Newton.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy.linalg as la\n",
    "import scipy.optimize as sopt\n",
    "import matplotlib.pyplot as pt\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "\n",
    "def f(x):\n",
    "    return np.exp(x[0] + 3 * x[1] - 0.1) +np.exp(x[0] - 3 * x[1] - 0.1) + np.exp(- x[0] - 0.1)\n",
    "\n",
    "def df(x):\n",
    "    dfx1 = np.exp(x[0] + 3 * x[1] - 0.1) +np.exp(x[0] - 3 * x[1] - 0.1) - np.exp(- x[0] - 0.1)\n",
    "    dfx2 = 3 * np.exp(x[0] + 3 * x[1] - 0.1) - 3 * np.exp(x[0] - 3 * x[1] -0.1)\n",
    "    return  np.array([dfx1, dfx2]) \n",
    "\n",
    "def ddf(x):\n",
    "    dfx11 = np.exp(x[0] + 3 * x[1] - 0.1) +np.exp(x[0] - 3 * x[1] - 0.1) - np.exp(- x[0] - 0.1)\n",
    "    dfx12 = 3 * np.exp(x[0] + 3 * x[1] - 0.1) - 3 * np.exp(x[0] - 3 * x[1] -0.1)\n",
    "    dfx21 = 3 * np.exp(x[0] + 3 * x[1] - 0.1) - 3 * np.exp(x[0] - 3 * x[1] -0.1)\n",
    "    dfx22 = 9 * np.exp(x[0] + 3 * x[1] - 0.1) - 9 * np.exp(x[0] - 3 * x[1] -0.1)\n",
    "    return np.array([[dfx11, dfx12], [dfx21, dfx22]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "final step size : 1.9244817692775262e-15\n"
     ]
    }
   ],
   "source": [
    "t = 1\n",
    "count = 1\n",
    "x0 = np.array([-1.3,1.3])\n",
    "dx0 = np.array([.1, 0.05])  #arbitrary descent direction \n",
    "a = 0.1\n",
    "b = 0.7\n",
    "\n",
    "\n",
    "def backtrack(x0, df, t, a, b, count):\n",
    "    \n",
    "    while (np.any(f(x0 + t * dx0) > f(x0) + a*t*df(x0)*dx0.T)):\n",
    "        t *= b\n",
    "        \n",
    "        count += 1\n",
    "    return t\n",
    "\n",
    "t = backtrack(x0, df, t, a, b,count)\n",
    "\n",
    "print(\"\\nfinal step size :\",  t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "1\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "2\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "3\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "4\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "5\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "6\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "7\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "8\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "9\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "10\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "11\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "12\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "13\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "14\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "15\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "16\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "17\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "18\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "19\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "20\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "21\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "22\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "23\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "24\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "25\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "26\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "27\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "28\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "29\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "30\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "31\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "32\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "33\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "34\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "35\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "36\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "37\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "38\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "39\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "40\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "41\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "42\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "43\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "44\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "45\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "46\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "47\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "48\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "49\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "50\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "51\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "52\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "53\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "54\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "55\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "56\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "57\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "58\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "59\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "60\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "61\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "62\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "63\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "64\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "65\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "66\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "67\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "68\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "69\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "70\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "71\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "72\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "73\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "74\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "75\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "76\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "77\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "78\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "79\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "80\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "81\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "82\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "83\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "84\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "85\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "86\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "87\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "88\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "89\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "90\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "91\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "92\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "93\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "94\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "95\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "96\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "97\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "98\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "99\n",
      "[ 8.86736863 36.5325071 ] [[-1.51322437e-13 -2.56845970e-12]\n",
      " [-6.23430495e-13 -7.70537910e-12]] 2.2880594276545232e-10 [-13.40885676 -23.0929488 ] [[  -78.63022645 -1334.62407504]\n",
      " [ -323.94720751 -4003.87222512]]\n",
      "100\n",
      "[-2.3  1.3]\n"
     ]
    }
   ],
   "source": [
    "def NGS(f,df,theta,H=None,mode=0,eps=1e-12,max_iter=1e2):\n",
    "     \n",
    "        x_pre=x_cur=theta=x0\n",
    "        g=df(x_cur)\n",
    "        \n",
    "        H = ddf(x0)\n",
    "        k=0\n",
    "        while k<max_iter and np.sum(np.abs(g))>eps:\n",
    "            d=-g*H\n",
    "            step = backtrack(x0, df, t, a, b,count)\n",
    "            x_cur = x_pre - np.linalg.inv(ddf(x0)) @ g\n",
    "            s=step*d\n",
    "            y=df(x_cur)-df(x_pre)\n",
    "            ys=np.sum(y*s.T)\n",
    "            print(g, s, ys, y, d)\n",
    "            if abs(ys)<eps:\n",
    "                break\n",
    "            \n",
    "            k+=1\n",
    "            print(k)\n",
    "        return x_cur\n",
    "H = ddf(x0)\n",
    "x_cur = NGS(f, df, H, mode = 0, eps = 1e-12, max_iter= 1e2)\n",
    "print(x_cur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x27fe42add30>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pt.figure()\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "\n",
    "xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]\n",
    "fmesh = f(np.array([xmesh, ymesh]))\n",
    "ax.plot_surface(xmesh, ymesh, fmesh,\n",
    "                alpha=0.3, cmap=pt.cm.coolwarm, rstride=3, cstride=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x27fe3cc1f28>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis(\"equal\")\n",
    "plt.contour(xmesh, ymesh, fmesh, 10)\n",
    "\n",
    "plt.plot(x_cur, \"x-\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comments:\n",
    "\n",
    "The Newton Raphson method converges extremely rapidly to the global solution.\n",
    "\n",
    "Newton's Method takes a long time per iteration and is memory-intensive. Newton's Method requires computing the second derivative, H, which is O(N2), where N is the number of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}