step04.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutable struct Variable\n",
    "    data::Array{Float64}\n",
    "end\n",
    "\n",
    "abstract type AbstractFunction end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "call! (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function call!(this::AbstractFunction, input::Variable)\n",
    "    x = input.data\n",
    "    y = forward!(this, x)\n",
    "    output = Variable(y)\n",
    "    return output\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "forward! (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mutable struct Square <: AbstractFunction end\n",
    "\n",
    "function forward!(this::Square, x::Array{Float64})\n",
    "    return x.^2\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "forward! (generic function with 2 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mutable struct Exp <: AbstractFunction end\n",
    "\n",
    "function forward!(this::Exp, x::Array{Float64})\n",
    "    return exp.(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numerical_diff (generic function with 2 methods)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function numerical_diff(f::AbstractFunction, x::Variable, eps=1e-4)\n",
    "    x0 = Variable(x.data .- eps)\n",
    "    x1 = Variable(x.data .+ eps)\n",
    "    y0 = call!(f, x0)\n",
    "    y1 = call!(f, x1)\n",
    "    return (y1.data - y0.data) ./ (2*eps)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 4.000000000004"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = Square()\n",
    "x = Variable([2.0])\n",
    "dy = numerical_diff(f, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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