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intro.json
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intro.json
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Meet PyMKS\n",
"\n",
"In this short introduction, we will demonstrate the functionality of PyMKS to compute 2-point statistics in order to objectively quantify microstructures, predict effective properties using homogenization and predict local properties using localization. If you would like more technical details amount any of these methods please see the [theory section](THEORY.html)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quantify Microstructures using 2-Point Statistics\n",
"\n",
"Lets make two dual phase microstructures with different morphologies."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks.datasets import make_microstructure\n",
"\n",
"X_1 = make_microstructure(n_samples=1, grain_size=(25, 25))\n",
"X_2 = make_microstructure(n_samples=1, grain_size=(15, 95))\n",
"\n",
"X = np.concatenate((X_1, X_2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Throughout PyMKS `X` is used to represent microstructures. Now that we have made the two microstructures, lets take a look at them."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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fpGGzsKxy1I32tmfAgJZe2nDbOtfAXabFILlcTplMRgsLC5qenlY+n9fy8rIq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\nEEEcAACAhQjiAAAALPQ/RoghqcR7pHsAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b48265190>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_microstructures\n",
"\n",
"draw_microstructures(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compute the 2-point statistics for these two periodic microstructures using the `correlate` function from `pymks.stats`. This function computes all of the autocorrelations and cross-correlation(s) for a microstructure. Before we compute the 2-point statistics, we will discretize them using the `PrimitiveBasis` function."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks import PrimitiveBasis\n",
"from pymks.stats import correlate\n",
"\n",
"prim_basis = PrimitiveBasis(n_states=2, domain=[0, 1])\n",
"X_ = prim_basis.discretize(X)\n",
"X_corr = correlate(X_, periodic_axes=[0, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at the two autocorrelations and the cross-correlation for these two microstructures."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(101, 101, 3)\n"
]
},
{
"data": {
"image/png": 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FF9bUqVOtJ554ItbxSJ8sCEI5Y9onv/DCC9aqVaus1tZWa/v27dZ//ud/Ws8++6y9/s47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\nt3lcPKPQ1lb/Mt1o0i+95o3G1LaUKah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uXGivW7ZsGUaPHo1Ro0Zh8eLF2LJlC5555hk8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\nLgw5aWpqwrp163DTTTehuroao0ePxnHHH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hRqampQUVGBk08+GZ/73Ofw0ksvdUXTU6e7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\nK33fOfDcmAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b1d2c2b50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_correlations\n",
"\n",
"print X_corr[0].shape\n",
"\n",
"draw_correlations(X_corr[0])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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zuoGIqJSh9jLVsTAxU2ClD3iZTaidAzP1qjodmSrwj+qzVuub9Cu+YvXfmu7K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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b1d2cc1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"draw_correlations(X_corr[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2-Point statistics provide an object way to compare microstructures, and have been shown as an effective input to machine learning methods."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Predict Homogenized Properties"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this section of the intro, we are going to predict the effective stiffness for two phase microstructures using the `MKSHomogenizationModel`, but we could have chosen any other effective material property. \n",
"\n",
"First we need to make some microstructures and their effective stress values to fit our model. Let's create 200 random instances 3 different types of microstructures, totaling to 600 microstructures."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks.datasets import make_elastic_stress_random\n",
"\n",
"grain_size = [(47, 6), (4, 49), (14, 14)]\n",
"n_samples = [200, 200, 200]\n",
"\n",
"X_train, y_train = make_elastic_stress_random(n_samples=n_samples, size=(51, 51),\n",
" grain_size=grain_size, seed=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once again, `X_train` is our microstructures. Throughout PyMKS `y` is used as either the prpoerty or the field we would like to predict. In this case `y_train` is the effective stress values for `X_train`. Let's look at one of each of the three different types of microstructures."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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/Oj2/tFoYaZSUpU/ay303ZQHRfh+D3bK3txcnJyexuroaL7/8cuzu7sb09HRERPzDP/xD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\nAACgZ/4fR2DQAZWM47AAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b073fb3d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"draw_microstructures(X_train[::200])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `MKSHomogenizationModel` uses 2-point statistics, so we need provide a discretization method for the microstructures by providing a basis function. We will also specify which correlations we want."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks import MKSHomogenizationModel\n",
"\n",
"prim_basis = PrimitiveBasis(n_states=2, domain=[0, 1])\n",
"homogenize_model = MKSHomogenizationModel(basis=prim_basis,\n",
" correlations=[(0, 0), (1, 1), (0, 1)])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's fit our model with the data we created."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"homogenize_model.fit(X_train, y_train, periodic_axes=[0, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's make some new data to see how good our model is."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_samples = [10, 10, 10]\n",
"X_test, y_test = make_elastic_stress_random(n_samples=n_samples, size=(51, 51),\n",
" grain_size=grain_size, seed=100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will try and predict the effective stress of our `X_test` microstructures."
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y_pred = homogenize_model.predict(X_test, periodic_axes=[0, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `MKSHomogenizationModel` generates low dimensional representations of microstructures and regression methods to predict effective properties. Take a look at the low dimensional representations."
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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xZdbGnj17+O233ygsLCQgIIDExERuv/126fyFCxdYt24dp0+fRq/XExwcTGJi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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b077280d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_components\n",
"\n",
"draw_components(homogenize_model.fit_data, homogenize_model.predict_data, \n",
" label_1='Training Data', label_2='Testing Data')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's look at a goodness of fit plot for our `MKSHomogenizationModel`."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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BRaFQ4OXl5bKE8IwZM5w/W61WOnfuzKJFizh37hzdunWjQ4cOSKVSfH19azxb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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b076c3810>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_goodness_of_fit\n",
"\n",
"fit_data = np.array([y_train, \n",
" homogenize_model.predict(X_train, periodic_axes=[0, 1])])\n",
"pred_data = np.array([y_test, y_pred])\n",
"\n",
"draw_goodness_of_fit(fit_data, pred_data, ['Training Data', 'Testing Data'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks good.\n",
"\n",
"The `MKSHomogenizationModel` can be used to predict effective properties and processing-structure evolutions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Predict Local Properties"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this section of the intro, we are going to predict the local strain field in a microstructure using `MKSLocalizationModel`, but we could have predicted another local property.\n",
"\n",
"First we need some data, so let's make some."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks.datasets import make_elastic_FE_strain_delta\n",
"\n",
"X_delta, y_delta = make_elastic_FE_strain_delta()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once again, `X_delta` is our microstructures and `y_delta` is our local strain fields. We need to discretize the microstructure again so we will also use the same basis function."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymks import MKSLocalizationModel\n",
"\n",
"prim_basis = PrimitiveBasis(n_states=2)\n",
"localize_model = MKSLocalizationModel(basis=prim_basis)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use the data to fit our `MKSLocalizationModel`."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"localize_model.fit(X_delta, y_delta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we have fit our model, we will create a random microstructure and compute its local strain field using finite element analysis. We will then try and reproduce the same strain field with our model."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from pymks.datasets import make_elastic_FE_strain_random\n",
"\n",
"X_test, y_test = make_elastic_FE_strain_random()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at the microstructure and its local strain field."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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C/7wsqvPZRTEIAAAcwW3jtDpOQDEIAAAcwSWKQSsUgwAAwBHc1IKWKAYBAIAj8DWxNYpB\nAADgCBSD1totBk2vZxuta7/auS5rTU3Ndz6PnWu/2nnOfD6fccbO2v7R2HnfmF6fOVqvp533s53r\nU0fT0peLjcZ73ObXpf2iKMM409jYaDT+1dfMr+W76nPz389hteaPf3Cq2XWWJem5C80zMw92M85s\nGWp+PePkZK9xZsOGKqPxodBB4zn69DG/ZvDp+8w/Oz6trDDOPNeww3ye4jeMM6+WPmicaZLhdaMP\nphiNpxi0RmcQAAA4AgeQWKMYBAAAjkBn0BrFIAAAcASKQWsUgwAAwBEoBq1RDAIAAEfgPIPW3Kd6\nAQAAADh16AwCAABHsHN6MSegGAQAAI7g5tQyligGAQCAI3AAiTWKQQAA4AgUg9YoBgEAgCNQDFqj\nGAQAAI7AASTWvvViMBAwv9i6z+czzlRXV0dlnpqaGqPx6enpxnPY0dxsfkHzaDx+u/PYed/YYed5\nM31N7XzY2Hn80Zonmn7+zv8Yjd/96GrjOf5P8WTjzJKf/ZfR+HmvFxrP8cLcF40z3YuuM86cm3K6\ncaZ492nGmcTYWOPM9OlPGWd+9z9zjTNvvvk3o/GNjUeM59i4catx5ro7rjLOHEk0jqjX7//XODOo\nYLRxpv7LeuPMjh11RuMTEzPVI6/j4zmAxBqdQQAA4AicdNoaxSAAAHAE9hm0RjEIAAAcoTMWg4sX\nL9bWrVuVlZWlqVOnRm6vr6/X/Pnz1djYqIKCAuXl5Wnt2rVasmSJkpKSNGfOHEnSmjVr9NJLL8nl\ncumCCy7QlVdeqYaGBj300EMKh8OKj4/XXXfdpS5dTl7ycTk6AADgCC6XK6o/7amqqtKhQ4dUVFSk\nxsZGVVZWRrYtX75cU6ZM0YwZM7Rs2TJJkt/v1wMPPNDiPjIzM1VcXKzi4mKtWbNGoVBI69atU05O\njgoLC9WvXz+tW7euzXXQGQQAAI7Q2Q4g2bJliwYPHixJysvLU3l5uXJyciQdPeDP7/dLkjwej8Lh\nsBISElrdR48ePSJ/jomJkdvtVlJSkoLBoCQpFAopKSmpzXXQGQQAAI7gdrmi+tOeYDAoj8cjSfJ6\nvZECTpKampoifz5xm5W1a9eqV69e8ng88vv92rp1q+6++25VVVVFisqToTMIAAAc4VTsM1hSUhL5\nc25urnJzcyN/93q9CofDko528I7v/LndX/frwuGwEhNPfh6hnTt36k9/+pOmT58uSXrvvfc0dOhQ\nXXXVVXrllVe0atUqjRw58qR5ikEAAOAIp+Kk0wUFBSfd5vf7VVpaqvz8fG3cuFGjR399Pkefz6fy\n8nL5fD6Fw+FIB/FE4XBYCxcu1G233aa4uLjIbccKy6SkJIVCoTbXyNfEAADAEdyu6P60JysrS3Fx\ncSosLFRMTIxycnK0aNEiSdL48eP1/PPPq7i4WBMmTJB09ICTuXPnKhAIqLi4WA0NDVqxYoVqa2v1\n2GOPqaioSLt27dJFF12kv/zlLyoqKtIHH3ygiy66qM110BkEAACO0NkOIJHU4nQykjRt2jRJUmpq\nqmbNmtViW3Z2tmbOnNnitgkTJkSKxePdd999HV4DxSAAAHCEzniewc6AYhAAADgCxaC1dotB0wvb\n29k503QOu/NUV1cbZ3w+n3HGVE1NjXEmPT3dOHP8YeodZefx23me7TyeaL1v7Mxjys66mpubjTN2\nnmdTKSkpqqszu9j8MRMberQ/6DhfFYxuf9AJhnXtbpzx3XeT0fjaD7Yaz3HhnZcaZw41HjHOnHf+\nT4wzz759v3GmwcbnzapVjxhnBpx1s3HmobfmGI1/7d9fNp5j8uRRxpny9z81zvTvb/4Z7fP1Ms6U\nln5snHGPsPHvZ7zZ8IzYBuUZjD8VB5D8PaAzCAAAHIHOoDWKQQAA4Aid8QCSzoBiEAAAOEJHTvfi\nRBSDAADAEfia2BrFIAAAcAQOILFGMQgAAByBzqA1ikEAAOAIFIPWKAYBAIAjcDSxNYpBAADgCHQG\nrVEMAgAAR+AAEmsUgwAAwBE4z6A1ikEAAOAIfE1srd1i0Oczu9B0TU2N8SLS09ONM51VIBAwzthp\nW9uZx/S1lOy9nnY02biofVpamnHGznNt+hzYeT9HY1122Xmv2bWhh9n74J1H3jCe48yxucaZnJzv\nGY0fNDjbeI5F28qMM8G3Ko0zt/5kvHHm/T+uNs5szU00zjS+9KlxpumI+WfH5dn9jMZP+v0vjefY\nf+SwcSa79zXGmZqaEuPM+B9ebJz55S+fMM4k/uhc40zf92uNxncbECf17/h4DiCxRmcQAAA4Ap1B\naxSDAADAETiAxBrFIAAAcAQ6g9YoBgEAgCNQDFqjGAQAAI7AASTWKAYBAIAjcJ5BaxSDAADAETiA\nxBrFIAAAcAT2GbRGMQgAAByBYtAaxSAAAHAEDiCxRjEIAAAcgc6gNYpBAADgCJ3xAJLFixdr69at\nysrK0tSpUyO319fXa/78+WpsbFRBQYHy8vK0du1aLVmyRElJSZozZ44kac2aNXrppZfkcrl0wQUX\n6Morr2zzfq20Www2NZldBDw9Pd1ovF2BQMA409zcbJwxfTzRevx23tA1NTXGGZ/PZ5yx89rYydh5\nru28B0yfg2g9z3ZE43cgJSVFdXV1xvNI0iS/wRXnJV1b8m/GcyzfUm6cCa+oMBpfVbXDeI5bfnWD\ncaZHj0zjTNeuccaZquaQceYPk+83zjz9erFx5rXXPjTOTLx8utH4h1+413iOAd26G2fWrHnSOJOX\nN804c+OzPzXO9O9v/nlbPGK0cWavz+yzIza2r9H4znZqmaqqKh06dEhFRUX63e9+p8rKSuXk5EiS\nli9frilTpsjn8+n+++9XXl6e/H6/HnjggUghKEmZmZkqLi6Wy+XS7Nmz9f3vf19ffvnlSe/Xivs7\nf6QAAACdgNvliupPe7Zs2aLBgwdLkvLy8lRe/vV/VgOBgPx+vzwejzwej8LhsBISEtSlS8s+Xo8e\nPSINopiYGLnd7jbv1/J5MXoWAQAA/k655YrqT3uCwaA8Ho8kyev1KhgMRrYd/83sidusrF27Vr16\n9ZLH42nzfq2wzyAAAHCEU3EASUlJSeTPubm5ys3Njfzd6/UqHA5LkkKhkBISEiLb3O6v+3XhcFiJ\niYknnWPnzp3605/+pOnTp7d7v1YoBgEAgCOcigNICgoKTrrN7/ertLRU+fn52rhxo0aP/no/S5/P\np/Lycvl8PoXD4Uin70ThcFgLFy7Ubbfdpri4uHbv1wpfEwMAAEfobPsMZmVlKS4uToWFhYqJiVFO\nTo4WLVokSRo/fryef/55FRcXa8KECZKOHnAyd+5cBQIBFRcXq6GhQStWrFBtba0ee+wxFRUVadeu\nXZb32xY6gwAAwBE643kGTzzty7RpR48QT01N1axZs1psy87O1syZM1vcNmHChEix2Nb9toViEAAA\nOEJnLAY7A4pBAADgCOwbZ41iEAAAOEJnvAJJZ0AxCAAAHIGvia1RDAIAAEegGLT2rReDdq59ake0\nrpm7fft244ypaFwvV2p5AsuOsnOdXTvsrC0ar020ROs90Nmfs88P7DcanxzX1XiOPm2cuPVkBv/k\nB0bj5/xsofEc3fYdMc4kpyYbZ5Yvf984U3FmvHEmI6OXceaT9z4xzkyebH7929jYGKPx7p3m12Z+\n63+rjTNVVV8YZ84/f4Bx5khzU/uDTlD4zN3GmSd+/UfjzLZtXxqNHzZslH72s7EdHk8xaI3OIAAA\ncISOXCLOiSgGAQCAI3AAiTWKQQAA4Ah8TWyNYhAAADiCm1rQEsUgAABwBDqD1igGAQCAI3AAiTWK\nQQAA4AgcQGKNYhAAADgCXxNboxgEAACOQDFojWIQAAA4AsWgNYpBAADgCC4OILFEMQgAAByB8wxa\na7cYNL2wfXNzs/EifD6fcaampsY4Y2dt6enpRuPtHKkUCASikonWa/OPtjZTdh6LnfdNdXW1caaz\nPmfH7PnY7DHF9DjNeI552//XOPNzd4bR+CNNTcZz/KVhj3Hm80rzz8GuXx0wznzvb2HjTEVDg3Fm\nSx/z/sTbb5u/nvv3mz2eUT8abTzHit9/ZJzJzu5jnBk8uJ9x5rP9+40zG1782DiTdEV/48wZ/2P2\nHjj99BSj8XxNbI3OIAAAcASKQWsUgwAAwBEoBq1RDAIAAEfgABJrFIMAAMAR6AxaoxgEAACOQDFo\njWIQAAA4AqeWsUYxCAAAHIHOoDWKQQAA4Ah2zunqBBSDAADAEdyd8GjixYsXa+vWrcrKytLUqVMj\nt9fX12v+/PlqbGxUQUGB8vLytHbtWi1ZskRJSUmaM2eOJGnr1q1asGCBDh48qEcffVSSVFFRoSVL\nlsjlciknJ0c333xzm2twf2ePDgAAACdVVVWlQ4cOqaioSI2NjaqsrIxsW758uaZMmaIZM2Zo2bJl\nkiS/368HHnigxX1873vf07//+7+re/fukdt69uypwsJCzZkzR3v37m33qm10BgEAgCN0tn0Gt2zZ\nosGDB0uS8vLyVF5erpycHElHLwXq9/slSR6PR+FwWAkJCa3uw+PxtLqtW7dukT936dJFMTExba6D\nziAAAHAEt8sV1Z/2BIPBSDHn9XoVDAYj25qOu8b5ids6qrq6Wvv27VPfvn3bHPetdwYzMswu6C6p\n3falFZ/PF5V5mpubv9PxkpSenm6cCQQCxhk7a7OTscPOTr3V1dXGmbS0NOOMKTuPxc57087vWjSe\ns5SUFNXV1RnPI0kLF/7JaPyPH51mPMeo1xuMM59P9BqNr6mpNZ4j1GC+rsE9exlnhv9sqHFm8hX3\nGWf69u3e/qATNBz3j19Hud3mPY309J5G4x+543fGcyx9scg4U1G+3ThzeqbZY5Gkmf/6pHHms/H9\njDOZpVuMMxkTzzYa3z3O7PPpVHQGS0pKIn/Ozc1Vbm5u5O9er1fhcFiSFAqFWnT+jn9vh8NhJSYm\nGs174MABLVq0SHfddVe7Y/maGAAAOMKpOJq4oKDgpNv8fr9KS0uVn5+vjRs3avTo0ZFtPp9P5eXl\n8vl8CofDll8Hn8yRI0c0f/583XjjjTrttNPaHc/XxAAAwBHcUf5pT1ZWluLi4lRYWKiYmBjl5ORo\n0aJFkqTx48fr+eefV3FxsSZMmCDp6AEnc+fOVSAQUHFxsRoaGlRXV9fitl27dmn16tWqrKzUM888\no6KiIpWXl7e5DjqDAADAETrbASSSWpxORpKmTTu6+0tqaqpmzZrVYlt2drZmzpzZ4rbu3bu3uq1n\nz54aMWJEh9dAMQgAAByhMxaDnQHFIAAAcASKQWsUgwAAwBG4HJ01ikEAAOAInfFydJ0BxSAAAHAE\nvia2RjEIAAAcgWLQGsUgAABwBDe1oCWKQQAA4AgcQGKNYhAAADgCB5BYczU3Nze3NSAmJsboDqur\nq40X4fP5jDPtLNuSnf8RmM5jZ46amhrjjJ3nLFpr68z/87LzvonGHNH6HTj+wucdZec90LdvX+OM\nJM1YVWg0ftvjfzGe47+XTDfONDc1GY0/4rLx2rjMX5vqfXuNM+POu904s3r9k8aZlTXbjDPvzHvD\nOBMXF2ucSUvraTS+tnaP8RyXXjrMOLNzp/k8X35Zb5y55KaLjTPbbLzX0hKTjDNPFj5rNH7o0BG6\n5ZZfdnh85VcvmS7pG8npNiGq89lFZxAAADgCB5BYoxgEAACOQDFojWIQAAA4QmfejelUohgEAACO\nwAEk1igGAQCAI3CeQWsUgwAAwBHYZ9AaxSAAAHAEikFrFIMAAMAROIDEGsUgAABwBDqD1igGAQCA\nI3A0sTWKQQAA4Ah0Bq1RDAIAAEfg1DLWXM3tXO3edGdLt9v8Yus1NTXGmXaWbcnn8xlnAoGAccaU\nnR1am5qajDN2Hv/27duNM9F6bey8b6Ixj505qqurjTOd9TlLSUlRXV2d8TyS9NynC4zGx8fEGs9R\nUlhinDnnXL/R+KpBycZzdH2t0jiTmnqacWb//pBx5qKLBhlnfvL5R8aZG7fFG2c++GCTcWbBizOM\nxg/Pmmo8x+bPnzPODMm60TizbJ3Z74wkvfH4G8aZT87rZpw59Pga48xdj//EaHyKO03DfJd2ePyB\nhv8xXdK0wXvkAAAXEElEQVQ3khjb8bWdSnQGAQCAI/A1sTWKQQAA4AgcQGKNYhAAADgCnUFrFIMA\nAMARKAatUQwCAABH4Aok1igGAQCAI3TGzuDixYu1detWZWVlaerUqZHb6+vrNX/+fDU2NqqgoEB5\neXlau3atlixZoqSkJM2ZM0eSdOTIES1cuFC7du3S0KFDdfXVV0fu489//rM++uijyNiTMT8PDAAA\nwN+j5ubo/rSjqqpKhw4dUlFRkRobG1VZ+fUpppYvX64pU6ZoxowZWrZsmSTJ7/frgQceaHEfa9as\nUVpamubMmaNPP/1UX331lSSpoaFB1dXVHeqGUgwCAABHaGpqjupPe7Zs2aLBgwdLkvLy8lReXh7Z\nFggE5Pf75fF45PF4FA6HlZCQoC5dWn6pW1FRoUGDjp4LdODAgdqyZYsk6a233tKoUaM6dO5fikEA\nAOAITU1NUf1pTzAYlMfjkSR5vV4Fg8EWaz3mxG3HC4VCio+Pj4wLhUJqbGzUJ598ooEDB3boeWGf\nQQAA4Agd6dZ920pKvr7qUW5urnJzcyN/93q9CofDko4WdQkJCZFtx1/RLRwOKzEx0fL+jxWAx+6j\nd+/eeu+99zRixIgOr5FiEAAAOIKdS7l+UwUFBSfd5vf7VVpaqvz8fG3cuFGjR4+ObPP5fCovL5fP\n51M4HI50EK3uY9OmTerXr582b96sESNG6NVXX9Xq1atVWlqqQCCgFStW6Ac/+MFJ10ExCAAAHOFU\ndAbbkpWVpbi4OBUWFiozM1M5OTlatGiRpk2bpvHjx2vBggU6fPhwpKCsqqrSM888o0AgoOLiYt17\n770655xz9OGHH2rWrFkaOnSounXrpuuvvz4yR2FhYZuFoCS5mtvZs9D0nDx2zuETCASMMz6fzzhT\nU1NjnInGOYk6snPnidLT06Myz/Ft6o6y83raWZud1yYa89j5n6ed97Mddl6btLQ0o/EpKSmqr683\nnkeSntzwW6PxCV3ijOd44idPGGd+9uStRuM3P/dX4zl69041znz44SfGmfXrK9sfdIJnVv6Hcebd\ngPnnbbONf6jL/3u1caZfv75G4+PjuxrPsXfvAePMtm1fGmcGDswyztSd3d04c1ZqD+PMP1/4S+PM\nHz4y+wxIcadpmO/SDo/fv/810yV9I0lJ46I6n110BgEAgCN0ts5gZ0ExCAAAHOFU7DP494BiEAAA\nOAKdQWsUgwAAwBHoDFqjGAQAAI5AZ9AaxSAAAHAEOoPWKAYBAIAj0Bm0RjEIAAAcgc6gNYpBAADg\nCHQGrVEMAgAAR6AzaI1iEAAAOAKdQWsUgwAAwBHoDFpzNTc3t1kmu91uozusqTG/OHlGRoZxxs48\ndvh8PqPxgUDgO1pJS3be0Onp6d/BSlozfc9I9l5P09dGsvf6tPMr0kq0nmc7j8XlchlnTB+/JPXt\n29c4I0n/tOIuo/Hxr1QZz7F/XJZxJvujeqPxq1ZtMJ7jgWd/YZz55ysKjTMjRuQZZ/bvDxlnsv/5\nQuNMj/h448wZ3VKNMz8aNd1o/Iq/LTCe4+c/vN84Y+d37bfP/tI4s3DdGuPM4MoG40zXrnHGmYQE\nj9H4Xr36a+TI6zo8/rPPnjZd0jdy5pk3RnU+u+gMAgAAR6AzaI1iEAAAOAL7DFqjGAQAAI5AZ9Aa\nxSAAAHAEOoPWKAYBAIAj0Bm0RjEIAAAcgc6gNYpBAADgCHQGrVEMAgAAR6AzaI1iEAAAOAKdQWsU\ngwAAwBHoDFqjGAQAAI5AZ9AaxSAAAHAEOoPW2i0GA4HAd74IOxfndrlc38FKWqupqTEab+ex+Hw+\n44zpuqLJzv+87DwH1dXVxpm0tDTjjOl7zc5rk56eHpVMNKSkpKiurs5Wtv/6A0bjt7vNPwc+3rnD\nOHN+z95G42+++TLjObZ9UG6c6do11jgz+z//r3Gme8IVxpll/3a1cWZAag/jzBdBs/eMJL3xt0eN\nxg/1/dB4jrKyp40zDcnm/Zk7b3rQODPzyZ8ZZ4aMNvsdkKRAzU7jTGyPBLPAYbP3DJ1Ba3QGAQCA\nI9AZtEYxCAAAHKEzdgYXL16srVu3KisrS1OnTo3cXl9fr/nz56uxsVEFBQXKy8tTOBzWvHnzFAwG\ndckll2jkyJEKhUJ65JFHdOjQIQ0bNkzjxo2TJL377rt677331NTUpNtvv12pqaknXYP7u36QAAAA\nnUFTU3NUf9pTVVWlQ4cOqaioSI2NjaqsrIxsW758uaZMmaIZM2Zo2bJlkqSVK1dqxIgRKioq0sqV\nK9XY2Kg333xTI0eOVGFhocrKyrR//37V19errKxMM2fOVGFhYZuFoEQxCAAAHKKpqSmqP+3ZsmWL\nBg8eLEnKy8tTefnX+w4HAgH5/X55PB55PB6Fw2FVVFRo0KBBcrvdysjI0I4dO1RbWxvZ7z4tLU2V\nlZVav369mpqaNHfuXC1atKjdtVAMAgAAR+hsncFgMCiPxyNJ8nq9CgaDx6316wLu2LZQKCSv19vi\ntj59+uiTTz5RU1OTysrKFAwGtXfvXjU2NmrmzJnq2rWr1qxZ0+Y62GcQAAA4wqnYZ7CkpCTy59zc\nXOXm5kb+7vV6FQ6HJUmhUEgJCV8fTe12f92vC4fDSkhIUHx8vEKhkJKTkyO3jRkzRk8++aQ+/vhj\npaSk6LTTTlMwGNRZZ50lSRo4cKAqKyt13nnnnXSNFIMAAMARTsXRxAUFBSfd5vf7VVpaqvz8fG3c\nuFGjR4+ObPP5fCovL5fP51M4HFZ8fLz8fr82btyo/Px8bdu2TX379lVMTIxuv/12NTU16ZFHHtGZ\nZ56pxMRErVy5UpK0detW9erVq801UgwCAABH6GxHE2dlZSkuLk6FhYXKzMxUTk6OFi1apGnTpmn8\n+PFasGCBDh8+HCkox4wZo3nz5mnFihUaO3asYmJiVFVVpaeffloul0vjx49XbGysMjMzFRcXp6Ki\nIiUlJemqq65qcx0UgwAAwBE643kGjz+djCRNmzZNkpSamqpZs2a12BYfH6977723xW3Z2dkqLCxs\ndb833nhjh9dAMQgAAByhs3UGOwuKQQAA4AidsTPYGVAMAgAAR6AzaM3V3NzcZpkcExNjdIc1NTXG\ni0hLSzPOuFzmF6i3w3SeQCBgPEc7L8G3Jj093Thj5/W0M4+d13P79u3GGTsfBKaP5/jTAXRUdXW1\ncebYSUZN2Hl/2tG3b19bufe3LzEaf98NvzGeY8JvrzfO3DFkmNH4YEOD8RxfBA8YZy4d+lPjzEUX\n5RlnXC7z93TyzUONM+tnv2qcmfX0nebz7NppNP69ua8Yz5GR0fbRm1b8/5RvnLklz/x5zhv4T8aZ\n0fOvM87E/bmy/UEn8Hq7Go3PzT1fN9zw8w6Pf+65maZL+kamTJkb1fnsojMIAAAcga+JrVEMAgAA\nR+BrYmsUgwAAwBHoDFqjGAQAAI5AZ9AaxSAAAHAEOoPWKAYBAIAj0Bm0RjEIAAAcgc6gNYpBAADg\nCHQGrVEMAgAAR6AzaI1iEAAAOAKdQWsUgwAAwBHoDFprtxg0vWZqtK5LG61r5nZW0Xosdq6za+f6\nt3Yej51rWtth+v60897szExfm5SUFNXV1dma66ZRvzQa/8L75tcm3ri71jhz/fXFRuPzfv594zlS\nunqMM/v2hYwzf/jDSuPM3vDrxpmSz8qMM+tsXKf9zcdKjTNjb73EaPyUx+4yniMhNcE48/Z282uU\n//IXTxhnevVKMc4kxZldM1iSnn3xPePMH1Y/aDT+NJfZddDpDFqjMwgAAByBzqA1ikEAAOAIdAat\nUQwCAABHoDNojWIQAAA4Ap1BaxSDAADAEegMWqMYBAAAjkBn0BrFIAAAcAQ6g9YoBgEAgCPQGbRG\nMQgAAByBzqA1ikEAAOAIdAatUQwCAABHoDNojWIQAAA4QmfsDC5evFhbt25VVlaWpk6dGrm9vr5e\n8+fPV2NjowoKCpSXl6dwOKx58+YpGAzqkksu0ciRI7Vv3z7NmzdPR44cUa9evXTrrbeqoaFBDz30\nkMLhsOLj43XXXXepS5eTl3ztFoMul8voQTXbuNC4HT6fLyrzRIPpcyxJNTU1xhk7z5md1zMjI8M4\ns337duOMnbXZeQ5Mn+tozBFNps/zN/kMaDpilq0/FDaeoyDrTOPMTUsGGo1//4vPjecor68zzgwd\neoZxJi2tp3Hmwf941jhTf1Ef48z69ZXGmaeWFxpnXljwZ6PxAV8v4zleTtlvnGl4aq1xZvL91xln\n/vKXjcaZi9PNP9f+lOgxzsQY/nvoktn4ztYZrKqq0qFDh1RUVKTf/e53qqysVE5OjiRp+fLlmjJl\ninw+n+6//37l5eVp5cqVGjFihIYPH66ioiINHz5c77//vkaNGqWRI0fqiSeeUHV1tWpra5WTk6NJ\nkyZp2bJlWrdunc4999yTrsMdrQcMAABwKjU1NUX1pz1btmzR4MGDJUl5eXkqLy+PbAsEAvL7/fJ4\nPPJ4PAqHw6qoqNCgQYPkdruVkZGhHTt2KCkpSaFQSJIUDoeVkJCgpKQkBYNBSVIoFFJSUlKb66AY\nBAAAjtDU1BzVn/YEg0F5PEc7qF6vN1LAHV3r18XksW2hUEher7fFbeeff75KS0t15513KjY2Vj16\n9JDf79fWrVt19913q6qqSn6/v811sM8gAABwhFOxz2BJSUnkz7m5ucrNzY383ev1Khw+urtLKBRS\nQkJCZJvb/XW/7ljHLz4+XqFQSMnJyZHbXn75ZU2ePFkXXHCBFi1apLKyMu3cuVNDhw7VVVddpVde\neUWrVq3SyJEjT7pGikEAAOAIp2KfwYKCgpNu8/v9Ki0tVX5+vjZu3KjRo0dHtvl8PpWXl8vn80UO\nBPH7/dq4caPy8/O1bds29enTR+FwWImJiZIU+cr4WKF4/G1toRgEAACO0NmOJs7KylJcXJwKCwuV\nmZmpnJwcLVq0SNOmTdP48eO1YMECHT58OFJQjhkzRvPmzdOKFSs0duxYdenSRZdddpkWLlyopUuX\nKikpSRMnTlQ4HNbDDz+sVatWqUuXLvqXf/mXNtdBMQgAAByhsx1NLKnF6WQkadq0aZKk1NRUzZo1\nq8W2+Ph43XvvvS1u69Wrl4qKilrclpiYqPvuu6/Da6AYBAAAjtDZOoOdBcUgAABwhM7YGewMKAYB\nAIAj0Bm0RjEIAAAcgc6gNYpBAADgCHQGrVEMAgAAR6AzaK3dYjA9Pd3oDl2GF5mWpJqaGuOM6brs\nam42e+OkpaV9Rys5Ney8ntXV1caZaL2edpg+B3b+5+nzmV8E3s7vjZ15tm/fbpyx66W/PmQ0PjGu\nq/Ecwy+8zTiz/L3fGI3v5U1of9AJ+nVLMc5c/Gjb5w6zsnZthXFmzNhzjDM7mg4aZypHDDLO/GRS\nsXHm9dfvNxrf0HjEeI6u2yuNMz9b/bRx5hrjhDT3+XuMMzfm/6txZl35EuNMwRXTjcZ///uX6+zZ\nYzo8ns6gNTqDAADAEegMWqMYBAAAjkBn0BrFIAAAcAQ6g9YoBgEAgCPQGbRGMQgAAByBzqA1ikEA\nAOAIdAatUQwCAABHoDNojWIQAAA4Ap1BaxSDAADAEegMWqMYBAAAjkBn0BrFIAAAcAQ6g9YoBgEA\ngCPQGbT2rReDNTU1xpmMjAzjTCAQMM6kp6cbZ6LBznPm8/miMo+d58zOa2Mn09xs/j88O89bNNh5\nLG632zhTXV1tnDF9D6SkpKiurs54HkmKMXxMV+X/i/Ecv/7zfcaZK4ebzfPnvzxsPEdPr9c4U3Za\nyDjz51dXG2dWnHbAOLPn8Y+MMw//4R7jzM+vv98484c/lBqND4UPGs/RkN/XOJOXl22c6Z2QYJyp\nOxg2zlx1Zb5xZv5/vmCc+e8/zTEa727saTSezqA1OoMAAMAR6AxaoxgEAACOQGfQGsUgAABwBDqD\n1igGAQCAI9AZtEYxCAAAHIHOoDWKQQAA4Ah0Bq1RDAIAAEegM2iNYhAAADhCZ+wMLl68WFu3blVW\nVpamTp0aub2+vl7z589XY2OjCgoKlJeXp3A4rHnz5ikYDOqSSy7RyJEjtW/fPs2bN09HjhxRr169\ndOutt7Z5v1bMz1oLAADwd6ipqSmqP+2pqqrSoUOHVFRUpMbGRlVWVka2LV++XFOmTNGMGTO0bNky\nSdLKlSs1YsQIFRUVaeXKlWpsbNT777+vUaNGafbs2XK73aqurm7zfq1QDAIAAEdoamqO6k97tmzZ\nosGDB0uS8vLyVF5eHtkWCATk9/vl8Xjk8XgUDodVUVGhQYMGye12KyMjQzt27FBSUpJCoaNXIwqH\nw0pISGjzfq1QDAIAAEfobJ3BYDAoj8cjSfJ6vQoGgy3WesyxbaFQSN7/f+nKY7edf/75Ki0t1Z13\n3qnY2Fj16NGjzfu1wj6DAADAEU7FPoMlJSWRP+fm5io3Nzfyd6/Xq3D46LWiQ6GQEo671vTx158/\n1vGLj49XKBRScnJy5LaXX35ZkydP1gUXXKBFixaprKyszfu10m4xGAgEOvhw7WtuNn9x3IYXtJek\n7du3G2dM2XksPp8vKvNkZGQYZ6qrq40zaWlpxhk7XC6XcaampsY4Y/r62Hmf2Xk97TzPdp6zaHwG\nHLPyD+8Zjc/O7mM8x6a6XcaZ3LMyjca/8azZ45CkPn26G2fi4mKNM/1uvcg4c2lGtnEm4anzjTP5\nZ0w1zrz66v3GmYoKs9/R8eMvNJ7j9jseMc4MLbzCOFP56kbjTMUW88+o/DsuMc7sPXTIOPPOSx8a\njU9LG6iMS0Z0ePypOJq4oKDgpNv8fr9KS0uVn5+vjRs3avTo0ZFtPp9P5eXl8vl8CofDio+Pl9/v\n18aNG5Wfn69t27apT58+CofDSkxMlCQlJSUpHA63eb9W6AwCAABH6GxHE2dlZSkuLk6FhYXKzMxU\nTk6OFi1apGnTpmn8+PFasGCBDh8+HCkox4wZo3nz5mnFihUaO3asunTpossuu0wLFy7U0qVLlZSU\npIkTJyomJqbV/baFYhAAADhCZzzP4ImnfZk2bZokKTU1VbNmzWqxLT4+Xvfee2+L23r16qWioqJ2\n77ctFIMAAMAROltnsLOgGAQAAI7QGTuDnQHFIAAAcAQ6g9YoBgEAgCPQGbRGMQgAAByBzqA1ikEA\nAOAIdAatUQwCAABHoDNojWIQAAA4Ap1BaxSDAADAEegMWqMYBAAAjkBn0Jqrubm5zTJ5x44d3/ki\n2lmCJZfL9R2spDXTtaWnp39HK2mppqbGOOPz+Ywz27ebX9Dczutph5157DwHpvO43W7jOey8nmlp\nacYZO0x/11JSUlRXV2drrquvvtBo/JQpY4znSE5OMM787W/lRuPr6/cbzxEbF2OcaR7XzzhTs2+v\ncSZ+WYVx5uAkv3Fm98PvG2f69etrnHG5zH5HN22qMp7jzbd+a5z5yxefG2eSYuOMMzd+/972B53g\nx0//1Dgz5PTexplgw2Gj8d1j0nVBxg86PD4pyWu6pG9k//5QVOezi84gAABwBDqD1igGAQCAI7DP\noDWKQQAA4Ah0Bq2Z79wEAACAfxh0BgEAgCPwNbE1ikEAAOAIfE1sjWIQAAA4wpEjFINW2GcQAADA\nwSgGAQAAHIxiEAAAwMEoBgEAAByMA0i+ZXl5ead6CSfVmdcWLXaeg2hcm9iOaL2eptcmTk5Otj1X\nenqW0fjExB7Gc8THxxtnunfvYzQ+NjZoPEeXLjauTdzV/PE3xXuMM137mF0vVpIOx/cyziRk5Bhn\nevc+3Thj+p4OBs1/pxsbbDzPSjLOdGmONc6cccaZxpmULqnGGTuPp8nVYDQ+zmX++4zWXM2m/9IB\nAADgHwZfEwMAADgYxSAAAICDUQwCAAA4GMUgAACAg1EMAgAAOBjFIAAAgIP9P+MjHnFEYyYiAAAA\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b0745b8d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_microstructure_strain\n",
"\n",
"draw_microstructure_strain(X_test[0], y_test[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's pass that same microstructure to our `MKSLocalizationModel` and compare the predicted and computed local strain field."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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IiIgUiTf+2BabTCIiIlIkjmTaFptMIiIiUiQ2mbbFJpOIiIgUiU2mbbHJJCIiIkXiczJt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\ny2EAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1b074e5610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pymks.tools import draw_strains_compare\n",
"\n",
"\n",
"y_pred = localize_model.predict(X_test)\n",
"draw_strains_compare(y_test[0], y_pred[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not bad.\n",
"\n",
"The `MKSLocalizationModel` can be used to predict local properties and local processing-structure evolutions."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}