Gradiend Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "from numpy.polynomial.polynomial import polyval\n",
    "import math\n",
    "sns.set(color_codes=True)\n",
    "sns.set(rc={'figure.figsize':(15,9)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.randint(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.04, -0.03, 0.04]\n"
     ]
    }
   ],
   "source": [
    "p = [random.randint(-5,5) for _ in range(random.randint(3,3))]\n",
    "p = [x/100 for x in p]\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10,10,100)\n",
    "y = polyval(x, p)\n",
    "\n",
    "sns.set()\n",
    "ax = sns.lineplot(x, y, color='skyblue', linewidth=2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.02, -0.05, 0.03]"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: polyval(x, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = math.inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations: 403\n",
      "e  = 0.0\n",
      "x* = -147762253174372.6\n"
     ]
    }
   ],
   "source": [
    "e = math.inf\n",
    "eps = 0.01\n",
    "\n",
    "x0 = -5\n",
    "dx = .01\n",
    "\n",
    "learning_rate = 1\n",
    "\n",
    "\n",
    "x = x0\n",
    "loop_counter = 0\n",
    "while e > eps:\n",
    "    loop_counter = loop_counter + 1\n",
    "    if loop_counter > 10000:\n",
    "        print(1)\n",
    "        break\n",
    "    # Calculate gradiend\n",
    "    df = f(x + dx) - f(x - dx)\n",
    "    df = df/(2*dx)\n",
    "    \n",
    "    new_x = x + learning_rate*df\n",
    "    e = abs(x - new_x)\n",
    "    x = new_x\n",
    "    \n",
    "    \n",
    "    \n",
    "print(\"Iterations: {}\".format(loop_counter))\n",
    "print(\"e  = {}\".format(e))\n",
    "print(\"x* = {}\".format(x))\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x + dx) - f(x - dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "531"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loop_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-144076285599684.06"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-144076285599684.06"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-144076285599684.06"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3021785906401291"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2247/7436"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current point: x = -500\n",
      "Gradient at the point: df = -40.02995999871928\n",
      "New point: x = -459.9700400012807\n",
      "Error at this point: e = 40.02995999871928\n",
      "\n",
      "Current point: x = -459.9700400012807\n",
      "Gradient at the point: df = -36.827563199040014\n",
      "New point: x = -423.1424768022407\n",
      "Error at this point: e = 36.827563199040014\n",
      "\n",
      "Current point: x = -423.1424768022407\n",
      "Gradient at the point: df = -33.881358142934914\n",
      "New point: x = -389.2611186593058\n",
      "Error at this point: e = 33.881358142934914\n",
      "\n",
      "Current point: x = -389.2611186593058\n",
      "Gradient at the point: df = -31.1708494919003\n",
      "New point: x = -358.0902691674055\n",
      "Error at this point: e = 31.1708494919003\n",
      "\n",
      "Current point: x = -358.0902691674055\n",
      "Gradient at the point: df = -28.67718153174792\n",
      "New point: x = -329.4130876356576\n",
      "Error at this point: e = 28.67718153174792\n",
      "\n",
      "Current point: x = -329.4130876356576\n",
      "Gradient at the point: df = -26.383007010736037\n",
      "New point: x = -303.03008062492154\n",
      "Error at this point: e = 26.383007010736037\n",
      "\n",
      "Current point: x = -303.03008062492154\n",
      "Gradient at the point: df = -24.272366449167748\n",
      "New point: x = -278.7577141757538\n",
      "Error at this point: e = 24.272366449167748\n",
      "\n",
      "Current point: x = -278.7577141757538\n",
      "Gradient at the point: df = -22.330577133288898\n",
      "New point: x = -256.4271370424649\n",
      "Error at this point: e = 22.330577133288898\n",
      "\n",
      "Current point: x = -256.4271370424649\n",
      "Gradient at the point: df = -20.544130962662166\n",
      "New point: x = -235.88300607980273\n",
      "Error at this point: e = 20.544130962662166\n",
      "\n",
      "Current point: x = -235.88300607980273\n",
      "Gradient at the point: df = -18.9006004861767\n",
      "New point: x = -216.98240559362603\n",
      "Error at this point: e = 18.9006004861767\n",
      "\n",
      "Current point: x = -216.98240559362603\n",
      "Gradient at the point: df = -17.388552447528127\n",
      "New point: x = -199.5938531460979\n",
      "Error at this point: e = 17.388552447528127\n",
      "\n",
      "Current point: x = -199.5938531460979\n",
      "Gradient at the point: df = -15.99746825195325\n",
      "New point: x = -183.59638489414465\n",
      "Error at this point: e = 15.99746825195325\n",
      "\n",
      "Current point: x = -183.59638489414465\n",
      "Gradient at the point: df = -14.717670791696946\n",
      "New point: x = -168.8787141024477\n",
      "Error at this point: e = 14.717670791696946\n",
      "\n",
      "Current point: x = -168.8787141024477\n",
      "Gradient at the point: df = -13.54025712839757\n",
      "New point: x = -155.33845697405013\n",
      "Error at this point: e = 13.54025712839757\n",
      "\n",
      "Current point: x = -155.33845697405013\n",
      "Gradient at the point: df = -12.457036557975698\n",
      "New point: x = -142.88142041607443\n",
      "Error at this point: e = 12.457036557975698\n",
      "\n",
      "Current point: x = -142.88142041607443\n",
      "Gradient at the point: df = -11.460473633292168\n",
      "New point: x = -131.42094678278227\n",
      "Error at this point: e = 11.460473633292168\n",
      "\n",
      "Current point: x = -131.42094678278227\n",
      "Gradient at the point: df = -10.543635742692459\n",
      "New point: x = -120.87731104008981\n",
      "Error at this point: e = 10.543635742692459\n",
      "\n",
      "Current point: x = -120.87731104008981\n",
      "Gradient at the point: df = -9.700144883254325\n",
      "New point: x = -111.17716615683548\n",
      "Error at this point: e = 9.700144883254325\n",
      "\n",
      "Current point: x = -111.17716615683548\n",
      "Gradient at the point: df = -8.924133292566694\n",
      "New point: x = -102.25303286426879\n",
      "Error at this point: e = 8.924133292566694\n",
      "\n",
      "Current point: x = -102.25303286426879\n",
      "Gradient at the point: df = -8.21020262918637\n",
      "New point: x = -94.04283023508242\n",
      "Error at this point: e = 8.21020262918637\n",
      "\n",
      "Current point: x = -94.04283023508242\n",
      "Gradient at the point: df = -7.553386418862829\n",
      "New point: x = -86.48944381621959\n",
      "Error at this point: e = 7.553386418862829\n",
      "\n",
      "Current point: x = -86.48944381621959\n",
      "Gradient at the point: df = -6.949115505335612\n",
      "New point: x = -79.54032831088398\n",
      "Error at this point: e = 6.949115505335612\n",
      "\n",
      "Current point: x = -79.54032831088398\n",
      "Gradient at the point: df = -6.393186264915585\n",
      "New point: x = -73.1471420459684\n",
      "Error at this point: e = 6.393186264915585\n",
      "\n",
      "Current point: x = -73.1471420459684\n",
      "Gradient at the point: df = -5.881731363729159\n",
      "New point: x = -67.26541068223924\n",
      "Error at this point: e = 5.881731363729159\n",
      "\n",
      "Current point: x = -67.26541068223924\n",
      "Gradient at the point: df = -5.411192854609226\n",
      "New point: x = -61.85421782763001\n",
      "Error at this point: e = 5.411192854609226\n",
      "\n",
      "Current point: x = -61.85421782763001\n",
      "Gradient at the point: df = -4.978297426191602\n",
      "New point: x = -56.87592040143841\n",
      "Error at this point: e = 4.978297426191602\n",
      "\n",
      "Current point: x = -56.87592040143841\n",
      "Gradient at the point: df = -4.580033632095137\n",
      "New point: x = -52.29588676934327\n",
      "Error at this point: e = 4.580033632095137\n",
      "\n",
      "Current point: x = -52.29588676934327\n",
      "Gradient at the point: df = -4.2136309415354845\n",
      "New point: x = -48.082255827807785\n",
      "Error at this point: e = 4.2136309415354845\n",
      "\n",
      "Current point: x = -48.082255827807785\n",
      "Gradient at the point: df = -3.8765404662086667\n",
      "New point: x = -44.20571536159912\n",
      "Error at this point: e = 3.8765404662086667\n",
      "\n",
      "Current point: x = -44.20571536159912\n",
      "Gradient at the point: df = -3.566417228924479\n",
      "New point: x = -40.63929813267464\n",
      "Error at this point: e = 3.566417228924479\n",
      "\n",
      "Current point: x = -40.63929813267464\n",
      "Gradient at the point: df = -3.281103850611089\n",
      "New point: x = -37.35819428206355\n",
      "Error at this point: e = 3.281103850611089\n",
      "\n",
      "Current point: x = -37.35819428206355\n",
      "Gradient at the point: df = -3.0186155425511174\n",
      "New point: x = -34.33957873951243\n",
      "Error at this point: e = 3.0186155425511174\n",
      "\n",
      "Current point: x = -34.33957873951243\n",
      "Gradient at the point: df = -2.777126299150723\n",
      "New point: x = -31.56245244036171\n",
      "Error at this point: e = 2.777126299150723\n",
      "\n",
      "Current point: x = -31.56245244036171\n",
      "Gradient at the point: df = -2.55495619523316\n",
      "New point: x = -29.00749624512855\n",
      "Error at this point: e = 2.55495619523316\n",
      "\n",
      "Current point: x = -29.00749624512855\n",
      "Gradient at the point: df = -2.3505596996145073\n",
      "New point: x = -26.656936545514043\n",
      "Error at this point: e = 2.3505596996145073\n",
      "\n",
      "Current point: x = -26.656936545514043\n",
      "Gradient at the point: df = -2.1625149236434993\n",
      "New point: x = -24.494421621870544\n",
      "Error at this point: e = 2.1625149236434993\n",
      "\n",
      "Current point: x = -24.494421621870544\n",
      "Gradient at the point: df = -1.989513729750314\n",
      "New point: x = -22.50490789212023\n",
      "Error at this point: e = 1.989513729750314\n",
      "\n",
      "Current point: x = -22.50490789212023\n",
      "Gradient at the point: df = -1.8303526313694363\n",
      "New point: x = -20.674555260750793\n",
      "Error at this point: e = 1.8303526313694363\n",
      "\n",
      "Current point: x = -20.674555260750793\n",
      "Gradient at the point: df = -1.6839244208597393\n",
      "New point: x = -18.990630839891054\n",
      "Error at this point: e = 1.6839244208597393\n",
      "\n",
      "Current point: x = -18.990630839891054\n",
      "Gradient at the point: df = -1.5492104671928075\n",
      "New point: x = -17.441420372698246\n",
      "Error at this point: e = 1.5492104671928075\n",
      "\n",
      "Current point: x = -17.441420372698246\n",
      "Gradient at the point: df = -1.4252736298168145\n",
      "New point: x = -16.016146742881432\n",
      "Error at this point: e = 1.4252736298168145\n",
      "\n",
      "Current point: x = -16.016146742881432\n",
      "Gradient at the point: df = -1.311251739432251\n",
      "New point: x = -14.704895003449181\n",
      "Error at this point: e = 1.311251739432251\n",
      "\n",
      "Current point: x = -14.704895003449181\n",
      "Gradient at the point: df = -1.2063516002758234\n",
      "New point: x = -13.498543403173358\n",
      "Error at this point: e = 1.2063516002758234\n",
      "\n",
      "Current point: x = -13.498543403173358\n",
      "Gradient at the point: df = -1.1098434722525141\n",
      "New point: x = -12.388699930920843\n",
      "Error at this point: e = 1.1098434722525141\n",
      "\n",
      "Current point: x = -12.388699930920843\n",
      "Gradient at the point: df = -1.021055994473663\n",
      "New point: x = -11.36764393644718\n",
      "Error at this point: e = 1.021055994473663\n",
      "\n",
      "Current point: x = -11.36764393644718\n",
      "Gradient at the point: df = -0.9393715149164095\n",
      "New point: x = -10.428272421530771\n",
      "Error at this point: e = 0.9393715149164095\n",
      "\n",
      "Current point: x = -10.428272421530771\n",
      "Gradient at the point: df = -0.8642217937220309\n",
      "New point: x = -9.56405062780874\n",
      "Error at this point: e = 0.8642217937220309\n",
      "\n",
      "Current point: x = -9.56405062780874\n",
      "Gradient at the point: df = -0.7950840502246592\n",
      "New point: x = -8.76896657758408\n",
      "Error at this point: e = 0.7950840502246592\n",
      "\n",
      "Current point: x = -8.76896657758408\n",
      "Gradient at the point: df = -0.7314773262070418\n",
      "New point: x = -8.037489251377039\n",
      "Error at this point: e = 0.7314773262070418\n",
      "\n",
      "Current point: x = -8.037489251377039\n",
      "Gradient at the point: df = -0.6729591401102297\n",
      "New point: x = -7.364530111266809\n",
      "Error at this point: e = 0.6729591401102297\n",
      "\n",
      "Current point: x = -7.364530111266809\n",
      "Gradient at the point: df = -0.6191224089020508\n",
      "New point: x = -6.7454077023647585\n",
      "Error at this point: e = 0.6191224089020508\n",
      "\n",
      "Current point: x = -6.7454077023647585\n",
      "Gradient at the point: df = -0.569592616189496\n",
      "New point: x = -6.1758150861752625\n",
      "Error at this point: e = 0.569592616189496\n",
      "\n",
      "Current point: x = -6.1758150861752625\n",
      "Gradient at the point: df = -0.5240252068943185\n",
      "New point: x = -5.651789879280944\n",
      "Error at this point: e = 0.5240252068943185\n",
      "\n",
      "Current point: x = -5.651789879280944\n",
      "Gradient at the point: df = -0.4821031903428086\n",
      "New point: x = -5.169686688938135\n",
      "Error at this point: e = 0.4821031903428086\n",
      "\n",
      "Current point: x = -5.169686688938135\n",
      "Gradient at the point: df = -0.44353493511506414\n",
      "New point: x = -4.726151753823071\n",
      "Error at this point: e = 0.44353493511506414\n",
      "\n",
      "Current point: x = -4.726151753823071\n",
      "Gradient at the point: df = -0.40805214030603665\n",
      "New point: x = -4.318099613517035\n",
      "Error at this point: e = 0.40805214030603665\n",
      "\n",
      "Current point: x = -4.318099613517035\n",
      "Gradient at the point: df = -0.3754079690815315\n",
      "New point: x = -3.942691644435503\n",
      "Error at this point: e = 0.3754079690815315\n",
      "\n",
      "Current point: x = -3.942691644435503\n",
      "Gradient at the point: df = -0.34537533155476474\n",
      "New point: x = -3.5973163128807384\n",
      "Error at this point: e = 0.34537533155476474\n",
      "\n",
      "Current point: x = -3.5973163128807384\n",
      "Gradient at the point: df = -0.31774530503037024\n",
      "New point: x = -3.279571007850368\n",
      "Error at this point: e = 0.31774530503037024\n",
      "\n",
      "Current point: x = -3.279571007850368\n",
      "Gradient at the point: df = -0.2923256806279806\n",
      "New point: x = -2.9872453272223876\n",
      "Error at this point: e = 0.2923256806279806\n",
      "\n",
      "Current point: x = -2.9872453272223876\n",
      "Gradient at the point: df = -0.2689396261777999\n",
      "New point: x = -2.7183057010445877\n",
      "Error at this point: e = 0.2689396261777999\n",
      "\n",
      "Current point: x = -2.7183057010445877\n",
      "Gradient at the point: df = -0.2474244560836114\n",
      "New point: x = -2.4708812449609763\n",
      "Error at this point: e = 0.2474244560836114\n",
      "\n",
      "Current point: x = -2.4708812449609763\n",
      "Gradient at the point: df = -0.22763049959689807\n",
      "New point: x = -2.243250745364078\n",
      "Error at this point: e = 0.22763049959689807\n",
      "\n",
      "Current point: x = -2.243250745364078\n",
      "Gradient at the point: df = -0.20942005962909516\n",
      "New point: x = -2.033830685734983\n",
      "Error at this point: e = 0.20942005962909516\n",
      "\n",
      "Current point: x = -2.033830685734983\n",
      "Gradient at the point: df = -0.19266645485882528\n",
      "New point: x = -1.8411642308761578\n",
      "Error at this point: e = 0.19266645485882528\n",
      "\n",
      "Current point: x = -1.8411642308761578\n",
      "Gradient at the point: df = -0.17725313847008484\n",
      "New point: x = -1.663911092406073\n",
      "Error at this point: e = 0.17725313847008484\n",
      "\n",
      "Current point: x = -1.663911092406073\n",
      "Gradient at the point: df = -0.16307288739247916\n",
      "New point: x = -1.5008382050135938\n",
      "Error at this point: e = 0.16307288739247916\n",
      "\n",
      "Current point: x = -1.5008382050135938\n",
      "Gradient at the point: df = -0.15002705640107528\n",
      "New point: x = -1.3508111486125185\n",
      "Error at this point: e = 0.15002705640107528\n",
      "\n",
      "Current point: x = -1.3508111486125185\n",
      "Gradient at the point: df = -0.13802489188896594\n",
      "New point: x = -1.2127862567235526\n",
      "Error at this point: e = 0.13802489188896594\n",
      "\n",
      "Current point: x = -1.2127862567235526\n",
      "Gradient at the point: df = -0.12698290053783645\n",
      "New point: x = -1.085803356185716\n",
      "Error at this point: e = 0.12698290053783645\n",
      "\n",
      "Current point: x = -1.085803356185716\n",
      "Gradient at the point: df = -0.11682426849485283\n",
      "New point: x = -0.9689790876908633\n",
      "Error at this point: e = 0.11682426849485283\n",
      "\n",
      "Current point: x = -0.9689790876908633\n",
      "Gradient at the point: df = -0.10747832701527016\n",
      "New point: x = -0.8615007606755931\n",
      "Error at this point: e = 0.10747832701527016\n",
      "\n",
      "Current point: x = -0.8615007606755931\n",
      "Gradient at the point: df = -0.09888006085405354\n",
      "New point: x = -0.7626206998215396\n",
      "Error at this point: e = 0.09888006085405354\n",
      "\n",
      "Current point: x = -0.7626206998215396\n",
      "Gradient at the point: df = -0.09096965598572038\n",
      "New point: x = -0.6716510438358192\n",
      "Error at this point: e = 0.09096965598572038\n",
      "\n",
      "Current point: x = -0.6716510438358192\n",
      "Gradient at the point: df = -0.08369208350686441\n",
      "New point: x = -0.5879589603289548\n",
      "Error at this point: e = 0.08369208350686441\n",
      "\n",
      "Current point: x = -0.5879589603289548\n",
      "Gradient at the point: df = -0.07699671682631637\n",
      "New point: x = -0.5109622435026384\n",
      "Error at this point: e = 0.07699671682631637\n",
      "\n",
      "Current point: x = -0.5109622435026384\n",
      "Gradient at the point: df = -0.07083697948022383\n",
      "New point: x = -0.4401252640224146\n",
      "Error at this point: e = 0.07083697948022383\n",
      "\n",
      "Current point: x = -0.4401252640224146\n",
      "Gradient at the point: df = -0.0651700211217951\n",
      "New point: x = -0.3749552429006195\n",
      "Error at this point: e = 0.0651700211217951\n",
      "\n",
      "Current point: x = -0.3749552429006195\n",
      "Gradient at the point: df = -0.05995641943205149\n",
      "New point: x = -0.314998823468568\n",
      "Error at this point: e = 0.05995641943205149\n",
      "\n",
      "Current point: x = -0.314998823468568\n",
      "Gradient at the point: df = -0.055159905877483206\n",
      "New point: x = -0.2598389175910848\n",
      "Error at this point: e = 0.055159905877483206\n",
      "\n",
      "Current point: x = -0.2598389175910848\n",
      "Gradient at the point: df = -0.050747113407287325\n",
      "New point: x = -0.20909180418379747\n",
      "Error at this point: e = 0.050747113407287325\n",
      "\n",
      "Current point: x = -0.20909180418379747\n",
      "Gradient at the point: df = -0.04668734433470323\n",
      "New point: x = -0.16240445984909424\n",
      "Error at this point: e = 0.04668734433470323\n",
      "\n",
      "Current point: x = -0.16240445984909424\n",
      "Gradient at the point: df = -0.04295235678792447\n",
      "New point: x = -0.11945210306116977\n",
      "Error at this point: e = 0.04295235678792447\n",
      "\n",
      "Current point: x = -0.11945210306116977\n",
      "Gradient at the point: df = -0.03951616824489357\n",
      "New point: x = -0.0799359348162762\n",
      "Error at this point: e = 0.03951616824489357\n",
      "\n",
      "Current point: x = -0.0799359348162762\n",
      "Gradient at the point: df = -0.03635487478530208\n",
      "New point: x = -0.04358106003097412\n",
      "Error at this point: e = 0.03635487478530208\n",
      "\n",
      "Current point: x = -0.04358106003097412\n",
      "Gradient at the point: df = -0.03344648480247542\n",
      "New point: x = -0.010134575228498699\n",
      "Error at this point: e = 0.03344648480247542\n",
      "\n",
      "Current point: x = -0.010134575228498699\n",
      "Gradient at the point: df = -0.030770766018282936\n",
      "New point: x = 0.020636190789784237\n",
      "Error at this point: e = 0.030770766018282936\n",
      "\n",
      "Current point: x = 0.020636190789784237\n",
      "Gradient at the point: df = -0.02830910473682058\n",
      "New point: x = 0.048945295526604815\n",
      "Error at this point: e = 0.02830910473682058\n",
      "\n",
      "Current point: x = 0.048945295526604815\n",
      "Gradient at the point: df = -0.026044376357871324\n",
      "New point: x = 0.07498967188447614\n",
      "Error at this point: e = 0.026044376357871324\n",
      "\n",
      "Current point: x = 0.07498967188447614\n",
      "Gradient at the point: df = -0.02396082624923912\n",
      "New point: x = 0.09895049813371526\n",
      "Error at this point: e = 0.02396082624923912\n",
      "\n",
      "Current point: x = 0.09895049813371526\n",
      "Gradient at the point: df = -0.02204396014930665\n",
      "New point: x = 0.12099445828302191\n",
      "Error at this point: e = 0.02204396014930665\n",
      "\n",
      "Current point: x = 0.12099445828302191\n",
      "Gradient at the point: df = -0.0202804433373574\n",
      "New point: x = 0.1412749016203793\n",
      "Error at this point: e = 0.0202804433373574\n",
      "\n",
      "Current point: x = 0.1412749016203793\n",
      "Gradient at the point: df = -0.018658007870375748\n",
      "New point: x = 0.15993290949075506\n",
      "Error at this point: e = 0.018658007870375748\n",
      "\n",
      "Current point: x = 0.15993290949075506\n",
      "Gradient at the point: df = -0.0171653672407443\n",
      "New point: x = 0.17709827673149936\n",
      "Error at this point: e = 0.0171653672407443\n",
      "\n",
      "Current point: x = 0.17709827673149936\n",
      "Gradient at the point: df = -0.0157921378614867\n",
      "New point: x = 0.19289041459298606\n",
      "Error at this point: e = 0.0157921378614867\n",
      "\n",
      "Current point: x = 0.19289041459298606\n",
      "Gradient at the point: df = -0.01452876683256249\n",
      "New point: x = 0.20741918142554855\n",
      "Error at this point: e = 0.01452876683256249\n",
      "\n",
      "Current point: x = 0.20741918142554855\n",
      "Gradient at the point: df = -0.013366465485956103\n",
      "New point: x = 0.22078564691150465\n",
      "Error at this point: e = 0.013366465485956103\n",
      "\n",
      "Current point: x = 0.22078564691150465\n",
      "Gradient at the point: df = -0.012297148247082668\n",
      "New point: x = 0.23308279515858732\n",
      "Error at this point: e = 0.012297148247082668\n",
      "\n",
      "Current point: x = 0.23308279515858732\n",
      "Gradient at the point: df = -0.011313376387309115\n",
      "New point: x = 0.24439617154589643\n",
      "Error at this point: e = 0.011313376387309115\n",
      "\n",
      "Current point: x = 0.24439617154589643\n",
      "Gradient at the point: df = -0.0104083062763341\n",
      "New point: x = 0.25480447782223054\n",
      "Error at this point: e = 0.0104083062763341\n",
      "\n",
      "Current point: x = 0.25480447782223054\n",
      "Gradient at the point: df = -0.009575641774221821\n",
      "New point: x = 0.26438011959645236\n",
      "Error at this point: e = 0.009575641774221821\n",
      "\n",
      "Iterations: 101\n",
      "e  = 0.009575641774221821\n",
      "x* = [-500, -459.9700400012807, -423.1424768022407, -389.2611186593058, -358.0902691674055, -329.4130876356576, -303.03008062492154, -278.7577141757538, -256.4271370424649, -235.88300607980273, -216.98240559362603, -199.5938531460979, -183.59638489414465, -168.8787141024477, -155.33845697405013, -142.88142041607443, -131.42094678278227, -120.87731104008981, -111.17716615683548, -102.25303286426879, -94.04283023508242, -86.48944381621959, -79.54032831088398, -73.1471420459684, -67.26541068223924, -61.85421782763001, -56.87592040143841, -52.29588676934327, -48.082255827807785, -44.20571536159912, -40.63929813267464, -37.35819428206355, -34.33957873951243, -31.56245244036171, -29.00749624512855, -26.656936545514043, -24.494421621870544, -22.50490789212023, -20.674555260750793, -18.990630839891054, -17.441420372698246, -16.016146742881432, -14.704895003449181, -13.498543403173358, -12.388699930920843, -11.36764393644718, -10.428272421530771, -9.56405062780874, -8.76896657758408, -8.037489251377039, -7.364530111266809, -6.7454077023647585, -6.1758150861752625, -5.651789879280944, -5.169686688938135, -4.726151753823071, -4.318099613517035, -3.942691644435503, -3.5973163128807384, -3.279571007850368, -2.9872453272223876, -2.7183057010445877, -2.4708812449609763, -2.243250745364078, -2.033830685734983, -1.8411642308761578, -1.663911092406073, -1.5008382050135938, -1.3508111486125185, -1.2127862567235526, -1.085803356185716, -0.9689790876908633, -0.8615007606755931, -0.7626206998215396, -0.6716510438358192, -0.5879589603289548, -0.5109622435026384, -0.4401252640224146, -0.3749552429006195, -0.314998823468568, -0.2598389175910848, -0.20909180418379747, -0.16240445984909424, -0.11945210306116977, -0.0799359348162762, -0.04358106003097412, -0.010134575228498699, 0.020636190789784237, 0.048945295526604815, 0.07498967188447614, 0.09895049813371526, 0.12099445828302191, 0.1412749016203793, 0.15993290949075506, 0.17709827673149936, 0.19289041459298606, 0.20741918142554855, 0.22078564691150465, 0.23308279515858732, 0.24439617154589643, 0.25480447782223054, 0.26438011959645236]\n"
     ]
    }
   ],
   "source": [
    "e = math.inf\n",
    "eps = 0.01\n",
    "\n",
    "x0 = -500\n",
    "dx = 0.001\n",
    "\n",
    "learning_rate = 1\n",
    "\n",
    "# History per iterations\n",
    "x  = []\n",
    "df = []\n",
    "\n",
    "# Initialize\n",
    "x.append(x0)\n",
    "\n",
    "loop_counter = 0\n",
    "while e > eps:\n",
    "    loop_counter = loop_counter + 1\n",
    "    if loop_counter > 10000:\n",
    "        print(1)\n",
    "        break\n",
    "    \n",
    "    \n",
    "    df_now = f(x[-1] + dx) - f(x[-1]) \n",
    "    df_now = df_now / dx\n",
    "    df.append(df_now)\n",
    "    \n",
    "    print(\"Current point: x = {}\".format(x[-1]))\n",
    "    print(\"Gradient at the point: df = {}\".format(df[-1]))\n",
    "    \n",
    "    \n",
    "    new_x = x[-1] - learning_rate*df_now\n",
    "    x.append(new_x)\n",
    "    e = abs(x[-1] - x[-2])\n",
    "    \n",
    "    print(\"New point: x = {}\".format(new_x))\n",
    "    print(\"Error at this point: e = {}\".format(e))\n",
    "    print(\"\")\n",
    "    \n",
    "    \n",
    "    \n",
    "print(\"Iterations: {}\".format(loop_counter))\n",
    "print(\"e  = {}\".format(e))\n",
    "print(\"x* = {}\".format(x))\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.8199397588458677e-05"
      ]
     },
     "execution_count": 275,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x[-1] + dx) - f(x[-1] - dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-30.049969999708992"
      ]
     },
     "execution_count": 276,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f(x0 + dx) - f(x0))/dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = []\n",
    "a.append(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-312644317773351.3]"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum at 0.37494891978302747\n"
     ]
    }
   ],
   "source": [
    "dx = 0.0001\n",
    "\n",
    "df = lambda x: (f(x + dx) - f(x))/dx\n",
    "\n",
    "\n",
    "next_x = 0\n",
    "\n",
    "\n",
    "loop_counter = 0\n",
    "\n",
    "step = math.inf\n",
    "\n",
    "while step > 0.0000001:\n",
    "    loop_counter = loop_counter + 1\n",
    "    if loop_counter > 10000:\n",
    "        print(1)\n",
    "        break\n",
    "    x = next_x\n",
    "    next_x = x - learning_rate * df(x)\n",
    "    step = abs(x - next_x)\n",
    "    \n",
    "print(\"Minimum at\", next_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 295,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loop_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.672501139228879"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = float(1e-6)\n",
    "learning_rate = 2\n",
    "df_calc = lambda x: (f(x + dx) - f(x))/dx\n",
    "\n",
    "\n",
    "x0 = -5\n",
    "\n",
    "tol = 1e-6\n",
    "\n",
    "x  = []\n",
    "df = []\n",
    "\n",
    "x.append(x0)\n",
    "\n",
    "loop_counter = 0\n",
    "diff = math.inf\n",
    "while diff > tol:\n",
    "    loop_counter = loop_counter + 1\n",
    "    if loop_counter > 10000:\n",
    "        break\n",
    "    df.append(df_calc(x[-1]))\n",
    "    x.append(x[-1] - learning_rate * df_calc(x[-1]))\n",
    "    diff = abs(x[-2] - x[-1])\n",
    "    \n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80"
      ]
     },
     "execution_count": 358,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loop_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.37499479325020957"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-06"
      ]
     },
     "execution_count": 360,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tol\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3749994890495145"
      ]
     },
     "execution_count": 344,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5,\n",
       " -4.140000079833612,\n",
       " -3.4176001468494377,\n",
       " -2.8107842031338492,\n",
       " -2.3010588107946717,\n",
       " -1.8728894809144592,\n",
       " -1.5132272439771732,\n",
       " -1.2111109649276486,\n",
       " -0.9573332905526932,\n",
       " -0.7441600440533058,\n",
       " -0.5650945170360089,\n",
       " -0.414679474309283,\n",
       " -0.2883308384360417,\n",
       " -0.18219798429197187,\n",
       " -0.09304638679874078,\n",
       " -0.018159044915528888,\n",
       " 0.04474632226359354,\n",
       " 0.0975868307046035,\n",
       " 0.14197285779449675,\n",
       " 0.1792571205411253,\n",
       " 0.21057590126272618,\n",
       " 0.2368836770538829,\n",
       " 0.2589822087251159,\n",
       " 0.27754497532673117,\n",
       " 0.293137699272088,\n",
       " 0.3062355873934042,\n",
       " 0.3172378134125342,\n",
       " 0.32647968326527277,\n",
       " 0.33424285394101805,\n",
       " 0.34076391731086453,\n",
       " 0.34624161055430314,\n",
       " 0.350842872856032,\n",
       " 0.3547079331972558,\n",
       " 0.35795458389554113,\n",
       " 0.36068177046933325,\n",
       " 0.3629726071841022,\n",
       " 0.3648969100400512,\n",
       " 0.3665133244312768,\n",
       " 0.3678711125215717,\n",
       " 0.369011654515754,\n",
       " 0.36996970978975696,\n",
       " 0.3707744762238052,\n",
       " 0.37145048003229153,\n",
       " 0.372018323221428,\n",
       " 0.37249531150363335,\n",
       " 0.37289598166734717,\n",
       " 0.3732325445976503,\n",
       " 0.3735152574507783,\n",
       " 0.37375273626516936,\n",
       " 0.37395221845982096,\n",
       " 0.37411978351887143,\n",
       " 0.3742605381490449,\n",
       " 0.37437877204394177,\n",
       " 0.3744780885156551,\n",
       " 0.3745615143513392,\n",
       " 0.374631592058865,\n",
       " 0.3746904573326315,\n",
       " 0.3747399041681465,\n",
       " 0.3747814394988769,\n",
       " 0.3748163291872375,\n",
       " 0.37484563652157465,\n",
       " 0.37487025467631163,\n",
       " 0.3748909339262907,\n",
       " 0.37490830450348955,\n",
       " 0.37492289577612414,\n",
       " 0.37493515245790476,\n",
       " 0.37494544806949026,\n",
       " 0.3749540963737852,\n",
       " 0.37496136096549115,\n",
       " 0.3749674632092015,\n",
       " 0.3749725890950284,\n",
       " 0.3749768948452292,\n",
       " 0.3749805116742877,\n",
       " 0.3749835497995946,\n",
       " 0.3749861018276279,\n",
       " 0.3749882455433884,\n",
       " 0.3749900462557454,\n",
       " 0.3749915588513497,\n",
       " 0.37499282943221246,\n",
       " 0.3749938967312394,\n",
       " 0.37499479325020957]"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda u: u[0]**2 + u[1]**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f([0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0009999999999195, 2.0009999999999195]"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df(f, [1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = [0,1]\n",
    "step = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5, 1]\n",
      "[0.5, 1.5]\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(u)):\n",
    "    new_u = u\n",
    "    new_u[i] = new_u[i] + step\n",
    "    print(new_u)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def calc_df(f, u, step=float(1e-6)):\n",
    "    \n",
    "    d = []\n",
    "    \n",
    "    for i, _ in enumerate(u):\n",
    "        v = [x for x in u]\n",
    "        v[i] = v[i] + step\n",
    "        derivative = f(v) - f(u)\n",
    "        derivative = derivative / step\n",
    "        d.append(derivative)\n",
    "        \n",
    "    return d\n",
    "    \n",
    "    \n",
    "\n",
    "def calc_diff(u,v):\n",
    "    if len(u) == 1:\n",
    "        return abs(u-v)\n",
    "    \n",
    "    acc = 0\n",
    "    for x in zip(u,v):\n",
    "        acc = acc + (x[1] - x[0])**2\n",
    "        \n",
    "    return acc ** (1/2)\n",
    "    \n",
    "    \n",
    "\n",
    "# Experiment for f(x,y) = x**2 + y**2\n",
    "\n",
    "\n",
    "f = lambda u: u[0]**2 + u[1]**2\n",
    "\n",
    "\n",
    "learning_rate = 0.1\n",
    "\n",
    "\n",
    "x0 = [-1, 5]\n",
    "\n",
    "tol = 1e-6\n",
    "\n",
    "x  = []\n",
    "df = []\n",
    "\n",
    "x.append(x0)\n",
    "df.append(math.inf)\n",
    "loop_counter = 0\n",
    "diff = math.inf\n",
    "while diff > tol:\n",
    "    loop_counter = loop_counter + 1\n",
    "    if loop_counter > 10000:\n",
    "        break\n",
    "        \n",
    "    new_df = calc_df(f, x[-1])\n",
    "    new_x  = [x[-1][i] - learning_rate*new_df[i] for i in range(len(x[-1]))]\n",
    "    \n",
    "    df.append(new_df)\n",
    "    x.append(new_x)\n",
    "    \n",
    "    diff = calc_diff(x[-2], x[-1])\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.127709859478127e-06, 2.6385511809792683e-06]"
      ]
     },
     "execution_count": 488,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'list' object cannot be interpreted as an integer",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-486-9a219a87931e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mlearning_rate\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnew_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'list' object cannot be interpreted as an integer"
     ]
    }
   ],
   "source": [
    "[x[-1][i] - learning_rate*new_df[i] for i in range(x[-1])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1e-06, 1e-06]"
      ]
     },
     "execution_count": 478,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_df(f, [0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 480,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0000009999243673, 2.0000009999243673]"
      ]
     },
     "execution_count": 480,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_df(f, [1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.9999990001906554, 2.0000009999243673]"
      ]
     },
     "execution_count": 481,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_df(f, [-1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 494,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_df(f, u, step=float(1e-6)):\n",
    "    d = []\n",
    "    for i, _ in enumerate(u):\n",
    "        v = [x for x in u]\n",
    "        v[i] = v[i] + step\n",
    "        derivative = f(v) - f(u)\n",
    "        derivative = derivative / step\n",
    "        d.append(derivative)        \n",
    "    return d\n",
    "    \n",
    "    \n",
    "\n",
    "def calc_diff(u,v):\n",
    "    if len(u) == 1:\n",
    "        return abs(u-v)\n",
    "    acc = 0\n",
    "    for x in zip(u,v):\n",
    "        acc = acc + (x[1] - x[0])**2\n",
    "    return acc ** (1/2)\n",
    "\n",
    "\n",
    "def find_minimum(f, x0, learning_rate=0.1, max_iterations=10000, tol=1e-6):\n",
    "    \n",
    "    x  = []\n",
    "    df = []\n",
    "\n",
    "    x.append(x0)\n",
    "    df.append(math.inf)\n",
    "    loop_counter = 0\n",
    "    diff = math.inf\n",
    "    while diff > tol:\n",
    "        loop_counter = loop_counter + 1\n",
    "        if loop_counter > 10000:\n",
    "            break\n",
    "\n",
    "        new_df = calc_df(f, x[-1])\n",
    "        new_x  = [x[-1][i] - learning_rate*new_df[i] for i in range(len(x[-1]))]\n",
    "\n",
    "        df.append(new_df)\n",
    "        x.append(new_x)\n",
    "\n",
    "        diff = calc_diff(x[-2], x[-1])\n",
    "    \n",
    "    return {\n",
    "        \"x\": x,\n",
    "        \"df\": df,\n",
    "        \"loop_counter\": loop_counter\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.1779899110628975e-06, 1.1299882945162842e-07]"
      ]
     },
     "execution_count": 497,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_minimum(f, [3, 0.5])['x'][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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