Variables-and-Gradients.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Dependencies\n",
    "import torch\n",
    "\n",
    "# A Variable is a wrapper around a Tensor that allows Accumulation of Gradients\n",
    "from torch.autograd import Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Defining a Variable**\n",
    "\n",
    "1. In the code below, we define a Variable using PyTorch. We give it the tensor of (3,3) Ones. \n",
    "2. Then we set the \"requires_grad\" flag to True. \n",
    "3. Setting this flag to true means that this Variable is trainable and when we do a backpropagation on this Variable, we'll see the gradients being updated and the change in weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]], requires_grad=True)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define a Variable\n",
    "a = Variable(torch.ones(3,3), requires_grad=True)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Not a Variable\n",
    "torch.ones((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]], requires_grad=True)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define a Variable\n",
    "b = Variable(torch.ones(3,3), requires_grad=True)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[5., 5., 5.],\n",
      "        [5., 5., 5.],\n",
      "        [5., 5., 5.]], grad_fn=<ThAddBackward>)\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[5., 5., 5.],\n",
       "        [5., 5., 5.],\n",
       "        [5., 5., 5.]], grad_fn=<ThAddBackward>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Variables behave similar to Tensors\n",
    "print(a*3 + b*2)\n",
    "print(\"\\n\")\n",
    "torch.add(a*3,b*2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[3., 3.],\n",
       "        [3., 3.]], requires_grad=True)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define a Variable from a Tensor\n",
    "x = Variable(torch.ones(2,2) * 3, requires_grad=True)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take an equation:\n",
    "\n",
    "    z = 2 x^2 + 9x\n",
    "\n",
    "The derivative of this will be:\n",
    "\n",
    "    dz/dx = 4x + 9\n",
    "\n",
    "Now, the value of derivative (gradient) for x = 3 is:\n",
    "\n",
    "    Gradient:   dz/dx = 12 + 9 = 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# New Variable using Previous Variable\n",
    "z = 2 * (x * x) + 9 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[45., 45.],\n",
       "        [45., 45.]], grad_fn=<ThAddBackward>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the Gradients using Backpropagation\n",
    "# The backprop will be computed w.r.t some values, so we provide ones(2,2)\n",
    "# So, the calculation becomes: d/dx.\n",
    "z.backward(torch.ones(2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[21., 21.],\n",
       "        [21., 21.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the Gradients of x\n",
    "x.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The computed gradient values match with the ones we derived above."
   ]
  }
 ],
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