0.1_Gradient Descent

0.1_Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sympy import symbols, Derivative, solve\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting example graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**4.+ 3.*(x**3.) + 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-3, 1.)\n",
    "y = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a5fc4f4e10>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2a5fc4f4e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Gradient discent')\n",
    "plt.plot(x, y, 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### get extreme points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = symbols('x, y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = Derivative(f(x), x).doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2.25000000000000, 0.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate  extreme point\n",
    "extreme = solve(d)\n",
    "extreme # x= 2.25 and x =0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The global optimum is -2.25\n",
      "The local optimum is 0.00\n"
     ]
    }
   ],
   "source": [
    "d2 = Derivative(f(x), x, 2).doit()\n",
    "for i in extreme:\n",
    "    if d2.subs({x:i}) > 0:\n",
    "        print('The global optimum is %.2f' %i)\n",
    "    else : \n",
    "        print('The local optimum is %.2f' %i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### get optimal point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "end at 0.00\n"
     ]
    }
   ],
   "source": [
    "cur_x = 1\n",
    "step_size = 0.01\n",
    "precision = .000001\n",
    "pre_step_size = cur_x\n",
    "\n",
    "while pre_step_size > precision:\n",
    "    pre_x = cur_x\n",
    "    cur_x = pre_x - step_size * d.subs({x:pre_x})\n",
    "    pre_step_size = abs(pre_x-cur_x)\n",
    "print('end at %.2f' %cur_x)"
   ]
  }
 ],
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