part2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 2: Bivariate optimization\n",
    "First import dependencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from random import randint\n",
    "\n",
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "rosenburg = lambda x0, x1: 100 * ((x1-x0**2)**2) + (1 - x0)**2\n",
    "rosenburg_grad = lambda x0, x1: np.array([-400*x0*(x1-x0**2)-2*(1-x0), 200*(x1 - x0**2)])\n",
    "rosenburg_hessian = lambda x0, x1: np.array([[-400*(x1-x0**2) + 800 * x0**2 + 2, -400*x0],[-400*x0, 200]])\n",
    "\n",
    "\n",
    "rastrigin = lambda x0, x1: (x0 ** 2 + 10 * (np.cos(2 * np.pi * x0))) + (x1 ** 2+ 10 * (1 - np.cos(2 * np.pi * x1)))\n",
    "rastrigin_grad = lambda x0, x1: np.array([2*x0 + 20*np.pi*np.sin(2*np.pi*x0), 2*x1 + 20*np.pi*np.sin(2*np.pi*x1)])\n",
    "rastrigin_hessian = lambda x0, x1: np.array([[2 + 40*(np.pi**2)*np.cos(2*np.pi*x0), 0],[0, 2 + 40*(np.pi**2)*np.cos(2*np.pi*x1)]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions\n",
    "Define all the functions we'll need. We have that the Rosenburg function is:\n",
    "$$f_1(x_0, x_1) = 100(x_1 - x_0^2)^2 + (1 - x_0)^2$$\n",
    "Which has the following Gradient and Hessian:\n",
    "$$\\nabla f_1(x_0, x_1) = \\begin{bmatrix} -400 x_0 (x_1 - x_0^2) - 2(1-x_0) \\\\ 200(x_1 - x_0^2) \\end{bmatrix}$$\n",
    "$$\\nabla^2 f_1(x_0, x_1) = \\begin{bmatrix} -400 (x_1 - x_0^2) + 800 x_0^2  + 2 && -400 x_0 \\\\ -400 x_0 && 200 \\end{bmatrix}$$\n",
    "\n",
    "And we also have the Rastrigin function:\n",
    "$$f_2(x_0, x_1) = (x_0^2 + 10(1- \\cos(2\\pi x_0))) + (x_1^2 + 10(1 - \\cos(2\\pi x_1)))$$\n",
    "\n",
    "Which has the following Gradient and Hessian:\n",
    "$$\\nabla f_2(x_0, x_1) = \\begin{bmatrix} x_0 + 20\\pi \\sin(2\\pi x_0) \\\\ x_1 + 20\\pi \\sin(2\\pi x_1) \\end{bmatrix}$$\n",
    "$$\\nabla^2 f_2(x_0, x_1) = \\begin{bmatrix} 2 + 40\\pi^2\\cos(2\\pi x_0) && 0 \\\\ 0 && 2 + 40\\pi^2\\cos(2\\pi x_1) \\end{bmatrix}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots\n",
    "Below the plots of the Rosenburg and Rastrigin function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def plot_rosenburg():\n",
    "    plot = plt.axes(projection=\"3d\")\n",
    "    X = np.arange(-2, 2, 0.001)\n",
    "    Y = np.arange(-1, 3, 0.001)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = rosenburg(X,Y)\n",
    "    plot.plot_surface(X, Y, Z, cmap=cm.gist_heat_r,\n",
    "                       linewidth=0, antialiased=False)\n",
    "\n",
    "plot_rosenburg()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def rosenburg_contour():\n",
    "    X = np.arange(-5, 5, 0.01)\n",
    "    Y = np.arange(-10, 3, 0.01)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = rosenburg(X,Y)\n",
    "    \n",
    "    plt.contourf(X,Y,Z)\n",
    "    plt.show()\n",
    "    \n",
    "rosenburg_contour()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def plot_rastign():\n",
    "    plot = plt.axes(projection=\"3d\")\n",
    "    X = np.arange(-1.5, 1.5, 0.001)\n",
    "    Y = np.arange(-1.5, 1.5, 0.001)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = rastrigin(X,Y)\n",
    "    plot.plot_surface(X, Y, Z, cmap=cm.gist_heat_r,\n",
    "                       linewidth=0, antialiased=False)\n",
    "\n",
    "plot_rastign()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QyvluyJDjwatnAOwjorsB/A2AhwD8m+4CRLQDwA+dc46I7sPmheZHGbYtxsmL+6Nv3D515UBy35+GgVgby22dUkxdk9XXVtg33s+tbxcfmTJ2Dko+SJdCcoXvnHsbwMMAngbwIoAvO+deIKKjRHR0ttiDAJ4noucAfA7AQy7giS/aoKwGk+sBhxBSgqXGQFtEjMYcLUs5JyU/eCVFinZj5SCXnL60TONinrT15BjGV+vUCkB4glg0jKnNo9PF2hS7XCTH49eag55Uw+9ru+hJ2+Lm0vEHpzV+O6Vrx9MPIqlx25KVrEZ1yO0e0OgasIg1s/fbkMrJmnMwxexjdDU9tcIiVl9biQ5k7knObaRPXTkwaqBZNIzYbdXQtdO0W04JOcgl1uxTvK9Yw/fEHvzYpp8TybdejdHvW5JxpFKL2Xe3ydluydp1OXlxv8o9mFRNizd8z1RNv9ZXHEobx9haShuEBf1CKd30rb7bdohqDB+IuwKWbPq1mn0XKeMAxtNS+n22VvSr+YLt0bjZnlPP4kbpcKh11McUXoDdR/KVh4COljEmVYN2QLh+LQc3SdFy0Sidqg0f0HkLj1bQSRpGDrPYdn5xLF3dPTQLB48Sjb8Eoy9duxpy0JOq56QN3yNtFIBc0Fk1jGUmsYxYE9HQEkjTM6XLoWm3iZULNhCv5xgttGb4HUowC0DHMGICLNUohrBqHtqUYPRDxOgn1cXTpYQc9OTsjivW8Ldu3+XuOfzI4P9SmphjvWx5XgDmugElaRgSRjEEV9daTL9pt5hSchDQq+rn6Xr6ycfqM/wuU68QazCLPiWYRw6aduVq18dKC22R4Rc3tcIQ3ZPACTbO4+BeTGsBJxVkY5lFf/uhepampWSTv3btSs5BYNwLdxWG3yUm2IDwKsOCWXT3I4SSzKIPR88StCzJHFKR0q7EHARsaFmd4XtqNf4SKsNbX7l23e+X964mr3PbeSdSMQLXn1MJPVPmTAnFunZAuPFPOQcB2Yt2tYbvkWxeAvJm0d9GKBpm0TcHznIxRiJZ7Xty6ak1C2KKOYToN2+ZWP0kW2qArRwE7LWuqzd8T0lm0V8Xl9AgiwmwUJPnrIdrHhpaArovzPFIG8TY+klV+57SctCj1RVn2vC3vOWyVhgAv2sAyGcW8wIwl7FImkUuo1i2bq55SLXctClVu+76JbQrLQcBWy20PqYNfxFaFSKQzywkK0apql7aLOZtL1RTrWpfCslKsGl3IxZyEJDvRp1HsYbfJabCAPSqfUmkgkzbLOZtn2MeJWkp3eQfUz9p7UrOQWDcrrgqDN8T27QE5EbzSFFTZbiIW1+5JmIcwDhaSk9nMQXtrOQgUM49F09Vhu+R7FP0jFlp1FrVz4OjJ/cCDugYyJSMvoukdqXkIGCnhVal4Xskm5aAfqVhuapfObMetNzG/rXobUhW+4CMnhqTnE1ZO+s5CNi6cFdt+J4SjWJo/Rw0gizUKOZ9JsZApLUE8ugpMSnWEE27TSzmIGDL7IGJGD5QjlEMrY+LdJDFmMWi9XDNQ0NL4Mbzv0jXXNPbNu3exULxZf3CzcX0bJm3vvcO98u3fwpAWnOyC6dfP/UtP7FBZznIchlGnxh9NbXUoFTtAL5+WtqNkYPAOGbv9f36xT8qc3rkruF3STX/MYxiWeBpvKauCzfIJM3CM2XTL9nsPVZN36ORg8D4918WGX6RXTqxzUmPVpdAF0svmLZo9n471roINJB+rN6qfhztcqCRg1pmH6vpTdFbNIBWIFuacnYeJexjCFqalorVi7U0JcS31j6maJrF8InofiJ6iYjOEtGxgf8TEX1u9v/vEdGBHNsF4g/e6rhlaUowDMltWjMOyf0pQbuWhzxSNU02fCLaAuDzAD4B4F4Av0lE9/YW+wSAfbOvIwD+OHW7jXexZmLaTMU0pnKc85h6nOcgR4V/H4CzzrlXnXMbAL4E4HBvmcMAvug2+Q6A9xPRnRm2DUCnkplisNXSHdDQZYpxo+EPOc5rDsPfCeD1zu/rs79xlwEAENERIjpFRKc23vlJht1rxJJrKGyjUTsagwFy5GMOwx860v7lLmSZzT8694Rz7qBz7uDKTe8L2gENY7I4uqPRsEgrFOySw/DXAezq/L4G4ELEMlHEBpfmcDBpOBejEo5bcjx3yXCPswTjreU5Ci6xMZuqaQ7DfwbAPiK6m4hWADwE4HhvmeMAPj0brfMRAJedc2+kblgroGsKNC4lmAYHa1pa259UaosXDlpappzjZMN3zr0N4GEATwN4EcCXnXMvENFRIjo6W+wEgFcBnAXwPwD8+9Ttphz0mBXhtbs2rvvKhWSVr5nE1p/WlKBpt5yc2knlIJcUH4rVtbipFTSnVQD059OxPIeH9OiLUgxDiilpB4TrV3MOAnmG23b1LXZqBXfzyqhNxDEmbfKfiw26q7tJbIjYxv41EeOYcjdAF452l/eusozCn2Mr+mmYfSk5yNVyiOs0uDh/OdOGnxOtyj5XEzEl6EIDLibQchuH9E13jUm3uqRWh5KmD+TVz6p2JeWgJ4fphzAJw9cwe6m+wNigkzR94Ppk55qH1v2XMatDQKdCTNVPUztA1uxLzUGPhulXb/jSZq910ycm6DimD8T3JQ6ZQOqMpkNomH1OPVPMX8P0gcXazft/DJLaWc9BILxfX9r0qzX8Wox+3nZDg07LOPrk7pcv3TAkL9hA004TDS0BmbmTip4eeYjLe1erNfvYfeAO+7P0IBN3f6xryR0KeHU3BR+TNe0AObMfe0il3wcO3NiU0LOaCj/mxFg3h2VwKg1rTcvQfQilNC2v3bVRZIUYiqTRWyKmxQ3whm7m1LNow0+5+pUcZH045lGCcUi20CxpKdk9B4xz0Z6Kdn2ktQSuP7exuhZl+DmaN9qV4J61S6zlz61vj9qOdLUPyBq/dAutFrOI1Q6wpZ+mdlo5CPCLLyBuauX++Q7V1vSTtlu373L3HH4k2/o0gowbXMuIDb7QoIt9SCuXecRexK0aRopZALwbgbVrN5Uc9OR6YPL0k4+V+aRtLqTNIXeAzVs3J/BCK43YKiO2wkhtpVm/aPc/yzULyWrfU6N2VnMQkO3m4VK14Ut330gG2aLthQYd1zxSgk16dEipF20Ns0jpGgB0JhOUquqt5yCg180TQpWGX5vRz9s+x/g1jEOKUivDedsq1SxikNKuxBwEZEfzhFCN4Ws8ij12kPXhBJ1mxZiLWox+3rYlzaJW7UrOQSDe+IE8+Vi04WvNlWItyPrsWbuUvdoHxjN+yRaaJS2lWmpA004bSS09Ocy/KMPXnvkQSA+yQzvOsJY/eXF/1Hakqn1AxzykW2i1mMXYFWLIdkLQ1E4rBwF+8QXEz8bZJVRb08Myb965y+0++mi29WkEGTe4lhEbfKFBFzujYy7z0JjkTNMwUswC4PXvN+2GKS0HgfRptbu8/Pijc4dlTsLwNar63EHWJybotAKOayAldMXl0DPF/GvUDgjXb4o5COQx/skafg1G34cbdGNVGRKUVhl2sXzB1kBSO+s5COga/yQNX9rstYOsDyfoSjeOmrSUvGAD5evH0a6kHAT0tJyU4Us/dDN2kHWZQrVfU2XYpWl3PSVp10eq+PJw9Vxk+NXMhx87P3apZg9s7g9nnzjHamGysZoNg7v9pt0m3JjXQCoHPTnn/q/C8DXmTLEWZF1qNP2azd5Tq+lLbduKbkNImz6Q57wWbfgpV75azN4jtY/W3wjFxZqW0qY/hn4cQo/Hmm5DaJl+iqZFPXjl0ZzuNlegPXjLswv//9SVA1m2EwLn4RAg7qnAGKbWJec5tONM8vj9RVjVT/thOI0c5GjJzcMusQ9tFXPTNlelotn8XxZgQ6QGneQNJEnTmKrZd7F284+DpNmnaldbHs7D61vsTVu34kZ9WbG22fvPxX4WkDU2CzcDG/FI6We1Cy4ll1JycCxCvDLJ8InoA0R0koh+MPt+25zlzhHR94nou0R0KmWbKWg1IXMEi0bAxY4YyE1J1b03ke5XLjT6gHNj6d0DXUrJQUBXy9QK/xiAbzrn9gH45uz3efyqc+4X5zU1rFFCF0ANlNRqmGcAJVWDJZ3vkrHqH6mGfxjAF2Y/fwHAryeur3hKSv5GOMt0bbrXSW26phr+B51zbwDA7Psdc5ZzAP6CiE4T0ZFFKySiI0R0iohO/fTqPyTuXqPRaDQ8S4dlEtE3AOwY+NfvMbbzK865C0R0B4CTRHTGOfftoQWdc08AeAIAVu9eszuEaA5PXTlQXVXQaDTqYKnhO+c+Pu9/RPRDIrrTOfcGEd0J4M0567gw+/4mEX0FwH0ABg2/MS1WX1spol952YVc8zmKFKzMs1MKpegaSuqDV8cBfAbAH86+/3l/ASLaCuAm59zV2c+/BuA/JG5XnJMX90ffeMlR5WsEWq7xv1OhtuTPQcwF+9z6dvGRKWPnoOSDdCmk9uH/IYBDRPQDAIdmv4OIPkREJ2bLfBDAXxHRcwD+GsBXnXNfD1k5baS/0rCLpsGlBIvlQJOoEGPWydHSavL1KfnBKylStBsrB7lo+lKS4TvnfuSc+1fOuX2z7z+e/f2Cc+6B2c+vOud+Yfb1Yefcf+RsY/W1leu+NEk1ipig0Qo0a4YhrW0ppi+FNe20TG6MHNSONY5HFjeXjj+g2H5fbnMypWsHuDF4+s3MnAYvGWgaF1tu94BG14AWpU6J0d2G1L2YknKQS8qFL0bXYubSmUebLXOT0g2ji+V5WSRo2oVhUbs+GnPoLNO02Ll0QogN6Jr6gGsyjJhtlqxl065c7fpYMPtlFF/hd9GY18NalVHzu21repdtH6vvQ81Jre+y7SOtJcDTs+oKv0vMjV3uybdUZdRs9gBfz1K0lH6frSX9Qim10te4cOfUs6oKv4vGyxjGqjSm8ALsPpKvPAR0tIwxqqbdYkrJQUCvlbaowq/W8D01dQtIBlkus9h2fjieru5Of6ZC2vQBGT1jK1Jts5fUDgjXz+oF22O9O27Shu8p1SwA25XhPJNYRoqJaGgJpOmZ0u3QtNvEmvFbzsMuzfBnaL1zM1fQWa0MY41iHjEGomX6fYa0zdmn3LS7ninkIJC3O65Yw9+6fZe75/AjN/w9tYk5hlksC8AcpiFpFrmNYgir5qFBaUY/BFc/be1CLgLW87DPkK6nn3ysLsPvEmv+WtW+FlJBpmEUfSSNA7ClpXQlaF2/Wi7YgF5Vv0zTRYZf3NQKfboHzwk07hQNXkxrQVeT0fe3HapnjJYWdCy9RbZs2yH6cbSzmoNAOS204g2/C9cogGmYBVCO2XeJMX7uBRzQN5ApaAds7oukdrXnIZBfz6oM3xNr/CUE3FTMootUxejR0FP66copaldrHgJyelZp+B6NrgGPdNBJGkZqcN36yjXW8pf3rkZtR6pi9OTWU2smxBT9NLUDwo3f2gW7ux0OVozeU7XheyS7BjwSQacxwVJMgHFNYtHnuQYiXe17+uc+RNccc7xrGH2Kfv3Pxugn3VIDppGHMZgepXPLtjX3Swd/62e/x1YXXaRHgPThBl6qaUgGWarRL4Orr9RokLGYknZAuH415yCQx+y7+v7lt363jlE6qdUFoFPtd9F6s0/JZtHfTqiuWtW+NFPUDpCt9rtovkLQalecpyjD75PaNSDVt6+NVJBpmcW87XKMv0QtJSvBWrWzoNsQGlV9Dk2rmR751leusU/ItvOOdeKtzUbInTq1BMOI3QduAo2tZY1mH7sPnDy0NP2zh5uDMa20XJoWXeEPIdm0BOxUiDUbfReOntKjsnIgXQla0q/2ar9ELaup8PvEVPscxqo0aq/q5yFd7UtrGbMNrnZW9ZPSbsxqv0SzByqs8LtIVhgezUrDcjfAypn1oOU29q9Fb+PWV66Jawnkrfil5kvpMnXtLOcgYKvoqtrwPSUaxdD6OWgEWahRDH0m1jyktQTy6Kk1T32KQXD16y4fo5+06QO2chCwZfZAxV06fSS7BDwSzUvpJqum2fc/H7sODS2Bd7sMOBqkdjNoXahz6BeDtHaWctCa2QMTqfBjGLM67K4nhtBAiwmyVKMYWl9KV4EW1kaGxJJTv9jWGqfSj6GkHNTGdIVPb21kqUY8mje1UoLFaqDlNvuU9WpV+ZpIV4SW9AsltYU2xme55PKlEK9MMnwi+hQRvUBE7xDR4KO8s+XuJ6KXiOgsER2L2VYu49c0Cu3uAA7WRnRM3fSl90/SlGPQir8xclC7K4fjjakV/vMAfgPAt+ctQERbAHwewCcA3AvgN4no3tgNWgvcEEICKIfRl1jda2+jBqxdrAG7Vb5HKwe14Z73JMN3zr3onHtpyWL3ATjrnHvVObcB4EsADqdsV9MYcpnovMrB4pODjbpoF9JNasvBGF01+vB3Ani98/v67G+DENERIjpFRKc23vmJ+M41Go3GVFhq+ET0DSJ6fuArtEofGuoyt2x2zj3hnDvonDu4ctP7BpfRHNUR+5L0IYZGDYz9eHijfkoYBaVFTTkYo+vSYZnOuY9H7c27rAPY1fl9DcCF2JWVGLzLAsr/P7VZeXU3ifXjb+xfE+8aKFHbxiaS2uUourRyUBtuXmp06TwDYB8R3U1EKwAeAnA8ZkU5gkpy/G+fa3dtsKoHzUpD8zyEEKMt5xhyttQk4OxfjHbWLqbaechZNjUPpbXss7F/LVjf1GGZnySidQAfBfBVInp69vcPEdEJAHDOvQ3gYQBPA3gRwJedcy+ErN/dvPKzgxkjYFNMIjZoUgNO0tikNLBmRiVgyfStVvcpuVRi8RXik0lP2jrnvgLgKwN/vwDggc7vJwCcSNlWDjQqwlyBotHEvLx3lT3EzwdUru6dWLPQru5DdLXcJefJ3TUn3TKLJUcepuSghpYxmH7SNiclmX3qOjWalKlVXUqrTcvsfYUYqgF3+SG0tBtLP2ntcnTJDK0zBu2unRAmMZeORpBJElNpcCqMmEofuN70NabYBcq5cGtVh7HaAfzWmmXtLOYgoKdlKFUbPveqadHs+9uyZvoejX74Ei/cJRhF6dpZzkGAryUg9zR1tV060mYv0XSU2K7FZmUM0oahUSFyt9G0W0wpOQjwY1JKz+oq/JgTxQ0yC3AqDX98IVWGdIXBpZbKsL/Npt2NlJaHMVpybuRK6FlNhX9572pUgJUWZF1qr/ZrM/uU7XO1G1s/rnahxzdWVb8Ibg7GVPu59Cy6wk85CSUbfR9utW+lP3HZdkMpVUuNCrFpp4O0lsD15zZW16IMP8dVTrsS3LN2ibX8ufXtUdvhBBynmwDQM/5mFk27IUrJQUCuq7VP/3yH6kvO2Xs4wLN1+y53z+FHsq1PI8i4wbWM2OALDbrYh0NyGUjsRdyqYaSYBcAbzdO0G6a0HATyvsvi9JOPnXbODb6QqqgKP5bSAmxo3dygC600YquM2OZlaivN+kW7/9kY3QCZat8TWx0OfZZDqXnYXS9HTw0tuVRt+NLdN5JGv2hboUHHDbjYYNO4QdjMYj6pZmFJP8s52N0eV0uNbp4QqjT8mox+0fY5xm+pyuAiafZjXLQlzWIq2pWYg4DMcFwO1Ri+xpOVYwdZH07QWWxehu5HCCVpKWkWtWtXcg4C8cYP5NG0aMPXmr7YWpD14Rr/2FVG6HZDKVVLqZYakN8oQpHSzpJuQ0hq6cmhaRGGL/2awXmkBtmhHWeiPnfy4v6oz+1Zu5S92gd0zEO6hWbZMKRaah7pC7dl7cbIQUBOS8+8c75MY9PDMm/eucvtPvpolnVpNPljg2sRsYEXWmnEzuGewzw0ZrMc46Idq5mH08dfs36x2lnJQ+4IrVzvvnj58UfnDsus3vBLNfohuEGnYRyeEAPRehGJx4JhSF+wgTxGoaGfpHZWcxDQN/7JGr602WsFWR/Lxi+FtNFraCltFlPUrpQcBPSMf3KGX6vR9+EEXcnGUZthSF6wAVv6SWlXYg4COlpOwvA1nqq0EmR9ajX+2oy+T80tNcmiy4J2faRysEuoposMv/jpkWOnS92zdqn4IPNw9o1zzGNNOMbVtESzBzb3Q1K7MfULhZOH3POlCVfHmG7HHJoWWeFrToaVM8AevOXZwb8/deVAlvVLVhlaFePUKkNP024xubSTzkFAp9r3DGlbdJfOjv/0cNZ1agbZvOBaRkrwSQeblHlIz39j2ew9TbthUrQbIwcBXdPvc/6zx8o0/NW719ydf/Db2danEWSxATaPmMCz1J+4jFLuvYTomqNKLEk7wK7Z58zDWF3HMv1m+CgvyLrUaPop3XLWq0PAdivNM4Z+0tpZykFgHNOfvOGXGmRdrJo+wDOOEu6/TK061NKv5eFycpj+IsMvfpTOMqTnUNEIstjtaPVb+9EDi8wgxwiD0sw+ZX1So3eGCNVOa9SPVbPX2I60X1Vt+KUO15uHZLDlCrSuOWgbRSpS51fLjFKR1E7SyKyfX66vSJ6rJMMnok8R0QtE9A4RDTYhZsudI6LvE9F3iehUyjYtMUagcbdp/SIWSundAdItNMuzgXLgaldCDloitcJ/HsBvAPh2wLK/6pz7xXl9S43xqcU0GrZocWWn8EoyfOfci865l3LtTE5q685pNBrTQeoimWWUDhF9C8DvOOcGu2uI6P8B+DsADsB/d849sWBdRwAcmf3689hsRdTK7QD+duydEKQdX9m04yuT3c65weE+S994RUTfALBj4F+/55z788Ad+BXn3AUiugPASSI645wb7AaaXQyemG37VM1dQO34yqYdX9nUfnxDLDV859zHUzfinLsw+/4mEX0FwH0I6/dvNBqNRibEh2US0VYi2uZ/BvBrqLubptFoNEySOizzk0S0DuCjAL5KRE/P/v4hIjoxW+yDAP6KiJ4D8NcAvuqc+3rgJub29VdCO76yacdXNrUf3w2Ynlqh0Wg0Gvmo+knbRqPRaLxLM/xGo9GYCGYMv/ZpGhjHdz8RvUREZ4nomOY+pkBEHyCik0T0g9n32+YsV5R+y/SgTT43+//3iCjfq5MUCDi+jxHR5Zle3yWix8fYz1iI6E+I6E0iGhwoUrp+bJxzJr4A3APgXwD4FoCDC5Y7B+D2sfdX4vgAbAHwCoCfA7AC4DkA946974HH918AHJv9fAzAfy5dvxA9ADwA4GsACMBHAPyfsfc78/F9DMD/GntfE47xXwI4AOD5Of8vVr+YLzMVvjM8TUMOAo/vPgBnnXOvOuc2AHwJwGH5vcvCYQBfmP38BQC/Pt6uZCNEj8MAvug2+Q6A9xPRndo7GknJ8RaE23zA88cLFilZPzZmDJ+BA/AXRHR6Ng1DTewE8Hrn9/XZ30rgg865NwBg9v2OOcuVpF+IHiVrFrrvHyWi54joa0T0YZ1dU6Nk/dgsfdI2J9rTNGiT4fho4G9mxs0uOj7GaszqN0CIHqY1W0LIvj+LzblZ/p6IHgDwZwD2Se+YIiXrx0bV8F3l0zRkOL51ALs6v68BuJC4zmwsOj4i+iER3emce2PWJH5zzjrM6jdAiB6mNVvC0n13zl3p/HyCiP6IiG53ztUy6VjJ+rEpqktnAtM0PANgHxHdTUQrAB4CcHzkfQrlOIDPzH7+DIAbWjQF6heix3EAn56N9vgIgMu+a6sAlh4fEe0gIpr9fB82PeNH6nsqR8n68Rn7rrH/AvBJbF5trwH4IYCnZ3//EIATs59/DpsjCZ4D8AI2u0pG3/dcxzf7/QEAL2Nz9ERJx/fPAXwTwA9m3z9Qg35DegA4CuDo7GcC8PnZ/7+PBSPMLH4FHN/DM62eA/AdAL889j4zj+9PAbwB4J9m+ffvatKP+9WmVmg0Go2JUFSXTqPRaDTiaYbfaDQaE6EZfqPRaEyEZviNRqMxEZrhNxqNxkRoht9oNBoToRl+o9FoTIT/D2anXxgArvpOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rastign_contour():\n",
    "    X = np.arange(-1.5, 1.5, 0.01)\n",
    "    Y = np.arange(-1.5, 1.5, 0.01)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = rastrigin(X,Y)\n",
    "    \n",
    "    plt.contourf(X,Y,Z)\n",
    "    plt.show()\n",
    "    \n",
    "rastign_contour()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton-Rapson method\n",
    "Below we create the Newton-Rapson method, which has the following stopping conditions: if the change per iteration is below a certain $\\epsilon_1$ (default: $\\epsilon_1 = 0.0001$), if it reaches it maximum number of iterations (default is 10.000), or if the norm of the step size is below an $\\epsilon_2$ (default: $\\epsilon_2 = 0.001$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mini_NR(func, x0, gradient, hessian, iteration_err = 0.0001, max_iterations = 10000, min_change = 0.001, advanced = False):\n",
    "    x: list = [np.inf, x0]\n",
    "    i = 0\n",
    "    \n",
    "    while np.abs(np.linalg.norm(x[-1] - x[-2])) > iteration_err and i < max_iterations or (advanced is True and i < max_iterations):\n",
    "        x.append(x[-1] - np.linalg.inv(hessian(x[-1][0], x[-1][1])).dot(gradient(x[-1][0], x[-1][1])))\n",
    "        i += 1\n",
    "\n",
    "        if np.linalg.norm(np.linalg.inv(hessian(x[-1][0], x[-1][1])).dot(gradient(x[-1][0], x[-1][1]))) < min_change and advanced is False:\n",
    "            break\n",
    "\n",
    "    print(f\"Newton Iterations: {i}\")\n",
    "\n",
    "    if advanced:\n",
    "        return np.array(x)\n",
    "\n",
    "    return x[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Differential Evolution\n",
    "Below we create the differential evolution method. There are two stopping conditions: maximum number of generations, or little diversity in the population (i.e. variance is below value)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def randint_multiple(start, stop, size):\n",
    "    \"\"\"Generate random int\"\"\"\n",
    "    random_ints = []\n",
    "    for _ in range(size):\n",
    "        random_ints.append(randint(start, stop))\n",
    "\n",
    "    return random_ints\n",
    "\n",
    "def generate_rand_bound(bound, size):\n",
    "    \"\"\"Generate random values in bound\"\"\"\n",
    "    length = np.abs(bound[0] - bound[1])\n",
    "    return np.add(np.random.rand(size) * length, bound[0])\n",
    "\n",
    "def generate_random_points(bound, size):\n",
    "    \"\"\"The most inefficient way to create random points in a bound!\"\"\"\n",
    "    a = []\n",
    "    for b in bound:\n",
    "        a.append(generate_rand_bound(b, size))\n",
    "        \n",
    "    c = np.zeros((size, bound.shape[0]))\n",
    "\n",
    "    for i in range(size):\n",
    "        for j in range(bound.shape[0]):\n",
    "            c[i][j] = a[j][i]\n",
    "\n",
    "    return c\n",
    "\n",
    "def get_values(func, estimations):\n",
    "    \"\"\"Calculate values of estimations\"\"\"\n",
    "    values = np.zeros(estimations.shape[0])\n",
    "\n",
    "    for i in range(estimations.shape[0]):\n",
    "        values[i] = func(estimations[i][0], estimations[i][1])\n",
    "\n",
    "    return values\n",
    "\n",
    "def mini_de(func, bound, popsize, mutation, max_generations = 100, max_std = 0.00000001, advanced = False, return_iterations=False):\n",
    "    \"\"\"Minimize\"\"\"\n",
    "    iterations = 0\n",
    "    # init with random points from bound.\n",
    "    x = [generate_random_points(bound, popsize)]\n",
    "    for i in range(1, max_generations):\n",
    "        z = np.zeros((popsize, bound.shape[0]))\n",
    "\n",
    "        for j in range(popsize):\n",
    "            r0, r1, r2 = randint_multiple(0, popsize - 1, 3)\n",
    "            z[j] = np.add(x[-1][r0], (x[-1][r1] - x[-1][r2]) * mutation)\n",
    "\n",
    "            if not (func(z[j][0], z[j][1]) <= func(x[-1][j][0], x[-1][j][1])):\n",
    "                z[j] = x[-1][j]\n",
    "\n",
    "        x.append(z)\n",
    "\n",
    "        if np.std(get_values(func, x[-1])) < max_std:\n",
    "            if return_iterations is False:\n",
    "                print(f\"DE iterations: {i}\")\n",
    "            iterations = i\n",
    "            break\n",
    "\n",
    "        if i == max_generations -1:\n",
    "            iterations = i\n",
    "            if return_iterations is False:\n",
    "                print(f\"DE evolutions: {i}\")\n",
    "\n",
    "    if advanced:\n",
    "        z = []\n",
    "        for a in x:\n",
    "            z.append(a[np.argmin(get_values(func, a))])\n",
    "        return np.array(z)\n",
    "\n",
    "    if return_iterations:\n",
    "        return x[-1][np.argmin(get_values(func, x[-1]))], iterations\n",
    "\n",
    "    return x[-1][np.argmin(get_values(func, x[-1]))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Population size\n",
    "We can test how the population size impacts the convergence speed, and quality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True: [1 1]\n",
      "\n",
      "Population 10:\n",
      "x Mean: -0.07818364754818696, x Est. std.: 0.07892380073768945, Avg. Iterations: 116.88\n",
      "\n",
      "Population 25:\n",
      "x Mean: 1.0000212618963464, x Est. std.: 7.635877880884934e-06, Avg. Iterations: 75.18\n",
      "\n",
      "Population 50:\n",
      "x Mean: 0.9999993767788082, x Est. std.: 3.815156101594219e-07, Avg. Iterations: 79.02\n",
      "\n",
      "Population 100:\n",
      "x Mean: 0.9999928843685496, x Est. std.: 2.96151120815491e-06, Avg. Iterations: 82.14\n",
      "\n",
      "Population 250:\n",
      "x Mean: 1.0000039717297813, x Est. std.: 1.202857918602973e-06, Avg. Iterations: 85.02\n",
      "\n",
      "Population 1000:\n",
      "x Mean: 1.00000031119419, x Est. std.: 9.687411728354078e-08, Avg. Iterations: 84.86\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def population_change():\n",
    "    n = 50\n",
    "\n",
    "    true_value = np.array([1, 1])\n",
    "    print(f\"True: {true_value}\")\n",
    "    print(\"\")\n",
    "    \n",
    "    print(\"Population 10:\")\n",
    "    pop10 = np.zeros((n, 2))\n",
    "    iter10 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop10[i], iter10[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 10, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop10[:][0].mean()}, x Est. std.: {pop10[:][0].std()}, Avg. Iterations: {iter10.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Population 25:\")\n",
    "    pop25 = np.zeros((n, 2))\n",
    "    iter25 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop25[i], iter25[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 25, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop25[:][0].mean()}, x Est. std.: {pop25[:][0].std()}, Avg. Iterations: {iter25.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Population 50:\")\n",
    "    pop50 = np.zeros((n, 2))\n",
    "    iter50 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop50[i], iter50[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 50, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop50[:][0].mean()}, x Est. std.: {pop50[:][0].std()}, Avg. Iterations: {iter50.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Population 100:\")\n",
    "    pop100 = np.zeros((n, 2))\n",
    "    iter100 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop100[i], iter100[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop100[:][0].mean()}, x Est. std.: {pop100[:][0].std()}, Avg. Iterations: {iter100.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Population 250:\")\n",
    "    pop250 = np.zeros((n, 2))\n",
    "    iter250 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop250[i], iter250[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 250, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop250[:][0].mean()}, x Est. std.: {pop250[:][0].std()}, Avg. Iterations: {iter250.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Population 1000:\")\n",
    "    pop1000 = np.zeros((n, 2))\n",
    "    iter1000 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        pop1000[i], iter1000[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 250, 0.8, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {pop1000[:][0].mean()}, x Est. std.: {pop1000[:][0].std()}, Avg. Iterations: {iter1000.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "population_change()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that for small poplulations, a lot of iterations are needed. However after populations of 25 we can see that the average iterations needed increase again. This makes sense, as there are more points and the main stopping condition is that the standard deviation is below a certain threshold. However if we look at the std. deviation of the estimation, it seems that the estimations with larger population sizes are much closer together (and also closer to the true value).\n",
    "\n",
    "### Mutation\n",
    "We can test how the mutation impacts the convergence speed, and quality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True: [1 1]\n",
      "\n",
      "Mutation 0.1:\n",
      "x Mean: 1.0000009528603058, x Est. std.: 3.3403557475608636e-07, Avg. Iterations: 49.7\n",
      "\n",
      "Mutation 0.25:\n",
      "x Mean: 0.9999922763932891, x Est. std.: 2.5596553510642828e-06, Avg. Iterations: 45.03\n",
      "\n",
      "Mutation 0.5:\n",
      "x Mean: 1.0000113547565546, x Est. std.: 3.4021191070987555e-06, Avg. Iterations: 57.02\n",
      "\n",
      "Mutation 0.75:\n",
      "x Mean: 1.0000100267782535, x Est. std.: 3.30490805444672e-06, Avg. Iterations: 78.75\n",
      "\n",
      "Mutation 1:\n",
      "x Mean: 0.9999967848409184, x Est. std.: 1.3530444133991182e-06, Avg. Iterations: 106.9\n",
      "\n",
      "Mutation 1.25:\n",
      "x Mean: 1.0000058061158388, x Est. std.: 1.9054934622397823e-06, Avg. Iterations: 144.3\n",
      "\n",
      "Mutation 1.5:\n",
      "x Mean: 0.9999985363871788, x Est. std.: 8.771165795895541e-07, Avg. Iterations: 186.31\n",
      "\n",
      "Mutation 1.75:\n",
      "x Mean: 0.20752274839193596, x Est. std.: 0.041675146786874784, Avg. Iterations: 28.74\n",
      "\n",
      "Mutation 2:\n",
      "x Mean: 4.318127911688428, x Est. std.: 1.69475195467408, Avg. Iterations: 23.42\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def mutation_change():\n",
    "    n = 100\n",
    "\n",
    "    true_value = np.array([1, 1])\n",
    "    print(f\"True: {true_value}\")\n",
    "    print(\"\")\n",
    "    \n",
    "    print(\"Mutation 0.1:\")\n",
    "    mut01 = np.zeros((n, 2))\n",
    "    iter01 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut01[i], iter01[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.1, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut01[:][0].mean()}, x Est. std.: {mut01[:][0].std()}, Avg. Iterations: {iter01.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 0.25:\")\n",
    "    mut025 = np.zeros((n, 2))\n",
    "    iter025 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut025[i], iter025[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.25, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut025[:][0].mean()}, x Est. std.: {mut025[:][0].std()}, Avg. Iterations: {iter025.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 0.5:\")\n",
    "    mut05 = np.zeros((n, 2))\n",
    "    iter05 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut05[i], iter05[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.5, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut05[:][0].mean()}, x Est. std.: {mut05[:][0].std()}, Avg. Iterations: {iter05.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 0.75:\")\n",
    "    mut075 = np.zeros((n, 2))\n",
    "    iter075= np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut075[i], iter075[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.75, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut075[:][0].mean()}, x Est. std.: {mut075[:][0].std()}, Avg. Iterations: {iter075.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 1:\")\n",
    "    mut1 = np.zeros((n, 2))\n",
    "    iter1 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut1[i], iter1[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 1, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut1[:][0].mean()}, x Est. std.: {mut1[:][0].std()}, Avg. Iterations: {iter1.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 1.25:\")\n",
    "    mut125 = np.zeros((n, 2))\n",
    "    iter125 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut125[i], iter125[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 1.25, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut125[:][0].mean()}, x Est. std.: {mut125[:][0].std()}, Avg. Iterations: {iter125.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 1.5:\")\n",
    "    mut15 = np.zeros((n, 2))\n",
    "    iter15 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut15[i], iter15[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 1.5, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut15[:][0].mean()}, x Est. std.: {mut15[:][0].std()}, Avg. Iterations: {iter15.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 1.75:\")\n",
    "    mut175 = np.zeros((n, 2))\n",
    "    iter175 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut175[i], iter175[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 10, 1.75, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut175[:][0].mean()}, x Est. std.: {mut175[:][0].std()}, Avg. Iterations: {iter175.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "    print(\"Mutation 2:\")\n",
    "    mut2 = np.zeros((n, 2))\n",
    "    iter2 = np.zeros(n)\n",
    "    for i in range(n):\n",
    "        mut2[i], iter2[i] = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 10, 2, max_generations=1000, return_iterations=True)\n",
    "    print(f\"x Mean: {mut2[:][0].mean()}, x Est. std.: {mut2[:][0].std()}, Avg. Iterations: {iter2.mean()}\")\n",
    "    print(\"\")\n",
    "\n",
    "mutation_change()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that for a mutation closer to 1 means a lower std. dev. for the estimation. We can also see that the average iterations sharply increase until a mutation of $1.5$, afterwards it lowers to it's lowest value. However the standard deviation also increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rosenberg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Newton Iterations: 4\n",
      "DE iterations: 89\n",
      "Newton min: [1.         0.99999936]\n",
      "Be min: [1.00001206 1.00002444]\n"
     ]
    }
   ],
   "source": [
    "def rosenburg_min():\n",
    "    x0 = np.array([5, 5])\n",
    "    x_min_newton = mini_NR(rosenburg, x0, rosenburg_grad, rosenburg_hessian, 0.00001)\n",
    "    x_min_be = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.8)\n",
    "\n",
    "    print(f\"Newton min: {x_min_newton}\")\n",
    "    print(f\"Be min: {x_min_be}\")\n",
    "\n",
    "rosenburg_min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rastrigin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Newton Iterations: 1\n",
      "DE evolutions: 99\n",
      "Newton min: [-1.31137202e-05 -1.31137202e-05]\n",
      "DE min: [4.97483779e-01 4.97889002e-05]\n"
     ]
    }
   ],
   "source": [
    "def rastrigin_min():\n",
    "    x0=np.array([0.01, 0.01])\n",
    "    x_min_newton = mini_NR(rastrigin, x0, rastrigin_grad, rastrigin_hessian, 0.000001)\n",
    "    x_min_de = mini_de(rastrigin, np.array([[-5, 5], [-5, 5]]), 100, 0.8)\n",
    "\n",
    "    print(f\"Newton min: {x_min_newton}\")\n",
    "    print(f\"DE min: {x_min_de}\")\n",
    "\n",
    "rastrigin_min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Newton Iterations: 25\n",
      "DE iterations: 81\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAecElEQVR4nO3de3TVZ53v8fc3IQkhl3LbIRhIIQES0HppI7XqsdVapU4rjuMFvNYyRV3i8Sw950zVc87oeGbqmlnjnDPTqqWWoT3jgKh1pBXFseqga7BCO3YKEyhpSiXlkgAtkAC5fs8fewfSkB12si+/3/7tz2stVtkPye/3Za/dTx6e5/k9j7k7IiISfUVBFyAiIrmhwBcRKRAKfBGRAqHAFxEpEAp8EZECMSXoAsYze/ZsX7BgQdBliIjklccff/y4u8dGt4c68BcsWMDu3buDLkNEJK+Y2XNjtYdySMfMbjWz9adOnQq6FBGRyAhl4Lv7w+6+9oorrgi6FBGRyAhl4IuISOaFMvA1pCMiknmhDHwN6YiIZF4oA19ERDIvlIGvIR0RkcwLZeAHPaSz5/lTPLjzIAeP9wRyfxGRbAj1g1dBePLQi3zoW49xpncAgIZYBTc21/CW5jm0LJhBSXEof0aKiFyWAn+EvYdP8eH7H2N6RQkbb1/OUx0v8ui+Th741+e471fPUjV1CtcviXHj0hpuWFLDjIrSoEsWEUmZhfHEKzO7Fbh10aJFdxw4cCAn99x/9Ayr1u+kvKSY73z8OubPnHbhz7p7B/j1geP8fN8xfr6vi+PdvRQZXF0/g7csreHG5jksmVOJmeWkVhGR8ZjZ4+7eckl7GAN/WEtLi+diL51nurp5/72/ochgy8evY8HsiqRfOzTkPPX8KR7d18nP9x1jz/OnAaibXs6NS2t4S3MNr2uYxdSS4qzXLSIyFgV+Es+d6OF99+5kcMjZvPY6FtVUTuj7j546zy/2d/Joaye/buvifP8Q5SXFvP+18/nSO1+epapFRJJT4I+h44WzvP/e33C2b4DNa6+jqbYqreud7x9kZ/sJ1v9LO7sOnqT1Kys0ySsiOZcs8As2jY6cOscH7nuMM+f7+X9rrk077AGmlhTz5qYa3vfaeQwMOc+dOJuBSkVEMiNngW9mDWZ2v5l9L1f3TKbzzHk+eN9jnOzp48E11/KKusyu92+MxYeFnunqzuh1RUTSkVbgm9kGM+s0sz2j2leY2X4zazOzOwHcvd3d16Rzv0w40d3LB+97jKOnz7PxY6/l1fOnZ/weDQp8EQmhdHv4G4EVIxvMrBi4B7gZWAasNrNlad4nI14828eH7v8tvz95lm99tIWWBTOzcp/KsinMqS6jvUtP6opIeKQV+O6+Azg5qnk50Jbo0fcBm4GVqV7TzNaa2W4z293V1ZVOeS9x+nw/H9nwW57p7Gb9R1p4fePsjF17LI2xSvXwRSRUsjGGXwccGvG6A6gzs1lm9k3gNWb2+WTf7O7r3b3F3VtisUvO4J2U7t4BbtvwW/7j8Gm+8aGruX5JZq47nsZYJc90dhPmVVAiUliysbXCWI+burufAD6R0gUuPmmbdjHn+gZZs3EXT3ac4u7Vr+HGpXPSvmYqGmMVnD4/wPHuPmJVZTm5p4jIeLLRw+8A5o94PQ84nIX7XNb5/kHueHA3uw6e5GvvexU3XzU3Z/fWxK2IhE02An8XsNjMFppZKbAK2JqF+4yrb2CIT/7D4/y67Th/+Z5XsfLVdTm9f2PiiV1N3IpIWKS7LHMTsBNoMrMOM1vj7gPAOmA70Apscfe9E7luuvvh9w8O8elNT/CL/V38xR9exXuumTep66RjbvVUykuK1cMXkdBIawzf3Vcnad8GbJvsddMdw//CQ0+xfe8xvnTrMj5wbf1ky0hLUZHREKtQ4ItIaIRya4V0e/jvuWYe//OWZdz2hoUZrmxitDRTRMIklIGf7pm21zbMYs0bgw17iJ+W1fHCOc73DwZdiohIOAM/6DNtM6UxVok7HDyhiVsRCV4oAz8qLmyi1qnAF5HghTLw0x3SCYuFsysw01p8EQmHUAZ+VIZ0ykuLqZtersAXkVAIZeBHSYNW6ohISIQy8KMypAPxPXXau3q0iZqIBC6UgR+VIR2IT9ye7Rvk6OnzQZciIgUulIEfJVqpIyJhkY3tkYN3+N/gzDEoq4TSCiitSvy+EkqmQVHufs411lQA8ZU6b1yc3UNXRETGE83Af+xeeHJTkj+0xA+BxA+DssoRPxAS7WVVMKWMsbf2n5gY8IWydhY8uR3OZf/gFcmQqdWw9J0wM/gntkUyxcI4mThi87Q7Dhw4MPELnHoeuo9CXw/0dkNfN/Seib/u6060nRn/zwcyN+Y+mHiPiy39HyCSI57YDqP+9fCqVfDyd8HU/J9TksJgZo+7e8sl7WEM/GEtLS2+e/fuoMtI22e3/I6dz5xg5+dvDLoUSdWLh+CpLfDkZjj+NBSXQfM74FWrofEtUFwSdIUiSSUL/GgO6YRMY6ySh554nu7eASrL9Jbnhenz4T99Dt742fic0JObYc/3YO8PoCIGV7033vOvfSXoX26SJ5Q+OTC8UufZrh6umqdhgbxiBnVXx3+97X9D28/i80O7vgW/+TrElsaD/5Xvg+qXBV2tyLhyFvhmVgF8HegDfunu387VvYPWGLu4UkeBn8emlMaHdZrfAedeiPf2n9wMP/tT+NmXoOGG+JDP0lviCwBEQibdIw43mFmnme0Z1b7CzPabWZuZ3ZlofjfwPXe/A3hnOvfNN/WzplFcZNpiIUrKZ0DL7bDmp/DpJ+D6/w4n2+EHa+GvFsMP18HZk0FXKfIS6S5I3wisGNlgZsXAPcDNwDJgtZktA+YBhxJfVlAngpRNKaZ+5jQdaB5VsxrhzV+AzzwJH/sJXPVH8Z7/vddDR/4vOpDoSCvw3X0HMLobsxxoc/d2d+8DNgMrgQ7ioT/ufc1srZntNrPdXV1d6ZQXKo063zb6zODK6+Cdfwdrtscf49iwAnZ+HUK8Gk4KRzYeOa3jYk8e4kFfBzwE/JGZfQN4ONk3u/t6d29x95ZYLDoPKjXGKmk/3sPgkP7HLwh118DHd8Dit8H2z8N3PgTnXgy6Kilw2Qj8sdaoubv3uPvH3P2Tl5uwjdJumcMaYhX0DQzx/Avngi5FcqV8Bqz6Nrz9L+Dpn8C9b4Lnnwi6Kilg2Qj8DmD+iNfzgMNZuE9eubCJmoZ1CosZXPep+Ni+D8GGt8Nj6zXEI4HIRuDvAhab2UIzKwVWAVuzcJ+8osAvcPNfGx/iaXwL/Pi/wXdvg/PR+Res5Id0l2VuAnYCTWbWYWZr3H0AWAdsB1qBLe6+dyLXjdJ++MNmVJQys6KUZ7RSp3BNmwmrNsFNfwatD8dX8Rz+XdBVSQFJd5XOanef6+4l7j7P3e9PtG9z9yXu3ujufz7R60ZxDB+0UkeIb839hs/Ax7bBQC/cfxPsul9DPJIToTwAJYo9fICG2ZW0K/AFoP518Ilfw8I3wY8+C99fE9+xVSSLQhn4ke3h11RwvLuPU2f7gy5FwqBiFnzgu3Dj/4pv03Dv9XD0qaCrkggLZeBHtYd/YeL2uHr5klBUFN+V86OPxM9j+NZb4fGNGuKRrNBumTl08Xzbbq6unxFwNRIqC94QH+J56A54+DOwbxvMWBB0VflrajVctw7KpwddSaiEMvBHnHgVdCkZNW9GOaXFRVqpI2OrjMGHHoJf/TX89l449FjQFeWv3tPxlVAf2AIzrgy6mtDQiVc5dtPX/oUFsyu47yOXHEYjIpny7I74dhbFZfCBzfGtLgpIshOvQjmGH2WNsUotzRTJtoVvgjX/DCXl8Pd/EO/tSzgDP6qrdCC+Uuf3J87SPzgUdCki0RZrgj9+FOa8HL7zYfjXuwt+MjyUgR/VVToQ7+EPDDm/P3k26FJEoq8yBrc9AktvhZ9+Ebb9VxgcCLqqwIQy8KNs5EodEcmBknJ47wPw+v8cP4t48+qCfchNgZ9jDRfOt9VKHZGcKSqCt30FbvkbaHsU/v5mOF14m/gq8HOsamoJNVVlmrgVCULL7fGlmicPwn03FtyTzaEM/ChP2kLi9CsFvkgwFr8Vbv9J/KyCDSvg6Z8GXVHOhDLwozxpC/GVOs909RDmZyBEIq32FfEVPDMbYNP742P7BSCUgR91jbFKTp3r50RPX9CliBSu6rnwsR/Hzx3+0edg+xdhKNrLpRX4AWjQSh2RcCirhFX/CMvXws67YcuHoS+6S6ZzFvhm1mBm95vZ93J1z7Bq1EodkfAoKoZ3/BWs+Crs+xE8cAt0dwZdVVaktHmamW0AbgE63f0VI9pXAP8XKAa+5e5fTXYNd28H1ijw4WVXlDO1pEgTtyJh8rpPwvR6+P4fwzffCDMbg63nHX8JtVdl9JKp7pa5EbgbeHC4wcyKgXuAm4AOYJeZbSUe/neN+v7b3T2aPzInoajIaJitPXVEQqf5D+C2H8Ev74L+c0FXk3EpBb677zCzBaOalwNtiZ47ZrYZWOnudxH/18CkmNlaYC1AfX39ZC8Teg2xCv69I5rLTkXyWt3V8MHvBl1FVqQzhl8HHBrxuiPRNiYzm2Vm3wReY2afT/Z17r7e3VvcvSUWi6VRXrg1xio59MJZzvcPBl2KiBSIdA5AsTHaki4sd/cTwCdSunBED0AZqbGmEnc4eKKH5trqoMsRkQKQTg+/A5g/4vU8oPA2p5ik4ZU67VqpIyI5kk7g7wIWm9lCMysFVgFbM1NW9DXM1lp8EcmtlALfzDYBO4EmM+swszXuPgCsA7YDrcAWd9+biaKivrUCQHlpMXXTy7VSR0RyJtVVOquTtG8DtmW0IgpjDB/iK3X08JWI5Eoot1YohB4+XNw1U5uoiUguhDLwo7498rDGmkp6+gY5dro36FJEpACEMvALp4c/vKeOxvFFJPtCGfiF4sL5tgp8EcmBUAZ+oQzp1FSVUVk2RUszRSQnQhn4hTKkY2Y0aqWOiORIKAO/kDTGtGumiORGKAO/UIZ0IL5S58ip8/T0DgRdiohEXCgDv1CGdAAaZsdX6jx7XMM6IpJdoQz8QtJYo5U6IpIbCvyAXTlrGkWmTdREJPsU+AErm1JM/cxpWqkjIlkXysAvpElb0EodEcmNUAZ+IU3aQnzXzGeP9zA4pE3URCR7Qhn4haYxVknvwBCHXzwXdCkiEmEK/BAYXqnTpmEdEcminAa+mb3LzO4zsx+a2dtyee8wu7CJmlbqiEgWpRz4ZrbBzDrNbM+o9hVmtt/M2szszvGu4e7/5O53ALcB759UxRE0s6KUGdNKaNfDVyKSRSkdcZiwEbgbeHC4wcyKgXuAm4AOYJeZbQWKgbtGff/t7t6Z+P3/SHyfJDTEKtXDF5GsSjnw3X2HmS0Y1bwcaHP3dgAz2wysdPe7gFtGX8PMDPgq8GN3f2LSVUdQY6yCn+/rCroMEYmwdMfw64BDI153JNqS+TTwVuA9ZvaJsb7AzNaa2W4z293VVTgB2Bir5Hh3L6fO9gddiohE1ESGdMZiY7QlXUzu7n8L/O14F3T39WZ2BLi1tLT0mjTryxsXJm6Pd3N1/YyAqxGRKEq3h98BzB/xeh5wOM1rFqThpZnt2mJBRLIk3cDfBSw2s4VmVgqsAramW1ShPWkLMH9GOSXFpi0WRCRrJrIscxOwE2gysw4zW+PuA8A6YDvQCmxx973pFlVoe+kATCku4spZFVqpIyJZM5FVOquTtG8DtmWsogLWGKugTYEvIlkSyq0VCnFIB+ITt8+dOEv/4FDQpYhIBIUy8AtxSAfigT8w5Bw6eTboUkQkgkIZ+IXaw2+Ixc+31WEoIpINoQz8QtUQ0/m2IpI9oQz8Qh3SuaK8hFhVmVbqiEhWhDLwC3VIB+IrddTDF5FsCGXgF7L4+bY9uOu4QxHJrFAGfqEO6UB8HP/UuX5O9vQFXYqIREwoA7/Qh3RAK3VEJPNCGfiFrFErdUQkSxT4IVM3vZyyKUVaqSMiGafAD5miImPh7AqdbysiGRfKwC/kSVuI742vTdREJNNCGfiFPGkLsLimkkMvnOVs30DQpYhIhIQy8Atdc2017nDgmHr5IpI5CvwQaq6tAmDf0dMBVyIiUZKzwDezpWb2TTP7npl9Mlf3zUf1M6dRXlLMvqNngi5FRCIkpcA3sw1m1mlme0a1rzCz/WbWZmZ3jncNd291908A7wNaJl9y9BUVGU21Vew7osAXkcxJtYe/EVgxssHMioF7gJuBZcBqM1tmZleZ2SOjftUkvuedwK+BRzP2N4io5toq9h09rT11RCRjUgp8d98BnBzVvBxoc/d2d+8DNgMr3f0pd79l1K/OxHW2uvvrgQ9m8i8RRc21Vbxwtp+uM71BlyIiEZHyIeZjqAMOjXjdAVyb7IvN7Abg3UAZ4xx6bmZrgbUA9fX1aZSX35pqqwFoPXqGmuqpAVcjIlGQTuDbGG1Jxx/c/ZfALy93UXdfb2ZHgFtLS0uvmXR1ee7CSp0jp7l+SSzgakQkCtJZpdMBzB/xeh5wOL1yZNiMilJqq6eyXyt1RCRD0gn8XcBiM1toZqXAKmBrJooq9CdthzXVVtGqwBeRDEl1WeYmYCfQZGYdZrbG3QeAdcB2oBXY4u57M1FUoe+lM6x5bhVtnWfoHxwKuhQRiYCUxvDdfXWS9m2MMwEr6VlaW03/oPPs8R6WzKkKuhwRyXOh3FpBQzpxTYmJ29Yj2mJBRNIXysDXkE5cY6ySKUWmiVsRyYhQBr56+HGlU4pojFVqTx0RyYhQBr5c1Dy3in0a0hGRDAhl4GtI56Lm2moOnzrPqXP9QZciInkulIGvIZ2Lhp+41Ti+iKQrlIEvFzXP1WEoIpIZoQx8DelcVFs9lSvKSzRxKyJpC2Xga0jnIrPhw1DUwxeR9IQy8OWlltZW8fSxboaGdBiKiEyeAj8PNM+tprt3gOdfPBd0KSKSxxT4eUBbLIhIJoQy8DVp+1JNc7Q0U0TSF8rA16TtS1WUTaF+5jSt1BGRtIQy8OVSzbVVtGotvoikQYGfJ5rnVnPweA/n+weDLkVE8lROA9/MKszscTO7JZf3jYLm2iqGHA4c6w66FBHJU6kecbjBzDrNbM+o9hVmtt/M2szszhQu9SfAlskUWuiG99TRsI6ITFZKRxwCG4G7gQeHG8ysGLgHuAnoAHaZ2VagGLhr1PffDrwS+A9ganolF6YrZ1UwtaRIK3VEZNJSPdN2h5ktGNW8HGhz93YAM9sMrHT3u4BLhmzM7M1ABbAMOGdm29xdp3OnqLjIWDKnSpuoicikpdrDH0sdcGjE6w7g2mRf7O5fBDCz24DjycLezNYCawHq6+vTKC96mmur+Pm+zqDLEJE8lc6krY3RdtnNXtx9o7s/Ms6frwe+DDxRWlqaRnnR01RbzfHuPrrO9AZdiojkoXQCvwOYP+L1POBweuXIeJbWam98EZm8dAJ/F7DYzBaaWSmwCtiaiaL0pO3YmnT6lYikIdVlmZuAnUCTmXWY2Rp3HwDWAduBVmCLu+/NRFHaS2dssyrLiFWV0XpEgS8iE5fqKp3VSdq3AdsyWpGMq7lWK3VEZHJCubWChnSSWzq3mgOd3QwMakWriExMKANfkmuaU0XfwBAHT/QEXYqI5JlQBr7G8JNrnju8Ukfj+CIyMaEMfA3pJLeoppLiImOfJm5FZIJCGfjq4SdXNqWYhtkVmrgVkQkLZeCrhz++5rnVGtIRkQkLZeDL+Jprq+h44Rynz/cHXYqI5JFQBr6GdMY3vDf+0+rli8gEhDLwNaQzvua51YBW6ojIxIQy8GV8L7tiKlVTp2jiVkQmRIGfh8yM5toqbaImIhOiwM9TzbXV7DtyBvfLHkEgIgKENPA1aXt5TbVVnOkd4PkXzwVdiojkiVAGviZtL2/pXO2NLyITE8rAl8tbMkd76ojIxCjw81TV1BLmzSin9YhW6ohIanIW+GZ2g5n9ysy+aWY35Oq+UdZcW60hHRFJWapHHG4ws04z2zOqfYWZ7TezNjO78zKXcaAbmEr8AHRJU3NtFe3HezjfPxh0KSKSB1Lt4W8EVoxsMLNi4B7gZmAZsNrMlpnZVWb2yKhfNcCv3P1m4E+AL2fur1C4mudWMTjktHV2B12KiOSBVM+03WFmC0Y1Lwfa3L0dwMw2Ayvd/S7glnEu9wJQNolaZZTm2vgWC/uPnuEVdVrRJCLjSynwk6gDDo143QFcm+yLzezdwNuB6cDd43zdWmAtQH19fRrlRd+CWdMonVKkLRZEJCXpBL6N0Zb0sU93fwh46HIXdff1ZnYEuLW0tPSaNOqLvCnFRSyZU6mlmSKSknRW6XQA80e8ngccTq8cmajmWh2GIiKpSSfwdwGLzWyhmZUCq4CtmShKT9qmrrm2iq4zvZzo7g26FBEJuVSXZW4CdgJNZtZhZmvcfQBYB2wHWoEt7r43E0VpL53UjZy4FREZT6qrdFYnad8GbMtoRfHrPgw83NLSckemrx01TYnTr1qPnuH1i2YHXI2IhFkot1ZQDz91saoyZleWsk9bLIjIZYQy8DWGPzHNtdXsP6YhHREZXygDXz38iWlKnH41OKTDUEQkuVAGvnr4E9NcW0XvwBDPnegJuhQRCbFQBr56+BOzdG58pY7W44vIeEIZ+OrhT8yimkqKDE3cisi4Qhn4MjFTS4pZOLtCPXwRGVcoA19DOhOnLRZE5HJCGfga0pm45toqfn/yLN29A0GXIiIhFcrAl4lrTkzcPq31+CKShAI/IpoTWyzsO6LAF5GxKfAjom56OZVlU9ivw1BEJIlQBr4mbSeuqMhoqq2iVRO3IpJEKANfk7aT01Rbxb4jp3HXFgsicqlQBr5MztLaKk6fH+Do6fNBlyIiIaTAj5DhlTqauBWRsSjwI2TJnOHDUDRxKyKXSunEq0wwsyLgK0A1sNvdH8jVvQvFFeUl1E0v13GHIjKmVM+03WBmnWa2Z1T7CjPbb2ZtZnbnZS6zEqgD+oGOyZUrlxOfuFXgi8ilUh3S2QisGNlgZsXAPcDNwDJgtZktM7OrzOyRUb9qgCZgp7t/Fvhk5v4KMlJzbRXPdHXTNzAUdCkiEjKpHmK+w8wWjGpeDrS5ezuAmW0GVrr7XcAto69hZh1AX+LlYLJ7mdlaYC1AfX19KuXJCM1zqxkYcp7p6r6wT76ICKQ3aVsHHBrxuiPRlsxDwNvN7O+AHcm+yN3XA18GnigtLU2jvMJ0YYsFTdyKyCjpTNraGG1Jn/hx97PAmjTuJylYOLuC0uIibZUsIpdIp4ffAcwf8XoecDi9cuL0pO3klRQXsaimUhO3InKJdAJ/F7DYzBaaWSmwCtiaiaK0l056mmurNKQjIpdIdVnmJmAn0GRmHWa2xt0HgHXAdqAV2OLuezNRlHr46ZldVcbpczoIRUReKtVVOquTtG8DtmW0IuI9fODWRYsWZfrSIiIFK5RbK6iHLyKSeaEMfI3hi4hkXigDXz18EZHMC2Xgq4cvIpJ5oQx89fBFRDIvlIEvIiKZF8rA15COiEjmhTLwNaSTPk++rZGIFChzD28wmFkX8Nwkv302cDyD5USd3q+J0fs1MXq/Jibd9+tKd4+Nbgx14KfDzHa7e0vQdeQLvV8To/drYvR+TUy23q9QDumIiEjmKfBFRApElAN/fdAF5Bm9XxOj92ti9H5NTFber8iO4YuIyEtFuYcvIiIjKPBFRApEJAPfzFaY2X4zazOzO4OuJ+zM7KCZPWVmvzOz3UHXEzZmtsHMOs1sz4i2mWb2z2Z2IPHfGUHWGCZJ3q8vmdnzic/Y78zsHUHWGCZmNt/MfmFmrWa218w+k2jP+GcscoFvZsXAPcDNwDJgtZktC7aqvPBmd3+11kqPaSOwYlTbncCj7r4YeDTxWuI2cun7BfA3ic/YqxOn5UncAPA5d18KvA74VCKzMv4Zi1zgA8uBNndvd/c+YDOwMuCaJI+5+w7g5KjmlcADid8/ALwrlzWFWZL3S5Jw9yPu/kTi92eInxFeRxY+Y1EM/Drg0IjXHYk2Sc6Bn5rZ42a2Nuhi8sQcdz8C8f9hgZqA68kH68zs3xNDPhoCG4OZLQBeAzxGFj5jUQx8G6NNa0/H9wZ3v5r4MNinzOxNQRckkfMNoBF4NXAE+OtAqwkhM6sEvg/8F3c/nY17RDHwO4D5I17PAw4HVEtecPfDif92Aj8gPiwm4ztmZnMBEv/tDLieUHP3Y+4+6O5DwH3oM/YSZlZCPOy/7e4PJZoz/hmLYuDvAhab2UIzKwVWAVsDrim0zKzCzKqGfw+8Ddgz/ncJ8c/URxO//yjwwwBrCb3h4Er4Q/QZu8DMDLgfaHX3r434o4x/xiL5pG1iydf/AYqBDe7+58FWFF5m1kC8Vw8wBfhHvV8vZWabgBuIb1l7DPhT4J+ALUA98Hvgve6uiUqSvl83EB/OceAg8PHh8elCZ2ZvBH4FPAUMJZq/QHwcP6OfsUgGvoiIXCqKQzoiIjIGBb6ISIFQ4IuIFAgFvohIgVDgi4gUCAW+iEiBUOCLiBSI/w98S/7c7/+CSQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def distance(est, true):\n",
    "    retur = np.zeros(est.shape[0])\n",
    "    for i, e in enumerate(est):\n",
    "        retur[i] = np.linalg.norm(e - true)\n",
    "\n",
    "    return retur\n",
    " \n",
    "def convergence_plot():\n",
    "    x0 = np.array([5, 5])\n",
    "    warnings.filterwarnings('ignore')\n",
    "    y_min_newton = mini_NR(rosenburg, x0, rosenburg_grad, rosenburg_hessian, 0, max_iterations=25, advanced=True)\n",
    "    y_min_de = mini_de(rosenburg, np.array([[-5, 5], [-5, 5]]), 100, 0.8, advanced=True)\n",
    "\n",
    "    true = np.array([1, 1])\n",
    "\n",
    "    x = np.linspace(0, 20, 20)\n",
    "    plt.plot(x, distance(y_min_newton, true)[1:21])\n",
    "    plt.plot(x, distance(y_min_de, true)[:20])\n",
    "    plt.yscale('log')\n",
    "    plt.xticks([0, 5, 10, 15, 20])\n",
    "    plt.show()\n",
    "\n",
    "convergence_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly you can see that the Newtons Method (blue) converges much quicker then then the Differential Evolution (orange) method."
   ]
  }
 ],
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