{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Local Crystallography Analysis for Lattice Atomic Defects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Authors: Artem Maksov, Maxim Ziatdinov*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*_Correspondence to: ziatdinovmax@gmail.com_\n",
    "\n",
    "_Date: 02/28/2018_    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we demonstrate how to study statistically significant deformation of the nearest neighborhood for each extracted defect structure using principal component analysis (PCA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import h5py\n",
    " \n",
    "import numpy as np\n",
    "from scipy import ndimage\n",
    "import cv2\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pylab as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "import pylab as P\n",
    "\n",
    "from keras.models import load_model\n",
    "\n",
    "from scipy.spatial import cKDTree\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structure of the defects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Finding coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use a pretrained convolutional neural network model for atomic coordinates identification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "atomgen = load_model('AtomGen_small5-8.h5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "totdefim = np.load('defim.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "totdefim2 = totdefim[:, :, :].reshape(totdefim.shape[0], totdefim.shape[1], totdefim.shape[2], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "totpred = atomgen.predict(totdefim2).reshape(len(totdefim2), 32, 32, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting coordinates of atoms in all the defect structures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def coord_edges(coordinates, dist_edge):\n",
    "    return [coordinates[0] > target_size[0] - dist_edge, coordinates[0] < dist_edge,\n",
    "            coordinates[1] > target_size[0] - dist_edge, coordinates[1] < dist_edge]\n",
    "    \n",
    "def get_coordinates(input_imgs, decoded_imgs, channel = 0, threshold = 0.75, dist_edge = 0):\n",
    "    d_list = list()\n",
    "    for i in range(input_imgs.shape[0]):\n",
    "        input_img = input_imgs[i,:,:,0]\n",
    "        decoded_img = decoded_imgs[i,:,:,channel]\n",
    "        _,thresh = cv2.threshold(decoded_img, threshold, 1, cv2.THRESH_BINARY) \n",
    "        labels, nlabels = ndimage.label(thresh)\n",
    "        coord = np.array(ndimage.center_of_mass(thresh, labels, np.arange(nlabels)+1))\n",
    "        coord = coord.reshape(coord.shape[0], 2)\n",
    "       \n",
    "        coord_to_rem = [idx for idx, c in enumerate(coord) if any(coord_edges(c, dist_edge))]\n",
    "        coord_to_rem = np.array(coord_to_rem, dtype = int)\n",
    "        coord = np.delete(coord, coord_to_rem, axis = 0)\n",
    "             \n",
    "        d_list.append(coord)\n",
    "                  \n",
    "    return d_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "target_size = (32, 32)\n",
    "atomic_coord = get_coordinates(totdefim2, totpred, channel = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Finding structural elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able to compare structure of the images we need to:\n",
    "    1. Choose fixed origin - in this case it will be the center of extracted image which corresponds to our initial defect coordinate\n",
    "    2. Choose fixed number of atoms to work with - in this case we are going to look at 7\n",
    "    3. Find the average positions of atoms we are going to look at.\n",
    "    4. For each image, find the atomic coordinates corresponding to those.\n",
    "    \n",
    "First, let us look at how the code works:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define center of the image and number of neighbors to look at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "clusters = np.load('clusters.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "imcenter = [15.5, 15.5]\n",
    "nn = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get the average image for a cluster and find the atoms to look at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numcluster = 1\n",
    "cl = totdefim[clusters == numcluster]\n",
    "cla = np.mean(cl, axis=0)\n",
    "cla2 = cla.reshape(1, cla.shape[0], cla.shape[1], 1)\n",
    "clapred = atomgen.predict(cla2).reshape(1, cla.shape[0], cla.shape[0], 2)\n",
    "cla_coord = get_coordinates(cla2, clapred, channel = 1)[0]\n",
    "\n",
    "T = cKDTree(cla_coord)\n",
    "d, ix = T.query(imcenter, nn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x21160911860>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZbGKy8b0LmKxun972jU59b04TXMJPYHQlr+BrWKFf1/cvOcj69EV4bGjbYf5lZPXwZeMq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21162c3c240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig441 = plt.figure(441)\n",
    "ax = fig441.add_subplot(121)\n",
    "ax.imshow(cla)\n",
    "ax.scatter(cla_coord[:, 1], cla_coord[:, 0], c='green')\n",
    "ax.scatter(cla_coord[ix, 1], cla_coord[ix, 0], c='red')\n",
    "ax = fig441.add_subplot(122)\n",
    "ax.imshow(clapred[0,:,:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, for an example of defect from this class, we can find nearest atoms to those of the average image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "T2 = cKDTree(atomic_coord[0])\n",
    "d2, ix2 = T2.query(cla_coord[ix], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x211629e2a20>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZeuiPCyF6hBCbD7P9hxCiUwixPvHnshPrJsOMPxzbTK6RzBP67wBcorH/RErZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21161954c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig442 = plt.figure(442)\n",
    "ax = fig442.add_subplot(121)\n",
    "ax.imshow(cla)\n",
    "ax.scatter(cla_coord[:, 1], cla_coord[:, 0], c='green')\n",
    "ax.scatter(cla_coord[ix, 1], cla_coord[ix, 0], c='red')\n",
    "ax = fig442.add_subplot(122)\n",
    "ax.imshow(totdefim[0])\n",
    "ax.scatter(atomic_coord[0][:, 1], atomic_coord[0][:, 0], c='green' )\n",
    "ax.scatter(atomic_coord[0][ix2, 1], atomic_coord[0][ix2, 0], c='red' )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This allows us to create a matrix of positions of the same atoms in each individual example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ndefs = (clusters == numcluster).sum()\n",
    "coormat = np.zeros(shape=(ndefs, 14))\n",
    "defcount = 0\n",
    "for i in range(len(atomic_coord)):\n",
    "    if clusters[i] == numcluster:\n",
    "        T2 = cKDTree(atomic_coord[i])\n",
    "        d2, ix2 = T2.query(cla_coord[ix], 1)\n",
    "        coormat[defcount, 0:7] = atomic_coord[i][ix2, 1]\n",
    "        coormat[defcount, 7:] = atomic_coord[i][ix2, 0]\n",
    "        defcount += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute mean values to ensure that this worked as planned:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meancoor = coormat.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ErXvcskymics1bCm5ZMZdDgCJMY8MleKykS+qjylb4tlckPVEgQ1wOTIf5bYY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21157765780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig443 = plt.figure(443)\n",
    "ax = fig443.add_subplot(111)\n",
    "ax.imshow(cla)\n",
    "ax.scatter(cla_coord[ix, 1], cla_coord[ix, 0], c='black')\n",
    "for i in range(7):\n",
    "    ax.scatter(meancoor[i], meancoor[i+7], c='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, black dots represent coordinates inferred from the average image, and red dots are the average values for coordinates found in all images of this cluster. As we can see, those 2 sets correspond very closely."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will define a function that will do this analysis automatically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def clustAnalysis(totdefim, clusters, atomic_coord,  atomgen, imcenter, nn, numcluster, thresh=0.5):\n",
    "    \n",
    "    \n",
    "    cl = totdefim[clusters == numcluster]\n",
    "    cla = np.mean(cl, axis=0)\n",
    "    cla2 = cla.reshape(1, cla.shape[0], cla.shape[1], 1)\n",
    "    clapred = atomgen.predict(cla2).reshape(1, cla.shape[0], cla.shape[0], 2)\n",
    "    cla_coord = get_coordinates(cla2, clapred, channel = 1, threshold=thresh)[0]\n",
    "\n",
    "    T = cKDTree(cla_coord)\n",
    "    d, ix = T.query(imcenter, nn)\n",
    "    \n",
    "    ndefs = (clusters == numcluster).sum()\n",
    "    coormat = np.zeros(shape=(ndefs, 14))\n",
    "    defcount = 0\n",
    "    for i in range(len(atomic_coord)):\n",
    "        if clusters[i] == numcluster:\n",
    "            T2 = cKDTree(atomic_coord[i])\n",
    "            d2, ix2 = T2.query(cla_coord[ix], 1)\n",
    "            coormat[defcount, 0:7] = atomic_coord[i][ix2, 1]\n",
    "            coormat[defcount, 7:] = atomic_coord[i][ix2, 0]\n",
    "            defcount += 1\n",
    "            \n",
    "    return cla, cla_coord[ix], coormat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. PCA on structures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perfrom PCA on resulting matrices for each cluster to identify most important variations in those coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cla, cla_coord, coormat = clustAnalysis(totdefim, clusters, atomic_coord,  atomgen, imcenter, nn, 1, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each sample, we subtract center of mass of all atoms from each individual atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "coormat2 = np.zeros_like(coormat)\n",
    "for i, coor in enumerate(coormat):\n",
    "    coormat2[i, 0:7] = coor[0:7] - coor[0:7].mean()\n",
    "    coormat2[i, 7:] = coor[7:] - coor[7:].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use SVD to compute eigenvectors. The first one shows average positions, and later ones show directions of significant variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "U, s, V = np.linalg.svd(coormat2, full_matrices=False)\n",
    "e_vec = s*V.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "colors = ['red', 'blue', 'green', 'black', 'magenta', 'cyan', 'darkviolet', 'darkorange', 'gold', 'pink']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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df+/ujdHFRbQeKCVvM7cxCljh7q+7+05gNiF7qtx9o7s/H53/O7CMcFjDcYRf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\nAUpcGqsCbaO3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21162ae57f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of PCA components to display\n",
    "n_comp = 2\n",
    "fig444 = plt.figure(444, figsize=(5, 5))\n",
    "ax = fig444.add_subplot(111)\n",
    "ax.axis([-620, 620, - 620, 620])\n",
    "scale = 5\n",
    "for i in range(7):\n",
    "    ax.scatter(e_vec[i, 0], e_vec[i+7, 0], c='k')\n",
    "        \n",
    "    for i2 in range(n_comp):\n",
    "        P.arrow(e_vec[i, 0], e_vec[i + 7, 0], \n",
    "            scale * (e_vec[i, i2 + 1]), scale *( e_vec[i+7, i2 + 1]), \n",
    "            head_width=5, head_length=10, ec=colors[i2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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