{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 202 Variable\n",
    "\n",
    "View more, visit my tutorial page: https://morvanzhou.github.io/tutorials/\n",
    "My Youtube Channel: https://www.youtube.com/user/MorvanZhou\n",
    "\n",
    "Dependencies:\n",
    "* torch: 0.1.11\n",
    "\n",
    "Variable in torch is to build a computational graph,\n",
    "but this graph is dynamic compared with a static graph in Tensorflow or Theano.\n",
    "So torch does not have placeholder, torch can just pass variable to the computational graph.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.autograd import Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " 1  2\n",
      " 3  4\n",
      "[torch.FloatTensor of size 2x2]\n",
      "\n",
      "Variable containing:\n",
      " 1  2\n",
      " 3  4\n",
      "[torch.FloatTensor of size 2x2]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tensor = torch.FloatTensor([[1,2],[3,4]])            # build a tensor\n",
    "variable = Variable(tensor, requires_grad=True)      # build a variable, usually for compute gradients\n",
    "\n",
    "print(tensor)       # [torch.FloatTensor of size 2x2]\n",
    "print(variable)     # [torch.FloatTensor of size 2x2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Till now the tensor and variable seem the same.\n",
    "\n",
    "However, the variable is a part of the graph, it's a part of the auto-gradient.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.5\n",
      "Variable containing:\n",
      " 7.5000\n",
      "[torch.FloatTensor of size 1]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "t_out = torch.mean(tensor*tensor)       # x^2\n",
    "v_out = torch.mean(variable*variable)   # x^2\n",
    "print(t_out)\n",
    "print(v_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v_out.backward()    # backpropagation from v_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ v_{out} = {{1} \\over {4}} sum(variable^2) $$\n",
    "\n",
    "the gradients w.r.t the variable, \n",
    "\n",
    "$$ {d(v_{out}) \\over d(variable)} = {{1} \\over {4}} 2 variable = {variable \\over 2}$$\n",
    "\n",
    "let's check the result pytorch calculated for us below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 0.5000  1.0000\n",
       " 1.5000  2.0000\n",
       "[torch.FloatTensor of size 2x2]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variable.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 1  2\n",
       " 3  4\n",
       "[torch.FloatTensor of size 2x2]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variable # this is data in variable format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       " 1  2\n",
       " 3  4\n",
       "[torch.FloatTensor of size 2x2]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variable.data # this is data in tensor format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.],\n",
       "       [ 3.,  4.]], dtype=float32)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variable.data.numpy() # numpy format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we did `.backward()` on `v_out` but `variable` has been assigned new values on it's `grad`.\n",
    "\n",
    "As this line \n",
    "```\n",
    "v_out = torch.mean(variable*variable)\n",
    "``` \n",
    "will make a new variable `v_out` and connect it with `variable` in computation graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.autograd.variable.Variable"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(v_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.FloatTensor"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(v_out.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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