projected_gradient_descent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "701efa6f",
   "metadata": {},
   "source": [
    "# HW4 Report Yufeng Yang"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228ba60c",
   "metadata": {},
   "source": [
    "## Part I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "cc8a44a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f6f14efe",
   "metadata": {},
   "outputs": [],
   "source": [
    "#generate matrix following the rule\n",
    "def matrix_generator(n, epsilon):\n",
    "    A = np.random.normal(0,1,n)\n",
    "    return np.matmul(np.transpose(A), np.transpose(A))+ epsilon*np.identity(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1403a37f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up FW update for quadratic function.\n",
    "def Frank_Wolfe_Quadratic(x, Q, eta):\n",
    "    eq = np.matmul(Q,x)\n",
    "    return (1-eta)*x+eta*(eq/np.linalg.norm(eq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "423480e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Test starts here.\n",
    "np.random.seed(123)\n",
    "n = 50\n",
    "epsilon = 0.6\n",
    "Q = matrix_generator(n, epsilon)\n",
    "lr = 0.1\n",
    "eta = lr\n",
    "x0 = 0.3*np.random.normal(0,0.5,n)\n",
    "max_iter = 1000\n",
    "eig_val, eig_vec = np.linalg.eigh(Q)\n",
    "lambda1 = eig_val.max()\n",
    "count = 0\n",
    "while count < max_iter:\n",
    "    x0 = Frank_Wolfe_Quadratic(x0, Q, eta)\n",
    "    count += 1\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "66071794",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.629531304419418e-12\n"
     ]
    }
   ],
   "source": [
    "# print the 2-norm difference between Qx and \\lambda_{max}x\n",
    "print(np.linalg.norm(np.matmul(Q, x0)-lambda1* x0))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce32539d",
   "metadata": {},
   "source": [
    "## Part II"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "8e26e104",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "58e31ffb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function to generate experimental data.\n",
    "# Input args: m,n are matrix shape; mu and sigma are for noise data.\n",
    "def data_generator(m,n,mu, sigma):\n",
    "    # A is a matrix with size R^{m*n}\n",
    "    \n",
    "    A = np.empty([m,n])\n",
    "    # ground truth \n",
    "    z = np.random.rand(n,1)\n",
    "    # create noise vector with the length equals to m\n",
    "    for i in range(m):\n",
    "        for j in range(n):\n",
    "            A[i,j] = np.random.normal(mu, 1)\n",
    "        norm_A_i = np.linalg.norm(A[i,:],2)\n",
    "        # scale each row of A such that the norm of each row is equal to 1.\n",
    "        A[i,:] = A[i,:]/norm_A_i\n",
    "    delta = np.random.normal(mu, sigma, size=(m,1))\n",
    "    return A, z, delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "1848b995",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute L_{\\infty} norm projection\n",
    "def projection_L_infinity(x):\n",
    "    n_row = np.shape(x)[0]\n",
    "    proj_x = np.zeros((n_row,1))\n",
    "    for indx in range(n_row):\n",
    "        if np.absolute(x[indx]) <=  1:\n",
    "            proj_x[indx] = x[indx]\n",
    "        elif x[indx] <= -1:\n",
    "            proj_x[indx] = -1\n",
    "        else:\n",
    "            proj_x[indx] = 1\n",
    "    return proj_x\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "6ffe6fef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute training loss.\n",
    "def least_square(A,x,b):\n",
    "    residual = np.matmul(A,x)-b\n",
    "    loss = 0.5*np.linalg.norm(residual,2)**2\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8775a209",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function compute gradient\n",
    "def least_square_grad(A,x,b):\n",
    "    residual = np.matmul(A,x)-b\n",
    "    # gradient is A^T(Ax-b)\n",
    "    grad = np.matmul(np.transpose(A),residual)\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a109b761",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify m, n\n",
    "m = 500\n",
    "n = 50\n",
    "# Specify the mean and variance of noise \\delta, which follows normal distribution.\n",
    "mu = 0\n",
    "# This can be changed.\n",
    "sigma = 0.8\n",
    "np.random.seed(123)\n",
    "#####\n",
    "A, z, delta = data_generator(m,n,mu,sigma)\n",
    "# generate observations\n",
    "b = np.matmul(A,z)+delta\n",
    "\n",
    "# generate initial guess\n",
    "x0 = z+np.random.normal(1,1,size = (z.shape[0],z.shape[1]))\n",
    "#print(x0)\n",
    "# specify learning rate\n",
    "lr = 0.1\n",
    "max_iter = 1000\n",
    "count = 0\n",
    "training_loss = np.empty(0)\n",
    "###\n",
    "err = least_square(A,x0,b)\n",
    "training_loss = np.append(training_loss,err)\n",
    "while count < max_iter:\n",
    "    grad = least_square_grad(A,x0,b)\n",
    "    x0 = x0 - lr*grad\n",
    "    x0 = projection_L_infinity(x0)\n",
    "    #print(x0)\n",
    "    err = least_square(A,x0,b)\n",
    "    training_loss = np.append(training_loss,err)\n",
    "    count += 1\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ce05a29d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(training_loss)\n",
    "plt.xlabel('Iteration Number')\n",
    "plt.ylabel('loss function')\n",
    "plt.title('loss function plot')\n",
    "plt.savefig(\"Visualization of loss function\", dpi = 150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "11d1d192",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(training_loss)\n",
    "plt.xlabel('Iteration Number')\n",
    "plt.ylabel('loss function')\n",
    "plt.title('loglog plot for loss function plot')\n",
    "plt.savefig(\"Visualization of loss function\", dpi = 150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c2163cc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}