw_microstructure_strain(X_delta[0], strains_delta[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/tj7L6bvsO8IxVXV88/37gXftageel+TN9C4fTye5u6reMewghkFJktRp810Z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\nzDAoSZK0DzMMSpIk7cMMg5IkSfuw/w86mAXEUbUx3wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x149d8780>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because `slice(None)` (the default slice operator in Python, equivalent to array[:]) was passed in to the `make_elasticFEstrain_delta` function as the argument for `strain_index`, the function returns all the strain fields. Let's also take a look at the $\\varepsilon_{yy}$ and $\\varepsilon_{xy}$ strain fields."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Calibrating First Order Influence Coefficients\n",
      "\n",
      "Now that we have the delta microstructures and their strain fields, we will calibrate the influence coefficients by creating an instance of the `MKSRegressionModel` class. Because we are going to calibrate the influence coefficients with delta microstructures, we can create an instance of `DiscreteIndicatorBasis` with `n_states` equal to 3, and use it to create an instance of `MKSRegressionModel`. The delta microstructures and their strain fields will then be passed to the `fit` method. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymks import MKSRegressionModel\n",
      "from pymks import DiscreteIndicatorBasis\n",
      "\n",
      "basis = DiscreteIndicatorBasis(n_states=3, domain=[0, 2])\n",
      "MKSmodel = MKSRegressionModel(basis=basis)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "MKSmodel.fit(X_delta, strains_delta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's it, the influence coefficient have be calibrated. Let's take a look at them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymks.tools import draw_coeff\n",
      "\n",
      "draw_coeff(MKSmodel.coeff)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SASuuzTG4SpIkSVIBK67NMbhKkiRJUgErrs0xuEqSJElSASuuzTG4SpIkSVIB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\nSZIkSeprBldJkiRJUl/7/xFp+6BGSsRVAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x14d47208>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The influence coefficients for $h=0$ and $h = 1$ have a Gaussian-like shape, while the influence coefficients for $h=2$ are constant-valued. The constant-valued influence coefficients may seem superfluous, but are equally as import. 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 `MKSRegressionModel` 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",
     "collapsed": false,
     "input": [
      "from pymks.datasets import make_elastic_FE_strain_random\n",
      "\n",
      "np.random.seed(101)\n",
      "X, strain = make_elastic_FE_strain_random(n_samples=1, elastic_modulus=elastic_modulus,\n",
      "                                          poissons_ratio=poissons_ratio, size=size, \n",
      "                                          macro_strain=macro_strain)\n",
      "draw_microstructure_strain(X[0] , strain[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Mbi5pYbfniyTV/1XXKGaMpMUrFtgeJ2lnSXN6aW+0Xlr4LSq23xDFIAAAqLT+\nvoDk5l/frd/9+p6ykL4e1qrv6It5xSHiSyR9OiKeyfWwvA8UgwAAoNL6ewaSPd+8o/Z8844vPj/1\nfy6qD3lI0thuz8eqNlpXFjOmWCbbwyVdKumCiLi8D13qcVuNcDUxAACotBYP7KOBuZIm2B5ne4Rq\nF3fMqouZJekwSbK9u6SlEbHYtWHNsyTdGxGnluxm95ZnSTrE9gjbW0maIOmWnhIZGQQAAJU22OcM\nRkSH7SmSrpbUKumsiJhn+6hi/ZkRcaXtScXFHs9KOrxI31PSoZJ+b/uOYtnxEXGV7YMkzZC0oaSf\n274jIt4ZEffa/pGkeyV1SPpUlFyBSTEIAAAqbbCLQUmKiNmSZtctO7Pu+ZQGeTephyO5EfETST/p\nYd1Jkk7qS98oBgEAQKUxA0k5ikEAAFBpQ2FkcCijGAQAAJXW31cTv9pRDAIAgEpjZLAcxSAAAKi0\nHm73goLL5nq1nZ4IdiBO0uzqajjPcqlm5rTNamae4WZk55ttZg7czs7OdM5A7X9W9r1v5jPczOer\nmXay78uJJ56YbqOZObZtKyKa/uW3HVOuO67P8f/62u3Tbfz0gfx8q3FlPmfUqLVS8X/848Leg+rs\n9dn90zmbrZXr150X9Tbb1csNf9v4dM53/vW0VPxVc3PxkrTwjgXpnGHDct9nO+y6bbqNvz2Tn/v6\n8X/k5ma+49FH022c84mZ6ZyTTjoynXPqqZem4mfPntPU94zteHrZ1dm0lbL2iP1X6jtxoDEyCAAA\nKo3DxOUoBgEAQKVxAUk5ikEAAFBpjAyWoxgEAACVRjFYjmIQAABUGjOQlKMYBAAAlcbIYDmKQQAA\nUG0DcHu5VzOKQQAAUGldXRSDZSgGAQBApTUzWcWqhGIQAABUGiOD5SgGAQBApTEyWI5iEAAAVBoj\ng+UcJVfY2I7svXk6OjrSnWhtzU0I3tLSkm6js7MzndPe3p7OyWpra+v3NqZPn97vbTRjIPZdkso+\n440MG5b/G6mZz9dQfV+yn/sjjzxSM2fOXKlJ2W3HJX88o8/x133rqnQbf99/TDrns2/cLZ3zod0+\nl4o///wvpdsYs9OW6Zx/PPRkKn7p0mfSbXSNWyed89oRuZwNNxqVbuPc7+c/L+uvv3Yq/m9/W5pu\n4+stf0nnfH557nO8y3v/Jd1G54Il6ZzrrrsjnfP5Yw9Oxa8+/B1Nfc/Yjqee+nk2baWss867Vuo7\ncaAxMgjgLX5IAAASTklEQVQAACqNkcFyFIMAAKDSOGewHMUgAACoNEYGy1EMAgCASmNksBzFIAAA\nqDRGBstRDAIAgEpjZLAcxSAAAKg0RgbLUQwCAIBKY2SwHMUgAACoNEYGy+Wn8gAAAHgV6erqGtBH\nI7YPsH2f7fttH9tDzIxi/V22d+62/Gzbi23fXRf/Bts32/697Vm21y6Wj7P9vO07isfpZa8PxSAA\nAKi0rq4Y0Ec9262STpN0gKTtJH3Y9uvqYiZJ2iYiJkj6hKTuc3SeU+TW+56kL0bEjpJ+IukL3dbN\nj4idi8enyl4fikEAAFBpQ2BkcFfVirMFEbFc0kWSDqyLmSzpXEmKiDmSRtnetHj+a0mNJo2eUKyT\npGslvb+Z16fXcwY7OjpyGxyWPw3Rzs3lnO2TJE2fPj2d09bW1u9ttLa2pnMGwtSpU9M5A/F6DYRm\n9r2ZfWlvb0/nZPs2EO+jJM2cOTOdU2/BT+/qc6zf99r09rcduVo65/vtF6dzbrzxW6n4r371B+k2\nvjzu0HTO6ltukIof/9qx6TZ+OO/u3oPqbDIi9/3//e9flW7j4x9/dzpnwYJHU/Hjx49Ot3H9lnun\nc/5814JU/Cm3zUm38e23NhqAKnfFFb9J55x/ztXpnGYNgXMGN5e0sNvzRZJ260PM5pLKPox/sH1g\nRFwh6YOSuv/ibmX7DklPSvpyRNzU00a4gAQAAFTaELiauK/VaP1fR73lHSFphu0TJM2StKxY/rCk\nsRGxxPZESZfb3j4inm60EYpBAABQaf09MnjLLffp1lvvKwt5SC8dtRur2shfWcyYYlmPIuKPkvaX\nJNvbSnpXsXyZisIwIm63/YCkCZJub7QdikEAAFBp/T0yuMsu22qXXbZ98fkZZ1xRHzJX0gTb41Qb\ntTtY0ofrYmZJmiLpItu7S1oaEYvL2rW9UUT83XaLpC+ruOjE9oaSlkREp+3xqhWCD/a0HYpBAABQ\naYN9zmBEdNieIulqSa2SzoqIebaPKtafGRFX2p5ke76kZyUdviLf9oWS9pG0ge2Fktoi4hzVrkr+\nzyLs0oj4fvHvvSVNt71cUpekoyJiaU/9oxgEAACVNgTOGVREzJY0u27ZmXXPp/SQWz+KuGL5DEkz\nGiy/TNJlfe0bxSAAAKi0wR4ZHOooBgEAQKUNhZHBoYxiEAAAVBojg+UoBgEAQKUxMliOYhAAAFQa\nI4PlKAYBAEClMTJYzhE9V8u2Y9q0aakNNjPfamdnZyp+qM5pOxD7Lkll71kjzcwX3Uy/svMsNzNv\nbjOyc+02M190M69XS0tLOic7j/dAfQHaVkTkOvfS/FjecW2f4w+47KJ0G9v/5ol0zgc/sG865+mn\nn0vF//WvpfeUbeiurYenc3TZvFT4uqPWSjdx/pbPp3PeMCs3B/CU0/493ca2Xaunc8aO3TgVv99+\nn0+3sddXD0rnPP6DhhNI9CiamMf7dRtsmM65/6yb0zmrrTYiFX/KKT9u6nvGdtxww6nZtJWy776f\nWanvxIHGyCAAAKg0RgbL5YcmAAAAUBmMDAIAgErjApJyFIMAAKDSOExcjmIQAABUGiOD5SgGAQBA\npTEyWI5iEAAAVBojg+UoBgEAQKUxMliOYhAAAFQaI4PlKAYBAEClMTJYjmIQAABUGiOD5SgGAQBA\npTEyWK7XYrC9vT21wc7OznQn7NxczlOnTk230YyI3F8S2ddKyu/7QDnxxBPTOR0dHan4YcMG5m+R\n7Oelra0t3UZra2s6Z9q0aemcE044IRXf0pKfcTL7ek2cODHdRiMfnX1Fn2O/vPH26e0vfOPf0jkj\nRw5P5zzwwJJUfDMjFo89/1w6Z/Ef/pKK32mnbdJtrDNiRDrnootyn+kTTzwv3YY+uV865fmncu/j\ngw8+km7jgnH5z/Fp/5orao7cYad0Gz+YMSuds8d/vi2d8/DP7k7nNIuRwXKMDAIAgEpjZLAcxSAA\nAKg0RgbLUQwCAIBKY2SwHMUgAACoNEYGy1EMAgCASmNksBzFIAAAqDRGBstRDAIAgEpjZLAcxSAA\nAKg0RgbLUQwCAIBKY2SwXH56AgAAgFeRrq4Y0Ecjtg+wfZ/t+20f20PMjGL9XbZ37rb8bNuLbd9d\nF7+r7Vts32H7Vtv/0m3d8cW27rP9jrLXh2IQAABUWldX14A+6tlulXSapAMkbSfpw7ZfVxczSdI2\nETFB0ickndFt9TlFbr1vSDohInaW1FY8l+3tJB1ctHWApNNt91jzUQwCAIBKGwIjg7tKmh8RCyJi\nuaSLJB1YFzNZ0rmSFBFzJI2yvWnx/NeSGk2Y/YikdYt/j5L0UPHvAyVdGBHLI2KBpPlFHxrq9ZzB\ntra23kJeusFh+dMQOzo6hlwbzbTT2dmZbiMif1Jra2trv7cxbdq0dE57e3sqvpnXayDYTudkf0+k\n/OvVjKlTpw5Izivhm295e59jvz7nt+nt33bmz9I5e33toHTOTTN/noqfMvM/0m142iXpnC222DgV\n/9aj90+38bF11knnPOXc98B7P/2udBu/mHltOmf9d+6Wij/ssPzrNXz9NdI5X9l071T8f15/dbqN\n9+22XTpnuzFbpHNOffRX6ZxmDYFzBjeXtLDb80WS6j9kjWI2l/RoyXaPk3ST7f9TbYBvj2L5aEm/\na7CthriABAAAVFp/X008f/5DeuCBh8tC+tqB+tGI3vLOknRMRPzE9gclnS2pp7+se9wWxSAAAKi0\n/h4ZHD9+M40fv9mLz6+5Zm59yEOSxnZ7Pla10bqymDH652HfnuwaEfsV/75E0vea2RbnDAIAgEob\nAucMzpU0wfY42yNUu7hjVl3MLEmHSZLt3SUtjYjFvezafNv7FP9+q6Q/ddvWIbZH2N5K0gRJt/S0\nEUYGAQBApQ32OYMR0WF7iqSrJbVKOisi5tk+qlh/ZkRcaXuS7fmSnpV0+Ip82xdK2kfSBrYXSmqL\niHNUu+r4/9keKen54rki4l7bP5J0r6QOSZ+KkgsIKAYBAEClDYUZSCJitqTZdcvOrHs+pYfcD/ew\nfK5efiHKinUnSTqpL32jGAQAAJU22CODQx3FIAAAqLShMDI4lFEMAgCASmNksBzFIAAAqDRGBstR\nDAIAgEpjZLAcxSAAAKg0RgbLuWzeWtuRnae1mXlwB6KNlpb8/bWbmc84KzvPsJSfO7aZeXOHqoGY\nl7qZ96SZeZYHop1m2mjmL2jbioj8pM7/zI8bF57b5/ht19sg3cZqTbwWz3bmvwMWLG00l3zPTvnM\n93oPqvPnP5dNVdrYf11wTCr+gK22Trdxx2/npXP23nvHVPzjjz+dbuO4476bztnw396Yir/k8Pz7\nuNdph6RzVrv8/lT8Y+/eMt3GC9952ewZvdro6D3TOfO/8otU/G9/+4emvmdsxxe/mH+tV8Y3vnHR\nSn0nDjRGBgEAQKUxMliOYhAAAFQa5wyWoxgEAACVxshgOYpBAABQaYwMlqMYBAAAlcbIYDmKQQAA\nUGmMDJajGAQAAJXGyGA5ikEAAFBpjAyWoxgEAACVxshgOYpBAABQaYwMlqMYBAAAlcbIYDmKQQAA\nUGmMDJbrtRicOnVqaoMnnHBCvhPDcjVpM2/q9OnT+z3Hzs9J3dnZmc7J9quZfW9vb0/nZPe/o6Mj\n3UZE//9110wbra2t6Zzs75aUfy+b2ZeWlpZU/JFHHpluo5En73yoz7H/cfbM9Pbvn7x5Ome3Xz+d\nzvnWt6Yk449Jt7Fs2bJ0zumnX5GKf/uxY9JtjB69QTrn2oULUvGbr7V2uo0bb7wrnfOuQ9+Qit96\n69HpNt474TXpnL1OeVsq/rpZc9JtbH78R9I5P4u/p3MO/cHnU/Hv2OqIdBsrMDJYjpFBAABQaYwM\nlqMYBAAAlcbIYDmKQQAAUGmMDJajGAQAAJXGyGA5ikEAAFBpjAyWoxgEAACVxshgOYpBAABQaYwM\nlqMYBAAAlcbIYLnc3WUBAABeZbq6ugb00YjtA2zfZ/t+28f2EDOjWH+X7Z27LT/b9mLbdzfIOdr2\nPNv32P56sWyc7edt31E8Ti97fRgZBAAAlTbYI4O2WyWdJmk/SQ9JutX2rIiY1y1mkqRtImKC7d0k\nnSFp92L1OZK+Lem8uu2+RdJkSTtGxHLbG3VbPT8idlYfUAwCAIBKGwLnDO6qWnG2QJJsXyTpQEnz\nusVMlnSuJEXEHNujbG8aEY9GxK9tj2uw3U9K+lpELC/y8vMCisPEAACg4rq6YkAfDWwuaWG354uK\nZdmYehMk7W37d7ZvsL1Lt3VbFYeIb7C9V9lGeh0ZnDp1am8hLxHR/0OxttM5bW1t6ZzW1tZUfPa1\nkgZmX7L7ITW3L9l+nXjiiek2Ojo60jnDhuUGwIfAX5A9yr6XzXy+su/9xIkTNXPmzHQ79RYu/Fuf\nYzfdZL309mO9DdI5y5Y9ns455pgZqfjV/3XHdBun7L1fOuexx55KxX/z5B+n21i89ybpnDPeNikV\nf9qMS9NtXDP3tHTOtT/+TSr+kaPflG5j4ZX3pHMuVC5nzi33pdsY+dH8Z3KNYcPTOfttOS6d06wh\n8L3e1+Ko/ku7t7xhktaLiN1t/4ukH0kaL+lhSWMjYontiZIut719RDzd00YAAAAqq7/PGVyy5Gkt\nXfpMWchDksZ2ez5WtZG/spgxxbIyiyRdJkkRcavtLtsbRMTjkpYVy2+3/YBqo4i3N9oIxSAAAKi0\n/h4ZXHfdNbXuumu++Pwvf1lcHzJX0oTivL+HJR0s6cN1MbMkTZF0ke3dJS2NiJdtqM7lkt4q6Ve2\nt5U0IiIet72hpCUR0Wl7vGqF4IM9bYRiEAAAVNpgX00cER22p0i6WlKrpLMiYp7to4r1Z0bElbYn\n2Z4v6VlJh6/It32hpH0kbWB7oaS2iDhH0tmSzi5uObNM0mFFyt6SptteLqlL0lERsbSn/lEMAgCA\nShsC5wwqImZLml237My651N6yK0fRVyxfLmkjzZYfpmKw8d9QTEIAAAqbbBHBoc6ikEAAFBpQ2Fk\ncCijGAQAAJXGyGA5ikEAAFBpjAyWoxgEAACVxshgOYpBAABQaYwMlqMYBAAAlcbIYDmXzSVsO7Jz\nm06bNi3diRNOOCEVP3369HQbzcjOs9xMv5qZA7i9vb3f2xgI2f1oVnb/B2ru62bm8R6I+bKbnWM7\nIvIv3D/z42tzvtrn+CPGvS7dxolfOS+d88n/eG8658EHH07F7/D6rdJtXLW0txmqXu6BC25JxR92\n7PvTbYwdvkY655GHc/M/L1r093QbI1+3UTpnszXXTsVvOnz1dBtPP/VsOueUU3JzRj/11HPpNq7f\nNb8v571zcjrn9OPOTcWff/61TX3P2I7tttsym7ZS7r33Lyv1nTjQGBkEAACVxshgOYpBAABQaZwz\nWI5iEAAAVBojg+UoBgEAQKUxMliOYhAAAFQaI4PlKAYBAEClMTJYrmWwOwAAAIDBw8ggAACoNA4T\nl6MYBAAAlcZh4nIUgwAAoNIYGSxHMQgAACqNkcFyFIMAAKDSGBks54ieXyDbkZ20fvr06elOZCv2\n9vb2dBttbW3pnGb2ZSCccMIJqfhhw/I1f/Z9l/LvSzNtZPddyu//QOx7s+2U/b42MhC/j5Jke6Um\nZbcdnV2/7HP8t267Jd3G/ztkRjrnttvOTOf88IfXpeI/9LG3p9t4vqMjndOZfF+/9Kn/l27jwLaD\n0jlr3P9kKn7R2BHpNvZbc9N0zrHHfjcV/85p7023MeKOxemc/d63Zyr+up/cnG5j0gf2Sud8YNal\n6ZwNL5mfir/kkhub+p6xHeuvv3Y2baU88cTTK/WdONAYGQQAAJXGyGA5ikEAAFBpnDNYjmIQAABU\nGiOD5SgGAQBApTEyWI5iEAAAVBojg+UoBgEAQKUxMliOYhAAAFQaI4PlKAYBAEClMTJYjmIQAABU\nGiOD5SgGAQBAZb2aZgIZLC2D3QEAAAAMnl5HBjfbbLPUBidOnNh0Z/oq26eh3k5/a+Y9aWbfs+0M\n1Os7EP0aqNc4OzfxQPw+vnLW6nPkxmtskt769tu/Pp3T0rJuOmfDDcek4lu9TrqN4S2d6ZxW5c6Z\nGjduQrqN9UZulM5Zbd3VU/EvrJ4/oDVy5PrpnPHjt03Fb7Daxuk2hq+f35fhyc/k+uuPTrfRzGdy\nwnpbpnNGbZUdj7ox3Qb6xmX/udjmIDuAPlmZQzF81wDoCw759o/SYhAAAADVxjmDAAAAqzCKQQAA\ngFUYxSAAAMAqjGIQAABgFUYxCAAAsAr7/2rRW3uNc2AHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x180c2828>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "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 `MKSRegressionModel` just pass the same microstructure to the `predict` method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "strain_pred = MKSmodel.predict(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally let's compare the results from finite element simulation and the MKS model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymks.tools import draw_strains_compare\n",
      "\n",
      "draw_strains_compare(strain[0], strain_pred[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KHTZwn1D8iy/OCcVXVKwJxadp1rBR2bFtmzYNb79Ti63Cba656/FQfNeOn4dz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x14fefb38>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot the difference between the two strain fields."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymks.tools import draw_diff\n",
      "\n",
      "draw_diff((strain[0] - strain_pred[0]), title='Finite Element - MKS')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1i+6yX22ftMOexz2feAT7psUDLS1p9ywYPrzaO4zannkm7Xl05N4LB+1xQFJ8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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x18317080>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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 random microstructure and its strain field."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 3 * L \n",
      "size = (N, N)\n",
      "print size\n",
      "\n",
      "X, strain = make_elastic_FE_strain_random(n_samples=1, elastic_modulus=elastic_modulus,\n",
      "                                          poissons_ratio=poissons_ratio, size=size, \n",
      "                                          macro_strain=macro_strain)\n",
      "\n",
      "draw_microstructure_strain(X[0] , strain[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(63, 63)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1fr8t6SdaunOyv9vnUdK9l/FcqN/24zy2wne5c7Z2vYi9efPrVCKdJwu3q/BB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\n+g/9MVFKRQMYBaAtgOoAeiilqhnLtANQSWudCOBBAIFZTh9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lmjfY9JF5+e5c7TCPh1c7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\nIAiCIAh/Yv4fQninzMkzxFwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x183b6390>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The influence coefficients that have already been calibrated on a $L$ by $L$ delta microstructures, need to be resized to match the shape of the new larger $N$ by $N$ 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",
     "collapsed": false,
     "input": [
      "MKSmodel.resize_coeff(X[0].shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's now take a look that ther resized influence coefficients."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_coeff(MKSmodel.coeff)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ccW2OwVWSJEmSCjji2hyDqyRJkiQVcMS1OQZXSZIkSSrgiGtzDK6SJEmSVMAR\n1+YYXCVJkiSpgCOuzTG4SpIkSVIBR1ybY3CVJEmSpAKOuDbH4CpJkiRJBRxxbY7BdS/YtWtX002Q\ntA+xz5G0t9jfaF/jiGtzDK6SJEmSVMAR1+YYXCVJkiSpgCOuzTG4SpIkSVIBR1ybM6vpBkiSJEnS\nMBgdHR2a11giYnlEbI6IuyPi/C5lVlfbN0TE8f3qRsRhEXFNRNwVEV+KiEOq9ftHxGci4vaI2BgR\nF0zm3BtcJUmSJKnA6GgOzasuIkaAS4DlwLHAmRFxTK3MCuCozFwCvBm4tKDuBcA1mXk0cG21DPA6\ngMx8MfAy4NyIOGKi595LhSVJkiSpwJDPcV0KbMnMrQARcQWwEtjUVuY04HKAzLw5Ig6JiHnA4h51\nTwNOqupfDlxHK7zeDxxUhd6DgKeBH0+08QZXSZIkSSow5HNcFwD3ti3fB5xYUGYBML9H3bmZub16\nvx2YC5CZV0fEG2gF2AOBP8nMRyfaeIOrJEmSJBUY5BHXzZu/z+bN3+9VpDR1R2GZPfaXmRkRCRAR\nrwcOAA4HDgNuiIhrM/OewnZ0MLhKkiRJUoFBHnE9+uhFHH30ot3La9f+U73INmBR2/IiWiOnvcos\nrMrMHmP9tur99oiYl5kPRMThwIPV+lcAn8/MXcBDEXEjcAIwoeDqzZkkSZIkqUDTdwqe5F2FbwWW\nRMSRETEHOANYWyuzFjgLICKWAY9WlwH3qrsWOLt6fzZwVfV+M/Cr1b4OApbROZ92XBxxlSRJkqQC\ngzzi2k9m7oyIVcDVwAhwWWZuiohzq+1rMnNdRKyIiC3A48A5vepWu34fcGVEvAnYCpxerV8DXBYR\nd9AaMP14Zt450fYbXCVJkiSpwCDPcS2RmeuB9bV1a2rLq0rrVusfBk4eY/1TwOsn0952BldJkiRJ\nKjDMI67DzuAqSZIkSQWGfcR1mBlcJUmSJKmAI67NMbhKkiRJUgFHXJtjcJUkSZKkAo64NsfgKkmS\nJEkFHHFtjsFVkiRJkgo44tocg6skSZIkFXDEtTkGV0mSJEkq4IhrcwyukiRJklTAEdfmGFwlSZIk\nqYAjrs0xuEqSJElSAUdcmzOr6QZIkiRJktSLI66SJEmSVMBLhZtjcJUkSZKkAl4q3ByDqyRJkiQV\ncMS1OQZXSZIkSSrgiGtzDK6SJEmSVMAR1+YYXCVJkiSpgCOuzTG4SpIkSVIBR1ybY3CVJEmSpAKO\nuDbH4CpfAd0kAAAGc0lEQVRJkiRJBRxxbY7BVZIkSZIKOOLanFlNN0CSJEmShsHoaA7NaywRsTwi\nNkfE3RFxfpcyq6vtGyLi+H51I+KwiLgmIu6KiC9FxCFt2y6sym+OiFMnc+4NrpIkSZJUYHR0dGhe\ndRExAlwCLAeOBc6MiGNqZVYAR2XmEuDNwKUFdS8ArsnMo4Frq2Ui4ljgjKr8cuCjETHh/OmlwpIk\nSZJUYMjnuC4FtmTmVoCIuAJYCWxqK3MacDlAZt4cEYdExDxgcY+6pwEnVfUvB66jFV5XAp/JzB3A\n1ojYUrXhpok03uAqSZIkSQWGfI7rAuDetuX7gBMLyiwA5veoOzczt1fvtwNzq/fz6Qypz+xrQgyu\nkiRJklRgkEdc77//RzzwwMO9ipQ2PgrL7LG/zMyI6HWcCZ9Ag6skSZIkFRjkEde5cw9l7txDdy9v\n2PCdepFtwKK25UW0RkF7lVlYlZk9xvpt1fvtETEvMx+IiMOBB3vsaxsT5M2ZJEmSJKlA03cKnuRd\nhW8FlkTEkRExh9aNk9bWyqwFzgKIiGXAo9VlwL3qrgXOrt6fDVzVtv51ETEnIhYDS4BvTPTcO+Iq\nSZIkSQUGecS1n8zcGRGrgKuBEeCyzNwUEedW29dk5rqIWFHdSOlx4Jxedatdvw+4MiLeBGwFTq/q\nbIyIK4GNwE7gvMz0UmFJkiRJmk6DPMe1RGauB9bX1q2pLa8qrVutfxg4uUudi4GLJ9redgZXSZIk\nSSowzCOuw87gKkmSJEkFhn3EdZgZXCVJkiSpgCOuzTG4SpIkSVIBR1ybY3CVJEmSpAKOuDbH4CpJ\nkiRJBRxxbY7BVZIkSZIKOOLaHIOrJEmSJBVwxLU5BldJkiRJKuCIa3MMrpIkSZJUwBHX5hhcJUmS\nJKmAI67NMbhKkiRJUgFHXJtjcJUkSZKkAo64NsfgKkmSJEkFHHFtjsFVkiRJkgo44tocg6skSZIk\nFXDEtTkGV0mSJEkq4IhrcwyukiRJklTAEdfmGFwlSZIkqYAjrs0xuEqSJElSAUdcm2NwlSRJkqQC\njrg2x+AqSZIkSQUccW2OwVWSJEmSCjji2hyDqyRJkiQVcMS1ObOaboAkSZIkDYPR0dGheY1HRBwW\nEddExF0R8aWIOKRLueURsTki7o6I80vqR8SFVfnNEXFq2/pzIuKOiNgQEesj4rm92mhwlSRJkqQC\no6M5NK9xugC4JjOPBq6tljtExAhwCbAcOBY4MyKO6VU/Io4FzqjKLwc+Gi1zgA8AJ2XmS4DbgVW9\nGmhwlSRJkqQCTY+iTteIK3AacHn1/nLgt8cosxTYkplbM3MHcAWwsk/9lcBnMnNHZm4FtlT72Qk8\nAhwcEQE8B9jWq4HOcZUkSZKkAjN4juvczNxevd8OzB2jzALg3rbl+4AT+9SfD9xUq7MwM2+OiLcA\ndwKPAXcBf9SrgQZXSZIkSSowyHcVfvLJp3nyyae7bo+Ia4B5Y2y6qH0hMzMixkro9XUxxrpe9XcX\niYjnAKuBl2TmPRHxEeBC4L3dKhlcJUmSJKnAII+4zpkzmzlzZu9e/vGPf9qxPTNP6VY3IrZHxLzM\nfCAiDgceHKPYNmBR2/JCnr28t1v9bnWOAe7JzHuq9X8PnE8PznGVJEmSpAJNz1udxjmua4Gzq/dn\nA1eNUeZWYElEHFndXOmMql6v+muB10XEnIhYDCwBvgF8F3hRRDyvKncKsLFXAx1xlSRJkqQCgzzi\nOknvA66MiDcBW4HTASJiPvA/M/M3MnNnRKwCrgZGgMsyc1Ov+pm5MSKupBVKdwLnZWYCD0XE24Gv\nRsRoVeeNvRpocJUkSZKkAoM8x3UyMvNh4OQx1v8A+I225fXA+tL61baLgYvHWP9J4JOlbTS4SpIk\nSVKBGTziOvAMrpIkSZJUYKaOuA4Dg6skSZIkFXDEtTkGV0mSJEkq4Ihrc6J1U6cuG3s/OFbSkMrM\naLoNY7HPkWamQexz7G+kmWk6+5uIyIMPPmC6dj/lHnvsiYHsfyeq54jrTPqgkgaffY6kvcX+RtJE\nOOLaHC8VliRJkqQCznFtjsFVkiRJkgo44tocg6skSZIkFXDEtTkGV0mSJEkq4IhrcwyukiRJklTA\nEdfmzGq6AZIkSZIk9dLzOa6SJEmSJDXNEVdJkiRJ0kAzuEqSJEmSBprBVZIkSZI00AyukiRJkqSB\nZnCVJEmSJA20/w8BDxKJQDPKzAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x183ad630>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because the coefficients have been resized, they will no longer work for our original $L$ by $L$ sized microstructures they were calibrated on, but they can now be used on the $N$ by $N$ microstructures. Just like before, just pass the microstructure as the argument of the `predict` method to get the strain field."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "strain_pred = MKSmodel.predict(X)\n",
      "\n",
      "draw_strains_compare(strain[0], strain_pred[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gdmL7cs5RBICBg/gchfhylmDzauyRNNuZKT9yOwMAO3Jw/SrZin8rT6/ia3F9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t+HUXJG3lgzUxtrbq/jBVu3b3PwMQCMGsOLRDat3Uv+RAID97cq83lJSDOB+jOHOKj41Cm+Vvp+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\nwtM1sg2Ah7ojI9n7yRh7Oio6l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       "text": [
        "<matplotlib.figure.Figure at 0x183ad128>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, let's plot the difference between the two strain fields."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "draw_diff((strain[0] - strain_pred[0]), title='Finite Element - MKS')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vfg/aA3j4cNb+ACAlhc/7619vpvhLX/oYxb/61asU6/zZaxfwUkEA4NQtOVDBfrozilhT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\nFNM6jj/qW57muhi1mOuvMIefb238P1isxxtgPV7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       "text": [
        "<matplotlib.figure.Figure at 0x14d46240>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you can see, the results from the strain field computed with the resized influence coefficients is not as accurate as they were before they were resized. This decrease in accuracy is expected when using spectral interpolation [4]."
     ]
    },
    {
     "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 behavior 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\u20131276 [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\u20131784 [doi:10.1016/j.actamat.2008.12.017](http://dx.doi.org/10.1016/j.actamat.2008.12.017)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}