assets/GD/GradientDescent 2 code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "import math\n",
    "import numpy as np \n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eta = .05\n",
    "x0 = 5\n",
    "c_sin = 5\n",
    "title = '$f(x) = x^2 + %dsin(x)$; ' %c_sin\n",
    "title += '$x_0 =  %.2f$; ' %x0\n",
    "title += r'$\\eta = %.2f$ ' % eta \n",
    "file_name = 'gd_14.gif'\n",
    "def grad(x):\n",
    "    return 2*x+ 10*np.cos(x)\n",
    "\n",
    "def grad2(x):\n",
    "    return 2 - 10*np.sin(x)\n",
    "\n",
    "def cost(x):\n",
    "    return x**2 + 10*np.sin(x)\n",
    "\n",
    "\n",
    "\n",
    "def GD_newton(x0):\n",
    "    x = [x0]    \n",
    "    for it in range(100):\n",
    "        g1 = grad(x[-1])\n",
    "        g2 = grad2(x[-1])\n",
    "        if abs(g2) < 1e-3:\n",
    "            break\n",
    "        x_new = x[-1] - g1/grad2(x[-1])\n",
    "        print(grad(x[-1]))\n",
    "        x.append(x_new)\n",
    "    return (x, it)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple Newton method with function x^3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x0 = 5\n",
    "\n",
    "def cost(x):\n",
    "    return x**2 + 10*np.sin(x)\n",
    "\n",
    "def grad(x):\n",
    "    return 2*x + 10*np.cos(x)\n",
    "\n",
    "def myGD1(x0, eta = 0.1):\n",
    "    x = [x0]\n",
    "    for it in range(100):\n",
    "        x_new = x[-1] - eta*grad(x[-1])\n",
    "        if abs(grad(x_new)) < 1e-3:\n",
    "            break\n",
    "        x.append(x_new)\n",
    "    x = np.asarray(x)\n",
    "    return (x, it)\n",
    "\n",
    "def GD_newton(x0):\n",
    "    x = [x0]\n",
    "    for it in range(100):\n",
    "        if abs(cost(x[-1])) < 1e-6 or abs(grad(x[-1])) < 1e-6:\n",
    "            break\n",
    "        x_new = x[-1] - 3*cost(x[-1])/grad(x[-1])\n",
    "        print(x_new, cost(x[-1]), grad(x[-1]))\n",
    "        x.append(x_new)\n",
    "    return (x, it)\n",
    "\n",
    "def Momentum(x0, eta = 0.1, gamma = 0.9):\n",
    "    v = [0]\n",
    "    x = [x0]\n",
    "    for it in range(100):\n",
    "        g = grad(x[-1])\n",
    "        if abs(g) < 1e-6:\n",
    "            break\n",
    "        v_new = gamma*v[-1] + eta*g\n",
    "        x_new = x[-1] - v_new\n",
    "        v.append(v_new)\n",
    "        x.append(x_new)\n",
    "    return (np.asarray(x), v, it)\n",
    "\n",
    "(x, v, it) = Momentum(5, 0.1, 0.9)\n",
    "# print(it, x)\n",
    "\n",
    "# print(GD_newton(x0))\n",
    "\n",
    "# GD_newton(-10)\n",
    "\n",
    "def plot_fn(fn, xmin = -5, xmax = 5, xaxis = True, opts = 'b-'):\n",
    "    x = np.linspace(xmin, xmax, 1000)\n",
    "    y = fn(x)\n",
    "    ymin = np.min(y) - .5\n",
    "    ymax = np.max(y) + .5\n",
    "    plt.axis([xmin, xmax, ymin, ymax])\n",
    "    if xaxis:\n",
    "        x0 = np.linspace(xmin, xmax, 2)\n",
    "        plt.plot([xmin, xmax], [0, 0], 'k')\n",
    "    plt.plot(x, y, opts)\n",
    "# plot_fn(cost, -10, 10)\n",
    "\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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e8NRTMHKkzbWyeHHoiDI3ZQrccw/86U9NX3QjSWJN4qr6vKr+TVWfAGprvz8X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\n/YIncQBVvUVVN1PV1VS1u6p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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb24e4b550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Momentum example\n",
    "import matplotlib.animation as animation\n",
    "from matplotlib.animation import FuncAnimation \n",
    "def viz_alg_1d(x, cost, filename = 'momentum1d2.gif'):\n",
    "#     x = x.asarray()\n",
    "    it = len(x)\n",
    "    y = cost(x)\n",
    "    xmin, xmax = np.min(x), np.max(x)\n",
    "    ymin, ymax = np.min(y), np.max(y)\n",
    "    \n",
    "    xmin, xmax = -4, 6\n",
    "    ymin, ymax = -12, 25\n",
    "    \n",
    "    x0 = np.linspace(xmin-1, xmax+1, 1000)\n",
    "    y0 = cost(x0)\n",
    "       \n",
    "    fig, ax = plt.subplots(figsize=(4, 4))  \n",
    "    \n",
    "    def update(i):\n",
    "        ani = plt.cla()\n",
    "        plt.axis([xmin, xmax, ymin, ymax])\n",
    "        plt.plot(x0, y0)\n",
    "        ani = plt.title('$f(x) = x^2 + 10\\sin(x); x_0 = 5; \\eta = 0.1; \\gamma = 0.9$')\n",
    "        if i == 0:\n",
    "            ani = plt.plot(x[i], y[i], 'ro', markersize = 7)\n",
    "        else:\n",
    "            ani = plt.plot(x[i-1], y[i-1], 'ok', markersize = 7)\n",
    "            ani = plt.plot(x[i-1:i+1], y[i-1:i+1], 'k-')\n",
    "            ani = plt.plot(x[i], y[i], 'ro', markersize = 7)\n",
    "        label = 'GD with Momemtum: iter %d/%d' %(i, it)\n",
    "        ax.set_xlabel(label)\n",
    "        return ani, ax \n",
    "        \n",
    "    anim = FuncAnimation(fig, update, frames=np.arange(0, it), interval=200)\n",
    "    anim.save(filename, dpi = 100, writer = 'imagemagick')\n",
    "    plt.show()\n",
    "    \n",
    "# x = np.asarray(x)\n",
    "(x, v, it) = Momentum(-5, 0.1, .9)\n",
    "viz_alg_1d(x, cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5KmTDZkesimVG0vYZ0W3BdOoEW2zhVSputeuus/7U114bOpL4HX44PP44PPmk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\nbQoDBni9eLIVK2yY/aBB3jf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb24f1a950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## GD example\n",
    "import matplotlib.animation as animation\n",
    "from matplotlib.animation import FuncAnimation \n",
    "def viz_alg_1d_2(x, cost, filename = 'nomomentum1d.gif'):\n",
    "#     x = x.asarray()\n",
    "    it = len(x)\n",
    "    y = cost(x)\n",
    "    xmin, xmax = np.min(x), np.max(x)\n",
    "    ymin, ymax = np.min(y), np.max(y)\n",
    "    xmin, xmax = -4, 6\n",
    "    ymin, ymax = -12, 25\n",
    "    x0 = np.linspace(xmin-1, xmax+1, 1000)\n",
    "    y0 = cost(x0)\n",
    "       \n",
    "    fig, ax = plt.subplots(figsize=(4, 4))  \n",
    "    \n",
    "    def update(i):\n",
    "        ani = plt.cla()\n",
    "        plt.axis([-4 , 6, -13, 26])\n",
    "        plt.plot(x0, y0)\n",
    "        plt.axis([xmin, xmax, ymin, ymax])\n",
    "        ani = plt.title('$f(x) = x^2 + 10\\sin(x); x_0 = 5; \\eta = 0.1$')\n",
    "        if i == 0:\n",
    "            ani = plt.plot(x[i], y[i], 'ro', markersize = 7)\n",
    "        else:\n",
    "            ani = plt.plot(x[i-1], y[i-1], 'ok', markersize = 7)\n",
    "            ani = plt.plot(x[i-1:i+1], y[i-1:i+1], 'k-')\n",
    "            ani = plt.plot(x[i], y[i], 'ro', markersize = 7)\n",
    "        label = 'GD without Momemtum: iter %d/%d' %(i, it)\n",
    "        ax.set_xlabel(label)\n",
    "        return ani, ax \n",
    "        \n",
    "    anim = FuncAnimation(fig, update, frames=np.arange(0, it), interval=200)\n",
    "    anim.save(filename, dpi = 100, writer = 'imagemagick')\n",
    "    plt.show()\n",
    "    \n",
    "# x = np.asarray(x)\n",
    "(x, it) = myGD1(5, 0.1)\n",
    "viz_alg_1d_2(x, cost)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}