Tutorial_21_FindingRoots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving Non-linear Equations\n",
    "\n",
    "The [Roots.jl](https://github.com/JuliaMath/Roots.jl) package provides methods for solving a non-linear equation (one variable, one function). \n",
    "\n",
    "For a system of non-linear equations, use [NLsolve.jl](https://github.com/JuliaNLSolvers/NLsolve.jl)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "@doc2"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Printf, Roots, NLsolve\n",
    "\n",
    "include(\"src/printmat.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining and Plotting the Function\n",
    "\n",
    "In the next few cells, we define a fairly simple function and then plot it. \n",
    "\n",
    "If possible, plot your function before trying to find the roots. Maybe you see something strange, perhaps there are several roots? It also helps you set the initial guesses (or brackets) for root solving."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fn1 (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fn1(x,c) = 2*(x - 1.1)^2 - c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"480\" height=\"320\" viewBox=\"0 0 1920 1280\">\n",
       "<defs>\n",
       "  <clipPath id=\"clip090\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"1920\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip090)\" d=\"M0 1280 L1920 1280 L1920 0 L0 0  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip091\">\n",
       "    <rect x=\"384\" y=\"0\" width=\"1345\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip090)\" d=\"M170.645 1106.38 L1872.76 1106.38 L1872.76 123.472 L170.645 123.472  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip092\">\n",
       "    <rect x=\"170\" y=\"123\" width=\"1703\" height=\"984\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"218.818,1106.38 218.818,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"620.259,1106.38 620.259,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1021.7,1106.38 1021.7,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1423.14,1106.38 1423.14,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1824.58,1106.38 1824.58,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"170.645,1026 1872.76,1026 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"170.645,815.73 1872.76,815.73 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"170.645,605.464 1872.76,605.464 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"170.645,395.198 1872.76,395.198 \"/>\n",
       "<polyline clip-path=\"url(#clip092)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"170.645,184.933 1872.76,184.933 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,1106.38 1872.76,1106.38 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"218.818,1106.38 218.818,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"620.259,1106.38 620.259,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1021.7,1106.38 1021.7,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1423.14,1106.38 1423.14,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1824.58,1106.38 1824.58,1087.48 \"/>\n",
       "<path clip-path=\"url(#clip090)\" d=\"M188.575 1148.11 L218.251 1148.11 L218.251 1152.05 L188.575 1152.05 L188.575 1148.11 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M229.154 1161 L236.793 1161 L236.793 1134.64 L228.482 1136.31 L228.482 1132.05 L236.746 1130.38 L241.422 1130.38 L241.422 1161 L249.061 1161 L249.061 1164.94 L229.154 1164.94 L229.154 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M620.259 1133.46 Q616.648 1133.46 614.82 1137.02 Q613.014 1140.56 613.014 1147.69 Q613.014 1154.8 614.82 1158.37 Q616.648 1161.91 620.259 1161.91 Q623.894 1161.91 625.699 1158.37 Q627.528 1154.8 627.528 1147.69 Q627.528 1140.56 625.699 1137.02 Q623.894 1133.46 620.259 1133.46 M620.259 1129.75 Q626.07 1129.75 629.125 1134.36 Q632.204 1138.94 632.204 1147.69 Q632.204 1156.42 629.125 1161.03 Q626.07 1165.61 620.259 1165.61 Q614.449 1165.61 611.371 1161.03 Q608.315 1156.42 608.315 1147.69 Q608.315 1138.94 611.371 1134.36 Q614.449 1129.75 620.259 1129.75 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1012.08 1161 L1019.72 1161 L1019.72 1134.64 L1011.41 1136.31 L1011.41 1132.05 L1019.68 1130.38 L1024.35 1130.38 L1024.35 1161 L1031.99 1161 L1031.99 1164.94 L1012.08 1164.94 L1012.08 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1417.79 1161 L1434.11 1161 L1434.11 1164.94 L1412.17 1164.94 L1412.17 1161 Q1414.83 1158.25 1419.41 1153.62 Q1424.02 1148.97 1425.2 1147.63 Q1427.45 1145.1 1428.33 1143.37 Q1429.23 1141.61 1429.23 1139.92 Q1429.23 1137.16 1427.29 1135.43 Q1425.36 1133.69 1422.26 1133.69 Q1420.06 1133.69 1417.61 1134.45 Q1415.18 1135.22 1412.4 1136.77 L1412.4 1132.05 Q1415.23 1130.91 1417.68 1130.33 Q1420.13 1129.75 1422.17 1129.75 Q1427.54 1129.75 1430.73 1132.44 Q1433.93 1135.13 1433.93 1139.62 Q1433.93 1141.75 1433.12 1143.67 Q1432.33 1145.56 1430.23 1148.16 Q1429.65 1148.83 1426.54 1152.05 Q1423.44 1155.24 1417.79 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1828.83 1146.31 Q1832.19 1147.02 1834.06 1149.29 Q1835.96 1151.56 1835.96 1154.89 Q1835.96 1160.01 1832.44 1162.81 Q1828.92 1165.61 1822.44 1165.61 Q1820.27 1165.61 1817.95 1165.17 Q1815.66 1164.75 1813.21 1163.9 L1813.21 1159.38 Q1815.15 1160.52 1817.46 1161.1 Q1819.78 1161.68 1822.3 1161.68 Q1826.7 1161.68 1828.99 1159.94 Q1831.31 1158.2 1831.31 1154.89 Q1831.31 1151.84 1829.15 1150.13 Q1827.03 1148.39 1823.21 1148.39 L1819.18 1148.39 L1819.18 1144.55 L1823.39 1144.55 Q1826.84 1144.55 1828.67 1143.18 Q1830.5 1141.79 1830.5 1139.2 Q1830.5 1136.54 1828.6 1135.13 Q1826.72 1133.69 1823.21 1133.69 Q1821.28 1133.69 1819.09 1134.11 Q1816.89 1134.52 1814.25 1135.4 L1814.25 1131.24 Q1816.91 1130.5 1819.22 1130.13 Q1821.56 1129.75 1823.62 1129.75 Q1828.95 1129.75 1832.05 1132.19 Q1835.15 1134.59 1835.15 1138.71 Q1835.15 1141.58 1833.51 1143.57 Q1831.86 1145.54 1828.83 1146.31 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1038.32 1208.4 L1025.42 1225.74 L1038.98 1244.04 L1032.08 1244.04 L1021.7 1230.04 L1011.32 1244.04 L1004.42 1244.04 L1018.26 1225.39 L1005.6 1208.4 L1012.5 1208.4 L1021.96 1221.1 L1031.41 1208.4 L1038.32 1208.4 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,1106.38 170.645,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,1026 189.543,1026 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,815.73 189.543,815.73 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,605.464 189.543,605.464 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,395.198 189.543,395.198 \"/>\n",
       "<polyline clip-path=\"url(#clip090)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"170.645,184.933 189.543,184.933 \"/>\n",
       "<path clip-path=\"url(#clip090)\" d=\"M129.901 1011.79 Q126.29 1011.79 124.461 1015.36 Q122.655 1018.9 122.655 1026.03 Q122.655 1033.14 124.461 1036.7 Q126.29 1040.24 129.901 1040.24 Q133.535 1040.24 135.341 1036.7 Q137.169 1033.14 137.169 1026.03 Q137.169 1018.9 135.341 1015.36 Q133.535 1011.79 129.901 1011.79 M129.901 1008.09 Q135.711 1008.09 138.767 1012.7 Q141.845 1017.28 141.845 1026.03 Q141.845 1034.76 138.767 1039.36 Q135.711 1043.95 129.901 1043.95 Q124.091 1043.95 121.012 1039.36 Q117.956 1034.76 117.956 1026.03 Q117.956 1017.28 121.012 1012.7 Q124.091 1008.09 129.901 1008.09 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M125.526 829.074 L141.845 829.074 L141.845 833.01 L119.901 833.01 L119.901 829.074 Q122.563 826.32 127.146 821.69 Q131.753 817.038 132.933 815.695 Q135.179 813.172 136.058 811.436 Q136.961 809.676 136.961 807.987 Q136.961 805.232 135.017 803.496 Q133.095 801.76 129.993 801.76 Q127.794 801.76 125.341 802.524 Q122.91 803.288 120.132 804.839 L120.132 800.116 Q122.956 798.982 125.41 798.403 Q127.864 797.825 129.901 797.825 Q135.271 797.825 138.466 800.51 Q141.66 803.195 141.66 807.686 Q141.66 809.815 140.85 811.737 Q140.063 813.635 137.956 816.227 Q137.378 816.899 134.276 820.116 Q131.174 823.311 125.526 829.074 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M132.262 592.258 L120.456 610.707 L132.262 610.707 L132.262 592.258 M131.035 588.184 L136.915 588.184 L136.915 610.707 L141.845 610.707 L141.845 614.596 L136.915 614.596 L136.915 622.744 L132.262 622.744 L132.262 614.596 L116.66 614.596 L116.66 610.082 L131.035 588.184 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M130.317 393.335 Q127.169 393.335 125.318 395.488 Q123.489 397.641 123.489 401.39 Q123.489 405.117 125.318 407.293 Q127.169 409.446 130.317 409.446 Q133.466 409.446 135.294 407.293 Q137.146 405.117 137.146 401.39 Q137.146 397.641 135.294 395.488 Q133.466 393.335 130.317 393.335 M139.6 378.682 L139.6 382.942 Q137.841 382.108 136.035 381.668 Q134.253 381.229 132.493 381.229 Q127.864 381.229 125.41 384.354 Q122.98 387.479 122.632 393.798 Q123.998 391.784 126.058 390.719 Q128.118 389.631 130.595 389.631 Q135.804 389.631 138.813 392.803 Q141.845 395.951 141.845 401.39 Q141.845 406.715 138.697 409.932 Q135.549 413.15 130.317 413.15 Q124.322 413.15 121.151 408.566 Q117.98 403.96 117.98 395.233 Q117.98 387.039 121.868 382.178 Q125.757 377.293 132.308 377.293 Q134.067 377.293 135.85 377.641 Q137.655 377.988 139.6 378.682 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M129.993 185.801 Q126.66 185.801 124.739 187.583 Q122.841 189.366 122.841 192.491 Q122.841 195.616 124.739 197.398 Q126.66 199.18 129.993 199.18 Q133.327 199.18 135.248 197.398 Q137.169 195.592 137.169 192.491 Q137.169 189.366 135.248 187.583 Q133.35 185.801 129.993 185.801 M125.318 183.81 Q122.308 183.069 120.618 181.009 Q118.952 178.949 118.952 175.986 Q118.952 171.843 121.892 169.435 Q124.855 167.028 129.993 167.028 Q135.155 167.028 138.095 169.435 Q141.035 171.843 141.035 175.986 Q141.035 178.949 139.345 181.009 Q137.679 183.069 134.692 183.81 Q138.072 184.597 139.947 186.889 Q141.845 189.18 141.845 192.491 Q141.845 197.514 138.767 200.199 Q135.711 202.884 129.993 202.884 Q124.276 202.884 121.197 200.199 Q118.142 197.514 118.142 192.491 Q118.142 189.18 120.04 186.889 Q121.938 184.597 125.318 183.81 M123.605 176.426 Q123.605 179.111 125.271 180.616 Q126.961 182.12 129.993 182.12 Q133.003 182.12 134.692 180.616 Q136.405 179.111 136.405 176.426 Q136.405 173.741 134.692 172.236 Q133.003 170.731 129.993 170.731 Q126.961 170.731 125.271 172.236 Q123.605 173.741 123.605 176.426 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M76.9143 613.239 Q83.28 615.722 85.2216 618.077 Q87.1631 620.432 87.1631 624.379 L87.1631 629.058 L82.2615 629.058 L82.2615 625.62 Q82.2615 623.201 81.1157 621.865 Q79.9699 620.528 75.7048 618.905 L73.0312 617.854 L37.9562 632.273 L37.9562 626.066 L65.838 614.926 L37.9562 603.786 L37.9562 597.579 L76.9143 613.239 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M572.05 14.324 L572.05 27.2059 L587.403 27.2059 L587.403 32.9987 L572.05 32.9987 L572.05 57.6282 Q572.05 63.1779 573.549 64.7578 Q575.088 66.3376 579.747 66.3376 L587.403 66.3376 L587.403 72.576 L579.747 72.576 Q571.118 72.576 567.837 69.3758 Q564.556 66.1351 564.556 57.6282 L564.556 32.9987 L559.087 32.9987 L559.087 27.2059 L564.556 27.2059 L564.556 14.324 L572.05 14.324 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M634.92 45.1919 L634.92 72.576 L627.467 72.576 L627.467 45.4349 Q627.467 38.994 624.955 35.7938 Q622.443 32.5936 617.42 32.5936 Q611.384 32.5936 607.901 36.4419 Q604.417 40.2903 604.417 46.9338 L604.417 72.576 L596.923 72.576 L596.923 9.54393 L604.417 9.54393 L604.417 34.2544 Q607.091 30.163 610.696 28.1376 Q614.342 26.1121 619.081 26.1121 Q626.899 26.1121 630.91 30.9732 Q634.92 35.7938 634.92 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M688.595 48.0275 L688.595 51.6733 L654.324 51.6733 Q654.81 59.3701 658.942 63.421 Q663.115 67.4314 670.528 67.4314 Q674.822 67.4314 678.832 66.3781 Q682.883 65.3249 686.853 63.2184 L686.853 70.267 Q682.842 71.9684 678.629 72.8596 Q674.417 73.7508 670.082 73.7508 Q659.226 73.7508 652.866 67.4314 Q646.546 61.1119 646.546 50.3365 Q646.546 39.1965 652.542 32.6746 Q658.578 26.1121 668.786 26.1121 Q677.941 26.1121 683.248 32.0264 Q688.595 37.9003 688.595 48.0275 M681.141 45.84 Q681.06 39.7232 677.698 36.0774 Q674.376 32.4315 668.867 32.4315 Q662.628 32.4315 658.861 35.9558 Q655.134 39.4801 654.567 45.8805 L681.141 45.84 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M750.168 9.54393 L750.168 15.7418 L743.039 15.7418 Q739.028 15.7418 737.449 17.3622 Q735.909 18.9825 735.909 23.1955 L735.909 27.2059 L748.184 27.2059 L748.184 32.9987 L735.909 32.9987 L735.909 72.576 L728.415 72.576 L728.415 32.9987 L721.285 32.9987 L721.285 27.2059 L728.415 27.2059 L728.415 24.0462 Q728.415 16.471 731.939 13.0277 Q735.464 9.54393 743.12 9.54393 L750.168 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M794.121 45.1919 L794.121 72.576 L786.667 72.576 L786.667 45.4349 Q786.667 38.994 784.156 35.7938 Q781.644 32.5936 776.621 32.5936 Q770.585 32.5936 767.101 36.4419 Q763.617 40.2903 763.617 46.9338 L763.617 72.576 L756.123 72.576 L756.123 27.2059 L763.617 27.2059 L763.617 34.2544 Q766.291 30.163 769.896 28.1376 Q773.542 26.1121 778.282 26.1121 Q786.1 26.1121 790.11 30.9732 Q794.121 35.7938 794.121 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M811.459 65.6895 L824.827 65.6895 L824.827 19.5497 L810.284 22.4663 L810.284 15.0127 L824.746 12.096 L832.928 12.096 L832.928 65.6895 L846.296 65.6895 L846.296 72.576 L811.459 72.576 L811.459 65.6895 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M879.676 9.62495 Q874.248 18.942 871.615 28.0566 Q868.981 37.1711 868.981 46.5287 Q868.981 55.8863 871.615 65.0818 Q874.288 74.2369 879.676 83.5134 L873.194 83.5134 Q867.118 73.9938 864.08 64.7983 Q861.082 55.6027 861.082 46.5287 Q861.082 37.4952 864.08 28.3401 Q867.078 19.1851 873.194 9.62495 L879.676 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M931.852 27.2059 L915.445 49.2833 L932.702 72.576 L923.912 72.576 L910.706 54.752 L897.5 72.576 L888.709 72.576 L906.331 48.8377 L890.208 27.2059 L898.999 27.2059 L911.03 43.369 L923.061 27.2059 L931.852 27.2059 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M945.138 62.2867 L953.686 62.2867 L953.686 69.2543 L947.042 82.2172 L941.817 82.2172 L945.138 69.2543 L945.138 62.2867 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M988.159 17.4837 Q981.84 17.4837 978.639 23.7221 Q975.48 29.92 975.48 42.3968 Q975.48 54.833 978.639 61.0714 Q981.84 67.2693 988.159 67.2693 Q994.519 67.2693 997.679 61.0714 Q1000.88 54.833 1000.88 42.3968 Q1000.88 29.92 997.679 23.7221 Q994.519 17.4837 988.159 17.4837 M988.159 11.0023 Q998.327 11.0023 1003.67 19.0636 Q1009.06 27.0843 1009.06 42.3968 Q1009.06 57.6687 1003.67 65.73 Q998.327 73.7508 988.159 73.7508 Q977.991 73.7508 972.604 65.73 Q967.256 57.6687 967.256 42.3968 Q967.256 27.0843 972.604 19.0636 Q977.991 11.0023 988.159 11.0023 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1023.44 62.2867 L1031.99 62.2867 L1031.99 72.576 L1023.44 72.576 L1023.44 62.2867 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1049.89 12.096 L1082.02 12.096 L1082.02 18.9825 L1057.39 18.9825 L1057.39 33.8088 Q1059.17 33.2012 1060.95 32.9176 Q1062.74 32.5936 1064.52 32.5936 Q1074.65 32.5936 1080.56 38.1433 Q1086.47 43.6931 1086.47 53.1722 Q1086.47 62.9348 1080.4 68.3631 Q1074.32 73.7508 1063.26 73.7508 Q1059.45 73.7508 1055.49 73.1026 Q1051.56 72.4545 1047.34 71.1582 L1047.34 62.9348 Q1050.99 64.9198 1054.88 65.892 Q1058.77 66.8642 1063.1 66.8642 Q1070.11 66.8642 1074.2 63.1779 Q1078.29 59.4916 1078.29 53.1722 Q1078.29 46.8528 1074.2 43.1664 Q1070.11 39.4801 1063.1 39.4801 Q1059.82 39.4801 1056.54 40.2093 Q1053.3 40.9384 1049.89 42.4778 L1049.89 12.096 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1100.37 9.62495 L1106.85 9.62495 Q1112.93 19.1851 1115.92 28.3401 Q1118.96 37.4952 1118.96 46.5287 Q1118.96 55.6027 1115.92 64.7983 Q1112.93 73.9938 1106.85 83.5134 L1100.37 83.5134 Q1105.76 74.2369 1108.39 65.0818 Q1111.06 55.8863 1111.06 46.5287 Q1111.06 37.1711 1108.39 28.0566 Q1105.76 18.942 1100.37 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1183.25 9.54393 L1183.25 15.7418 L1176.12 15.7418 Q1172.11 15.7418 1170.53 17.3622 Q1168.99 18.9825 1168.99 23.1955 L1168.99 27.2059 L1181.27 27.2059 L1181.27 32.9987 L1168.99 32.9987 L1168.99 72.576 L1161.5 72.576 L1161.5 32.9987 L1154.37 32.9987 L1154.37 27.2059 L1161.5 27.2059 L1161.5 24.0462 Q1161.5 16.471 1165.02 13.0277 Q1168.55 9.54393 1176.2 9.54393 L1183.25 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1188.72 54.671 L1188.72 27.2059 L1196.17 27.2059 L1196.17 54.3874 Q1196.17 60.8284 1198.68 64.0691 Q1201.2 67.2693 1206.22 67.2693 Q1212.26 67.2693 1215.74 63.421 Q1219.26 59.5726 1219.26 52.9291 L1219.26 27.2059 L1226.72 27.2059 L1226.72 72.576 L1219.26 72.576 L1219.26 65.6084 Q1216.55 69.7404 1212.94 71.7658 Q1209.38 73.7508 1204.64 73.7508 Q1196.82 73.7508 1192.77 68.8897 Q1188.72 64.0286 1188.72 54.671 M1207.48 26.1121 L1207.48 26.1121 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1279.78 45.1919 L1279.78 72.576 L1272.33 72.576 L1272.33 45.4349 Q1272.33 38.994 1269.82 35.7938 Q1267.31 32.5936 1262.28 32.5936 Q1256.25 32.5936 1252.76 36.4419 Q1249.28 40.2903 1249.28 46.9338 L1249.28 72.576 L1241.79 72.576 L1241.79 27.2059 L1249.28 27.2059 L1249.28 34.2544 Q1251.95 30.163 1255.56 28.1376 Q1259.21 26.1121 1263.94 26.1121 Q1271.76 26.1121 1275.77 30.9732 Q1279.78 35.7938 1279.78 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1327.3 28.9478 L1327.3 35.9153 Q1324.14 34.1734 1320.94 33.3227 Q1317.78 32.4315 1314.54 32.4315 Q1307.29 32.4315 1303.28 37.0496 Q1299.27 41.6271 1299.27 49.9314 Q1299.27 58.2358 1303.28 62.8538 Q1307.29 67.4314 1314.54 67.4314 Q1317.78 67.4314 1320.94 66.5807 Q1324.14 65.6895 1327.3 63.9476 L1327.3 70.8341 Q1324.18 72.2924 1320.82 73.0216 Q1317.5 73.7508 1313.73 73.7508 Q1303.48 73.7508 1297.45 67.3098 Q1291.41 60.8689 1291.41 49.9314 Q1291.41 38.832 1297.49 32.472 Q1303.6 26.1121 1314.22 26.1121 Q1317.66 26.1121 1320.94 26.8413 Q1324.22 27.5299 1327.3 28.9478 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1347.64 14.324 L1347.64 27.2059 L1362.99 27.2059 L1362.99 32.9987 L1347.64 32.9987 L1347.64 57.6282 Q1347.64 63.1779 1349.14 64.7578 Q1350.67 66.3376 1355.33 66.3376 L1362.99 66.3376 L1362.99 72.576 L1355.33 72.576 Q1346.7 72.576 1343.42 69.3758 Q1340.14 66.1351 1340.14 57.6282 L1340.14 32.9987 L1334.67 32.9987 L1334.67 27.2059 L1340.14 27.2059 L1340.14 14.324 L1347.64 14.324 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1372.79 27.2059 L1380.25 27.2059 L1380.25 72.576 L1372.79 72.576 L1372.79 27.2059 M1372.79 9.54393 L1380.25 9.54393 L1380.25 18.9825 L1372.79 18.9825 L1372.79 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1413.42 32.4315 Q1407.43 32.4315 1403.94 37.1306 Q1400.46 41.7891 1400.46 49.9314 Q1400.46 58.0738 1403.9 62.7728 Q1407.39 67.4314 1413.42 67.4314 Q1419.38 67.4314 1422.86 62.7323 Q1426.35 58.0333 1426.35 49.9314 Q1426.35 41.8701 1422.86 37.1711 Q1419.38 32.4315 1413.42 32.4315 M1413.42 26.1121 Q1423.15 26.1121 1428.69 32.4315 Q1434.24 38.7509 1434.24 49.9314 Q1434.24 61.0714 1428.69 67.4314 Q1423.15 73.7508 1413.42 73.7508 Q1403.66 73.7508 1398.11 67.4314 Q1392.6 61.0714 1392.6 49.9314 Q1392.6 38.7509 1398.11 32.4315 Q1403.66 26.1121 1413.42 26.1121 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip090)\" d=\"M1484.31 45.1919 L1484.31 72.576 L1476.86 72.576 L1476.86 45.4349 Q1476.86 38.994 1474.35 35.7938 Q1471.84 32.5936 1466.81 32.5936 Q1460.78 32.5936 1457.29 36.4419 Q1453.81 40.2903 1453.81 46.9338 L1453.81 72.576 L1446.32 72.576 L1446.32 27.2059 L1453.81 27.2059 L1453.81 34.2544 Q1456.48 30.163 1460.09 28.1376 Q1463.74 26.1121 1468.47 26.1121 Q1476.29 26.1121 1480.3 30.9732 Q1484.31 35.7938 1484.31 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip092)\" style=\"stroke:#ff0000; stroke-linecap:round; stroke-linejoin:round; stroke-width:8; stroke-opacity:1; fill:none\" points=\"218.818,151.29 258.962,237.499 299.106,319.503 339.251,397.301 379.395,470.894 419.539,540.282 459.683,605.464 499.827,666.441 539.971,723.213 580.115,775.779 620.259,824.14 660.403,868.296 700.548,908.247 740.692,943.992 780.836,975.532 820.98,1002.87 861.124,1026 901.268,1044.92 941.412,1059.64 981.556,1070.15 1021.7,1076.46 1061.84,1078.56 1101.99,1076.46 1142.13,1070.15 1182.28,1059.64 1222.42,1044.92 1262.57,1026 1302.71,1002.87 1342.85,975.532 1383,943.992 1423.14,908.247 1463.29,868.296 1503.43,824.14 1543.57,775.779 1583.72,723.213 1623.86,666.441 1664.01,605.464 1704.15,540.282 1744.29,470.894 1784.44,397.301 1824.58,319.503 \"/>\n",
       "</svg>\n"
      ],
      "text/html": [
       "<img src=\"data:image/png;base64,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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(-1,3,length=41)\n",
    "\n",
    "p1 = plot( x,fn1.(x,0.5),\n",
    "           linecolor = :red,\n",
    "           linewidth = 2,\n",
    "           legend = nothing,\n",
    "           title = \"the fn1(x,0.5) function\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"y\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There seems to be two roots: around 0.6 and 1.6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving a Non-Linear Equation\n",
    "\n",
    "The Roots package wants a function with only one input and one output. An easy way to turn ```fn1(a,0.5)``` into that form is by defining an anonymous function:\n",
    "```\n",
    "x->fn1(x,0.5)\n",
    "```\n",
    "\n",
    "Then, running \n",
    "```\n",
    "find_zero(x->fn1(x,0.5),(x₀,x₁))\n",
    "```\n",
    "searches for a root in the `[x₀,x₁]` interval. Alternatively, you can do \n",
    "```\n",
    "find_zero(x->fn1(x,0.5),x₂)\n",
    "``` \n",
    "where `x₂` is a single starting guess."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at which x is fn1(x,0.5) = 0?      0.600\n",
      "at which x is fn1(x,0.5) = 0?      1.600\n",
      "\n",
      "\u001b[34m\u001b[1myes, there are several roots. Just look at it (in the plot)\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "xRoot1 = find_zero(x->fn1(x,0.5),(-1,1))         #searches for roots in [-1,1]\n",
    "printlnPs(\"at which x is fn1(x,0.5) = 0? \",xRoot1)\n",
    "\n",
    "xRoot2 = find_zero(x->fn1(x,0.5),2)              #searches for roots around 2\n",
    "printlnPs(\"at which x is fn1(x,0.5) = 0? \",xRoot2)\n",
    "\n",
    "printblue(\"\\nyes, there are several roots. Just look at it (in the plot)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance Tips (extra)\n",
    "\n",
    "Anonymous functions like `x->fn1(x,b)` where `b` is a global variable might be slow when used as above. To speed up, either wrap the call in another function or by create *both* `b` and the anonymous function `x->fn1(x,b)` inside a loop. See the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     0.600          \n",
      "\n",
      "     0.600\n",
      "     0.746\n",
      "\n"
     ]
    }
   ],
   "source": [
    "FindTheRoot(b) = find_zero(x->fn1(x,b),(-1,1))        #approach 1: a short wrapping function\n",
    "b = 0.5\n",
    "printlnPs(FindTheRoot(b),\"\\n\")\n",
    "\n",
    "xRoot4 = fill(NaN,2)                                  #appraoch 2: create things inside a loop\n",
    "for i = 1:2                                           #are local to the loop\n",
    "    local b\n",
    "    b = 0.5/i\n",
    "    xRoot4[i] = find_zero(x->fn1(x,b),(-1,1))\n",
    "end\n",
    "printmat(xRoot4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Many Roots\n",
    "\n",
    "Instead, running\n",
    "```\n",
    "find_zeros(x->fn1(x,0.5),x₀,x₁)\n",
    "```\n",
    "searches for all roots between x₀ and x₁. (Notice the *s* in `find_zeros`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at which x is fn1(x,0.5) = 0?      0.600     1.600\n"
     ]
    }
   ],
   "source": [
    "xRootsAll = find_zeros(x->fn1(x,0.5),-1,3)            #find_zeros (notice the \"s\")\n",
    "\n",
    "printlnPs(\"at which x is fn1(x,0.5) = 0? \",xRootsAll)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving a System of Non-Linear Equations\n",
    "\n",
    "The NLsolve,jl package has many options. The cells below illustrate a very simple case (2 non-linear equations with 2 unknowns, no information about the derivatives).\n",
    "\n",
    "The two equations are\n",
    "\n",
    "$ \n",
    "y-x^2-1=0\n",
    "$\n",
    "\n",
    "$\n",
    "y-x-1=0\n",
    "$\n",
    "\n",
    "and the roots are at $(x,y)=(0,1)$ and also at $(1,2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fn2 (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fn2(p)             #p is a vector with 2 elements, the output too\n",
    "    (x,y) = (p[1],p[2])\n",
    "    z = [y-x^2-1;y-x-1]     #equal to [0,0]\n",
    "    return z\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There is a solution at             -0.000     1.000\n",
      "There is a another solution at      1.000     2.000\n"
     ]
    }
   ],
   "source": [
    "Sol2a = nlsolve(fn2,[0.0,0.5])\n",
    "printlnPs(\"There is a solution at         \",Sol2a.zero)\n",
    "\n",
    "Sol2b = nlsolve(fn2,[1.0,0.0])  #try again, using another starting guess\n",
    "printlnPs(\"There is a another solution at \",Sol2b.zero)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}