minimize-function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimizing a function using mini-autograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from autograd.tensor import Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function\n",
    "def sum_of_squares(x: Tensor) -> float:\n",
    "    return (x * x).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "371.0\n"
     ]
    }
   ],
   "source": [
    "x_1 = Tensor([10, -10, 10, -5, 6, 3, 1], requires_grad=True)\n",
    "y = sum_of_squares(x_1)\n",
    "print(y.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1264.0\n"
     ]
    }
   ],
   "source": [
    "x_2 = Tensor([11, -6, 12, -31, -1, 0, 1], requires_grad=True)\n",
    "y = sum_of_squares(x_2)\n",
    "print(y.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For what value of x is the function sum_of_squares(x) will be minimum ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "439.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = Tensor([12, 0, 11, 5, 8, -9, 2], requires_grad=True) # initialization\n",
    "print(sum_of_squares(x).data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_vals = []\n",
    "\n",
    "for i in range(20):\n",
    "    x.zero_grad()\n",
    "\n",
    "    y = sum_of_squares(x)\n",
    "    y.backward()\n",
    "\n",
    "    delta_x = Tensor(0.1) * x.grad\n",
    "    x = x - delta_x\n",
    "\n",
    "    y_vals.append(y.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(range(1, len(y_vals) + 1), y_vals, marker='o', linestyle='-', color='b', label=\"sum_of_squares(x) per Iteration\")\n",
    "plt.xlabel(\"Iteration\", fontsize=12)\n",
    "plt.ylabel(\"sum_of_squares(x)\", fontsize=12)\n",
    "plt.title(\"Minimization of sum_of_squares (Convergence Plot)\", fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.legend(fontsize=12)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.13835058,  0.        ,  0.12682137,  0.05764608,  0.09223372,\n",
       "       -0.10376294,  0.02305843])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv-3.9.20",
   "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": "3.9.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}