Tutorial_24_Derivatives.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical Integration and Differentiation\n",
    "\n",
    "This notebook illustrates how to perform numerical integration and differentiation. \n",
    "\n",
    "There are several packages for doing this. Here, the focus is on `QuadGK.jl` and `FiniteDiff.jl` packages. Towards the end of the notebook, there are also some (extra) comments about the `ForwardDiff.jl` and `ReverseDiff.jl` packages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf\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": [
    "# Numerical Integration\n",
    "\n",
    "with the [QuadGK.jl](https://github.com/JuliaMath/QuadGK.jl) package. \n",
    "\n",
    "There are many alternative packages (for instance, [HCubature.jl](https://github.com/JuliaMath/HCubature.jl)), but they are not discussed in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using QuadGK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Pdf of the N() Distribution\n",
    "\n",
    "As a simple illustration, the next cells plot and integrate the $N(0,\\sigma)$ pdf.\n",
    "\n",
    "Notice: the function takes $\\mu$ and $\\sigma$ (not $\\sigma^2$) as inputs, similar to the `Distributions.jl` package. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ϕNS (generic function with 3 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function ϕNS(x,μ=0,σ=1)       #pdf of N(μ,σ), defaults to N(0,1)\n",
    "    z   = (x - μ)/σ\n",
    "    pdf = exp(-0.5*z^2)/(sqrt(2*pi)*σ)\n",
    "    return pdf\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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=\"clip830\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"1920\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip830)\" d=\"M0 1280 L1920 1280 L1920 0 L0 0  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip831\">\n",
       "    <rect x=\"384\" y=\"0\" width=\"1345\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip830)\" d=\"M151.798 1106.38 L1872.76 1106.38 L1872.76 123.472 L151.798 123.472  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip832\">\n",
       "    <rect x=\"151\" y=\"123\" width=\"1722\" height=\"984\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,1106.38 151.798,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"438.625,1106.38 438.625,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"725.451,1106.38 725.451,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1012.28,1106.38 1012.28,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1299.1,1106.38 1299.1,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1585.93,1106.38 1585.93,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1872.76,1106.38 1872.76,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,1106.38 1872.76,1106.38 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,872.354 1872.76,872.354 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,638.329 1872.76,638.329 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,404.303 1872.76,404.303 \"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"151.798,170.277 1872.76,170.277 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,1106.38 1872.76,1106.38 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,1106.38 151.798,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"438.625,1106.38 438.625,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"725.451,1106.38 725.451,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1012.28,1106.38 1012.28,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1299.1,1106.38 1299.1,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1585.93,1106.38 1585.93,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1872.76,1106.38 1872.76,1087.48 \"/>\n",
       "<path clip-path=\"url(#clip830)\" d=\"M121.266 1148.11 L150.942 1148.11 L150.942 1152.05 L121.266 1152.05 L121.266 1148.11 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M175.201 1146.31 Q178.557 1147.02 180.432 1149.29 Q182.33 1151.56 182.33 1154.89 Q182.33 1160.01 178.812 1162.81 Q175.293 1165.61 168.812 1165.61 Q166.636 1165.61 164.321 1165.17 Q162.03 1164.75 159.576 1163.9 L159.576 1159.38 Q161.52 1160.52 163.835 1161.1 Q166.15 1161.68 168.673 1161.68 Q173.071 1161.68 175.363 1159.94 Q177.678 1158.2 177.678 1154.89 Q177.678 1151.84 175.525 1150.13 Q173.395 1148.39 169.576 1148.39 L165.548 1148.39 L165.548 1144.55 L169.761 1144.55 Q173.21 1144.55 175.039 1143.18 Q176.868 1141.79 176.868 1139.2 Q176.868 1136.54 174.969 1135.13 Q173.094 1133.69 169.576 1133.69 Q167.655 1133.69 165.456 1134.11 Q163.257 1134.52 160.618 1135.4 L160.618 1131.24 Q163.28 1130.5 165.594 1130.13 Q167.932 1129.75 169.993 1129.75 Q175.317 1129.75 178.418 1132.19 Q181.52 1134.59 181.52 1138.71 Q181.52 1141.58 179.877 1143.57 Q178.233 1145.54 175.201 1146.31 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M408.567 1148.11 L438.243 1148.11 L438.243 1152.05 L408.567 1152.05 L408.567 1148.11 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M452.363 1161 L468.682 1161 L468.682 1164.94 L446.738 1164.94 L446.738 1161 Q449.4 1158.25 453.983 1153.62 Q458.59 1148.97 459.77 1147.63 Q462.016 1145.1 462.895 1143.37 Q463.798 1141.61 463.798 1139.92 Q463.798 1137.16 461.854 1135.43 Q459.932 1133.69 456.83 1133.69 Q454.631 1133.69 452.178 1134.45 Q449.747 1135.22 446.969 1136.77 L446.969 1132.05 Q449.793 1130.91 452.247 1130.33 Q454.701 1129.75 456.738 1129.75 Q462.108 1129.75 465.303 1132.44 Q468.497 1135.13 468.497 1139.62 Q468.497 1141.75 467.687 1143.67 Q466.9 1145.56 464.793 1148.16 Q464.215 1148.83 461.113 1152.05 Q458.011 1155.24 452.363 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M695.208 1148.11 L724.884 1148.11 L724.884 1152.05 L695.208 1152.05 L695.208 1148.11 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M735.786 1161 L743.425 1161 L743.425 1134.64 L735.115 1136.31 L735.115 1132.05 L743.379 1130.38 L748.055 1130.38 L748.055 1161 L755.694 1161 L755.694 1164.94 L735.786 1164.94 L735.786 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1012.28 1133.46 Q1008.67 1133.46 1006.84 1137.02 Q1005.03 1140.56 1005.03 1147.69 Q1005.03 1154.8 1006.84 1158.37 Q1008.67 1161.91 1012.28 1161.91 Q1015.91 1161.91 1017.72 1158.37 Q1019.55 1154.8 1019.55 1147.69 Q1019.55 1140.56 1017.72 1137.02 Q1015.91 1133.46 1012.28 1133.46 M1012.28 1129.75 Q1018.09 1129.75 1021.14 1134.36 Q1024.22 1138.94 1024.22 1147.69 Q1024.22 1156.42 1021.14 1161.03 Q1018.09 1165.61 1012.28 1165.61 Q1006.47 1165.61 1003.39 1161.03 Q1000.33 1156.42 1000.33 1147.69 Q1000.33 1138.94 1003.39 1134.36 Q1006.47 1129.75 1012.28 1129.75 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1289.49 1161 L1297.12 1161 L1297.12 1134.64 L1288.81 1136.31 L1288.81 1132.05 L1297.08 1130.38 L1301.75 1130.38 L1301.75 1161 L1309.39 1161 L1309.39 1164.94 L1289.49 1164.94 L1289.49 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1580.58 1161 L1596.9 1161 L1596.9 1164.94 L1574.96 1164.94 L1574.96 1161 Q1577.62 1158.25 1582.2 1153.62 Q1586.81 1148.97 1587.99 1147.63 Q1590.24 1145.1 1591.11 1143.37 Q1592.02 1141.61 1592.02 1139.92 Q1592.02 1137.16 1590.07 1135.43 Q1588.15 1133.69 1585.05 1133.69 Q1582.85 1133.69 1580.4 1134.45 Q1577.97 1135.22 1575.19 1136.77 L1575.19 1132.05 Q1578.01 1130.91 1580.47 1130.33 Q1582.92 1129.75 1584.96 1129.75 Q1590.33 1129.75 1593.52 1132.44 Q1596.72 1135.13 1596.72 1139.62 Q1596.72 1141.75 1595.91 1143.67 Q1595.12 1145.56 1593.01 1148.16 Q1592.43 1148.83 1589.33 1152.05 Q1586.23 1155.24 1580.58 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1877 1146.31 Q1880.36 1147.02 1882.24 1149.29 Q1884.13 1151.56 1884.13 1154.89 Q1884.13 1160.01 1880.61 1162.81 Q1877.1 1165.61 1870.61 1165.61 Q1868.44 1165.61 1866.12 1165.17 Q1863.83 1164.75 1861.38 1163.9 L1861.38 1159.38 Q1863.32 1160.52 1865.64 1161.1 Q1867.95 1161.68 1870.48 1161.68 Q1874.87 1161.68 1877.17 1159.94 Q1879.48 1158.2 1879.48 1154.89 Q1879.48 1151.84 1877.33 1150.13 Q1875.2 1148.39 1871.38 1148.39 L1867.35 1148.39 L1867.35 1144.55 L1871.56 1144.55 Q1875.01 1144.55 1876.84 1143.18 Q1878.67 1141.79 1878.67 1139.2 Q1878.67 1136.54 1876.77 1135.13 Q1874.9 1133.69 1871.38 1133.69 Q1869.46 1133.69 1867.26 1134.11 Q1865.06 1134.52 1862.42 1135.4 L1862.42 1131.24 Q1865.08 1130.5 1867.4 1130.13 Q1869.74 1129.75 1871.8 1129.75 Q1877.12 1129.75 1880.22 1132.19 Q1883.32 1134.59 1883.32 1138.71 Q1883.32 1141.58 1881.68 1143.57 Q1880.04 1145.54 1877 1146.31 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1028.89 1208.4 L1016 1225.74 L1029.56 1244.04 L1022.65 1244.04 L1012.28 1230.04 L1001.9 1244.04 L994.994 1244.04 L1008.84 1225.39 L996.172 1208.4 L1003.08 1208.4 L1012.53 1221.1 L1021.98 1208.4 L1028.89 1208.4 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,1106.38 151.798,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,1106.38 170.696,1106.38 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,872.354 170.696,872.354 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,638.329 170.696,638.329 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,404.303 170.696,404.303 \"/>\n",
       "<polyline clip-path=\"url(#clip830)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"151.798,170.277 170.696,170.277 \"/>\n",
       "<path clip-path=\"url(#clip830)\" d=\"M65.8226 1092.18 Q62.2115 1092.18 60.3828 1095.74 Q58.5773 1099.28 58.5773 1106.41 Q58.5773 1113.52 60.3828 1117.09 Q62.2115 1120.63 65.8226 1120.63 Q69.4569 1120.63 71.2624 1117.09 Q73.0911 1113.52 73.0911 1106.41 Q73.0911 1099.28 71.2624 1095.74 Q69.4569 1092.18 65.8226 1092.18 M65.8226 1088.47 Q71.6328 1088.47 74.6883 1093.08 Q77.767 1097.66 77.767 1106.41 Q77.767 1115.14 74.6883 1119.75 Q71.6328 1124.33 65.8226 1124.33 Q60.0125 1124.33 56.9338 1119.75 Q53.8782 1115.14 53.8782 1106.41 Q53.8782 1097.66 56.9338 1093.08 Q60.0125 1088.47 65.8226 1088.47 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M85.9845 1117.78 L90.8688 1117.78 L90.8688 1123.66 L85.9845 1123.66 L85.9845 1117.78 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M111.054 1092.18 Q107.443 1092.18 105.614 1095.74 Q103.809 1099.28 103.809 1106.41 Q103.809 1113.52 105.614 1117.09 Q107.443 1120.63 111.054 1120.63 Q114.688 1120.63 116.494 1117.09 Q118.322 1113.52 118.322 1106.41 Q118.322 1099.28 116.494 1095.74 Q114.688 1092.18 111.054 1092.18 M111.054 1088.47 Q116.864 1088.47 119.92 1093.08 Q122.998 1097.66 122.998 1106.41 Q122.998 1115.14 119.92 1119.75 Q116.864 1124.33 111.054 1124.33 Q105.244 1124.33 102.165 1119.75 Q99.1095 1115.14 99.1095 1106.41 Q99.1095 1097.66 102.165 1093.08 Q105.244 1088.47 111.054 1088.47 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M67.0495 858.153 Q63.4384 858.153 61.6097 861.718 Q59.8041 865.259 59.8041 872.389 Q59.8041 879.495 61.6097 883.06 Q63.4384 886.602 67.0495 886.602 Q70.6837 886.602 72.4892 883.06 Q74.3179 879.495 74.3179 872.389 Q74.3179 865.259 72.4892 861.718 Q70.6837 858.153 67.0495 858.153 M67.0495 854.449 Q72.8596 854.449 75.9152 859.056 Q78.9938 863.639 78.9938 872.389 Q78.9938 881.116 75.9152 885.722 Q72.8596 890.305 67.0495 890.305 Q61.2393 890.305 58.1606 885.722 Q55.1051 881.116 55.1051 872.389 Q55.1051 863.639 58.1606 859.056 Q61.2393 854.449 67.0495 854.449 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M87.2114 883.755 L92.0956 883.755 L92.0956 889.634 L87.2114 889.634 L87.2114 883.755 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M103.091 885.699 L110.73 885.699 L110.73 859.333 L102.42 861 L102.42 856.741 L110.683 855.074 L115.359 855.074 L115.359 885.699 L122.998 885.699 L122.998 889.634 L103.091 889.634 L103.091 885.699 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M67.4198 624.127 Q63.8087 624.127 61.98 627.692 Q60.1745 631.234 60.1745 638.363 Q60.1745 645.47 61.98 649.035 Q63.8087 652.576 67.4198 652.576 Q71.0541 652.576 72.8596 649.035 Q74.6883 645.47 74.6883 638.363 Q74.6883 631.234 72.8596 627.692 Q71.0541 624.127 67.4198 624.127 M67.4198 620.424 Q73.23 620.424 76.2855 625.03 Q79.3642 629.613 79.3642 638.363 Q79.3642 647.09 76.2855 651.697 Q73.23 656.28 67.4198 656.28 Q61.6097 656.28 58.531 651.697 Q55.4754 647.09 55.4754 638.363 Q55.4754 629.613 58.531 625.03 Q61.6097 620.424 67.4198 620.424 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M87.5818 649.729 L92.466 649.729 L92.466 655.609 L87.5818 655.609 L87.5818 649.729 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M106.679 651.673 L122.998 651.673 L122.998 655.609 L101.054 655.609 L101.054 651.673 Q103.716 648.919 108.299 644.289 Q112.906 639.636 114.086 638.294 Q116.332 635.771 117.211 634.035 Q118.114 632.275 118.114 630.586 Q118.114 627.831 116.17 626.095 Q114.248 624.359 111.146 624.359 Q108.947 624.359 106.494 625.123 Q104.063 625.886 101.285 627.437 L101.285 622.715 Q104.109 621.581 106.563 621.002 Q109.017 620.424 111.054 620.424 Q116.424 620.424 119.619 623.109 Q122.813 625.794 122.813 630.285 Q122.813 632.414 122.003 634.336 Q121.216 636.234 119.109 638.826 Q118.531 639.498 115.429 642.715 Q112.327 645.91 106.679 651.673 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M66.4708 390.102 Q62.8597 390.102 61.031 393.666 Q59.2254 397.208 59.2254 404.338 Q59.2254 411.444 61.031 415.009 Q62.8597 418.551 66.4708 418.551 Q70.105 418.551 71.9105 415.009 Q73.7392 411.444 73.7392 404.338 Q73.7392 397.208 71.9105 393.666 Q70.105 390.102 66.4708 390.102 M66.4708 386.398 Q72.2809 386.398 75.3365 391.004 Q78.4151 395.588 78.4151 404.338 Q78.4151 413.064 75.3365 417.671 Q72.2809 422.254 66.4708 422.254 Q60.6606 422.254 57.5819 417.671 Q54.5264 413.064 54.5264 404.338 Q54.5264 395.588 57.5819 391.004 Q60.6606 386.398 66.4708 386.398 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M86.6327 415.703 L91.5169 415.703 L91.5169 421.583 L86.6327 421.583 L86.6327 415.703 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M115.869 402.949 Q119.225 403.666 121.1 405.935 Q122.998 408.203 122.998 411.537 Q122.998 416.652 119.48 419.453 Q115.961 422.254 109.48 422.254 Q107.304 422.254 104.989 421.814 Q102.697 421.398 100.244 420.541 L100.244 416.027 Q102.188 417.162 104.503 417.74 Q106.818 418.319 109.341 418.319 Q113.739 418.319 116.031 416.583 Q118.345 414.847 118.345 411.537 Q118.345 408.481 116.193 406.768 Q114.063 405.032 110.244 405.032 L106.216 405.032 L106.216 401.189 L110.429 401.189 Q113.878 401.189 115.707 399.824 Q117.535 398.435 117.535 395.842 Q117.535 393.18 115.637 391.768 Q113.762 390.333 110.244 390.333 Q108.322 390.333 106.123 390.75 Q103.924 391.166 101.285 392.046 L101.285 387.879 Q103.947 387.139 106.262 386.768 Q108.6 386.398 110.66 386.398 Q115.984 386.398 119.086 388.828 Q122.188 391.236 122.188 395.356 Q122.188 398.227 120.545 400.217 Q118.901 402.185 115.869 402.949 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M65.3365 156.076 Q61.7254 156.076 59.8967 159.641 Q58.0912 163.182 58.0912 170.312 Q58.0912 177.418 59.8967 180.983 Q61.7254 184.525 65.3365 184.525 Q68.9707 184.525 70.7763 180.983 Q72.605 177.418 72.605 170.312 Q72.605 163.182 70.7763 159.641 Q68.9707 156.076 65.3365 156.076 M65.3365 152.372 Q71.1467 152.372 74.2022 156.979 Q77.2809 161.562 77.2809 170.312 Q77.2809 179.039 74.2022 183.645 Q71.1467 188.229 65.3365 188.229 Q59.5264 188.229 56.4477 183.645 Q53.3921 179.039 53.3921 170.312 Q53.3921 161.562 56.4477 156.979 Q59.5264 152.372 65.3365 152.372 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M85.4984 181.678 L90.3827 181.678 L90.3827 187.557 L85.4984 187.557 L85.4984 181.678 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M113.415 157.071 L101.609 175.52 L113.415 175.52 L113.415 157.071 M112.188 152.997 L118.068 152.997 L118.068 175.52 L122.998 175.52 L122.998 179.409 L118.068 179.409 L118.068 187.557 L113.415 187.557 L113.415 179.409 L97.8132 179.409 L97.8132 174.895 L112.188 152.997 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M764.119 65.7705 L764.119 89.8329 L756.625 89.8329 L756.625 27.2059 L764.119 27.2059 L764.119 34.0924 Q766.468 30.0415 770.033 28.0971 Q773.638 26.1121 778.621 26.1121 Q786.885 26.1121 792.029 32.6746 Q797.215 39.2371 797.215 49.9314 Q797.215 60.6258 792.029 67.1883 Q786.885 73.7508 778.621 73.7508 Q773.638 73.7508 770.033 71.8063 Q766.468 69.8214 764.119 65.7705 M789.477 49.9314 Q789.477 41.7081 786.075 37.0496 Q782.712 32.3505 776.798 32.3505 Q770.884 32.3505 767.481 37.0496 Q764.119 41.7081 764.119 49.9314 Q764.119 58.1548 767.481 62.8538 Q770.884 67.5124 776.798 67.5124 Q782.712 67.5124 786.075 62.8538 Q789.477 58.1548 789.477 49.9314 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M839.425 34.0924 L839.425 9.54393 L846.879 9.54393 L846.879 72.576 L839.425 72.576 L839.425 65.7705 Q837.075 69.8214 833.47 71.8063 Q829.905 73.7508 824.882 73.7508 Q816.659 73.7508 811.474 67.1883 Q806.329 60.6258 806.329 49.9314 Q806.329 39.2371 811.474 32.6746 Q816.659 26.1121 824.882 26.1121 Q829.905 26.1121 833.47 28.0971 Q837.075 30.0415 839.425 34.0924 M814.026 49.9314 Q814.026 58.1548 817.388 62.8538 Q820.791 67.5124 826.705 67.5124 Q832.619 67.5124 836.022 62.8538 Q839.425 58.1548 839.425 49.9314 Q839.425 41.7081 836.022 37.0496 Q832.619 32.3505 826.705 32.3505 Q820.791 32.3505 817.388 37.0496 Q814.026 41.7081 814.026 49.9314 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M885.2 9.54393 L885.2 15.7418 L878.071 15.7418 Q874.06 15.7418 872.48 17.3622 Q870.941 18.9825 870.941 23.1955 L870.941 27.2059 L883.215 27.2059 L883.215 32.9987 L870.941 32.9987 L870.941 72.576 L863.447 72.576 L863.447 32.9987 L856.317 32.9987 L856.317 27.2059 L863.447 27.2059 L863.447 24.0462 Q863.447 16.471 866.971 13.0277 Q870.495 9.54393 878.152 9.54393 L885.2 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M935.391 32.4315 Q929.396 32.4315 925.912 37.1306 Q922.428 41.7891 922.428 49.9314 Q922.428 58.0738 925.871 62.7728 Q929.355 67.4314 935.391 67.4314 Q941.346 67.4314 944.83 62.7323 Q948.313 58.0333 948.313 49.9314 Q948.313 41.8701 944.83 37.1711 Q941.346 32.4315 935.391 32.4315 M935.391 26.1121 Q945.113 26.1121 950.663 32.4315 Q956.213 38.7509 956.213 49.9314 Q956.213 61.0714 950.663 67.4314 Q945.113 73.7508 935.391 73.7508 Q925.628 73.7508 920.078 67.4314 Q914.569 61.0714 914.569 49.9314 Q914.569 38.7509 920.078 32.4315 Q925.628 26.1121 935.391 26.1121 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M991.536 9.54393 L991.536 15.7418 L984.407 15.7418 Q980.396 15.7418 978.817 17.3622 Q977.277 18.9825 977.277 23.1955 L977.277 27.2059 L989.551 27.2059 L989.551 32.9987 L977.277 32.9987 L977.277 72.576 L969.783 72.576 L969.783 32.9987 L962.653 32.9987 L962.653 27.2059 L969.783 27.2059 L969.783 24.0462 Q969.783 16.471 973.307 13.0277 Q976.832 9.54393 984.488 9.54393 L991.536 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1024.47 12.096 L1035.49 12.096 L1062.31 62.6918 L1062.31 12.096 L1070.25 12.096 L1070.25 72.576 L1059.23 72.576 L1032.41 21.9802 L1032.41 72.576 L1024.47 72.576 L1024.47 12.096 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1104.11 9.62495 Q1098.68 18.942 1096.05 28.0566 Q1093.42 37.1711 1093.42 46.5287 Q1093.42 55.8863 1096.05 65.0818 Q1098.72 74.2369 1104.11 83.5134 L1097.63 83.5134 Q1091.55 73.9938 1088.52 64.7983 Q1085.52 55.6027 1085.52 46.5287 Q1085.52 37.4952 1088.52 28.3401 Q1091.51 19.1851 1097.63 9.62495 L1104.11 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1137.13 17.4837 Q1130.81 17.4837 1127.61 23.7221 Q1124.45 29.92 1124.45 42.3968 Q1124.45 54.833 1127.61 61.0714 Q1130.81 67.2693 1137.13 67.2693 Q1143.49 67.2693 1146.65 61.0714 Q1149.85 54.833 1149.85 42.3968 Q1149.85 29.92 1146.65 23.7221 Q1143.49 17.4837 1137.13 17.4837 M1137.13 11.0023 Q1147.29 11.0023 1152.64 19.0636 Q1158.03 27.0843 1158.03 42.3968 Q1158.03 57.6687 1152.64 65.73 Q1147.29 73.7508 1137.13 73.7508 Q1126.96 73.7508 1121.57 65.73 Q1116.22 57.6687 1116.22 42.3968 Q1116.22 27.0843 1121.57 19.0636 Q1126.96 11.0023 1137.13 11.0023 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1173.26 62.2867 L1181.81 62.2867 L1181.81 69.2543 L1175.16 82.2172 L1169.94 82.2172 L1173.26 69.2543 L1173.26 62.2867 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1200.2 65.6895 L1213.57 65.6895 L1213.57 19.5497 L1199.02 22.4663 L1199.02 15.0127 L1213.49 12.096 L1221.67 12.096 L1221.67 65.6895 L1235.04 65.6895 L1235.04 72.576 L1200.2 72.576 L1200.2 65.6895 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1249.34 9.62495 L1255.82 9.62495 Q1261.89 19.1851 1264.89 28.3401 Q1267.93 37.4952 1267.93 46.5287 Q1267.93 55.6027 1264.89 64.7983 Q1261.89 73.9938 1255.82 83.5134 L1249.34 83.5134 Q1254.72 74.2369 1257.36 65.0818 Q1260.03 55.8863 1260.03 46.5287 Q1260.03 37.1711 1257.36 28.0566 Q1254.72 18.942 1249.34 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip832)\" style=\"stroke:#ff0000; stroke-linecap:round; stroke-linejoin:round; stroke-width:8; stroke-opacity:1; fill:none\" points=\"151.798,1096.01 180.481,1092.45 209.163,1087.86 237.846,1081.99 266.529,1074.59 295.211,1065.36 323.894,1053.97 352.577,1040.09 381.259,1023.36 409.942,1003.45 438.625,980.027 467.307,952.822 495.99,921.616 524.672,886.281 553.355,846.797 582.038,803.275 610.72,755.979 639.403,705.333 668.086,651.935 696.768,596.55 725.451,540.106 754.133,483.672 782.816,428.427 811.499,375.626 840.181,326.549 868.864,282.457 897.547,244.533 926.229,213.835 954.912,191.24 983.594,177.409 1012.28,172.753 1040.96,177.409 1069.64,191.24 1098.32,213.835 1127.01,244.533 1155.69,282.457 1184.37,326.549 1213.06,375.626 1241.74,428.427 1270.42,483.672 1299.1,540.106 1327.79,596.55 1356.47,651.935 1385.15,705.333 1413.83,755.979 1442.52,803.275 1471.2,846.797 1499.88,886.281 1528.56,921.616 1557.25,952.822 1585.93,980.027 1614.61,1003.45 1643.29,1023.36 1671.98,1040.09 1700.66,1053.97 1729.34,1065.36 1758.03,1074.59 1786.71,1081.99 1815.39,1087.86 1844.07,1092.45 1872.76,1096.01 \"/>\n",
       "<path clip-path=\"url(#clip832)\" d=\"M151.798 1096.01 L180.481 1092.45 L209.163 1087.86 L237.846 1081.99 L266.529 1074.59 L295.211 1065.36 L323.894 1053.97 L352.577 1040.09 L381.259 1023.36 L409.942 1003.45 L438.625 980.027 L467.307 952.822 L495.99 921.616 L524.672 886.281 L553.355 846.797 L582.038 803.275 L610.72 755.979 L639.403 705.333 L668.086 651.935 L696.768 596.55 L725.451 540.106 L754.133 483.672 L782.816 428.427 L811.499 375.626 L840.181 326.549 L868.864 282.457 L897.547 244.533 L926.229 213.835 L954.912 191.24 L983.594 177.409 L1012.28 172.753 L1040.96 177.409 L1069.64 191.24 L1098.32 213.835 L1127.01 244.533 L1155.69 282.457 L1184.37 326.549 L1213.06 375.626 L1241.74 428.427 L1270.42 483.672 L1299.1 540.106 L1327.79 596.55 L1356.47 651.935 L1385.15 705.333 L1413.83 755.979 L1442.52 803.275 L1471.2 846.797 L1471.2 1106.38 L1442.52 1106.38 L1413.83 1106.38 L1385.15 1106.38 L1356.47 1106.38 L1327.79 1106.38 L1299.1 1106.38 L1270.42 1106.38 L1241.74 1106.38 L1213.06 1106.38 L1184.37 1106.38 L1155.69 1106.38 L1127.01 1106.38 L1098.32 1106.38 L1069.64 1106.38 L1040.96 1106.38 L1012.28 1106.38 L983.594 1106.38 L954.912 1106.38 L926.229 1106.38 L897.547 1106.38 L868.864 1106.38 L840.181 1106.38 L811.499 1106.38 L782.816 1106.38 L754.133 1106.38 L725.451 1106.38 L696.768 1106.38 L668.086 1106.38 L639.403 1106.38 L610.72 1106.38 L582.038 1106.38 L553.355 1106.38 L524.672 1106.38 L495.99 1106.38 L467.307 1106.38 L438.625 1106.38 L409.942 1106.38 L381.259 1106.38 L352.577 1106.38 L323.894 1106.38 L295.211 1106.38 L266.529 1106.38 L237.846 1106.38 L209.163 1106.38 L180.481 1106.38 L151.798 1106.38  Z\" fill=\"#ff0000\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip832)\" style=\"stroke:#e26f46; stroke-linecap:round; stroke-linejoin:round; stroke-width:8; stroke-opacity:1; fill:none\" points=\"151.798,1096.01 180.481,1092.45 209.163,1087.86 237.846,1081.99 266.529,1074.59 295.211,1065.36 323.894,1053.97 352.577,1040.09 381.259,1023.36 409.942,1003.45 438.625,980.027 467.307,952.822 495.99,921.616 524.672,886.281 553.355,846.797 582.038,803.275 610.72,755.979 639.403,705.333 668.086,651.935 696.768,596.55 725.451,540.106 754.133,483.672 782.816,428.427 811.499,375.626 840.181,326.549 868.864,282.457 897.547,244.533 926.229,213.835 954.912,191.24 983.594,177.409 1012.28,172.753 1040.96,177.409 1069.64,191.24 1098.32,213.835 1127.01,244.533 1155.69,282.457 1184.37,326.549 1213.06,375.626 1241.74,428.427 1270.42,483.672 1299.1,540.106 1327.79,596.55 1356.47,651.935 1385.15,705.333 1413.83,755.979 1442.52,803.275 1471.2,846.797 \"/>\n",
       "<path clip-path=\"url(#clip830)\" d=\"M1338.36 479.389 L1338.36 486.75 L1347.13 486.75 L1347.13 490.06 L1338.36 490.06 L1338.36 504.134 Q1338.36 507.305 1339.21 508.208 Q1340.09 509.111 1342.75 509.111 L1347.13 509.111 L1347.13 512.676 L1342.75 512.676 Q1337.82 512.676 1335.95 510.847 Q1334.07 508.995 1334.07 504.134 L1334.07 490.06 L1330.95 490.06 L1330.95 486.75 L1334.07 486.75 L1334.07 479.389 L1338.36 479.389 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1374.28 497.028 L1374.28 512.676 L1370.02 512.676 L1370.02 497.167 Q1370.02 493.486 1368.59 491.657 Q1367.15 489.829 1364.28 489.829 Q1360.83 489.829 1358.84 492.028 Q1356.85 494.227 1356.85 498.023 L1356.85 512.676 L1352.57 512.676 L1352.57 476.657 L1356.85 476.657 L1356.85 490.778 Q1358.38 488.44 1360.44 487.282 Q1362.52 486.125 1365.23 486.125 Q1369.7 486.125 1371.99 488.903 Q1374.28 491.657 1374.28 497.028 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1404.95 498.648 L1404.95 500.731 L1385.37 500.731 Q1385.65 505.129 1388.01 507.444 Q1390.39 509.736 1394.63 509.736 Q1397.08 509.736 1399.37 509.134 Q1401.69 508.532 1403.96 507.329 L1403.96 511.356 Q1401.67 512.329 1399.26 512.838 Q1396.85 513.347 1394.37 513.347 Q1388.17 513.347 1384.54 509.736 Q1380.93 506.125 1380.93 499.967 Q1380.93 493.602 1384.35 489.875 Q1387.8 486.125 1393.63 486.125 Q1398.86 486.125 1401.9 489.505 Q1404.95 492.861 1404.95 498.648 M1400.69 497.398 Q1400.65 493.903 1398.73 491.819 Q1396.83 489.736 1393.68 489.736 Q1390.11 489.736 1387.96 491.75 Q1385.83 493.764 1385.51 497.421 L1400.69 497.398 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1438.8 499.643 Q1433.63 499.643 1431.64 500.824 Q1429.65 502.004 1429.65 504.852 Q1429.65 507.12 1431.13 508.463 Q1432.64 509.782 1435.21 509.782 Q1438.75 509.782 1440.88 507.282 Q1443.03 504.759 1443.03 500.592 L1443.03 499.643 L1438.8 499.643 M1447.29 497.884 L1447.29 512.676 L1443.03 512.676 L1443.03 508.741 Q1441.57 511.102 1439.4 512.236 Q1437.22 513.347 1434.07 513.347 Q1430.09 513.347 1427.73 511.125 Q1425.39 508.879 1425.39 505.129 Q1425.39 500.754 1428.31 498.532 Q1431.25 496.31 1437.06 496.31 L1443.03 496.31 L1443.03 495.893 Q1443.03 492.954 1441.09 491.356 Q1439.17 489.736 1435.67 489.736 Q1433.45 489.736 1431.34 490.268 Q1429.24 490.801 1427.29 491.866 L1427.29 487.93 Q1429.63 487.028 1431.83 486.588 Q1434.03 486.125 1436.11 486.125 Q1441.74 486.125 1444.51 489.042 Q1447.29 491.958 1447.29 497.884 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1471.09 490.731 Q1470.37 490.315 1469.51 490.13 Q1468.68 489.921 1467.66 489.921 Q1464.05 489.921 1462.11 492.282 Q1460.18 494.62 1460.18 499.018 L1460.18 512.676 L1455.9 512.676 L1455.9 486.75 L1460.18 486.75 L1460.18 490.778 Q1461.53 488.417 1463.68 487.282 Q1465.83 486.125 1468.91 486.125 Q1469.35 486.125 1469.88 486.194 Q1470.42 486.241 1471.06 486.356 L1471.09 490.731 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1496.69 498.648 L1496.69 500.731 L1477.11 500.731 Q1477.38 505.129 1479.74 507.444 Q1482.13 509.736 1486.36 509.736 Q1488.82 509.736 1491.11 509.134 Q1493.42 508.532 1495.69 507.329 L1495.69 511.356 Q1493.4 512.329 1490.99 512.838 Q1488.59 513.347 1486.11 513.347 Q1479.91 513.347 1476.27 509.736 Q1472.66 506.125 1472.66 499.967 Q1472.66 493.602 1476.09 489.875 Q1479.54 486.125 1485.37 486.125 Q1490.6 486.125 1493.63 489.505 Q1496.69 492.861 1496.69 498.648 M1492.43 497.398 Q1492.38 493.903 1490.46 491.819 Q1488.56 489.736 1485.42 489.736 Q1481.85 489.736 1479.7 491.75 Q1477.57 493.764 1477.24 497.421 L1492.43 497.398 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1515.46 499.643 Q1510.3 499.643 1508.31 500.824 Q1506.32 502.004 1506.32 504.852 Q1506.32 507.12 1507.8 508.463 Q1509.3 509.782 1511.87 509.782 Q1515.42 509.782 1517.54 507.282 Q1519.7 504.759 1519.7 500.592 L1519.7 499.643 L1515.46 499.643 M1523.96 497.884 L1523.96 512.676 L1519.7 512.676 L1519.7 508.741 Q1518.24 511.102 1516.06 512.236 Q1513.89 513.347 1510.74 513.347 Q1506.76 513.347 1504.4 511.125 Q1502.06 508.879 1502.06 505.129 Q1502.06 500.754 1504.98 498.532 Q1507.92 496.31 1513.73 496.31 L1519.7 496.31 L1519.7 495.893 Q1519.7 492.954 1517.75 491.356 Q1515.83 489.736 1512.34 489.736 Q1510.11 489.736 1508.01 490.268 Q1505.9 490.801 1503.96 491.866 L1503.96 487.93 Q1506.29 487.028 1508.49 486.588 Q1510.69 486.125 1512.78 486.125 Q1518.4 486.125 1521.18 489.042 Q1523.96 491.958 1523.96 497.884 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1566.46 487.745 L1566.46 491.727 Q1564.65 490.731 1562.82 490.245 Q1561.02 489.736 1559.16 489.736 Q1555.02 489.736 1552.73 492.375 Q1550.44 494.991 1550.44 499.736 Q1550.44 504.481 1552.73 507.12 Q1555.02 509.736 1559.16 509.736 Q1561.02 509.736 1562.82 509.25 Q1564.65 508.741 1566.46 507.745 L1566.46 511.68 Q1564.67 512.514 1562.75 512.93 Q1560.85 513.347 1558.7 513.347 Q1552.85 513.347 1549.4 509.666 Q1545.95 505.986 1545.95 499.736 Q1545.95 493.393 1549.42 489.759 Q1552.91 486.125 1558.98 486.125 Q1560.95 486.125 1562.82 486.542 Q1564.7 486.935 1566.46 487.745 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1583.91 489.736 Q1580.48 489.736 1578.49 492.421 Q1576.5 495.083 1576.5 499.736 Q1576.5 504.389 1578.47 507.074 Q1580.46 509.736 1583.91 509.736 Q1587.31 509.736 1589.3 507.051 Q1591.29 504.366 1591.29 499.736 Q1591.29 495.13 1589.3 492.444 Q1587.31 489.736 1583.91 489.736 M1583.91 486.125 Q1589.47 486.125 1592.64 489.736 Q1595.81 493.347 1595.81 499.736 Q1595.81 506.102 1592.64 509.736 Q1589.47 513.347 1583.91 513.347 Q1578.33 513.347 1575.16 509.736 Q1572.01 506.102 1572.01 499.736 Q1572.01 493.347 1575.16 489.736 Q1578.33 486.125 1583.91 486.125 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1599.81 486.75 L1604.33 486.75 L1612.43 508.509 L1620.53 486.75 L1625.04 486.75 L1615.32 512.676 L1609.54 512.676 L1599.81 486.75 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1653.1 498.648 L1653.1 500.731 L1633.52 500.731 Q1633.79 505.129 1636.16 507.444 Q1638.54 509.736 1642.78 509.736 Q1645.23 509.736 1647.52 509.134 Q1649.84 508.532 1652.1 507.329 L1652.1 511.356 Q1649.81 512.329 1647.41 512.838 Q1645 513.347 1642.52 513.347 Q1636.32 513.347 1632.68 509.736 Q1629.07 506.125 1629.07 499.967 Q1629.07 493.602 1632.5 489.875 Q1635.95 486.125 1641.78 486.125 Q1647.01 486.125 1650.04 489.505 Q1653.1 492.861 1653.1 498.648 M1648.84 497.398 Q1648.79 493.903 1646.87 491.819 Q1644.97 489.736 1641.83 489.736 Q1638.26 489.736 1636.11 491.75 Q1633.98 493.764 1633.66 497.421 L1648.84 497.398 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1675.11 490.731 Q1674.4 490.315 1673.54 490.13 Q1672.71 489.921 1671.69 489.921 Q1668.08 489.921 1666.13 492.282 Q1664.21 494.62 1664.21 499.018 L1664.21 512.676 L1659.93 512.676 L1659.93 486.75 L1664.21 486.75 L1664.21 490.778 Q1665.55 488.417 1667.71 487.282 Q1669.86 486.125 1672.94 486.125 Q1673.38 486.125 1673.91 486.194 Q1674.44 486.241 1675.09 486.356 L1675.11 490.731 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1696.11 487.514 L1696.11 491.542 Q1694.3 490.616 1692.36 490.153 Q1690.41 489.69 1688.33 489.69 Q1685.16 489.69 1683.56 490.662 Q1681.99 491.634 1681.99 493.579 Q1681.99 495.06 1683.12 495.917 Q1684.26 496.75 1687.68 497.514 L1689.14 497.838 Q1693.68 498.81 1695.58 500.592 Q1697.5 502.352 1697.5 505.523 Q1697.5 509.134 1694.63 511.241 Q1691.78 513.347 1686.78 513.347 Q1684.7 513.347 1682.43 512.93 Q1680.18 512.537 1677.68 511.727 L1677.68 507.329 Q1680.04 508.555 1682.34 509.18 Q1684.63 509.782 1686.87 509.782 Q1689.88 509.782 1691.5 508.764 Q1693.12 507.722 1693.12 505.847 Q1693.12 504.111 1691.94 503.185 Q1690.78 502.259 1686.83 501.403 L1685.34 501.055 Q1681.39 500.222 1679.63 498.509 Q1677.87 496.773 1677.87 493.764 Q1677.87 490.106 1680.46 488.116 Q1683.05 486.125 1687.82 486.125 Q1690.18 486.125 1692.27 486.472 Q1694.35 486.819 1696.11 487.514 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1347.63 554.284 L1347.63 538.59 L1351.89 538.59 L1351.89 554.122 Q1351.89 557.803 1353.32 559.655 Q1354.76 561.483 1357.63 561.483 Q1361.08 561.483 1363.07 559.284 Q1365.08 557.085 1365.08 553.289 L1365.08 538.59 L1369.34 538.59 L1369.34 564.516 L1365.08 564.516 L1365.08 560.534 Q1363.53 562.895 1361.47 564.053 Q1359.43 565.187 1356.72 565.187 Q1352.26 565.187 1349.94 562.409 Q1347.63 559.631 1347.63 554.284 M1358.34 537.965 L1358.34 537.965 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1382.23 560.627 L1382.23 574.377 L1377.95 574.377 L1377.95 538.59 L1382.23 538.59 L1382.23 542.525 Q1383.58 540.21 1385.61 539.099 Q1387.67 537.965 1390.52 537.965 Q1395.24 537.965 1398.18 541.715 Q1401.14 545.465 1401.14 551.576 Q1401.14 557.687 1398.18 561.437 Q1395.24 565.187 1390.52 565.187 Q1387.67 565.187 1385.61 564.076 Q1383.58 562.942 1382.23 560.627 M1396.72 551.576 Q1396.72 546.877 1394.78 544.215 Q1392.86 541.53 1389.48 541.53 Q1386.1 541.53 1384.15 544.215 Q1382.23 546.877 1382.23 551.576 Q1382.23 556.275 1384.15 558.96 Q1386.1 561.622 1389.48 561.622 Q1392.86 561.622 1394.78 558.96 Q1396.72 556.275 1396.72 551.576 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1427.49 531.229 L1427.49 538.59 L1436.26 538.59 L1436.26 541.9 L1427.49 541.9 L1427.49 555.974 Q1427.49 559.145 1428.34 560.048 Q1429.22 560.951 1431.89 560.951 L1436.26 560.951 L1436.26 564.516 L1431.89 564.516 Q1426.96 564.516 1425.08 562.687 Q1423.21 560.835 1423.21 555.974 L1423.21 541.9 L1420.08 541.9 L1420.08 538.59 L1423.21 538.59 L1423.21 531.229 L1427.49 531.229 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1451.91 541.576 Q1448.48 541.576 1446.49 544.261 Q1444.5 546.923 1444.5 551.576 Q1444.5 556.229 1446.47 558.914 Q1448.46 561.576 1451.91 561.576 Q1455.31 561.576 1457.3 558.891 Q1459.29 556.206 1459.29 551.576 Q1459.29 546.97 1457.3 544.284 Q1455.31 541.576 1451.91 541.576 M1451.91 537.965 Q1457.46 537.965 1460.64 541.576 Q1463.81 545.187 1463.81 551.576 Q1463.81 557.942 1460.64 561.576 Q1457.46 565.187 1451.91 565.187 Q1446.33 565.187 1443.16 561.576 Q1440.01 557.942 1440.01 551.576 Q1440.01 545.187 1443.16 541.576 Q1446.33 537.965 1451.91 537.965 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1507.49 538.59 L1498.11 551.206 L1507.97 564.516 L1502.95 564.516 L1495.4 554.331 L1487.86 564.516 L1482.83 564.516 L1492.9 550.951 L1483.69 538.59 L1488.71 538.59 L1495.59 547.826 L1502.46 538.59 L1507.49 538.59 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1514.55 542.988 L1544.22 542.988 L1544.22 546.877 L1514.55 546.877 L1514.55 542.988 M1514.55 552.432 L1544.22 552.432 L1544.22 556.368 L1514.55 556.368 L1514.55 552.432 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1555.13 560.581 L1562.76 560.581 L1562.76 534.215 L1554.45 535.882 L1554.45 531.622 L1562.72 529.956 L1567.39 529.956 L1567.39 560.581 L1575.03 560.581 L1575.03 564.516 L1555.13 564.516 L1555.13 560.581 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1584.48 558.636 L1589.36 558.636 L1589.36 564.516 L1584.48 564.516 L1584.48 558.636 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1610.13 545.372 Q1606.98 545.372 1605.13 547.525 Q1603.3 549.678 1603.3 553.428 Q1603.3 557.155 1605.13 559.331 Q1606.98 561.483 1610.13 561.483 Q1613.27 561.483 1615.1 559.331 Q1616.95 557.155 1616.95 553.428 Q1616.95 549.678 1615.1 547.525 Q1613.27 545.372 1610.13 545.372 M1619.41 530.72 L1619.41 534.979 Q1617.65 534.146 1615.84 533.706 Q1614.06 533.266 1612.3 533.266 Q1607.67 533.266 1605.22 536.391 Q1602.79 539.516 1602.44 545.835 Q1603.81 543.821 1605.87 542.757 Q1607.93 541.669 1610.4 541.669 Q1615.61 541.669 1618.62 544.84 Q1621.65 547.988 1621.65 553.428 Q1621.65 558.752 1618.5 561.969 Q1615.36 565.187 1610.13 565.187 Q1604.13 565.187 1600.96 560.604 Q1597.79 555.997 1597.79 547.27 Q1597.79 539.076 1601.68 534.215 Q1605.57 529.331 1612.12 529.331 Q1613.88 529.331 1615.66 529.678 Q1617.46 530.025 1619.41 530.72 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1642.56 534.03 L1630.75 552.479 L1642.56 552.479 L1642.56 534.03 M1641.33 529.956 L1647.21 529.956 L1647.21 552.479 L1652.14 552.479 L1652.14 556.368 L1647.21 556.368 L1647.21 564.516 L1642.56 564.516 L1642.56 556.368 L1626.95 556.368 L1626.95 551.854 L1641.33 529.956 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip830)\" d=\"M1659.92 529.956 L1678.27 529.956 L1678.27 533.891 L1664.2 533.891 L1664.2 542.363 Q1665.22 542.016 1666.24 541.854 Q1667.25 541.669 1668.27 541.669 Q1674.06 541.669 1677.44 544.84 Q1680.82 548.011 1680.82 553.428 Q1680.82 559.006 1677.35 562.108 Q1673.87 565.187 1667.56 565.187 Q1665.38 565.187 1663.11 564.817 Q1660.87 564.446 1658.46 563.706 L1658.46 559.006 Q1660.54 560.141 1662.76 560.696 Q1664.99 561.252 1667.46 561.252 Q1671.47 561.252 1673.81 559.145 Q1676.14 557.039 1676.14 553.428 Q1676.14 549.817 1673.81 547.71 Q1671.47 545.604 1667.46 545.604 Q1665.59 545.604 1663.71 546.02 Q1661.86 546.437 1659.92 547.317 L1659.92 529.956 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
      ],
      "text/html": [
       "<img src=\"data:image/png;base64,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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x  = -3:0.1:3\n",
    "xb = filter(<=(1.645),x)          #same as x[x.<=1.645]\n",
    "\n",
    "p1 = plot( x,ϕNS.(x),\n",
    "           linecolor = :red,\n",
    "           linewidth = 2,\n",
    "           ylims = (0,0.42),\n",
    "           xlims = (-3,3),\n",
    "           legend = nothing,\n",
    "           title = \"pdf of N(0,1)\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"\",\n",
    "           annotation = (1.75,0.25,text(\"the area covers\\nup to x=1.645\",8)) )\n",
    "plot!(xb,ϕNS.(xb),fillcolor=:red,linewidth=2,legend=nothing,fill=(0,:red))\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating Prob(x<=1.645)\n",
    "\n",
    "Let $\\phi(x,\\mu,\\sigma)$ be the pdf of an $N(\\mu,\\sigma)$ variable. The next cell calculates\n",
    "\n",
    "$\n",
    "\\displaystyle\\int_{-\\infty}^{1.645}\\phi(x,0,\\sigma)dx\n",
    "$,\n",
    "\n",
    "by numeric integration.\n",
    "\n",
    "The input to `quadgk` should be a function with only one argument. We do that by creating an anonymous function `x->ϕNS(x,0,2)` or just `ϕNS` is we want to use the default values of the (`μ,σ`) inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Pr(x<=1.645) according to N(0,1):     0.950\n",
      "\n",
      "Pr(x<=1.645) according to N(0,2):     0.795\n"
     ]
    }
   ],
   "source": [
    "cdf1, = quadgk(ϕNS,-Inf,1.645)              #N(0,1), default values\n",
    "printlnPs(\"\\nPr(x<=1.645) according to N(0,1):\", cdf1)\n",
    "\n",
    "cdf2, = quadgk(x->ϕNS(x,0,2),-Inf,1.645)    #N(0,σ=2)\n",
    "printlnPs(\"\\nPr(x<=1.645) according to N(0,2):\", cdf2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical Derivatives\n",
    "\n",
    "We use the [FiniteDiff.jl](https://github.com/JuliaDiff/FiniteDiff.jl) package to calculate numerical derivatives.\n",
    "\n",
    "The `FiniteDiff.jl` package does not export its functions and the names are very long, for instance, `FiniteDiff.finite_difference_derivative`. In the next cell we therefore rename the relevant functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "using FiniteDiff: finite_difference_derivative as δ, finite_difference_gradient as ∇"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Derivative of a Function with One Input and One Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fn1 (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fn1(x,a)                 #a simple function, to be differentiated\n",
    "   return (x - 1.1)^2 - a         #see below for a plot\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The derivative at x=2.0 is:      1.800\n"
     ]
    }
   ],
   "source": [
    "x₀ = 2.0\n",
    "dydx_A = δ(x->fn1(x,0.5),x₀)              #make sure x₀ is a Float64\n",
    "\n",
    "printlnPs(\"The derivative at x=$x₀ is: \",dydx_A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = -3:6/99:6          #calculate the derivative at many points\n",
    "\n",
    "dydx_A = [δ(z->fn1(z,0.5),xᵢ) for xᵢ in x];               #xᵢ should be Float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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=\"clip890\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"1920\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M0 1280 L1920 1280 L1920 0 L0 0  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip891\">\n",
       "    <rect x=\"384\" y=\"0\" width=\"1345\" height=\"1280\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M142.909 1106.38 L1872.76 1106.38 L1872.76 123.472 L142.909 123.472  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip892\">\n",
       "    <rect x=\"142\" y=\"123\" width=\"1731\" height=\"984\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"373.806,1106.38 373.806,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"737.682,1106.38 737.682,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1101.56,1106.38 1101.56,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1465.43,1106.38 1465.43,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"1829.31,1106.38 1829.31,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,984.105 1872.76,984.105 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,836.516 1872.76,836.516 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,688.926 1872.76,688.926 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,541.337 1872.76,541.337 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,393.748 1872.76,393.748 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"142.909,246.159 1872.76,246.159 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,1106.38 1872.76,1106.38 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"373.806,1106.38 373.806,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"737.682,1106.38 737.682,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1101.56,1106.38 1101.56,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1465.43,1106.38 1465.43,1087.48 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1829.31,1106.38 1829.31,1087.48 \"/>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M343.748 1148.11 L373.424 1148.11 L373.424 1152.05 L343.748 1152.05 L343.748 1148.11 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M387.544 1161 L403.863 1161 L403.863 1164.94 L381.919 1164.94 L381.919 1161 Q384.581 1158.25 389.164 1153.62 Q393.771 1148.97 394.951 1147.63 Q397.197 1145.1 398.076 1143.37 Q398.979 1141.61 398.979 1139.92 Q398.979 1137.16 397.035 1135.43 Q395.113 1133.69 392.011 1133.69 Q389.812 1133.69 387.359 1134.45 Q384.928 1135.22 382.15 1136.77 L382.15 1132.05 Q384.974 1130.91 387.428 1130.33 Q389.882 1129.75 391.919 1129.75 Q397.289 1129.75 400.484 1132.44 Q403.678 1135.13 403.678 1139.62 Q403.678 1141.75 402.868 1143.67 Q402.081 1145.56 399.974 1148.16 Q399.396 1148.83 396.294 1152.05 Q393.192 1155.24 387.544 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M737.682 1133.46 Q734.071 1133.46 732.242 1137.02 Q730.437 1140.56 730.437 1147.69 Q730.437 1154.8 732.242 1158.37 Q734.071 1161.91 737.682 1161.91 Q741.316 1161.91 743.122 1158.37 Q744.95 1154.8 744.95 1147.69 Q744.95 1140.56 743.122 1137.02 Q741.316 1133.46 737.682 1133.46 M737.682 1129.75 Q743.492 1129.75 746.548 1134.36 Q749.626 1138.94 749.626 1147.69 Q749.626 1156.42 746.548 1161.03 Q743.492 1165.61 737.682 1165.61 Q731.872 1165.61 728.793 1161.03 Q725.738 1156.42 725.738 1147.69 Q725.738 1138.94 728.793 1134.36 Q731.872 1129.75 737.682 1129.75 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1096.21 1161 L1112.53 1161 L1112.53 1164.94 L1090.59 1164.94 L1090.59 1161 Q1093.25 1158.25 1097.83 1153.62 Q1102.44 1148.97 1103.62 1147.63 Q1105.86 1145.1 1106.74 1143.37 Q1107.65 1141.61 1107.65 1139.92 Q1107.65 1137.16 1105.7 1135.43 Q1103.78 1133.69 1100.68 1133.69 Q1098.48 1133.69 1096.03 1134.45 Q1093.6 1135.22 1090.82 1136.77 L1090.82 1132.05 Q1093.64 1130.91 1096.1 1130.33 Q1098.55 1129.75 1100.59 1129.75 Q1105.96 1129.75 1109.15 1132.44 Q1112.35 1135.13 1112.35 1139.62 Q1112.35 1141.75 1111.54 1143.67 Q1110.75 1145.56 1108.64 1148.16 Q1108.06 1148.83 1104.96 1152.05 Q1101.86 1155.24 1096.21 1161 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1468.44 1134.45 L1456.64 1152.9 L1468.44 1152.9 L1468.44 1134.45 M1467.22 1130.38 L1473.1 1130.38 L1473.1 1152.9 L1478.03 1152.9 L1478.03 1156.79 L1473.1 1156.79 L1473.1 1164.94 L1468.44 1164.94 L1468.44 1156.79 L1452.84 1156.79 L1452.84 1152.28 L1467.22 1130.38 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1829.72 1145.8 Q1826.57 1145.8 1824.72 1147.95 Q1822.89 1150.1 1822.89 1153.85 Q1822.89 1157.58 1824.72 1159.75 Q1826.57 1161.91 1829.72 1161.91 Q1832.86 1161.91 1834.69 1159.75 Q1836.55 1157.58 1836.55 1153.85 Q1836.55 1150.1 1834.69 1147.95 Q1832.86 1145.8 1829.72 1145.8 M1839 1131.14 L1839 1135.4 Q1837.24 1134.57 1835.43 1134.13 Q1833.65 1133.69 1831.89 1133.69 Q1827.26 1133.69 1824.81 1136.81 Q1822.38 1139.94 1822.03 1146.26 Q1823.4 1144.25 1825.46 1143.18 Q1827.52 1142.09 1829.99 1142.09 Q1835.2 1142.09 1838.21 1145.26 Q1841.24 1148.41 1841.24 1153.85 Q1841.24 1159.18 1838.1 1162.39 Q1834.95 1165.61 1829.72 1165.61 Q1823.72 1165.61 1820.55 1161.03 Q1817.38 1156.42 1817.38 1147.69 Q1817.38 1139.5 1821.27 1134.64 Q1825.16 1129.75 1831.71 1129.75 Q1833.47 1129.75 1835.25 1130.1 Q1837.05 1130.45 1839 1131.14 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1024.45 1208.4 L1011.56 1225.74 L1025.12 1244.04 L1018.21 1244.04 L1007.83 1230.04 L997.457 1244.04 L990.55 1244.04 L1004.4 1225.39 L991.727 1208.4 L998.634 1208.4 L1008.09 1221.1 L1017.54 1208.4 L1024.45 1208.4 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,1106.38 142.909,123.472 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,984.105 161.807,984.105 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,836.516 161.807,836.516 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,688.926 161.807,688.926 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,541.337 161.807,541.337 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,393.748 161.807,393.748 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"142.909,246.159 161.807,246.159 \"/>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M53.3921 984.556 L83.0679 984.556 L83.0679 988.491 L53.3921 988.491 L53.3921 984.556 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M93.2067 966.825 L111.563 966.825 L111.563 970.76 L97.4891 970.76 L97.4891 979.232 Q98.5076 978.885 99.5261 978.723 Q100.545 978.538 101.563 978.538 Q107.35 978.538 110.73 981.709 Q114.109 984.88 114.109 990.297 Q114.109 995.875 110.637 998.977 Q107.165 1002.06 100.846 1002.06 Q98.6697 1002.06 96.4012 1001.69 Q94.1558 1001.32 91.7484 1000.57 L91.7484 995.875 Q93.8317 997.01 96.0539 997.565 Q98.2761 998.121 100.753 998.121 Q104.758 998.121 107.096 996.014 Q109.433 993.908 109.433 990.297 Q109.433 986.686 107.096 984.579 Q104.758 982.473 100.753 982.473 Q98.878 982.473 97.003 982.889 Q95.1512 983.306 93.2067 984.186 L93.2067 966.825 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M102.165 822.314 Q98.5539 822.314 96.7252 825.879 Q94.9197 829.421 94.9197 836.55 Q94.9197 843.657 96.7252 847.221 Q98.5539 850.763 102.165 850.763 Q105.799 850.763 107.605 847.221 Q109.433 843.657 109.433 836.55 Q109.433 829.421 107.605 825.879 Q105.799 822.314 102.165 822.314 M102.165 818.611 Q107.975 818.611 111.031 823.217 Q114.109 827.8 114.109 836.55 Q114.109 845.277 111.031 849.884 Q107.975 854.467 102.165 854.467 Q96.3549 854.467 93.2762 849.884 Q90.2206 845.277 90.2206 836.55 Q90.2206 827.8 93.2762 823.217 Q96.3549 818.611 102.165 818.611 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M93.2067 671.646 L111.563 671.646 L111.563 675.582 L97.4891 675.582 L97.4891 684.054 Q98.5076 683.707 99.5261 683.544 Q100.545 683.359 101.563 683.359 Q107.35 683.359 110.73 686.531 Q114.109 689.702 114.109 695.119 Q114.109 700.697 110.637 703.799 Q107.165 706.878 100.846 706.878 Q98.6697 706.878 96.4012 706.507 Q94.1558 706.137 91.7484 705.396 L91.7484 700.697 Q93.8317 701.831 96.0539 702.387 Q98.2761 702.943 100.753 702.943 Q104.758 702.943 107.096 700.836 Q109.433 698.73 109.433 695.119 Q109.433 691.507 107.096 689.401 Q104.758 687.294 100.753 687.294 Q98.878 687.294 97.003 687.711 Q95.1512 688.128 93.2067 689.007 L93.2067 671.646 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M62.8134 554.682 L70.4522 554.682 L70.4522 528.317 L62.1421 529.983 L62.1421 525.724 L70.4059 524.057 L75.0818 524.057 L75.0818 554.682 L82.7207 554.682 L82.7207 558.617 L62.8134 558.617 L62.8134 554.682 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M102.165 527.136 Q98.5539 527.136 96.7252 530.701 Q94.9197 534.242 94.9197 541.372 Q94.9197 548.478 96.7252 552.043 Q98.5539 555.585 102.165 555.585 Q105.799 555.585 107.605 552.043 Q109.433 548.478 109.433 541.372 Q109.433 534.242 107.605 530.701 Q105.799 527.136 102.165 527.136 M102.165 523.432 Q107.975 523.432 111.031 528.039 Q114.109 532.622 114.109 541.372 Q114.109 550.099 111.031 554.705 Q107.975 559.289 102.165 559.289 Q96.3549 559.289 93.2762 554.705 Q90.2206 550.099 90.2206 541.372 Q90.2206 532.622 93.2762 528.039 Q96.3549 523.432 102.165 523.432 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M63.8087 407.093 L71.4476 407.093 L71.4476 380.727 L63.1374 382.394 L63.1374 378.135 L71.4013 376.468 L76.0772 376.468 L76.0772 407.093 L83.716 407.093 L83.716 411.028 L63.8087 411.028 L63.8087 407.093 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M93.2067 376.468 L111.563 376.468 L111.563 380.403 L97.4891 380.403 L97.4891 388.876 Q98.5076 388.528 99.5261 388.366 Q100.545 388.181 101.563 388.181 Q107.35 388.181 110.73 391.352 Q114.109 394.524 114.109 399.94 Q114.109 405.519 110.637 408.621 Q107.165 411.699 100.846 411.699 Q98.6697 411.699 96.4012 411.329 Q94.1558 410.959 91.7484 410.218 L91.7484 405.519 Q93.8317 406.653 96.0539 407.209 Q98.2761 407.764 100.753 407.764 Q104.758 407.764 107.096 405.658 Q109.433 403.551 109.433 399.94 Q109.433 396.329 107.096 394.223 Q104.758 392.116 100.753 392.116 Q98.878 392.116 97.003 392.533 Q95.1512 392.95 93.2067 393.829 L93.2067 376.468 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M66.0309 259.504 L82.3503 259.504 L82.3503 263.439 L60.406 263.439 L60.406 259.504 Q63.068 256.749 67.6513 252.12 Q72.2578 247.467 73.4383 246.124 Q75.6837 243.601 76.5633 241.865 Q77.4661 240.106 77.4661 238.416 Q77.4661 235.661 75.5216 233.925 Q73.6004 232.189 70.4985 232.189 Q68.2995 232.189 65.8458 232.953 Q63.4152 233.717 60.6375 235.268 L60.6375 230.546 Q63.4615 229.411 65.9152 228.833 Q68.3689 228.254 70.4059 228.254 Q75.7763 228.254 78.9707 230.939 Q82.1651 233.624 82.1651 238.115 Q82.1651 240.245 81.3549 242.166 Q80.5679 244.064 78.4614 246.657 Q77.8827 247.328 74.7809 250.546 Q71.6791 253.74 66.0309 259.504 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M102.165 231.958 Q98.5539 231.958 96.7252 235.523 Q94.9197 239.064 94.9197 246.194 Q94.9197 253.3 96.7252 256.865 Q98.5539 260.407 102.165 260.407 Q105.799 260.407 107.605 256.865 Q109.433 253.3 109.433 246.194 Q109.433 239.064 107.605 235.523 Q105.799 231.958 102.165 231.958 M102.165 228.254 Q107.975 228.254 111.031 232.861 Q114.109 237.444 114.109 246.194 Q114.109 254.921 111.031 259.527 Q107.975 264.11 102.165 264.11 Q96.3549 264.11 93.2762 259.527 Q90.2206 254.921 90.2206 246.194 Q90.2206 237.444 93.2762 232.861 Q96.3549 228.254 102.165 228.254 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M564.968 9.54393 L564.968 15.7418 L557.838 15.7418 Q553.828 15.7418 552.248 17.3622 Q550.708 18.9825 550.708 23.1955 L550.708 27.2059 L562.983 27.2059 L562.983 32.9987 L550.708 32.9987 L550.708 72.576 L543.214 72.576 L543.214 32.9987 L536.085 32.9987 L536.085 27.2059 L543.214 27.2059 L543.214 24.0462 Q543.214 16.471 546.738 13.0277 Q550.263 9.54393 557.919 9.54393 L564.968 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M608.92 45.1919 L608.92 72.576 L601.466 72.576 L601.466 45.4349 Q601.466 38.994 598.955 35.7938 Q596.443 32.5936 591.42 32.5936 Q585.384 32.5936 581.9 36.4419 Q578.417 40.2903 578.417 46.9338 L578.417 72.576 L570.922 72.576 L570.922 27.2059 L578.417 27.2059 L578.417 34.2544 Q581.09 30.163 584.695 28.1376 Q588.341 26.1121 593.081 26.1121 Q600.899 26.1121 604.909 30.9732 Q608.92 35.7938 608.92 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M626.258 65.6895 L639.626 65.6895 L639.626 19.5497 L625.083 22.4663 L625.083 15.0127 L639.545 12.096 L647.728 12.096 L647.728 65.6895 L661.096 65.6895 L661.096 72.576 L626.258 72.576 L626.258 65.6895 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M694.475 9.62495 Q689.047 18.942 686.414 28.0566 Q683.781 37.1711 683.781 46.5287 Q683.781 55.8863 686.414 65.0818 Q689.087 74.2369 694.475 83.5134 L687.994 83.5134 Q681.917 73.9938 678.879 64.7983 Q675.881 55.6027 675.881 46.5287 Q675.881 37.4952 678.879 28.3401 Q681.877 19.1851 687.994 9.62495 L694.475 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M707.762 9.62495 L714.243 9.62495 Q720.32 19.1851 723.317 28.3401 Q726.356 37.4952 726.356 46.5287 Q726.356 55.6027 723.317 64.7983 Q720.32 73.9938 714.243 83.5134 L707.762 83.5134 Q713.15 74.2369 715.783 65.0818 Q718.456 55.8863 718.456 46.5287 Q718.456 37.1711 715.783 28.0566 Q713.15 18.942 707.762 9.62495 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M788.294 49.7694 Q779.26 49.7694 775.777 51.8354 Q772.293 53.9013 772.293 58.8839 Q772.293 62.8538 774.885 65.2034 Q777.518 67.5124 782.015 67.5124 Q788.213 67.5124 791.94 63.1374 Q795.707 58.7219 795.707 51.4303 L795.707 49.7694 L788.294 49.7694 M803.161 46.6907 L803.161 72.576 L795.707 72.576 L795.707 65.6895 Q793.155 69.8214 789.347 71.8063 Q785.539 73.7508 780.03 73.7508 Q773.062 73.7508 768.931 69.8619 Q764.839 65.9325 764.839 59.3701 Q764.839 51.7138 769.943 47.825 Q775.088 43.9361 785.256 43.9361 L795.707 43.9361 L795.707 43.2069 Q795.707 38.0623 792.304 35.2672 Q788.942 32.4315 782.825 32.4315 Q778.936 32.4315 775.25 33.3632 Q771.564 34.295 768.161 36.1584 L768.161 29.2718 Q772.252 27.692 776.101 26.9223 Q779.949 26.1121 783.595 26.1121 Q793.439 26.1121 798.3 31.2163 Q803.161 36.3204 803.161 46.6907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M856.228 45.1919 L856.228 72.576 L848.774 72.576 L848.774 45.4349 Q848.774 38.994 846.262 35.7938 Q843.751 32.5936 838.728 32.5936 Q832.692 32.5936 829.208 36.4419 Q825.724 40.2903 825.724 46.9338 L825.724 72.576 L818.23 72.576 L818.23 27.2059 L825.724 27.2059 L825.724 34.2544 Q828.398 30.163 832.003 28.1376 Q835.649 26.1121 840.389 26.1121 Q848.207 26.1121 852.217 30.9732 Q856.228 35.7938 856.228 45.1919 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M900.95 34.0924 L900.95 9.54393 L908.403 9.54393 L908.403 72.576 L900.95 72.576 L900.95 65.7705 Q898.6 69.8214 894.995 71.8063 Q891.43 73.7508 886.407 73.7508 Q878.183 73.7508 872.998 67.1883 Q867.854 60.6258 867.854 49.9314 Q867.854 39.2371 872.998 32.6746 Q878.183 26.1121 886.407 26.1121 Q891.43 26.1121 894.995 28.0971 Q898.6 30.0415 900.95 34.0924 M875.55 49.9314 Q875.55 58.1548 878.913 62.8538 Q882.315 67.5124 888.23 67.5124 Q894.144 67.5124 897.547 62.8538 Q900.95 58.1548 900.95 49.9314 Q900.95 41.7081 897.547 37.0496 Q894.144 32.3505 888.23 32.3505 Q882.315 32.3505 878.913 37.0496 Q875.55 41.7081 875.55 49.9314 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M950.128 27.2059 L957.581 27.2059 L957.581 72.576 L950.128 72.576 L950.128 27.2059 M950.128 9.54393 L957.581 9.54393 L957.581 18.9825 L950.128 18.9825 L950.128 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M980.55 14.324 L980.55 27.2059 L995.903 27.2059 L995.903 32.9987 L980.55 32.9987 L980.55 57.6282 Q980.55 63.1779 982.049 64.7578 Q983.588 66.3376 988.247 66.3376 L995.903 66.3376 L995.903 72.576 L988.247 72.576 Q979.618 72.576 976.337 69.3758 Q973.056 66.1351 973.056 57.6282 L973.056 32.9987 L967.587 32.9987 L967.587 27.2059 L973.056 27.2059 L973.056 14.324 L980.55 14.324 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1034.63 28.5427 L1034.63 35.5912 Q1031.47 33.9709 1028.07 33.1607 Q1024.66 32.3505 1021.02 32.3505 Q1015.47 32.3505 1012.67 34.0519 Q1009.92 35.7533 1009.92 39.156 Q1009.92 41.7486 1011.9 43.2475 Q1013.89 44.7058 1019.88 46.0426 L1022.44 46.6097 Q1030.38 48.3111 1033.7 51.4303 Q1037.06 54.509 1037.06 60.0587 Q1037.06 66.3781 1032.04 70.0644 Q1027.05 73.7508 1018.3 73.7508 Q1014.66 73.7508 1010.69 73.0216 Q1006.76 72.3329 1002.38 70.9151 L1002.38 63.2184 Q1006.52 65.3654 1010.53 66.4591 Q1014.54 67.5124 1018.47 67.5124 Q1023.73 67.5124 1026.57 65.73 Q1029.4 63.9071 1029.4 60.6258 Q1029.4 57.5877 1027.34 55.9673 Q1025.31 54.3469 1018.39 52.8481 L1015.79 52.2405 Q1008.87 50.7821 1005.79 47.7845 Q1002.71 44.7463 1002.71 39.4801 Q1002.71 33.0797 1007.25 29.5959 Q1011.78 26.1121 1020.13 26.1121 Q1024.26 26.1121 1027.9 26.7198 Q1031.55 27.3274 1034.63 28.5427 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1105.16 34.0924 L1105.16 9.54393 L1112.61 9.54393 L1112.61 72.576 L1105.16 72.576 L1105.16 65.7705 Q1102.81 69.8214 1099.2 71.8063 Q1095.64 73.7508 1090.61 73.7508 Q1082.39 73.7508 1077.2 67.1883 Q1072.06 60.6258 1072.06 49.9314 Q1072.06 39.2371 1077.2 32.6746 Q1082.39 26.1121 1090.61 26.1121 Q1095.64 26.1121 1099.2 28.0971 Q1102.81 30.0415 1105.16 34.0924 M1079.76 49.9314 Q1079.76 58.1548 1083.12 62.8538 Q1086.52 67.5124 1092.44 67.5124 Q1098.35 67.5124 1101.75 62.8538 Q1105.16 58.1548 1105.16 49.9314 Q1105.16 41.7081 1101.75 37.0496 Q1098.35 32.3505 1092.44 32.3505 Q1086.52 32.3505 1083.12 37.0496 Q1079.76 41.7081 1079.76 49.9314 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1166.77 48.0275 L1166.77 51.6733 L1132.5 51.6733 Q1132.99 59.3701 1137.12 63.421 Q1141.29 67.4314 1148.7 67.4314 Q1153 67.4314 1157.01 66.3781 Q1161.06 65.3249 1165.03 63.2184 L1165.03 70.267 Q1161.02 71.9684 1156.8 72.8596 Q1152.59 73.7508 1148.26 73.7508 Q1137.4 73.7508 1131.04 67.4314 Q1124.72 61.1119 1124.72 50.3365 Q1124.72 39.1965 1130.72 32.6746 Q1136.75 26.1121 1146.96 26.1121 Q1156.12 26.1121 1161.42 32.0264 Q1166.77 37.9003 1166.77 48.0275 M1159.32 45.84 Q1159.24 39.7232 1155.87 36.0774 Q1152.55 32.4315 1147.04 32.4315 Q1140.8 32.4315 1137.04 35.9558 Q1133.31 39.4801 1132.74 45.8805 L1159.32 45.84 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1205.29 34.1734 Q1204.04 33.4443 1202.54 33.1202 Q1201.08 32.7556 1199.3 32.7556 Q1192.98 32.7556 1189.58 36.8875 Q1186.21 40.9789 1186.21 48.6757 L1186.21 72.576 L1178.72 72.576 L1178.72 27.2059 L1186.21 27.2059 L1186.21 34.2544 Q1188.56 30.1225 1192.33 28.1376 Q1196.1 26.1121 1201.49 26.1121 Q1202.26 26.1121 1203.19 26.2337 Q1204.12 26.3147 1205.25 26.5172 L1205.29 34.1734 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1213.11 27.2059 L1220.57 27.2059 L1220.57 72.576 L1213.11 72.576 L1213.11 27.2059 M1213.11 9.54393 L1220.57 9.54393 L1220.57 18.9825 L1213.11 18.9825 L1213.11 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1230.81 27.2059 L1238.71 27.2059 L1252.89 65.2844 L1267.07 27.2059 L1274.97 27.2059 L1257.96 72.576 L1247.83 72.576 L1230.81 27.2059 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1305.88 49.7694 Q1296.84 49.7694 1293.36 51.8354 Q1289.88 53.9013 1289.88 58.8839 Q1289.88 62.8538 1292.47 65.2034 Q1295.1 67.5124 1299.6 67.5124 Q1305.8 67.5124 1309.52 63.1374 Q1313.29 58.7219 1313.29 51.4303 L1313.29 49.7694 L1305.88 49.7694 M1320.74 46.6907 L1320.74 72.576 L1313.29 72.576 L1313.29 65.6895 Q1310.74 69.8214 1306.93 71.8063 Q1303.12 73.7508 1297.61 73.7508 Q1290.65 73.7508 1286.51 69.8619 Q1282.42 65.9325 1282.42 59.3701 Q1282.42 51.7138 1287.53 47.825 Q1292.67 43.9361 1302.84 43.9361 L1313.29 43.9361 L1313.29 43.2069 Q1313.29 38.0623 1309.89 35.2672 Q1306.53 32.4315 1300.41 32.4315 Q1296.52 32.4315 1292.83 33.3632 Q1289.15 34.295 1285.74 36.1584 L1285.74 29.2718 Q1289.84 27.692 1293.68 26.9223 Q1297.53 26.1121 1301.18 26.1121 Q1311.02 26.1121 1315.88 31.2163 Q1320.74 36.3204 1320.74 46.6907 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1343.47 14.324 L1343.47 27.2059 L1358.82 27.2059 L1358.82 32.9987 L1343.47 32.9987 L1343.47 57.6282 Q1343.47 63.1779 1344.97 64.7578 Q1346.51 66.3376 1351.17 66.3376 L1358.82 66.3376 L1358.82 72.576 L1351.17 72.576 Q1342.54 72.576 1339.26 69.3758 Q1335.98 66.1351 1335.98 57.6282 L1335.98 32.9987 L1330.51 32.9987 L1330.51 27.2059 L1335.98 27.2059 L1335.98 14.324 L1343.47 14.324 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1368.63 27.2059 L1376.08 27.2059 L1376.08 72.576 L1368.63 72.576 L1368.63 27.2059 M1368.63 9.54393 L1376.08 9.54393 L1376.08 18.9825 L1368.63 18.9825 L1368.63 9.54393 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1386.33 27.2059 L1394.23 27.2059 L1408.41 65.2844 L1422.58 27.2059 L1430.48 27.2059 L1413.47 72.576 L1403.34 72.576 L1386.33 27.2059 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1479.58 48.0275 L1479.58 51.6733 L1445.31 51.6733 Q1445.8 59.3701 1449.93 63.421 Q1454.1 67.4314 1461.51 67.4314 Q1465.81 67.4314 1469.82 66.3781 Q1473.87 65.3249 1477.84 63.2184 L1477.84 70.267 Q1473.83 71.9684 1469.62 72.8596 Q1465.4 73.7508 1461.07 73.7508 Q1450.21 73.7508 1443.85 67.4314 Q1437.53 61.1119 1437.53 50.3365 Q1437.53 39.1965 1443.53 32.6746 Q1449.56 26.1121 1459.77 26.1121 Q1468.93 26.1121 1474.23 32.0264 Q1479.58 37.9003 1479.58 48.0275 M1472.13 45.84 Q1472.05 39.7232 1468.68 36.0774 Q1465.36 32.4315 1459.85 32.4315 Q1453.61 32.4315 1449.85 35.9558 Q1446.12 39.4801 1445.55 45.8805 L1472.13 45.84 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip892)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"191.867,355.08 202.894,369.641 213.92,383.985 224.947,398.112 235.974,412.023 247,425.717 258.027,439.193 269.053,452.453 280.08,465.497 291.106,478.323 302.133,490.932 313.159,503.325 324.186,515.501 335.213,527.46 346.239,539.202 357.266,550.727 368.292,562.035 379.319,573.127 390.345,584.002 401.372,594.659 412.398,605.1 423.425,615.325 434.452,625.332 445.478,635.122 456.505,644.696 467.531,654.053 478.558,663.193 489.584,672.116 500.611,680.822 511.638,689.312 522.664,697.584 533.691,705.64 544.717,713.479 555.744,721.101 566.77,728.506 577.797,735.694 588.823,742.666 599.85,749.421 610.877,755.958 621.903,762.279 632.93,768.384 643.956,774.271 654.983,779.941 666.009,785.395 677.036,790.632 688.062,795.652 699.089,800.455 710.116,805.041 721.142,809.41 732.169,813.563 743.195,817.499 754.222,821.217 765.248,824.72 776.275,828.005 787.301,831.073 798.328,833.925 809.355,836.559 820.381,838.977 831.408,841.178 842.434,843.162 853.461,844.929 864.487,846.48 875.514,847.813 886.541,848.93 897.567,849.83 908.594,850.513 919.62,850.979 930.647,851.229 941.673,851.261 952.7,851.077 963.726,850.676 974.753,850.058 985.78,849.223 996.806,848.171 1007.83,846.903 1018.86,845.417 1029.89,843.715 1040.91,841.796 1051.94,839.66 1062.97,837.307 1073.99,834.738 1085.02,831.951 1096.05,828.948 1107.07,825.728 1118.1,822.291 1129.12,818.637 1140.15,814.766 1151.18,810.679 1162.2,806.375 1173.23,801.853 1184.26,797.115 1195.28,792.16 1206.31,786.989 1217.34,781.6 1228.36,775.995 1239.39,770.173 1250.42,764.133 1261.44,757.878 1272.47,751.405 1283.5,744.715 1294.52,737.809 1305.55,730.685 1316.58,723.345 1327.6,715.788 1338.63,708.014 1349.66,700.024 1360.68,691.816 1371.71,683.392 1382.74,674.751 1393.76,665.892 1404.79,656.818 1415.82,647.526 1426.84,638.017 1437.87,628.292 1448.89,618.35 1459.92,608.19 1470.95,597.814 1481.97,587.222 1493,576.412 1504.03,565.386 1515.05,554.142 1526.08,542.682 1537.11,531.005 1548.13,519.111 1559.16,507 1570.19,494.673 1581.21,482.128 1592.24,469.367 1603.27,456.389 1614.29,443.194 1625.32,429.782 1636.35,416.154 1647.37,402.308 1658.4,388.246 1669.43,373.967 1680.45,359.471 1691.48,344.758 1702.51,329.828 1713.53,314.682 1724.56,299.319 1735.59,283.738 1746.61,267.941 1757.64,251.927 1768.67,235.697 1779.69,219.249 1790.72,202.585 1801.74,185.703 1812.77,168.605 1823.8,151.29 \"/>\n",
       "<polyline clip-path=\"url(#clip892)\" style=\"stroke:#ff0000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"191.867,1078.56 202.894,1074.98 213.92,1071.41 224.947,1067.83 235.974,1064.25 247,1060.67 258.027,1057.09 269.053,1053.52 280.08,1049.94 291.106,1046.36 302.133,1042.78 313.159,1039.2 324.186,1035.63 335.213,1032.05 346.239,1028.47 357.266,1024.89 368.292,1021.32 379.319,1017.74 390.345,1014.16 401.372,1010.58 412.398,1007 423.425,1003.43 434.452,999.848 445.478,996.27 456.505,992.692 467.531,989.114 478.558,985.536 489.584,981.958 500.611,978.38 511.638,974.802 522.664,971.224 533.691,967.646 544.717,964.068 555.744,960.49 566.77,956.912 577.797,953.335 588.823,949.757 599.85,946.179 610.877,942.601 621.903,939.023 632.93,935.445 643.956,931.867 654.983,928.289 666.009,924.711 677.036,921.133 688.062,917.555 699.089,913.977 710.116,910.4 721.142,906.822 732.169,903.244 743.195,899.666 754.222,896.088 765.248,892.51 776.275,888.932 787.301,885.354 798.328,881.776 809.355,878.198 820.381,874.62 831.408,871.042 842.434,867.465 853.461,863.887 864.487,860.309 875.514,856.731 886.541,853.153 897.567,849.575 908.594,845.997 919.62,842.419 930.647,838.841 941.673,835.263 952.7,831.685 963.726,828.107 974.753,824.53 985.78,820.952 996.806,817.374 1007.83,813.796 1018.86,810.218 1029.89,806.64 1040.91,803.062 1051.94,799.484 1062.97,795.906 1073.99,792.328 1085.02,788.75 1096.05,785.172 1107.07,781.594 1118.1,778.017 1129.12,774.439 1140.15,770.861 1151.18,767.283 1162.2,763.705 1173.23,760.127 1184.26,756.549 1195.28,752.971 1206.31,749.393 1217.34,745.815 1228.36,742.237 1239.39,738.659 1250.42,735.082 1261.44,731.504 1272.47,727.926 1283.5,724.348 1294.52,720.77 1305.55,717.192 1316.58,713.614 1327.6,710.036 1338.63,706.458 1349.66,702.88 1360.68,699.302 1371.71,695.724 1382.74,692.147 1393.76,688.569 1404.79,684.991 1415.82,681.413 1426.84,677.835 1437.87,674.257 1448.89,670.679 1459.92,667.101 1470.95,663.523 1481.97,659.945 1493,656.367 1504.03,652.789 1515.05,649.212 1526.08,645.634 1537.11,642.056 1548.13,638.478 1559.16,634.9 1570.19,631.322 1581.21,627.744 1592.24,624.166 1603.27,620.588 1614.29,617.01 1625.32,613.432 1636.35,609.854 1647.37,606.277 1658.4,602.699 1669.43,599.121 1680.45,595.543 1691.48,591.965 1702.51,588.387 1713.53,584.809 1724.56,581.231 1735.59,577.653 1746.61,574.075 1757.64,570.497 1768.67,566.919 1779.69,563.341 1790.72,559.764 1801.74,556.186 1812.77,552.608 1823.8,549.03 \"/>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M804.906 311.756 L1210.76 311.756 L1210.76 156.236 L804.906 156.236  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"804.906,311.756 1210.76,311.756 1210.76,156.236 804.906,156.236 804.906,311.756 \"/>\n",
       "<polyline clip-path=\"url(#clip890)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"824.126,208.076 939.449,208.076 \"/>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M975.174 189.337 L975.174 192.879 L971.1 192.879 Q968.809 192.879 967.906 193.805 Q967.026 194.731 967.026 197.138 L967.026 199.43 L974.04 199.43 L974.04 202.74 L967.026 202.74 L967.026 225.356 L962.744 225.356 L962.744 202.74 L958.67 202.74 L958.67 199.43 L962.744 199.43 L962.744 197.624 Q962.744 193.296 964.758 191.328 Q966.772 189.337 971.147 189.337 L975.174 189.337 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1000.29 209.708 L1000.29 225.356 L996.031 225.356 L996.031 209.847 Q996.031 206.166 994.596 204.337 Q993.16 202.509 990.29 202.509 Q986.841 202.509 984.85 204.708 Q982.86 206.907 982.86 210.703 L982.86 225.356 L978.577 225.356 L978.577 199.43 L982.86 199.43 L982.86 203.458 Q984.387 201.12 986.448 199.962 Q988.531 198.805 991.239 198.805 Q995.707 198.805 997.998 201.583 Q1000.29 204.337 1000.29 209.708 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1010.2 221.421 L1017.84 221.421 L1017.84 195.055 L1009.53 196.722 L1009.53 192.462 L1017.79 190.796 L1022.47 190.796 L1022.47 221.421 L1030.1 221.421 L1030.1 225.356 L1010.2 225.356 L1010.2 221.421 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1049.18 189.384 Q1046.08 194.708 1044.57 199.916 Q1043.07 205.124 1043.07 210.472 Q1043.07 215.819 1044.57 221.073 Q1046.1 226.305 1049.18 231.606 L1045.47 231.606 Q1042 226.166 1040.27 220.911 Q1038.55 215.657 1038.55 210.472 Q1038.55 205.31 1040.27 200.078 Q1041.98 194.847 1045.47 189.384 L1049.18 189.384 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1056.77 189.384 L1060.47 189.384 Q1063.95 194.847 1065.66 200.078 Q1067.4 205.31 1067.4 210.472 Q1067.4 215.657 1065.66 220.911 Q1063.95 226.166 1060.47 231.606 L1056.77 231.606 Q1059.85 226.305 1061.35 221.073 Q1062.88 215.819 1062.88 210.472 Q1062.88 205.124 1061.35 199.916 Q1059.85 194.708 1056.77 189.384 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip890)\" style=\"stroke:#ff0000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"824.126,259.916 939.449,259.916 \"/>\n",
       "<path clip-path=\"url(#clip890)\" d=\"M977.582 255.205 L977.582 241.177 L981.841 241.177 L981.841 277.196 L977.582 277.196 L977.582 273.307 Q976.239 275.622 974.179 276.756 Q972.142 277.867 969.272 277.867 Q964.573 277.867 961.61 274.117 Q958.67 270.367 958.67 264.256 Q958.67 258.145 961.61 254.395 Q964.573 250.645 969.272 250.645 Q972.142 250.645 974.179 251.779 Q976.239 252.89 977.582 255.205 M963.068 264.256 Q963.068 268.955 964.989 271.64 Q966.934 274.302 970.313 274.302 Q973.693 274.302 975.637 271.64 Q977.582 268.955 977.582 264.256 Q977.582 259.557 975.637 256.895 Q973.693 254.21 970.313 254.21 Q966.934 254.21 964.989 256.895 Q963.068 259.557 963.068 264.256 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1012.79 263.168 L1012.79 265.251 L993.207 265.251 Q993.485 269.649 995.846 271.964 Q998.23 274.256 1002.47 274.256 Q1004.92 274.256 1007.21 273.654 Q1009.53 273.052 1011.79 271.849 L1011.79 275.876 Q1009.5 276.848 1007.1 277.358 Q1004.69 277.867 1002.21 277.867 Q996.008 277.867 992.373 274.256 Q988.762 270.645 988.762 264.487 Q988.762 258.122 992.188 254.395 Q995.637 250.645 1001.47 250.645 Q1006.7 250.645 1009.73 254.025 Q1012.79 257.381 1012.79 263.168 M1008.53 261.918 Q1008.48 258.423 1006.56 256.339 Q1004.67 254.256 1001.52 254.256 Q997.952 254.256 995.799 256.27 Q993.67 258.284 993.346 261.941 L1008.53 261.918 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1034.8 255.251 Q1034.09 254.835 1033.23 254.65 Q1032.4 254.441 1031.38 254.441 Q1027.77 254.441 1025.82 256.802 Q1023.9 259.14 1023.9 263.538 L1023.9 277.196 L1019.62 277.196 L1019.62 251.27 L1023.9 251.27 L1023.9 255.298 Q1025.24 252.937 1027.4 251.802 Q1029.55 250.645 1032.63 250.645 Q1033.07 250.645 1033.6 250.714 Q1034.13 250.761 1034.78 250.876 L1034.8 255.251 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1039.27 251.27 L1043.53 251.27 L1043.53 277.196 L1039.27 277.196 L1039.27 251.27 M1039.27 241.177 L1043.53 241.177 L1043.53 246.571 L1039.27 246.571 L1039.27 241.177 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1049.39 251.27 L1053.9 251.27 L1062 273.029 L1070.1 251.27 L1074.62 251.27 L1064.9 277.196 L1059.11 277.196 L1049.39 251.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1092.28 264.163 Q1087.12 264.163 1085.13 265.344 Q1083.14 266.524 1083.14 269.372 Q1083.14 271.64 1084.62 272.983 Q1086.12 274.302 1088.69 274.302 Q1092.23 274.302 1094.36 271.802 Q1096.52 269.279 1096.52 265.112 L1096.52 264.163 L1092.28 264.163 M1100.78 262.404 L1100.78 277.196 L1096.52 277.196 L1096.52 273.261 Q1095.06 275.622 1092.88 276.756 Q1090.71 277.867 1087.56 277.867 Q1083.58 277.867 1081.22 275.645 Q1078.88 273.399 1078.88 269.649 Q1078.88 265.274 1081.79 263.052 Q1084.73 260.83 1090.54 260.83 L1096.52 260.83 L1096.52 260.413 Q1096.52 257.474 1094.57 255.876 Q1092.65 254.256 1089.16 254.256 Q1086.93 254.256 1084.83 254.788 Q1082.72 255.321 1080.78 256.386 L1080.78 252.45 Q1083.11 251.548 1085.31 251.108 Q1087.51 250.645 1089.6 250.645 Q1095.22 250.645 1098 253.562 Q1100.78 256.478 1100.78 262.404 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1113.76 243.909 L1113.76 251.27 L1122.53 251.27 L1122.53 254.58 L1113.76 254.58 L1113.76 268.654 Q1113.76 271.825 1114.62 272.728 Q1115.5 273.631 1118.16 273.631 L1122.53 273.631 L1122.53 277.196 L1118.16 277.196 Q1113.23 277.196 1111.35 275.367 Q1109.48 273.515 1109.48 268.654 L1109.48 254.58 L1106.35 254.58 L1106.35 251.27 L1109.48 251.27 L1109.48 243.909 L1113.76 243.909 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1128.14 251.27 L1132.4 251.27 L1132.4 277.196 L1128.14 277.196 L1128.14 251.27 M1128.14 241.177 L1132.4 241.177 L1132.4 246.571 L1128.14 246.571 L1128.14 241.177 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1138.25 251.27 L1142.77 251.27 L1150.87 273.029 L1158.97 251.27 L1163.48 251.27 L1153.76 277.196 L1147.97 277.196 L1138.25 251.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip890)\" d=\"M1191.54 263.168 L1191.54 265.251 L1171.96 265.251 Q1172.23 269.649 1174.59 271.964 Q1176.98 274.256 1181.22 274.256 Q1183.67 274.256 1185.96 273.654 Q1188.28 273.052 1190.54 271.849 L1190.54 275.876 Q1188.25 276.848 1185.84 277.358 Q1183.44 277.867 1180.96 277.867 Q1174.76 277.867 1171.12 274.256 Q1167.51 270.645 1167.51 264.487 Q1167.51 258.122 1170.94 254.395 Q1174.39 250.645 1180.22 250.645 Q1185.45 250.645 1188.48 254.025 Q1191.54 257.381 1191.54 263.168 M1187.28 261.918 Q1187.23 258.423 1185.31 256.339 Q1183.41 254.256 1180.27 254.256 Q1176.7 254.256 1174.55 256.27 Q1172.42 258.284 1172.09 261.941 L1187.28 261.918 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
      ],
      "text/html": [
       "<img src=\"data:image/png;base64,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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( [x x],[fn1.(x,0.5) dydx_A],\n",
    "           line = [:solid :dash],\n",
    "           linecolor = [:black :red],\n",
    "           label = [\"fn1()\" \"derivative\"],\n",
    "           legend = :top,\n",
    "           title = \"fn1() and its derivative\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Derivative of a Function with Many Inputs and One Output (Gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mThe gradient is:\u001b[22m\u001b[39m\n",
      "\n",
      " numerical     exact\n",
      "     4.000     4.000\n",
      "     9.000     9.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "fn2(w,Σ) = w'*Σ*w                 #a quadratic form. The derivative wrt w is 2Σw\n",
    "\n",
    "Σ = [1 0.5\n",
    "     0.5 2]\n",
    "w₀ = [1.0,2.0]                   #floats\n",
    "\n",
    "grad = ∇(z->fn2(z,Σ),w₀)\n",
    "\n",
    "printblue(\"The gradient is:\\n\")\n",
    "printmat(grad,2*Σ*w₀;colNames=[\"numerical\",\"exact\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comments on Using the ForwardDiff or ReverseDiff Packages (extra)\n",
    "\n",
    "The [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and [ReverseDiff.jl](https://github.com/JuliaDiff/ReverseDiff.jl) packages are exact and fast. (Use the former for functions with few inputs and many outputs, and the latter for vice versa.)\n",
    "\n",
    "However, they require that your code can handle also other types than Floats. In most cases, that is not a problem, but you may have to watch out if you create arrays to store (intermediate?) results inside the function. See the examples below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ForwardDiff: ForwardDiff.gradient as ForwardDiff_∇\n",
    "using ReverseDiff: ReverseDiff.gradient as ReverseDiff_∇"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    ForwardDiff    ReverseDiff          exact\n",
      "          4.000          4.000          4.000\n",
      "          9.000          9.000          9.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "grad_B = ForwardDiff_∇(z->fn2(z,Σ),w₀)                    #this works\n",
    "grad_C = ReverseDiff_∇(z->fn2(z,Σ),w₀)\n",
    "\n",
    "printmat(grad_B,grad_C,2*Σ*w₀;colNames=[\"ForwardDiff\",\"ReverseDiff\",\"exact\"],width=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Illustration of the Pitfall of ForwardDiff.jl and ReverseDiff.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fnDoesWork (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fnDoesNotWork(b,a)\n",
    "    z = zeros(length(b))              #will not work with ForwardDiff, since\n",
    "    for i in 1:length(z)              #since z cannot store dual numbers\n",
    "        z[i] = b[i]*i\n",
    "    end\n",
    "    return sum(z) + a\n",
    "end\n",
    "\n",
    "function fnDoesWork(b,a)\n",
    "    z = similar(b)                    #will work with ForwardDiff, since\n",
    "    z .= 0                            #when b is a dual number, so is z\n",
    "    for i in 1:length(z)\n",
    "        z[i] = b[i]*i\n",
    "    end\n",
    "    return sum(z) + a\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     1         1    \n"
     ]
    }
   ],
   "source": [
    "b0 = [2]              #should be a vector for use with the gradient functions\n",
    "\n",
    "grad_x1 = ForwardDiff_∇(b->fnDoesWork(b,1),b0)\n",
    "#grad_x1 = ForwardDiff_∇(b->fnDoesNotWork(b,1),b0)    #uncomment to get an error\n",
    "\n",
    "grad_x2 = ReverseDiff_∇(b->fnDoesWork(b,1),b0)\n",
    "#grad_x2 = ReverseDiff_∇(b->fnDoesNotWork(b,1),b0)    #uncomment to get an error\n",
    "\n",
    "printlnPs(grad_x1,grad_x2)"
   ]
  },
  {
   "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
}