09-梯度下降原理及代码实现.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "梯度下降法的原理介绍"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "    <img src='./img/5.jpg', width= 600, height = 200>\n",
    "    <img src='./img/6.jpg', width= 600, height = 200>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "梯度下降代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 构造我们的数据集\n",
    "X = np.linspace(-5, 5, 50)\n",
    "Y = x**2 + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J(x):\n",
    "    return x**2 + 5\n",
    "\n",
    "def dJ(x):\n",
    "    return 2 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00013292279957849163\n",
      "5.00000001766847\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 # 学习学率\n",
    "epsilon = 1e-8 # 相当于0的存在\n",
    "x = 1\n",
    "while True:\n",
    "    gradient = dJ(x)\n",
    "    last_x = x\n",
    "    x = x - eta * gradient # 进行迭代操作\n",
    "    \n",
    "    if abs(J(x) - J(last_x)) < epsilon:\n",
    "        break;\n",
    "\n",
    "# 进行测试一下\n",
    "print(x)\n",
    "print(J(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "进行绘图感性了解一下"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.3 # 学习学率\n",
    "epsilon = 1e-8 # 相当于0的存在\n",
    "x = 5\n",
    "history_x = [x]\n",
    "while True:\n",
    "    gradient = dJ(x)\n",
    "    last_x = x\n",
    "    x = x - eta * gradient # 进行迭代操作\n",
    "    history_x.append(x)\n",
    "    \n",
    "    if abs(J(x) - J(last_x)) < epsilon:\n",
    "        break;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x163f9236240>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MdjfhKo8UehkCvNy5OzKYb3cmcTIjx+g4QojKyM+HiRPLnBNa4vvdyZzIyOHfPe3r2nkJKfRyPNKjIUXaNF9QCGEDrjAnFKCwSPPJulhaBNXkxiYBBgQ0Pyn0coT4ejKwdV2+3JpAerZsrSuEVSuZE9qjxz/mhJb4bf9J4lLP8++eDVHKtjfhKo8U+hU82rMh2XmFLNgkW+sKYdXeess0J3TGjH/MCQXTFrkfr4sl3M+TW1v+c+WLvZBCv4KmdWrSu2ltPtsUz7ncAqPjCCHKkpwMb79d5pzQEhuPnGZvUgaP3NjQ5rfIvRIp9AqMvakR6dn5fLFZztKFsEovvggFBWXOCQXT2fn7q2Oo6+3Bne3rWTicZUmhV6BdqA89mgQwe0Mc5+UsXQjrcoU5oSU2xaax/dhZHuvZEHcXZwsHtCwp9EoY17sxZ87nsXCLnKULYVUmTjTNCX3hhTKfLjk7r1PTg7s7hlg4nOVVWOhKqRCl1Fql1AGl1H6l1Ljix32VUquUUjHFv9vfKv1iHcJ86N7Yn1nr48jOk7N0IazCmjXw889lzgktsTkuja1Hz/BvBzg7h8qdoRcAT2utmwGdgceVUs2B54A1WuvGwJri7+3WuN6NSTufx6ItCUZHEUJUMCe0xPurYwis6c4wBzg7h0oUutb6hNZ6Z/HXWcABoB4wGFhQfNgC4HZzhbQGkeG+3NDIn0/Xx3IhT4ZJC2GoRYtg165y54QCbI5NIzr+DP++sSEervZ/dg5XeQ1dKRUOtAOigUCt9QkwlT5Qu5yfeVgptV0ptT01NfX60hpsXJ/GnD6Xx6JouZYuhGFK5oS2b1/mnNAS7685TG0vd4ZHhVownLEqXehKqRrAt8B4rXVmZX9Oaz1Lax2ptY4MCLDt2207hvvStaEfn66PIydfztKFMMSHH5rmhM6YUeacUIDouDS2xJ3hUQc6O4dKFrpSyhVTmS/SWn9X/PAppVTd4ufrAg4xXXlc78akZuXyZbRcSxfC4tLSrjgntMT7a2II8HLn3k6Oc3YOlVvlooC5wAGt9TulnloO3F/89f3AD1Ufz/p0auBH5wa+fLIuVs7ShbC0V1+FrCzTBlzl2Hb0DJti03ikRwOHOjuHyp2hdwNGAjcppXYX/+oPvAH0VUrFAH2Lv3cI43o3ISUrlyVb5SxdCIspmRM6ejS0aFHuYe+vjsG/hjv3dQqzYDjr8M89Ji+jtd4IlLf5Qe+qjWMbujT0I6q+Lx+vi2V4VKjDnQUIYYhJk0xzQl95pdxDdhw7w8Yjp5ncvxnV3Bzv/5dyp+g1Gt+nMacy5Vq6EBYRHQ1ffVXunNASb/92GP8abtzX2bGunZeQQr9GXRv6062RHx+tPSI7MQphTlqbivwKc0IBNsacZlNsGo/3aoSnW4UXH+ySFPp1mNAvgrTzeXy2Md7oKELYrwrmhIJpz5a3fj1IkLeHw61sKU0K/Tq0C/Whb/NAZq2Pk6lGQphDyZzQpk3LnRMK8Ntfp9iTlMH4Pk0cYs+W8kihX6cJ/SI4l1fAJ+tk9qgQVW7OnCvOCQXTrNC3fztEg4Dqdr/feUWk0K9TRB0vbm9bj/mb4knJzDE6jhD2Iyvr7zmhAweWe9jyPckcPnWOp/tG4OLs2JXm2O++iozv05iCQs3MtUeMjiKE/Zg+HVJSTPNCyxnqnFdQxLurYmgRVJNbW9axcEDrI4VeBcL8qjOsYwiLtyaQeCbb6DhC2L6SOaHDhkFUVLmHfbU9kYQz2Uy4OQInO54VWllS6FXkiZsa46QU762OMTqKELbvpZeuOCcUICe/kA/WxNAx3IeeTWx747+qIoVeRep4e3B/13CW7Uoi5lSW0XGEsF379v09J7RBg3IPW7DpKClZuTxzc1NUOZdkHI0UehV69MaGeLq58PZvh42OIoTtevZZqFmz3DmhAJk5+Xy8LpYbmwQQVb/s8XOOSAq9CvlWd2NM9/r8sv8kexLTjY4jhO2pxJxQgDkb4knPzmdCvwgLhrN+UuhV7MEb6uNX3Y3Xfz6A1troOELYjkrOCU3JzGH2+jgGtKpLq2BvCwa0flLoVczLw5XxfRqzJe4Maw44xMwPIarGl1+a5oROnVrunFCAd1YdpqCoiGdvkbPzy0mhm8HwqFAaBFRn2s8HyC8sMjqOENYvJ+fvOaH33FPuYQdPZvLV9kT+1SWcML/qFgxoG6TQzcDV2Ynnb21GXOp5lmxLNDqOENbvgw8gIeGKc0IBXl95kBruLjxxUyMLhrMdUuhm0qdZbTrV9+W9VYfJysk3Oo4Q1qtkTmj//lecE7r+cCrrDqfyZO/G1PJ0s2BA2yGFbiZKKSYPaEba+Tw+WRdrdBwhrNdrr5n2bZk+vdxDCos001YeIMS3GiO7ON5oucqSQjej1sG1uL1tEHM2xHM8/YLRcYSwPrGx8NFHFc4J/XZnEgdPZjHxlqYOvT1uRaTQzWzCzRFoYMZvh4yOIoT1qcSc0Oy8At7+7RBtQ2oxoFX54+eEFLrZBft4Mrpbfb7bmcy+5Ayj4whhPSo5J3T2+nhOZebywoBmcot/BaTQLeCxXg3xre7Gaz/9JTcbCQGmOaHPPAO1a5sKvRwpmTl8uj6WW1vWITJcbvGviBS6BdSUm42EuNTy5bBhg2lOqJdXuYe9u/oweQVFTLylqQXD2S4pdAu5p/hmo6krD5BXIDcbCQdWek7omDHlHrYvOYMl2xIZ2SWMcH+5iagypNAtxNXZiRdva0786fPM+yPe6DhCGGfOHDh06IpzQrXWTFmxHx9PN8b3bmLhgLZLCt2CekbUpk+zQD5cE8MpmT8qHFEl54T+sPs4246e5dmbI/D2dLVcPhsnhW5hL97WnPwizesrDxgdRQjLe+utCueEnsstYNrKA7QO9ubuyBALB7RtUugWFurnycPdG/D97uNsO3rG6DhCWM7x45WaE/rh7zGkZOUyZVALmRN6laTQDfBYr4YEeXvw0g/7KSySZYzCQbz4oukD0SvMCY1NPce8jfEM6RBMu1AfC4azD1LoBvB0c2HSgGb8dSKTL7cmGB1HCPOrxJxQrTWvrPgLDxdnWaZ4jSosdKXUPKVUilJqX6nHXlZKJSuldhf/6m/emPZnQKu6dGngx9u/HeLs+Tyj4whhXhMnmtabT55c7iFrDqSw7nAq4/o0JsDL3YLh7EdlztDnA7eU8fi7Wuu2xb9WVm0s+6eU4uVBLcjKKeDtVbLPi7Bjv/8OK1eaytzPr8xDcvILeeXHv2hUuwb3dw23bD47UmGha63XA/LpnRlE1PFiZOcwvoxOYP9x2edF2KGiItOt/WFh8MQT5R42Z0McCWeyeXlgC1yd5Urwtbqef3NjlVJ7iy/JyKcX1+g/fZpQy9ONF3/YT5F8QCrsTSXmhCadzeajtbHc0qIONzT2t3BA+3Kthf4x0BBoC5wA3i7vQKXUw0qp7Uqp7ampqdf4cvbL29OV529tyo5jZ2VcnbAvlZgTqrXmxR/2A/DCbc0smc4uXVOha61Paa0LtdZFwGyg3EWlWutZWutIrXVkQEDAtea0a0M6BNO5gS+v/3yAlCy5g1TYiQ8/NM0JfeutcueErvzzJL8fTOHpfk0I9vG0cED7c02FrpQqvXnxHcC+8o4VFVNKMfWOVuTmF/HKir+MjiPE9UtLM11m6d8fbrqpzEMyLuTz8or9tKxXk1HyQWiVqMyyxcXAZiBCKZWklHoQmK6U+lMptRfoBfzHzDntXsOAGjzeqxE/7j3B2kOyxa6wcZWYEzr9l4Okncvl9Tta4yIfhFaJsrc6K0VrXdbFr7lmyOLwHu3ZgOV7knlh2T5WPdUDT7cK//MIYX0qMSd0x7EzLIpOYHS3+rQK9rZwQPslfyxaEXcXZ16/szXJ6Rd4f3WM0XGEuDaTJ5vmhE6ZUubT+YVFTPpuH0HeHjzdT7bGrUpS6FYmqr4v90SFMGdjvKxNF7Zn61ZYuhSefhqCgso8ZNb6OA6dyuKVwS2p7i5/C61KUuhW6LlbmuHj6cak7/6UzbuE7dDadBNR7dqmeaFlOJZ2ng/WxHBryzr0aR5o4YD2TwrdCnl7uvLiwObsScrgi81HjY4jROVUMCdUa83kZftwc3bi5UFlX1sX10cK3UoNbF2XG5sE8Navh0g6m210HCGurGROaEREuXNCv92ZzMYjp3n2lggCa5Z916i4PlLoVsq0Nr0lAM9+s1e2BRDWbe7cK84JPZFxgSkr9tMx3If7OoUZENAxSKFbsWAfT164rTmbYtNYFH3M6DhClC0rC156Cbp3h0GD/vG01pqJ3/5JQaFmxtA2MoXIjKTQrdzwjiH0aBLAtJUHSUiTSy/CCpXMCZ0xo8w5oUu3JbL+cCrP929KmF91AwI6Dil0K6eU4s27WuHirJjwzR659CKsSwVzQpPOZvPaTwfo0sCPEXKpxeyk0G1AXe9qvHhbc7bGn2H+pqNGxxHiby+9VO6c0KIizbPf7EVrzfQhreVSiwVIoduIIR2C6d20NtN/PUhc6jmj4wgB+/fDvHnw+ONlzgldFH2MTbFpTB7QnBBf2UnREqTQbYRSiml3tsLdxZkJX++RG46E8Z591rTe/IUX/vFUQlo201YepHtjf+6JCjEgnGOSQrchgTU9mDKoBTsT0pmzIc7oOMKRXWFOaFGRZsI3e3BxUrx5V2tUGR+UCvOQQrcxg9sGcXOLQN5edZhDJ7OMjiMcUcmc0NDQMueEzvsjnq3xZ/i/gc0JqlXNgICOSwrdxiileO32VtT0cOHJxbvIyS80OpJwNIsXlzsndF9yBtN/OUSfZoEM7RBsUEDHJYVugwK83JkxtA2HTmUx9acDRscRjiQnByZNMs0JvffeS546n1vAk4t34VPdlelD5FKLEaTQbVTPiNo81L0+X2w5xq/7TxodRziKK8wJnbJiP/Fp53l3WFt8q7sZFNCxSaHbsGdubkqret5M/HYvJzIuGB1H2LsrzAldsec4X21P4rGeDena0N+ggEIK3Ya5uTjxwT3tyCsoYvyS3bKUUZjX1KmmfVvefPOShxPPZDPpuz9pF1qL8X1kApGRpNBtXH3/6rwyuCXR8Wf479ojRscR9iouDmbOhAcegJYtLz6cX1jEk0t2AfDB8Ha4yrBnQ8m/fTtwV/t6DG4bxHtrYthx7IzRcYQ9mjTJNCf0lVcuefj91THsSkjntTtayt2gVkAK3Q6YljK2JKiWB08u3k3GhXyjIwl7Us6c0M2xaXz0vyMM7RDM4Lb1DAwoSkih2wkvD1c+GN6OU5k5TPhadmUUVaScOaEpmTmMW7KLcL/qMk7Oikih25F2oT5M6t+MVX+d4uN1sUbHEfZgxQrTnNCXX744JzS/sIjHv9xJVk4BH49oT3X3f04oEsaQQrczD3QLZ3DbIGb8doj1h1ONjiNsWUFBmXNCp/50gG1Hz/LGXa1oWqemgQHF5aTQ7YxSitfvbEVEoBdPLtlF4hmZciSu0Zw5cPCgaZmiqysA3+9KZv6mo4zuVl+um1shKXQ75OnmwicjOlBYpHl04Q7Z70VcvTLmhP51PJPnvttLVH1fnu/f1OCAoixS6HYq3L867w1ry/7jmbzw/T60lg9JxVWYMeOSOaEZ2fk8unAH3tVcmXmvrDe3VvJfxY71bhbIk70b882OJBZFJxgdR9iK48dNRX733RAVRVGRZvzSXZzIuMB/72tPbS+Piv8ZwhBS6HZufO/G9IwIYMqK/exMOGt0HGELSuaEvv46AB/8HsPaQ6n8323N6RDma3A4cSVS6HbOyUnx/rB21PWuxiNf7CDprHxIKq7gsjmhP+09wXurY7izfT1Gdg4zOp2oQIWFrpSap5RKUUrtK/WYr1JqlVIqpvh3H/PGFNfD29OVeaMiyckv5MH528nMkTtJRTlKzQndmXCW/3y1m8gwH6bd0Ur2N7cBlTlDnw/cctljzwFrtNaNgTXF3wsr1qi2F5+M6EBs6jkeX7ST/MIioyMJa1MyJ3TSJBJVNR5asJ263h58OrIDHq7ORqcTlVBhoWut1wOX7/g0GFhQ/PUC4PYqziXMoFsjf6be0ZINMad5afl+Wfki/lZUZLq1PzSUjIf+zajPtlJQpJk3qiN+NdyNTifHNqLpAAAN1klEQVQq6Vrv2Q3UWp8A0FqfUErVLu9ApdTDwMMAoaGh1/hyoqoM6xjK0bRsPv5fLPX9qvNQjwZGRxLWYPFi2LmTgvkL+Pc3+0k4k83nozvRMKCG0cnEVTD7h6Ja61la60itdWRAQIC5X05UwjP9IhjQqi7Tfj7AL/tkfJ3DK54Tqtu3Z3K1VmyKTeONO1vTpaGf0cnEVbrWQj+llKoLUPx7StVFEubm5KR4++42tA2pxfilu9iTmG50JGGkmTMhIYHl941n6c7jPHlTI+7qEGx0KnENrrXQlwP3F399P/BD1cQRluLh6szsf0XiX8OdBxdsIy71nNGRhBHOnIGpUznZtRfjUnwZ1CaI//SVMXK2qjLLFhcDm4EIpVSSUupB4A2gr1IqBuhb/L2wMf413FkwOgqtYcScaJLTZdC0w3ntNXRmJqOa3cUNjfyZPqS1LE+0YZVZ5XKP1rqu1tpVax2stZ6rtU7TWvfWWjcu/l3mntmohgE1+PzBKLJyCxgxJ5rUrFyjIwlLiYujaOZMvm7VB8/2bZn1L1meaOvkTlFBiyBv5j8QxanMHEbOjSY9O8/oSMIC0sZNIFc7sfzOR/nsgSg83WRQha2TQhcAdAjzYdbISOJSzzPqs22cyy0wOpIwo7jvf8Xvx2V80/Nu3nuqP97VXI2OJKqAFLq46IbG/sy8tx1/Jmfw8OfbZR91e6Q1p979iLp3Dyalpj995s3AX24cshtS6OIS/VrU4e2hbdgcl8bYL3eSVyBbBNiN9HTO3zGUwKfG8mdIc3L/2ELdkHLvCRQ2SApd/MPt7erx6uCWrD6QwsNfyJm6Xdi0ifzWbXBf8T3v9RlNzQ2/E9KyodGpRBWTQhdlGtE5jDfubMW6w6mM+myrXFO3VYWFMHUqukcPTp3L48Ex73LrF+/RNKiW0cmEGUihi3INjwrlvWFt2Xb0LCPnRpORLdvu2pTkZOjbF154gV+a3cADT3zCy1NHE1HHy+hkwkyk0MUVDW5bj//e1579yZncM3sLaedknbpNWLEC2rShcEs0kwc9xRsjX+Sz8X2p71/d6GTCjKTQRYVublGH2fdHEnf6HMNmbeFUZo7RkUR5cnLgySdh0CCyatdlwP3vsfXGQXz9aFeCfTyNTifMTApdVMqNTQJY8EAUJ9IvMPSTzRxLO290JHG5AwegUyf48EPiRzxE54Gv4dysKUse7kztmjLY2RFIoYtK69TAj0UPdSYzJ5/bP/qDrfGy44NV0BrmzoXISPTx4/w0bRa96g2maXgAXz7UWQZUOBApdHFV2obU4vvHuuHj6caIOdF8tzPJ6EiOLT0dhg+HMWMo6tyFV6cu5vGMIAa1CWLRmE5yB6iDkc0bxFUL96/Osse68ejCHTz11R7iUs/zVN8mODnJLn0WtWkT3HsvJCWRPeU1Rgf0ZEtcOuN6N2Z8n8aya6IDkjN0cU28PV1ZMDqKYZEhzFx7hCeW7JIbkCyleG05PXqAkxPJK35jgGc3diZl8t6wtvynbxMpcwclhS6umZuLE2/c1Yrnb23Kyj9PMGzWFlKyZAWMWZVaW87QoUR/t5r+WwvIuJDPlw914vZ29YxOKAwkhS6ui1KKR25syCcjOnD4ZBb939/IxpjTRseyT8Vry4mOpmjuPGaOmcI9Sw8Q4OXO9491IzLc1+iEwmBS6KJK3NyiDt8/3o1anq6MnBfN278doqBQNvaqEqXWlhMSQtqGzfyrqDkzVsUwoHUQyx7rSqifrDEXUuiiCkXU8WL52G4MaR/Mh78f4d7Z0ZzIkLF216XU2nLGj+ePhT9y88oUth09wxt3tuKD4W3x8pCVLMJECl1UKU83F94a2oZ3h7Vh3/EM+r+/gd8PnjI6lu0ptbac48cp/GE5b9/6KCMW7qaWpyvLx97A8KhQ+fBTXEIKXZjFHe2CWfHEDdTxrsbo+dt5efl+zsuOjZVTam05XbqQsHYLw4/78eHvRxjSPpjlY7vJBluiTLIOXZhNw4AaLHusK6+vPMD8TUdZ9dcpXrujJb0iZKhCuTZvNq0tT0ykcOo0Pul0F+8vOYy7ixPvDmvDHe2CjU4orJicoQuz8nB1Zsrglnz9aBc8XJ144LNtPLl4F6dl18ZLFRbCtGnQvTsoxaFvVjLAsxtvrYqhT7ParHnqRilzUSGltbbYi0VGRurt27db7PWEdcktKOTj/8Xy0dojVHd3YXL/ZgzpECzXgZOTYeRIWLuW/KHDmHHHeGbtTSPQy4NXb29J3+aBRicUBlNK7dBaR1Z4nBS6sLQjKVk89+2fbD92ls4NfJnUvxmtgx10gs6PP8KoUegLF9j57Ks84dqaE1m5jOwcxjM3R8gKFgFUvtDlkouwuEa1vfjqkS68dntLDp86x6CZf/DYoh0cSTlndDTLycmBceNg4ECyAuoy5slPuetCBD413Pnm0a68MrillLm4avKhqDCEk5NiROcwBrcNYs6GeOZsiOOXfScZ2iGEcX0aE1SrmtERzefgQdMqlj17+LHXUJ5qfy/1/Goxs18T+resK5uciWsml1yEVUg7l8tHa2NZuOUYKBjZOYzRN9Snnj0Vu9bouXMpenIc2c5ujLv5Sfa378643k0YGhmMq7P8hVmUTa6hC5uUdDab91bHXNxnvW/zQO7vGk6XBn42/eFpTmoaKfc9QOiqFfwR1pqX7nqOoYOiuL9rOB6uzkbHE1ZOCl3YtKSz2SzcksCSbQmkZ+fTJLAG/+oSzp3t6+HpZiNXCi9c4PSKnzn2xbeErvsFn3PpLOg/hmqTJnJ7ZKjtvA9hOCl0YRdy8gtZvuc4CzYdZf/xTLw8XOjXvA63tKxD98b+1nd2e/QoWd9+T+Z3ywnYtgm3/FyyXd2JadkJp0mTaHlXP5v+m4YwhkUKXSl1FMgCCoGCil5QCl1cK601OxPOsig6gdV/nSIzpwBPN2d6RgRwc4s69Gpam5pGrArJz4eNG8n89gcKf/wJn2NHADhaqy7bW3RB9+9P19F3Uq+Oj+WzCbtR2UKvir/z9dJaywbYwqyUUnQI86VDmC/5hUVsiUvjl30n+e2vU6z88ySuzoo2wbVoE2L61S6kFsE+1cxyNpyffJxTS5dR+ONP1N6ygWoXzuHh5EJ0SEv+un0sHoMH0umWztwV6CVn48KiquIMPbKyhS5n6KKqFRVpdiWe5bf9p9h+7Cz7kjPILTDtw+5b3Y02wd5E1KlJnZru1PH2ILCmB3W9q+Ffww2XK6wqybmQS+qheDIPx3IhNp7C+GOopER89++mUcIhAE7W8GVTRCeSuvSi5oCbualjI9mXXJiFpS65xANnAQ18qrWedaXjpdCFueUXFnHoZBa7E9PZk5jO7sR0jqadJ7/w0v+dOynwruaKk1L02beeR9Z+jnNRIe75uXjm5VA9NxtnfemAjgyPGhyv14ATXXvhPKA/Dfp0I9jXU87ChdlZ6pJLN631caVUbWCVUuqg1nr9ZUEeBh4GCA0Nvc6XE+LKXJ2daFnPm5b1vBnROQwwncWfyc7jZEYOpzJzOJmZw6mMHM5k5wHQsDCE7MQIipydyXfzoKCaJ04+tXAKC8O9QTheTRrg27Qh3v4+eAPNDHx/QlxJla1yUUq9DJzTWs8o7xg5QxdCiKtn9r1clFLVlVJeJV8D/YB91/rPE0IIcX2u55JLILCs+PqhC/Cl1vqXKkklhBDiql1zoWut44A2VZhFCCHEdZDdgIQQwk5IoQshhJ2QQhdCCDshhS6EEHZCCl0IIeyERbfPVUqlAscs9oJVxx9wpA3IHO39grxnR2Gr7zlMax1Q0UEWLXRbpZTaXpm7tOyFo71fkPfsKOz9PcslFyGEsBNS6EIIYSek0CvnitsC2yFHe78g79lR2PV7lmvoQghhJ+QMXQgh7IQU+lVQSk1QSmmllL/RWcxNKfWWUuqgUmqvUmqZUqqW0ZnMRSl1i1LqkFLqiFLqOaPzmJtSKkQptVYpdUAptV8pNc7oTJaglHJWSu1SSv1odBZzkUKvJKVUCNAXSDA6i4WsAlpqrVsDh4HnDc5jFkopZ+Aj4FagOXCPUqq5sanMrgB4WmvdDOgMPO4A7xlgHHDA6BDmJIVeee8Cz2Kan2r3tNa/aa0Lir/dAgQbmceMooAjWus4rXUesAQYbHAms9Jan9Ba7yz+OgtTydUzNpV5KaWCgQHAHKOzmJMUeiUopQYByVrrPUZnMcho4GejQ5hJPSCx1PdJ2Hm5laaUCgfaAdHGJjG79zCdkBVVdKAtu94h0XZDKbUaqFPGU5OBSZhG7NmVK71nrfUPxcdMxvRX9EWWzGZBqozHHOJvYUqpGsC3wHitdabRecxFKXUbkKK13qGU6ml0HnOSQi+mte5T1uNKqVZAfWBP8bi9YGCnUipKa33SghGrXHnvuYRS6n7gNqC3tt/1rUlASKnvg4HjBmWxGKWUK6YyX6S1/s7oPGbWDRiklOoPeAA1lVILtdYjDM5V5WQd+lVSSh0FIrXWtrjBT6UppW4B3gFu1FqnGp3HXJRSLpg+9O0NJAPbgHu11vsNDWZGynRmsgA4o7Ueb3QeSyo+Q5+gtb7N6CzmINfQRXlmAl7AKqXUbqXUJ0YHMofiD37HAr9i+nDwK3su82LdgJHATcX/bXcXn70KGydn6EIIYSfkDF0IIeyEFLoQQtgJKXQhhLATUuhCCGEnpNCFEMJOSKELIYSdkEIXQgg7IYUuhBB24v8B+52WyMVGubwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, Y)\n",
    "plt.plot(np.array(history_x), J(np.array(history_x)), color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "END"
   ]
  }
 ],
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