{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What are derivatives?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    \"\"\"Random quadratic\"\"\"\n",
    "    return 3*x ** 2 - 4*x + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fac624994b0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(-10, 10, 0.5)\n",
    "ys = f(xs)\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement a derivative in code, since the actual expression is too difficult:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0029999999995311555"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 10 ** -3\n",
    "x = 2/3\n",
    "(f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    }
   ],
   "source": [
    "a = 2.0\n",
    "b = -3.0\n",
    "c = 10.0\n",
    "d = a*b + c\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d1 4.0\n",
      "d2 4.0002\n",
      "slope 2.0000000000042206\n"
     ]
    }
   ],
   "source": [
    "h = 0.0001\n",
    "\n",
    "# Random inputs\n",
    "a = 2.0\n",
    "b = -3.0\n",
    "c= 10.0\n",
    "\n",
    "d1 = a*b + c\n",
    "b += h\n",
    "d2 = a*b + c\n",
    "\n",
    "print('d1', d1)\n",
    "print('d2', d2)\n",
    "print('slope', (d2 - d1) /h)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Value object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Value:\n",
    "    def __init__(self, data, _children=(), _op=''):\n",
    "        self.data = data\n",
    "        # Changing this variable doesn't change the loss\n",
    "        self.grad = 0.0\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op\n",
    "        self._backward = lambda: None\n",
    "\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data})\"\n",
    "\n",
    "    def __add__(self, other):\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "        def _backward():\n",
    "            self.grad = 1.0 * out.grad\n",
    "            other.grad = 1.0 * out.grad\n",
    "        out._backward = _backward\n",
    "        return out\n",
    "\n",
    "    def __mul__(self, other):\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward(): \n",
    "            self.grad = other.data * out.grad\n",
    "            other.grad = self.data * out.grad\n",
    "        out._backward = _backward\n",
    "        return out\n",
    "\n",
    "    def tanh(self):\n",
    "        n = self.data\n",
    "        t = (math.exp(2*n) - 1) / (math.exp (2*n + 1))\n",
    "        out = Value(t, (self, ), 'tanh')\n",
    "        def _backward():\n",
    "            # Local derivative \n",
    "            self.grad = (1 - t**2) * out.grad\n",
    "        \n",
    "        out._backward = _backward\n",
    "        return out\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "this is the alternative, and I do think it feels a bit sharper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Value(2.0)\n",
    "b = Value(-3.0)\n",
    "c = Value(10.0)\n",
    "d = a*b + c\n",
    "d._op"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9 (main, Dec 19 2022, 17:35:49) [GCC 12.2.0]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "632cf67f3dc7ae5e2d87dcad018c0f1b1cd2d0aa8b91fc5df1dd41dbdb2fa25c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}