Steepest.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(x, 0)\n",
    "\n",
    "def f(A, x, b):\n",
    "    residual = relu(np.dot(A, x) - b)\n",
    "    return np.linalg.norm(residual)**2\n",
    "\n",
    "def grad_f(A, x, b):\n",
    "    residual = relu(np.dot(A, x) - b)\n",
    "    return 2 * np.dot(np.transpose(A), residual)\n",
    "\n",
    "def calculate_alpha(f, x_k, A, b):\n",
    "    \"\"\"\n",
    "    Calculate the step size alpha using the formula:\n",
    "    alpha = (g_k.T @ g_k) / (g_k.T @ Q @ g_k)\n",
    "    where g_k is the gradient of the function f at x_k, and Q = g_k^2.\n",
    "\n",
    "    Parameters:\n",
    "    f (function): The objective function.\n",
    "    x_k (np.ndarray): The current point.\n",
    "\n",
    "    Returns:\n",
    "    float: The calculated step size alpha.\n",
    "    \"\"\"\n",
    "    # Calculate the gradient g_k at x_k\n",
    "    g_k = grad_f(A, x_k, b)\n",
    "    \n",
    "    # Calculate Q as the square of the gradient\n",
    "    Q = np.outer(g_k, g_k)\n",
    "    \n",
    "    # Calculate the numerator and denominator\n",
    "    numerator = np.dot(np.transpose(g_k), g_k)\n",
    "    denominator = np.dot(np.transpose(g_k), np.dot(Q, g_k))\n",
    "    \n",
    "    # Ensure the denominator is not zero to avoid division by zero\n",
    "    if denominator == 0:\n",
    "        raise ValueError(\"The denominator for calculating alpha is zero.\")\n",
    "    \n",
    "    alpha = numerator / denominator\n",
    "    return alpha\n",
    "\n",
    "def steepest_descent(f, grad_quadratic, x0, A, b, tol=0.7, max_iter=4000):\n",
    "    x = x0\n",
    "    minimum_values = []  # List to store the minimum values in each iteration\n",
    "    for i in range(max_iter):\n",
    "        gradient = grad_quadratic(A, x, b)  # Pass A and b to grad_quadratic\n",
    "        if np.linalg.norm(gradient) < tol:\n",
    "            print(\"Converged after\", i, \"iterations.\")\n",
    "            return x, minimum_values\n",
    "        alpha = calculate_alpha(f, x, A, b)\n",
    "        x = x - alpha * gradient\n",
    "        minimum_values.append(f(A, x, b))  # Append the minimum value to the list\n",
    "    print(\"Did not converge after\", max_iter, \"iterations.\")\n",
    "    return x, minimum_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Did not converge after 4000 iterations.\n",
      "Minimum: [[ 2.27204685]\n",
      " [-0.8565484 ]\n",
      " [ 0.51985982]\n",
      " [-0.52797471]\n",
      " [-0.86881327]\n",
      " [-0.00963642]\n",
      " [ 0.13760148]\n",
      " [ 2.90575775]\n",
      " [-0.18537329]\n",
      " [-1.13076241]\n",
      " [ 0.27527136]\n",
      " [-2.07463403]\n",
      " [-0.08782086]\n",
      " [ 0.01761694]\n",
      " [ 0.79253686]\n",
      " [ 0.96831396]\n",
      " [-0.50218332]\n",
      " [-0.15022234]\n",
      " [-0.76401704]\n",
      " [-1.1262625 ]\n",
      " [ 0.30903257]\n",
      " [-1.26860727]\n",
      " [-0.41894396]\n",
      " [-0.99123183]\n",
      " [ 0.55481226]\n",
      " [ 1.794149  ]\n",
      " [-1.30127535]\n",
      " [-1.84966215]\n",
      " [-0.1241033 ]\n",
      " [ 0.01716279]\n",
      " [ 0.21887644]\n",
      " [-0.44563109]\n",
      " [-0.19775223]\n",
      " [ 0.37055715]\n",
      " [ 1.03868968]\n",
      " [-1.95964992]\n",
      " [-0.36484919]\n",
      " [ 0.21593285]\n",
      " [-0.9152903 ]\n",
      " [ 1.7307132 ]\n",
      " [-0.63455853]\n",
      " [-0.04281206]\n",
      " [ 0.55575538]\n",
      " [-0.59277707]\n",
      " [-1.84160832]\n",
      " [-0.42705292]\n",
      " [ 1.02467775]\n",
      " [-0.33554192]\n",
      " [-0.84599383]\n",
      " [ 0.92448458]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = int(input(\"please enter n\")) \n",
    "n = int(input(\"please enter m\"))\n",
    "\n",
    "# Generate random A, x, and b\n",
    "np.random.seed(42)\n",
    "A = 10 * (np.random.randn(m, n) - np.random.randn(m, n))\n",
    "x_true = np.random.randn(n, 1) - np.random.randn(n, 1)\n",
    "b = np.dot(A, x_true) + 0.01 * np.eye(m).dot(np.maximum(np.dot(A, x_true) - np.random.randn(m, 1), 0))\n",
    "\n",
    "# Initial guess\n",
    "x0 = np.random.randn(n, 1)\n",
    "\n",
    "d = -grad_f(A, x0, b)\n",
    "minimum, minimum_values = steepest_descent(f, grad_f, x0, A, b)\n",
    "print(\"Minimum:\", minimum)\n",
    "\n",
    "# Plot the changes in the minimum value\n",
    "plt.plot(range(len(minimum_values)), minimum_values)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Minimum Value')\n",
    "plt.title('Changes in Minimum Value')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}