{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton_armijo(\n",
    "    f, grad, hess, x,\n",
    "    step = 1.0,\n",
    "    sigma = 0.1,\n",
    "    eta = 0.1,\n",
    "    epsilon = 1e-6,\n",
    "    return_niter = False,\n",
    "    tau = 0.1,\n",
    "    theta = 0.1\n",
    "    ):\n",
    "\n",
    "    g_k = grad( x )\n",
    "\n",
    "    niter = 0\n",
    "\n",
    "    while np.linalg.norm( g_k ) > epsilon:\n",
    "\n",
    "        step_k = step\n",
    "\n",
    "        d_k = np.linalg.solve( hess( x ), -g_k )\n",
    "        d_k_g_k = d_k @ g_k\n",
    "        if d_k_g_k > -tau * np.linalg.norm( g_k ) * np.linalg.norm( d_k ):\n",
    "            d_k = -g_k\n",
    "            d_k_g_k = d_k @ g_k\n",
    "        elif np.linalg.norm( d_k ) < theta * np.linalg.norm( g_k ):\n",
    "            d_k = -g_k\n",
    "            d_k_g_k = d_k @ g_k\n",
    "\n",
    "        f_k = f( x )\n",
    "\n",
    "        x_try = x - step_k * g_k\n",
    "        while f( x_try ) > f_k + sigma * step_k * d_k_g_k:\n",
    "            step_k = step_k * eta\n",
    "            x_try = x - step_k * g_k\n",
    "\n",
    "        x = x_try\n",
    "        g_k = grad( x )\n",
    "\n",
    "        niter = niter + 1\n",
    "\n",
    "    if return_niter:\n",
    "        return ( x, niter )\n",
    "    else:\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rosenbrock( x, a = 100, b = 1 ):\n",
    "\n",
    "    return a * ( x[ 1 ] - x[ 0 ] ** 2 ) ** 2 + ( x[ 0 ] - b ) ** 2\n",
    "\n",
    "def rosenbrock_grad( x, a = 100, b = 1 ):\n",
    "\n",
    "    return np.array(\n",
    "        (\n",
    "            -400 * ( x[ 1 ] - x[ 0 ] ** 2 ) * x[ 0 ] + 2 * ( x[ 0 ] - 1 ),\n",
    "            200 * ( x[ 1 ] - x[ 0 ] ** 2 )\n",
    "        )\n",
    "    )\n",
    "\n",
    "def rosenbrock_hess( x, a = 100, b = 1 ):\n",
    "\n",
    "    return np.array(\n",
    "        (\n",
    "            ( -400 * ( x[ 1 ] - x[ 0 ] ** 2 ) + 800 * x[ 0 ] ** 2 + 2, -400 * x[ 0 ] ),\n",
    "            ( -400 * x[ 0 ], 200 )\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([1., 1.]), 833)\n"
     ]
    }
   ],
   "source": [
    "print( newton_armijo( rosenbrock, rosenbrock_grad, rosenbrock_hess, np.zeros( ( 2, ) ), epsilon = 1e-10, return_niter = True ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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