Predict.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import re\n",
    "from IPython.display import display, Math, Latex, Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load properties file, result files created by predict() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "imgs = np.load('pred_imgs.npy')\n",
    "preds = np.load('pred_latex.npy')\n",
    "properties = np.load('properties.npy').tolist()\n",
    "displayPreds = lambda Y: display(Math(Y.split('#END')[0]))\n",
    "idx_to_chars = lambda Y: ' '.join(map(lambda x: properties['idx_to_char'][x],Y))\n",
    "#displayIdxs = lambda Y: display(Math(''.join(map(lambda x: properties['idx_to_char'][x],Y))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare Image display function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import PIL.Image\n",
    "from cStringIO import StringIO\n",
    "import IPython.display\n",
    "import numpy as np\n",
    "def showarray(a, fmt='png'):\n",
    "    a = np.uint8(a)\n",
    "    f = StringIO()\n",
    "    PIL.Image.fromarray(a).save(f, fmt)\n",
    "    IPython.display.display(IPython.display.Image(data=f.getvalue()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display original Input image, predicted latex tokens and render the corresponding result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original (Input) Image: 1\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAF0UlEQVR4nO1XbWhcVRp+zrn3zmSS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\nRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "2 f ^ { 2 } - 4 f ^ { 2 } - g ^ { 2 } ( 1 - \\Gamma ) \\, , \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$2 f ^ { 2 } - 4 f ^ { 2 } - g ^ { 2 } ( 1 - \\Gamma ) \\, , $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 2\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGu0lEQVR4nO1YW2xcVxVd99w7Yzv4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\nXgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\delta | \\Phi ^ { ( n ) } \\rangle \\ = \\ \\ { \\cal Q } \\left| \\Phi ^ { ( n + 1 ) } \\rangle \\; , \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\delta | \\Phi ^ { ( n ) } \\rangle \\ = \\ \\ { \\cal Q } \\left| \\Phi ^ { ( n + 1 ) } \\rangle \\; , $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 3\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGrklEQVR4nO1XbWxT1xl+z712HOcL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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "+ t _ { 2 } e _ { 1 } r _ { 2 } + t _ { 2 } 2 e _ { 2 } r _ { 3 } + t _ { 2 } e _ { 3 } r _ { 4 } \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$+ t _ { 2 } e _ { 1 } r _ { 2 } + t _ { 2 } 2 e _ { 2 } r _ { 3 } + t _ { 2 } e _ { 3 } r _ { 4 } $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 4\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAG70lEQVR4nO1YfWyV1Rl/znnf9962\ntPQrZUWcBeKcMF0YCiOTBm1BlBWMBpZtmXFxm2OWKVJgFWEtyOxqE4hmk2WajRgXHVMX1qzFAi24\nKiP7Yx/ZH0xbSFwpK+XSL3o/zsfz2x/3bXvp120Hxrr0l9w/zj3POe/ze57f+zznvAL0/wH3k3Yg\nOUBEIqmV+JRkhGUSg2smYllK+3HmFb2O4RxCkqRcK5GkkRqyZAgiuGM6BCMIguAkbgnRd3t7vlhQ\nsYydcbefsB9jeCdrNzVe/ml0AuGQrue6rjd2YIXnup7rer5LWmuttdAZ628//dcFj5sk2w+Jgq2X\nOAEjxw8BEZGVr7+0sDi/2jHxtYN8RrjL8lQjpYju4FNpo4gERBCR57LT/2OzO+6720oS5Hsj1cmi\n2bT6pcjM8cU1RETKBEsI4U1ANoJyj8zYkpczpv9DlnrBb37+9/TmR9Ru4w2bYymIBD1TX3u08pV7\niqIrrEOsdkaJKOXZFPPPndqrU4EkSR8gYuWfGyoSeFDngWX3JmUCeW93OS0vORpdax0I6tMkpSEK\neMFBE5+InPmvlV+k+Weqnk4ZCFh8SkBSt2u458jpzNfTvkMVXxGBNmf2gF/iXe8BevsXtcEk7wgh\nDoNCamYTH7AOFX+GnIaB8VhgdN0dXLrxrkN3lkLB6jVpN904a+acOTd5VVAjrGkn+kwlhcHDJk6u\nzE/LveHz5zmydJOJhZmLv//obwce8X5xRnVN1u+RxBX4RAw3uYFC39pyNKPwo3X0JGLjrjW2LqOw\nDriS4naBGe2B34UubaK2UMfizVAAMyPU0trS0tpyVqHeq0eYy70wOD5lz7a0trS0ftBe9Oaeqls+\n6AIs7YViXZx/buFG7ldKKYVQR19r65WkPOCXX+vc8eWmMycL2SEilmtOXErbX/mHFXa8dLKMpS8+\nTYim7njhchDG2xHZTyqfLgRpu96vpUOkvVOnBEgg+Ejq7me1cCCf2as9WJcI+pdKgAQtWZh26/vL\n/zYz5hx/qGU2y8ufrUT0x8OflUTkvrQMNwRUFRXBADBopDKO9fdcxVirQdj4P1ato2bEEMOj32DF\nNvLwOcMh2mbDvO8MNBDqHlrOWL4SuLj4nrBlBrpDiXtvXtpdcImBjWmARSgbUDWRwZXMPFyMo8An\ngkVl6Mimk2wAZTaLJhjAgrUeM6eMEBXDAJZr63TUwFyEQo2ogUIMFg3FBfPqWMXbgY7tc7+27yef\n22LBDLN9Xv6GPhufUSYsauBexHvV+StfjLCJ3XfX9jm/sknFdDUEiMjKxpILmWLvrqLj1oGweRxy\nIBLrNnR1h69Cx65ZYx0i7dWUv1B6VS2FcX9U05UFQdap++ob6zoX/DvH34U/yuuJyOwsAkGtbftT\nztdzD+j4WhZNt2W/+IO0y925sf4CCRKvRTdkJpXSMMTLr9hamqUCj+9rfLfQktPYVU7aI8HSPhdb\nUiIkEdyCNsnx51rrr+3hbwqXCOGAqIotKRGCvPDLWQEiYtldsqwktGF5BvvRkHNpBhEZR2iv+lh9\nymuHD8PXvaQiojKinHg7EkTfmszRZzCKgMGxYMjaGPZQEUyM99LzrACGXnHLq4vKWY+aS4VdFAZD\nYecT6+e9uqicNaOLtrECFKro5hseLO8fKrXsa53Rm506f/62WtjBrQxD+ybxsZnASzEMLhGRKXsq\nByJAT/6s8egqiBN5m4WrpdOL5oaic7srUkAi+nTYZ+7YkrXxamadoJXM/ce/ffDNVed2VwSV9wrN\nilv1UlNqtkzo9UM6dbq2bqe8xGOeE1eGSBhPGpIITu+F0kgkEukLPBZoIvfUsVube4Tn3D83PHex\njbH/aniDGHjODPsXR8jgNvpu9lIbY4ig7PJ+KFwiohT3xlwZqYzQyJOFdGbl5dGht8iOmLoWANpu\nGhqKtvCXiCi1aFcp1Ybzz2OHGNmK41qx/au/UHex/XsPmlD+eewQkVDLr4n+cdYAzJdSD4bOrrgz\nakesVSi7ub3zoPdW8iY3SWm5qqDCD47wVOch748fdhw40XjHseJOL127fkj1ENn4hUFQWt3q9bly\n7RuO9dK1C+fD93p3eQ3BxxwSnPv2/oolTzyEkedIl/a4y8TDF3L/JwWNl5Fh6AWAK1fCgOnLfAdb\nKDJWP2KgN9QNcG/mO9hC4WFzIYyeSgBdXUh4168LCLiqaysLGK0BwGhsva009fDYR0cGAM0Ddkpr\npbRf44z/G22ZBvTk69L4GHnVBQkiEAkiRv2RB1aNV9LHsxvnIjSK4q4Vye/sE21Nk29h1xVJvn9Y\nnsCFdxJ2Hx8+Ld+1kuKT1cN1xDSRqYZpIlMN00SmGqaJTDVME5lqmCYy1fBfpb8ZREshPp4AAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\Delta { \\cal L } _ { 0 } = \\left. \\tilde { C } _ { 0 } T e ^ { - 2 T e ^ { - D } } \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\Delta { \\cal L } _ { 0 } = \\left. \\tilde { C } _ { 0 } T e ^ { - 2 T e ^ { - D } } $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 5\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAHOUlEQVR4nO1Ye4xUVx3+zn3szD5m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\nuGqM/AfAAGOyiAfhzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\Psi _ { \\epsilon } ( N _ { L } , \\, A ) = e ^ { i P \\; N _ { L } } \\Psi _ { \\epsilon } ( A ) \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\Psi _ { \\epsilon } ( N _ { L } , \\, A ) = e ^ { i P \\; N _ { L } } \\Psi _ { \\epsilon } ( A ) $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 6\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGx0lEQVR4nO1YW2xcVxVd586dZ+zE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\nHxgh/wFMyxmgsv91CAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "{ \\cal F } ( - \\hat { k } _ { 1 } , - \\hat { k } _ { 1 } ) = { \\cal F } ( \\hat { k } _ { 1 } , \\hat { k } _ { 1 } ) , \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$${ \\cal F } ( - \\hat { k } _ { 1 } , - \\hat { k } _ { 1 } ) = { \\cal F } ( \\hat { k } _ { 1 } , \\hat { k } _ { 1 } ) , $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 7\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGcElEQVR4nO1YbWyV5Rm+nvd53/ZQ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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "M ( n _ { e } , n _ { m } ) = | n _ { e } a + n _ { m } a _ { D } | . \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$M ( n _ { e } , n _ { m } ) = | n _ { e } a + n _ { m } a _ { D } | . $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 8\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAFoElEQVR4nO2YXWwUVRiG3+/MbLvb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\nHt7gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\| \\varphi * f \\| _ { \\infty } \\leq \\| \\varphi \\| _ { 1 } \\| f \\| _ { \\infty } . \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\| \\varphi * f \\| _ { \\infty } \\leq \\| \\varphi \\| _ { 1 } \\| f \\| _ { \\infty } . $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 9\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAFpUlEQVR4nO1YXWwUVRj9ZnfbbrGU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\nIMV37TsXuLwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "[ { \\cal K } _ { 1 } { } ^ { ; { \\cal P } } , { \\cal K } _ { 2 } { \\cal { \\cal P } } ] = - i { \\cal K } _ { 3 } { { \\cdot P } } \\, , \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$[ { \\cal K } _ { 1 } { } ^ { ; { \\cal P } } , { \\cal K } _ { 2 } { \\cal { \\cal P } } ] = - i { \\cal K } _ { 3 } { { \\cdot P } } \\, , $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 10\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAF5ElEQVR4nO2YX2xcxRnFz9y5u5sY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\nIZD5pv8D7zDapKSwQwcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\vec { \\Gamma } _ { \\mu } ( x ) = \\partial _ { \\mu } \\vec { n } ( x ) \\wedge \\vec { n } ( x ) \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\vec { \\Gamma } _ { \\mu } ( x ) = \\partial _ { \\mu } \\vec { n } ( x ) \\wedge \\vec { n } ( x ) $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 11\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGAElEQVR4nO1Ya2xUVRCe+9ht6UMC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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\gamma _ { n } ^ { \\mu } = \\alpha _ { n } ^ { \\mu } + \\tilde { \\alpha } _ { n } ^ { \\mu } , \\quad n \\neq 0 . \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\gamma _ { n } ^ { \\mu } = \\alpha _ { n } ^ { \\mu } + \\tilde { \\alpha } _ { n } ^ { \\mu } , \\quad n \\neq 0 . $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 12\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGs0lEQVR4nO2YW2xUxx3Gvzlz9uL1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\nRK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\hat { R } K _ { 1 } \\hat { R } K _ { 1 } = q ^ { 2 } K _ { 1 } \\hat { R } K _ { 1 } \\hat { R } ^ { - 1 } \\, . \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\hat { R } K _ { 1 } \\hat { R } K _ { 1 } = q ^ { 2 } K _ { 1 } \\hat { R } K _ { 1 } \\hat { R } ^ { - 1 } \\, . $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 13\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGLElEQVR4nO1XbYxcVRl+zr13Zj/a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\nXki9YV5IvWFeSL1hXki9YV5IveE/zHrOUoAzinoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\sigma _ { 4 } ^ { - 1 } \\sigma _ { 3 } ^ { - 1 } \\sigma _ { 2 } \\sigma _ { 1 } = P _ { n + 1 , n + 2 } \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\sigma _ { 4 } ^ { - 1 } \\sigma _ { 3 } ^ { - 1 } \\sigma _ { 2 } \\sigma _ { 1 } = P _ { n + 1 , n + 2 } $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 14\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGk0lEQVR4nO1Ye3BUVx3+zn1sdhPS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\nG0aEDDd8bIT8D1fjaimtxHHTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "f ^ { \\mu } = B ^ { \\mu } e ^ { \\frac { 1 } { 2 } k ( \\sigma - v \\tau ) } + A ^ { \\mu } \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$f ^ { \\mu } = B ^ { \\mu } e ^ { \\frac { 1 } { 2 } k ( \\sigma - v \\tau ) } + A ^ { \\mu } $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 15\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAGUUlEQVR4nO1YXWxUxxX+zty7XgwY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\nAOpHSNUEcw9YAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "j ^ { \\mu a } = ( \\psi _ { + } \\left| \\gamma ^ { \\mu } T ^ { a } \\right| \\psi _ { + } \\right) , \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$j ^ { \\mu a } = ( \\psi _ { + } \\left| \\gamma ^ { \\mu } T ^ { a } \\right| \\psi _ { + } \\right) , $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Original (Input) Image: 16\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAoCAAAAACed+rAAAAHkUlEQVR4nO1YW2xU1xVd59552CWJ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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Latex\n",
      "\\{ \\psi ( { \\bf x } ) , \\psi ^ { \\dagger } ( { \\bf y } ) \\} = \\delta ( { \\bf x - y } ) . \n",
      "\n",
      "Rendering the predicted latex\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\{ \\psi ( { \\bf x } ) , \\psi ^ { \\dagger } ( { \\bf y } ) \\} = \\delta ( { \\bf x - y } ) . $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "batch_size=16\n",
    "from PIL import Image as Img\n",
    "for i in xrange(batch_size):\n",
    "    preds_chars = idx_to_chars(preds[i,1:]).replace('$','')\n",
    "    print \"Original (Input) Image: %d\"%(i+1)\n",
    "    showarray(imgs[i][0])\n",
    "    print \"Predicted Latex\"\n",
    "    print preds_chars.split('#END')[0]\n",
    "    print \"\\nRendering the predicted latex\"\n",
    "    displayPreds(preds_chars)\n",
    "    print \"\\n\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\f",
       "rac{l}{n}\\sigma^{\\prime}(0),$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "displayPreds('\\frac{l}{n}\\sigma^{\\prime}(0),')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}