Tutorial_25_Interpolation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interpolation\n",
    "\n",
    "This notebook uses the [Interpolations.jl](https://github.com/JuliaMath/Interpolations.jl) package. As alternatives, consider [Dierckx.jl](https://github.com/kbarbary/Dierckx.jl) and [DataInterpolations.jl](https://github.com/PumasAI/DataInterpolations.jl)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Interpolations\n",
    "\n",
    "include(\"jlFiles/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "\n",
    "gr(size=(480,320))\n",
    "default(fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interpolation of y = f(x)\n",
    "\n",
    "Interpolations are particularly useful when *(a)* we repeatedly want to evaluate a function $f(x)$ that is time consuming to calculate but we are willing to accept approximate results, or *(b)* when we only know $f(x)$ for a grid of $x$ values but we are willing to assume that the function is pretty smooth (perhaps even linear over short intervals).\n",
    "\n",
    "In either case, we do something like this:\n",
    "\n",
    "1. Calculate $f(x)$ values for a grid of $x$. This creates a \"look-up\" table.\n",
    "2. Replace the calculation of $f(z)$ by interpolating from the \"look-up\" table."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Values to Be Interpolated\n",
    "\n",
    "As a simple illustration, we interpolate the sine function. (In practice, the interpolation technique is typically applied to more complicated functions.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MTGmpqYFV9PV1bWwsBg2bFj59sLn87nYFOB+ci6Gl98vnIvJUfE3zIMHOHwYJ07gy5ecJXXqwNYW3bqhaVNYWsLcHJqa+Z+VmIj37xEaiqAgBAcjOBiBgbzAQN6SJWjeHFOmYPx4FLgTroKTs6Oo5GpU0DExMY8fP/7+++8B/PTTT0eOHOndu7dYLD5x4sTkyZNZpyOkipHJcOkSPDxw717OknbtMGYMHBzQsiVKPPNgYAADA7RsiVGjACAjA76+OHcOFy4gPByzZ8PNDePGYeZMlPq0ZFUkY8HR0dHCwkJbW7t27doWFhZ+fn4ymezo0aONGjWSr/Du3TtLS8sePXq0adPG1tY2PT294EY8PT0dHR3LnSE5Obncz2WLu8lTU1MlEgnrFOUhEokyMjJYpyinMr9hpFLZn3/K2raVATJAZmQkmz9f9vixYtKIxbKzZ2W9euVsXCCQTZggi4kpdF3uvtUVlZwnk8lU/3+FuLi49PT03IfGxsa6urppaWmJiYm5ZzOysrICAwOFQmH79u0L/WNh7969wcHBnp6e5cuQkpKir69fvueyxd3kaWlpdA5a9cr2hgkKwqxZOUfNpqaYNw+OjtDTU3ysJ0+wbRu8vZGdDaEQM2Zg0SLUqpV3Fe6+1RWVnM2virGxsUUe8rPpenp6ec81a2trd+/e3cbGhou/z4RwT3w8HB3RqRPu3UO9etizB5GRmDtXKe0MoFUr7N2L8HCMGIGsLGzYgGbNcOyYUvbFWdR9hBDg1Ck0bw4vL2howMUFL17AyQna2krfb+PGOH4cQUGwt0d8PEaPxvff4+1bpe+XI6igCanakpIwdiyGDcOXL+jTB48fY906qPjEQvv2uH4d+/ejZk1cuoRWrbB/v0oDqCsqaEKqMD8/tGmDI0egp4c9e3D1Kpo2ZZOEx8PEiXj6FD/9hORkTJ6MsWN5aWlswqgNKmhCqqqNG/Hdd4iJQefOePgQTk4lD55Ttnr14OODw4dRrRqOHNG1tcWTJ4wjMUUFTUjVk56OUaMwfz6kUri54Z9/0KQJ60x5jBmDwEC0asWPiECnTlX5k0MqaEKqmOhodOuG48ehr48zZ7BqFTTU6IK1HM2a4cGD7DFjkJ6OMWOwciVYDAhmjgqakKrk4UN06YJHj2BlhQcPMGgQ60BF09XN3LUL27eDz8eKFfjlF2Rlsc6kalTQhFQZ16/Dzg5xcejTBwEBpZ+0iKUZM3D+PPT1ceQIevfG16+sA6kUFTQhVcOff2LAACQnY/RoXLiQM/kcJwwYgH/+Qf36+Ocf2Nvj40fWgVSHCpqQKmD3bowahawsODvj8GFoabEOVEZt2+L+fTRvjsePYWeXf77TyosKmpBKTnPfPkyfDpkM69dj40b2Y+nKx9QU/v5o1w7Pn6NnT0RFsQ6kClTQhFRqu3cL580DgO3bMX8+6zQVU7s2btxAp06IikLPnoiMZB1I6aigCam8du/G9OkAsG1bzhdcV7MmfH1ha4t37/Ddd5X+XAcVNCGV1IED8lLOWr8eM2awTqM4+vq4eBFduiA6Gt99V7k/M6SCJqQyOn8eTk6QybBli8jRkXUaRatWDZcvo107vHgBBwckJLAOpCxU0IRUOrduYcQIiMVYvhyzZrFOoxwGBrh2Dc2bIzQU/fohzw1AKhMqaEIql9BQ/PADMjMxdSpWrGCdRplq14avLxo1woMHGDkSEgnrQIpHBU1IJfLmDfr2RVIShg3Djh2s0yifqSmuXoWhIf76C3PmsE6jeFTQhFQWKSkYOBBxcfj2Wxw+jCpyrzgrK5w7B6EQO3Zg40bWaRSsavwICan0JBKMHImwMDRvjtOnuXetYEV0744//gCfjwULcPo06zSKRAVNSKUwfz4uXYKRES5ehIEB6zQqN2wY1q6FVIpx4xASwjqNwlBBE8J9np7YsgXa2jhzBhYWrNMwMn8+Jk9GejoGD8anT6zTKAYVNCEcd/s2Zs4EAE9P9OjBOg1TO3eiWzfExGDIEIhErNMoABU0IVwWG4thw5CdDRcXjBvHOg1rWlo4fTpnYtJKMQCcCpoQzsrOxtChiI3Ft99i9WrWadSDsTHOnoWODjw94enJOk1FUUETwlnOzrhzB2ZmOH4cAgHrNGrDxgZeXgAwezaCg1mnqRAqaEK46fBh7NgBbW2cPo3atVmnUTOjR2P6dGRlYehQJCayTlN+VNCEcNCzZ5g6FQB27EDHjqzTqKWNG2Fjg6gojB/P3TuCU0ETwjUZGRgxAmlpGDcOkyezTqOutLVx8iRq1sT589i0iXWacqKCJoRr5sxBWBiaNcPOnayjqLdGjeDtDR4Pixbh3j3WacqDCpoQTvnzT+zdC6EQf/4JPT3WadTeDz9g3jxkZ2PUKCQlsU5TZlTQhHDH69dwcgKAzZvRpg3rNByxejU6dUJ0NH79lXWUMqOCJoQjxOKcw8ChQzFlCus03KGhgSNHUK0aTp3C4cOs05QNFTQhHPH773jwAGZm2LuXdRSusbTE9u0AMGMGXr9mnaYMqKAJ4YKgIHh4gM+Ht3dVnKyu4saPx8iRSE7GiBHIzmadprSooAlRe6mpGDUK2dmYNw/29qzTcNauXTA3R2AgPDxYRyktKmhC1J6zM16+RNu2WLWKdRQuMzDImdff3Z0rl4BTQROi3i5cgJcXhEIcOQJtbdZpOM7WFrNmITsb48YhM5N1mpJRQROixhIScsbVeXigVSvWaSoFDw80a4anT7F0KesoJaOCJkSNzZqF2Fh07YrZs1lHqSx0dHD0KDQ1sWkT/P1ZpykBFTQh6urCBRw5Al3dnDOnRFHat8fChZBKMWkS0tJYpykO/dQJUUt5T25YWrJOU+ksXYp27RAZiSVLWEcpDhU0IWop9+SG/H6DRLG0tODtDU1NbN+O27dZpykSFTQh6ufiRTq5oXRt22L+fEilcHREVhbrNIWjnz0haiYlBdOmAcDvv9PJDeVatgzNmiE8XG0HmFNBE6JmFi/G27fo2LFy3JdarQmFOHgQAgHWrlXPS1eooAlRJ/fuYdcuaGpi3z66D6wqdO6MadMgFsPRERIJ6zT5abDa8alTp3x8fKpVqzZr1qw2BWa2ffLkyZEjR3IfTp482ZL+1iOVnkiEX3+FVApXV5ruWXU8PHDhAkJCsG0b5s5lneY/2BxBnzhxYvbs2UOGDGnatKmtre379+/zrfDixYvTp0/X/JeGBrP/kRCiOh4eePoUVlacuMit8qhWDbt3A4CbG6KiWKf5DzbFt2nTJnd39yFDhgAICAjw8vJasWJFvnXMzMwWLlzIIBwhTDx/jjVrwOPl3NGKqFLfvhg2DCdPYvZs/PUX6zT/j8ERtFgsDgkJ6dmzp/xhjx49AgICCq725s2b6dOnL1u27MmTJ6oNSIjKyWSYPh1ZWZg8Gba2rNNUSVu2oEYNXLiAM2dYR/l/DI6g4+PjJRJJrVq15A+NjIxiY2PzrVOnTp2hQ4daWFg8ffq0c+fOPj4+Dg4O+dZ5/fr1xYsXe/Xqlbtk3bp1zZo1K2WMtLQ0Ho9X3m+CJe4mT09Pl0gkfA4O7M3OzpZIJGKxWEnb1zhxQnjjhqxWrfQlS2SpqYrdOHffMCpNrq+vuXy5trOzbPr09M6dZdWrV2RjpUmuq6tb4u8Cg4LW1dUFkPXvyPCMjIxq1arlW6dHjx49evSQf21kZOTh4VGwoE1MTKytrefMmZO7pGXLljo6OqWMIZPJCu6XE7ibnMfj6ejocLeghUo685CQADc3ALxNm/TMzRW+ee6+YVSdfPZsnDrFu3dPb80abNtWkS0pKjmDgq5Ro4a+vv6bN2+MjY0BvHnzpn79+sWs37Jly7wjOnIJhUJTU9PvvvtOWUEJUY3Fi/HxI2xt8csvrKNUbXw+9uxBhw7YtQvjx6N9e9aBGI3iGDJkiLe3N4D09PRTp07JPy1MT0/39vZOS0sD8OHDB/maIpHo0KFDHTt2ZJKTEKULDMTevdDSwq5d4OaJiEqlTRvMmgWJBFOmQCplnYZRQS9btuzatWvdu3dv06ZN8+bNf/zxRwAJCQkTJkz48uULgLlz5zZu3NjW1rZhw4YfP35cv349k5yEKJdEAicnSKWYNw8tWrBOQwAAK1bA1BSBgThwgHUURsPsGjZsGB4eHhISUqNGjebNm8sX1qtXLzY2tk6dOgCOHz8eERHx+fNnExOTRo0acfQjDkJKsGcPHj5Ew4byc9BELejrY+NGjBgBV1cMHgxDQ4ZZmF0AoqWl1blz57xL+Hy+/Ky0/OvSj8cghJO+fMHy5QCwZQt0dVmnIXkMHw5vb1y9ikWLsHcvwyDc+zydkEpi4UJ8+YK+ffHjj6yjkAK2bIGWFvbvx4MHDFNQQRPCwoMHOHgQ2trYupV1FFKYpk0xbx6kUsyYwfDTQipoQlROKsWsWTmfDVpZsU5DiuDmBnNzBAUx/LSQCpoQldu3DwEBaNAAixezjkKKpquLNWsAYPFiJCYyiUAFTYhqJSTk3Kh040bo6bFOQ4o1fDhsbREfjwKzuakGFTQhqrV8OT5/Rq9eGDqUdRRSEh4PO3dCQwM7dyIsTPX7p4ImRIWePcOePRAIsHkz6yikdFq2hKMjxGLkmfZHZaigCVGhOXOQnY0pU+iGKVyyahUMDXHjBnx8VLxnKmhCVOX8efj6olYtrFzJOgopi1q18PvvALBgATIzVblnKmhCVEIkgosL8O/hGOGWX39FmzZ4/Rpbtqhyt1TQhKjEpk14+RKtW8PRkXUUUna5Hxt4eCAuTmW7pYImRPni4uDhAQBbtoDugMxRvXph0CCkpOSMklQJKmhClM/NDSkp+PFH5LlDG+GejRuhrQ1vbwQFqWaHVNCEKFloKLy9oamJdetYRyEVY2GRc43+7NmQyVSwQypoQpTM2RkSCWbMoGk3KoMlS1CnDu7eVc2QOypoQpTpr79w4wYMDbF0KesoRBFq1MCqVQDg6op/73ytPFTQhChNdnbO0LoVK1CzJus0REEmTULr1oiMxPbtyt4VFTQhSrNzJyIi0KwZnJxYRyGKIxBAfpdUd3d8/qzUXVFBE6IcCQk5fwuvXw9NTdZpiEI5OKBfPyQmKvuiUCpoQpRj1Sp8/Qp7e3z/PesoRAk2boSGBvbswdOnytsJFTQhShAZiZ07wedj40bWUYhyNG+OyZMhFmPRIuXthAqaECVYtAgiEcaOhbU16yhEaVauRPXquHABN28qaQ9U0IQo2v37OH0aOjo556BJZVWnDhYuBABnZyXdWJYKmhCFkskwf37Ofxs0YJ2GKJmzM8zM8OgRjh1TxuapoAlRKB8f3LmDunVzRkCTyk0oxG+/AYCbmzKmiqaCJkRxsrNzbtT922/Q12edhqjE2LFo1w5v3mDbNoVvmwqaEMXZvRsvX6JZM0ycyDoKURU+H5s2AcDq1Qq/boUKmhAFSU7OuTHSunU06XPVYm+Pvn2RmJjzBlAcKmhCFGTtWsTHw9YWAweyjkJUbt06CATYvRuRkQrcKhU0IYrw/j22bAGPh9WrWUchLLRujV9+gUik2PutUEEToghubkhPx4gR6NKFdRTCyKpV0NXFyZO4f19Rm6SCJqTCwsJw+DC0tBR+CpJwiakpZs2CTJYzkkcRqKAJqTBXV0gkmDoVFhasoxCmFi6EoSFu3tS4dk0h26OCJqRi/P1x+TL09RV43ES4ysBAfg5ae8kSiMUV3x4VNCEVIJPlXDHo6oo6dVinIWpg2jQ0asR/8QKHD1d8Y1TQhFTAqVMIDISJCebMYR2FqAdtbbi7A4AiznLQcHpCyis7O2dM1YoV0NVlnYaojZEjM4RCnc6dK74lKmhCymvPHrx6haZNMWEC6yhEvYi/+04hk7HQKQ5CyiU1NWdQ3dq1dGE3URIqaELKZeNGfPqE7t3x44+so5BKiwqakLKLj8+52eCaNayjkMqMCpqQsvvtN6SkYNAgdOvGOgqpzKigCSmjqCjs3QuBgC7sJspGBU1IGS1eDJEIEyagZUvWUUglRwVNSFmEhuLkSUmH9voAACAASURBVAiFWLaMdRRS+VFBE1IWLi6QSjFrFt2xm6gAFTQhpebrC19f1KwJV1fWUUiVUFxB37hxIzg4WBl7zczM/O233wYMGDBr1qyPHz8Wus6pU6cGDx48atSoO3fuKCMDIWUjk2HRIgBwdUXNmqzTkCqhuIL28/OzsbHp2LGjl5dXamqqAvc6Y8YMf39/Z2fnrKwsBwcHmUyWb4W//vpr+vTp48aNs7e379+///PnzxW4d0LKQXDqFIKDYWKCGTNYZyFVhqxoWVlZJ0+e/O6773g8nr6+vqOjY3BwcDHrl1J8fLy2tnZ0dLRMJpNIJCYmJn///Xe+dezt7bdt2yb/2tHRcdasWQW34+np6ejoWO4YycnJ5X4uW9xNnpqaKpFIWKcoD1FamrRxYxkg27ePdZYy4+4bhpIXdwStpaU1dOhQX1/fFy9eTJs27ezZsx06dLCxsdm7d29FDqgfP35cu3Ztc3NzAHw+v2vXrkFBQfnWCQoK6vbvJQDdunULDAwsz55kMgQGKmTabFLF8fft40VGonlzjBvHOgupQko1yUuTJk3WrFmzcuXK06dPz50718nJacGCBePHj3d2djYzMyvrLj9+/FirVq3ch4aGhnFxcXlXSE9PT0lJyV2n4ApykZGRFy9e7NWrV+6S1atXt2jRIvehxpkzOuPHi6ZNyyrselzFnrRRJe4mT09PF4vFfD7HPprmpaXp/v47gAw3N3FGBus4ZcbdN0zlTq6rqysQCIpfp7SzcH348OHAgQP79u2Lj4/v0qWLtbX1oUOHDhw4cPHixZ49e5ZyI3J6enqZmZm5D9PT0+v891YUQqFQQ0Mj49/fhIyMDP3CJu6rX7++tbX1nH8nStfQ0GjXrp22tvb/r2FjA4FAa98+rXnzCr1ZXKGb5QSOJufz+To6OpwraGzejPh4aadOOiNHgsdjnaY8OPqGQZVPXsKvilQqvXLlyuDBg83NzdeuXdu3b9+HDx/evXt3586db9686dChw4YNG8q6ywYNGnz48EEkEskfRkdH169f/z+Z+HwTE5Po6Gj5w6ioqAaFjTnV1tY2NTX97l92dnb/aWcALVtizBiIRFi6tKwhCckRH48NGwCIf/+do+1MuKu4gr5w4YKFhUX//v1fvXq1ZcuW9+/f79mzp127dvJ/1dfXHzhwYFGD5IrRrl07U1PTP//8E8CzZ8+Cg4MHDRoE4NWrV8eOHZOvM2zYsAMHDgDIyso6evTosGHDyrqXHO7u0NHB8eMICSnnFkgVt2oVUlJkAwZIu3dnHYVUOcUVdGhoaNeuXW/duhUWFjZ9+vTq1avnW2Ho0KHbt28v6y55PN6OHTvmz5/frVu3nj17rlmzRn6KIyAgwM3NTb7OggULXr582bZt2+bNm5uZmY0YMaKse8lhaoqpUyGT0R2XSXlER2PvXvD5khUrWEchVRFPVmAMci6ZTMZT2t90aWlpL168aNCgQe3ateVLsrOzMzMzc0/cSKXSZ8+eCYVCS0vLQrewd+/e4OBgT0/PEvaUkIDGjZGQgL//xrff5i5OSUnh6Okt7iZPS0vj2Dno0aNx7BjGjcv28pJIJEKhkHWg8uDuG4aSF/erorx2BqCnp9e+ffvcdgagqamZ91vi8/mtWrUqqp3LoGZNzJ8PAIsWoej/GxGS3+PHOHECWlo0LxJhhTvHMhUxezbq1UNgIHx8WEch3OHqCqkU06cXOgSIEBWoGgWtp4flywHAzY2uWyGl4ueHK1dQowZ9ekEYqhoFDWDSJDRtihcvsH8/6yhE7clkWLgQAFxcYGTEOg2puqpMQWtowN0dAFauRFoa6zREvZ0+jYAA1KuHfy+DIoSJKlPQAH7+GV27IjYWW7awjkLUmFic86ngihXQ02OdhlRpVamgAcgn5Vi7Fp8+sY5C1NXevXj+HFZWmDiRdRRS1VWxgu7RAwMGICUFhU2fRAjS0rBqFQCsXg2N0s5UQ4iSVLGCBrB6Nfh87NrFj4lhHYWon82bEReHzp0xeDDrKIRUwYJu3RpjxiArS+u331hHIWomPh7r1wPA2rU0LxJRB1WvoAGsWgWhUPP0aZpBifzHqlVITsaAASjjDLqEKEmVLGgzM8yYAakU8+axjkLURlQUPD0hENDnE0R9VMmCBrBkiaxmTfj54do11lGIenB1hUiE8ePRqhXrKITkqKoFbWAgcnYGABcXSKWs0xDWAgNx6hR0dHKmBCBEPVTVggZETk4wN8fjx/j3LgGk6nJ1hUyGuXNR2L17CGGl6hY0hELIB3K4uSEri3Uaws6lS7hxA0ZGWLCAdRRC/qMKFzSAMWPQti3evEHZ7wtDKgmJBK6uALBkCWrUYJ2GkP+o2gXN52PdOgDw8MDXr6zTEBa8vfHkCSwsMG0a6yiE5Fe1CxpAnz7o0wcJCTlz3ZEqJSMDK1cCwOrV0NJinYaQ/Kp8QQNYvx58PnbsQGQk6yhEtTZswNu3+OYbDB3KOgohhaCCBtq0wdixEImwdCnrKESFPn3Chg0AsGYNXdhN1BMVNADA3R26ujhxAvfusY5CVGX5ciQnY9Ag2NuzjkJI4aigAQCmppg1CzIZFi1iHYWoxPPn2LcPGhpYvZp1FEKKRAX9L1dXGBnB3x/nzrGOQpTP1RViMX79Fc2asY5CSJGooP9Vo0bOZb4LFyI7m3Uaokx+fjh/Hvr6dGE3UXNU0HlMmYIWLRARgT17WEchSiOVwsUFAFxdUbcu6zSEFIcKOg8NDXh4AMDy5XTdSqV15AiCglC/Pt2xm6g/Kuj/+vFHfPstEhJoUuDKKSMjZzDlmjXQ1WWdhpASUEEXsGED+Hxs3UrXrVRCGzYgJgbW1hg5knUUQkpGBV1Au3YYPRoiEZYsYR2FKFRcXM4tB7dsAZ/e+YQD6G1aGPl1KydP4u5d1lGI4ixdipQUDBpEtxwkXEEFXZgGDeDikjODu0zGOg1RhEePcPAgtLRy5i8khAuooIuwcCHMzBAQgCNHWEchiuDiAokEM2eiSRPWUQgpLSroIujo4PffAWDRIqSlsU5DKsbHB3//jdq14ebGOgohZUAFXbQxY/DNN3j/PueTJcJRIlHOFCu//QYDA9ZpCCkDKuii8XjYsgU8Htatw5s3rNOQ8tq0CS9fokULTJ7MOgohZUMFXawuXTB8ODIyaJY7rvr4MWe+uq1boaHBOg0hZUMFXZK1a3Omir59m3UUUnZLliA5GT/8gO++Yx2FkDKjgi6JmRkWLIBMhlmzIJGwTkPKIjg4Z2gdfYpAuIkKuhQWLEDDhnj4EAcOsI5CSk0mw5w5kErh7AwrK9ZpCCkPKuhS0NHJubph0SJ8+cI6DSmdQ4dw+zaMjenzA8JdVNClM3Qo7Ozw5QtWrWIdhZRCSgoWLwaA9etRvTrrNISUExV0qW3dCoEAu3bh2TPWUUhJ3N3x4QO6dMHo0ayjEFJ+VNCl1qYNnJyQnY0ZM1hHIcWKiMDmzeDzsW0beDzWaQgpPyrosli1CkZGuHkTJ06wjkKKNmsWRCJMnAgbG9ZRCKkQKuiyqFUr555Yc+ciOZl1GlIYHx/873+oWTPnJ0UIl1FBl9GkSejcGXFxOVMpEbWSno758wHAwwO1a7NOQ0hFUUGXEZ+PHTsgEGDzZoSFsU5D/uv33xEdjQ4d8OuvrKMQogDMZifw8vI6c+aMnp6es7Nz165d8/1rSEiIp6dn7sM5c+Y0b95ctQGL1qEDJk+GpyfmzMH166zTkH+9eIGNG8HnY9cuCASs0xCiAGyOoA8ePOjh4eHs7Ozg4NCvX7/o6Oh8K0RFRfn7+3f4V3V1G8rq7g4jI9y4gWPHWEch/5o5EyIRJk/GN9+wjkKIYrA5gt66devvv//eu3dvAH5+fl5eXu7u7vnWMTExcXR0ZJGuFAwNsXYtJk3CvHno359mGWbvxAn4+sLQkD4bJJUJgyPo7OzssLCwLl26yB926dIlODi44GqRkZGjRo2aPXv2vXv3VBuwdCZMgL094uJyrlgjDCUnY948AFi3DoaGrNMQojDKOoL+8OHDlwLTVgiFwiZNmsTHx0ul0lq1askXGhoaxsXF5VvT1NR06tSpjRs3fvr0aZ8+fQ4dOjR48OB867x8+fLMmTOBgYHyh5qamlu3bm3VqlUpE6alpfEqdhUDf+1a3W7d4OmZMWSIRIV/Vlc8OSvp6ekSiYTPV/Bhgbazs+aHD5KuXTOGDkVqqmI3LpednS2RSMRisTI2rmzcfcNU7uS6urol/i4oq6D/+OOPkydP5lvYuHHj06dP6+vrA8jIyDAwMACQlpZW8BRz586dO3fuDGDo0KF6enobN24sWNANGzbs2bPn4jwHsG3atNHU1CxlQplMVq1atbJ8TwV07Ih587Bmjc6cOQgORql3XUEKSM4Ij8fT0dFRcEEHBMjnFBV4eVXT11fklvOQF7RQKFTS9pWKu28YSq6sgl60aNGiImYR09fXNzAweP36db169QBERUWZmZkVsykLC4vPnz8XXK6pqWlkZNShQweFBC6nZctw8iTCwrB9O5ydWSapmsRiODlBKsWCBWjRgnUaQhSMzSiOESNGyEfRJScnnzhxYsSIEQDS0tK2bNmSkpIC4OXLl1KpFEBqaqqnp2e3bt2Y5CyZjg527ACA5cvpvoUMbN6MR49gaUmfBJBKiU1BL1u27NGjR61atWratKmtrW3//v0BJCYmzp07NyEhAYC7u3vdunXbtm1ramrK5/PXrl3LJGep9OuHESOQmoopU1hHqWJev8aKFQCwcyd0dBiHIUQJ2Ayzq1evXmhoaEREhL6+vomJiXyhqalpRkaG/DSft7f3x48fP336ZGpqmvtxovrauhW+vrh6FUeOYMwY1mmqBpkMv/6K9HSMGYM+fVinIUQpmF3qzePxmjZtmtvOcnk/hKlbt27r1q050M4A6tTBxo0AMGcOPn1inaZq2LcPN27AyAibNrGOQoiy0FwcCjJuHBwc8OULfVSoCrGxWLgQAHbsoEmRSCVGBa04np6oVg1Hj+Kvv1hHqeymT0dCAgYMwPDhrKMQokRU0Ipjbo7ffgOA6dORmMg6TeV16hTOnkWNGsgznRYhlRIVtELNmoXOnfHuHebOZR2lkoqPz7nl2Nq1MDVlnYYQ5aKCViiBAN7e0NGBtzfOnmWdpjKaPh2fPqFXL6jtRFqEKA4VtKI1bYpVqwBg+nR8/co6TeVy7BhOnUL16jh4kO4GS6oCKmglmDsXPXsiNhZz5rCOUonExmLmTADYvBnFzg1ASKVBBa0EfD727YOuLg4fxrlzrNNUFo6O+PoV/ftj4kTWUQhRESpo5WjSBKtXA4CjIz5+ZJ2G+w4exMWLqFkTXl6soxCiOlTQSjNzJnr3Rnw8Jk6ETMY6DZe9eoXZswFg+3b899JTQio3Kmil4fHg7Q1DQ1y+jF27WKfhLLEYv/yClBQMGYLRo1mnIUSlqKCVycQk50/y+fMRFsY6DTetXIl791C/Pl2WQqogKmglGzwYEyYgMxPjxkEkYp2Ga+7cwerV4PNx6BA4MW0WIQpFBa18W7eicWM8fIgibjFDCpeUhDFjIJHA1RX29qzTEMIAFbTy6evj6FFoamLzZly4wDoNd0yejOhodOyYMys/IVUPFbRKdOqENWsgk2H8eMTEsE7DBTt24PRp1KiB48dVdjdeQtQNFbSqzJ2LH3/E168YNgzZ2azTqLegIMyfDwD796NxY9ZpCGGGClpVeDwcPIiGDfHgAZYuZZ1GjSUmYvhwZGVh1iz8/DPrNISwRAWtQjVr5pyMXreOTkYXTibDpEl4/RodO2L9etZpCGGMClq1unaFhwdkMowdi4gI1mnUz7p1OHMGBgb4809oabFOQwhjVNAqN28ehg1DUhIGD0ZKCus06uR//8OSJTmjnhs1Yp2GEPaooFVOfgm4tTWePcPYsTRNR47oaIweDYkEK1Zg4EDWaQhRC1TQLOjo4ORJ1KyJ8+exZg3rNGogNRUDB+LLFwwaBDc31mkIURdU0IxYWuLIEfD5cHOr6nNGy4eHP3mCFi1w6BDdKoWQXFTQ7PTvD3d3SKUYMwbBwazTsLNoEXx8YGCAs2ehr886DSFqhAqaKVdXODkhLQ0DB1bRKwz378fatdDUxMmTsLJinYYQ9UIFzdr27fj2W8TGon9/JCWxTqNaN29i2jQA2LYNvXuzTkOI2qGCZk1TE6dOoVkzPH2KkSOr0FXgYWEYNAgiERYvxpQprNMQoo6ooNVAzZq4eBG1a+PKFUyYAKmUdSDli45Gv35ITsaIEfj9d9ZpCFFTVNDqoXFjXL6cMzGp/P57lVhsLHr3xvv3sLPDwYM0bIOQolBBqw0bG/z1F4RC7NhRmWdATkxE//549Qrt2uHsWQiFrAMRor6ooNWJnR2OH4eGBlauxJYtrNMoHi81ld+/Px49QosW8PWFgQHrRISoNSpoNTNoELy8wOPB2RmbN7NOo1ApKdo//YQHD2BhAV9fGBmxDkSIuqOCVj/jx2PPnpyO3rCBdRoFSUqCg4Pg7l00aABfX5iYsA5ECAdQQaslR0d4eYHPh4sLVq1inabCEhPRpw/u3ZOZmUmvX4eFBetAhHADFbS6mjgR+/dDIMCyZXBz4/Ckd58+wc4OAQGwtMy4do1uYUVI6VFBq7Hx4+HtDQ0NuLtjwgROXsMSEYGuXREaimbN4O8vq1+fdSBCuIQKWr2NGYPz56Gnhz/+wMCBHJvg//ZtdO2KyEh07Ah/fzrvTEhZUUGrvf79cfMm6tTB//4HOzu8f886UOmcPInevfHlC374ISc/IaSMqKC5oGNH3L2LJk0QEoIOHQS3b7MOVCyJBG5uGDECmZmYMQNnzkBPj3UmQjiJCpojGjfGvXvo0wcfP+r+8AM2bWIdqAifPqFPH7i7QyDApk3Yvh0CAetMhHAVFTR3GBri8mUsXgyJJOfOswkJrDP91+3baN8eN27A2Bi+vpg7l3UgQriNCppTBAK4u2ccO4YaNXDqFFq3xtWrrDMBALKysHgx7O3x/j169kRICOzsWGcihPOooLlHPGAAgoLQtSvev0f//nByYjy6IyAA7dtj9WrIZHB1xfXrqFePZR5CKgsqaG6ytMStW1i7Ftra2LsXrVrhxAkGF7MkJmL+fHTtimfP0KwZbt/G6tXQ0FB1DEIqKSpozhIIsGABgoLQsSNiYjByJLp3R2CgivaenY1t29CkCTZuBIAFC/DwITp3VtHeCakaqKA5rmVL3L+P/ftRrx7u3kWnThg+HCEhStxjdjaOHUPLlpg9G58/51zGvXYtzexMiMKxKei///575cqVI0eO9PPzK2qdffv22dvb9+/f/6qafA6mtvh8TJyIFy+waBG0tXHyJDp0QO/e8PVV8I4SE7FuHSwsMHo0Xr5E8+b46y/cvIn27RW8I0IIAFYFffDgwa9fv969ezc6OrrQFf7888+VK1cuX758woQJw4cPf/z4sWoDcpC+Pjw88OoVXFxQvTr+/ht9+qBxY7i54enTCm05KwsXL2LcODRogIUL8e4dWrTAvn14/BgDByooPSGkEGw+zzl69CiAgICAolbYvn37kiVL7OzsAPj7++/evXv37t0qi8dhpqZYtw5LlmDPHmzfjtev4e4Od3e0aYPvvkPPnujaFbVrl7wdqRTh4bh/H35+uHABSUkAwOOhTx/MnQsHB7qRICEqoKYfuIeGhm7fvl3+defOnXfu3Mk2D8fUqIGFC+HiAn9/HDsGHx88fozHj7FpE3g8WFrCwgLm5jA3///bmujrIz4eHz7gwwfExODhQyQn//8G27XD0KEYNgyWlky+IUKqJmUV9JMnTzIyMvItrFu3rpmZWYnPTUtLS01NrVmzpvxhrVq14uLiCq4WERHh4+OT9zB8x44dbdq0KWXC1NTUUq6pbsqQ3MYGNjZYs0Zw547G/fuCu3f5gYG8ly/x8mWJT5U2aCDt1EnSsaO4Tx9p7iTOFRtwnZ6eLhaL+XzufTSdnZ0tkUiyuTjjaxV5q6uZ0iTX1dUVlDQRgrIK2sPDIyoqKt/CIUOGzJs3r8Tn6ujoaGpqpqenyx+mpaXVqFGj4GoWFha2traLFy+WP9TQ0GjZsqVGWQbh6uvrl35ltVLm5D/8gB9+AIDsbEREIDoab97gzRskJuaskJQEQ0PUq4cGDVCvHlq35terxwc0AG3Fxebz+To6OtwtaCFnR6pUobe62lBIcmUV9LFjx8r9XD6fX79+/cjIyBYtWgCIjIw0NzcvuJqGhoaRkVGHDh3KsYv09PStW7e6ubmVOyRDmzdvXrhwobZ2uZpTUxMtW6JlS0WHKpWTJ09269bNysqKyd4r4sGDBwkJCQM5+KHox48fjx8/PmfOHNZBymP16tUeHh6sU5THvn37Ro8eXafCs+yq0bHMs2fP9uzZI/965MiRnp6eUqk0LS3t0KFDI0eOVOy+Pn365OXlpdhtqsyePXu+fPnCOkV5nD9/nqMDcu7evXv9+nXWKcojMjLyxIkTrFOU0+rVq1lHKKcTJ05ERkZWfDtsCnrQoEE8Hu/+/fsTJkzg8XhXrlwB8OjRo3Xr1slXcHFxSU5OtrCwsLCwsLGxGTp0KJOchBDCEJtRHOfOnSu4cNSoUaNGjZJ/bWBgcOvWrXfv3mlra9cuzbAwQgipdNR0mJ1cfbrHKCGkCuPJVD8FmoK4urpu3bpVR0enHM+VSqWpqanVq1dXeCoVSEpKql69Oo+Dl4qkpaVpaWlpamqyDlJmWVlZUqm0fG82tiQSSXp6OkfHQiQmJhoYGLBOUR4pKSkljqKbMmVKiR+BcrigxWLx169fy/3bnpWVVc6BEKxxOrmWlhYX/9cikUhkMlmZBnGqD06/YSpxcl1d3RLX4XBBE0JI5aZGw+wIIYTkRQVNCCFqigqaEELUFCc/9FCg2NjYS5cuRUVFCYXCPn36dOrUiXWi0pJIJLdu3bp7965IJOrSpUvfvn1ZJyqDlJSUhw8fRkREdOjQwdramnWcEkRFRR05ckQikQwbNkw+/QAnyGSyly9fhoSEZGZmjh8/nnWcMpDJZIGBgTdv3kxNTW3Tps3PP//Moflb/P3979+/n5CQYG5uPnLkyAqOQuHMt60kt2/fvn//fs2aNTMyMvr27XvgwAHWiUrrwoULs2bNSk1N1dTUdHJymjt3LutEZfDjjz/OmDFj2bJl8otI1dmbN29sbGySkpIAdOnSJTQ0lHWi0rp06VL37t03btzIrfcGgNDQ0OHDh3/69ElPT2/lypU///wz60RlsH///uTk5Nq1a1++fNna2johIaFCm5ORf23evNnOzo51itJKS0uTSqXyr//55x+hUCgSidhGKr3s7GyZTPbTTz+5u7uzzlICFxeXX375Rf71woULx44dyzZP6clf5Hv37hkYGLDOUjaZmZlisVj+9bt37wDExMSwjVQOUqnU3Nz83LlzFdlIVT+CziUWix8+fNi8eXPWQUpLV1c3d0CxRCLR1tYucW5Z9cGhAcU3b950cHCQf+3g4HDz5k22eUqPQy9yPnnfzGKxmMfjcfESodevXyclJVVw7kYqaISHhzdu3NjQ0DAyMnLDhg2s45SZSCRycXFxdnbm0Hk6DomNjc2dNLJu3bpxcXFSqZRtpKpDJpPNmTNnwoQJRrm3/uECFxcXMzOzVq1abdy4sYLHfJX/V9rPz0+7MM+fP5evYGVl9eDBg+vXr2tpaanb2boGDRoUTL5q1arcFcRi8ejRo01MTHJvXKAm+vfvXzD5sGHDWOcqM4FAIJFI5F+LxWKBQMDFKyE5at68ebGxsVu2bGEdpGxWrFhx9+5dLy8vFxeXkJCQimyKq38ElZ6dnV3uzVnyyv0bSiAQGBkZGRkZrVmzxt7e3tPTU7UBi/PmzRtZgUs9c4+UJRLJ+PHjU1NTz507p25/z168eLFgci5Wm6mp6YcPH+Rff/jwwcTEhIvfBRctXrzYz8/v+vXrnJtIRE9PT09Pb8yYMZcuXfLx8Wnfvn25N1X5j6ABCAoj/6esrKzc1R4+fNigQQNGGQvH5/MLJpcXhEwmmzZt2sePH8+cOaOG8xUUmpyLJ2G+//7706dPy7/28fH5/vvv2eapIpYtW3bx4sVr167l3puUE8Rice7fW9nZ2U+fPq3glJxVfS6O4cOHf/361dzc/N27dwEBAUePHu3Xrx/rUKXy559/jhgxomvXrrq6uvIlR48erfgtdlRj27ZtFy5cePz4cfXq1Rs2bDhv3jy1Hcf95cuXLl26WFlZ6enp3b59++7du4XegE0NxcXFjR07Nikp6eHDh3Z2dvXr1z948CDrUKUSEBDQqVMna2trQ0ND+ZJNmza1bt2abarSePPmTffu3bt16yYUCu/cuWNiYnL16tWKfMJZ1Qs6LS3tzp07Hz58MDIy6t69O4fmNoyNjX369GneJd27d+fKXU2fP38uHz4l16JFCxMTE4Z5ipeamvq///0vOzu7b9++HHqHZGRk3LlzJ/ehrq5u165dGeYpvcTExKCgoLxLbGxsuPLKv3r1KiQkJCsry8rKquIXvlX1giaEELXFvXOChBBSRVBBE0KImqKCJoQQNUUFTQghaooKmhBC1BQVNCGEqCkqaEIIUVNU0IQQoqaooAkhRE1RQRPy/969e9ewYcMJEybkLrl165aRkdHmzZsZpiJVFl3qTch/nDp1atiwYfv37584ceLXr1+tra0bNWp0/fp1Dt2whlQaVNCE5Dd16lRvb+979+4tX7783r17jx49Uue5nEglRgVNSH6ZmZmdO3eOiopKTU29fPly7j0JCVExOgdNSH5CofDXX39NTk7u1q0btTNhiI6gCckvKiqqffv2DRo0CAsLO3z48JgxY1gnIlUUHUET8h/Z2dmjR482NDS8ffv2+PHjp0yZknt/YUJUjI6gCfmPefPm7dy54HIw2wAAAH1JREFU8+7du+3bt09LS/vmm28EAsGDBw8qcuMiQsqHjqAJ+X+XL1/evHnz+vXr5Xdi1tPTO3nyZGRk5Pz581lHI1URHUETQoiaoiNoQghRU1TQhBCipqigCSFETVFBE0KImqKCJoQQNUUFTQghaooKmhBC1BQVNCGEqKn/A4HQU79vbgAmAAAAAElFTkSuQmCC\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xGrid = range(-pi,3.0,length=101)  #uniformly spaced grid\n",
    "yGrid = sin.(xGrid)               #y values at xGrid\n",
    "\n",
    "p1 = plot( xGrid,yGrid,\n",
    "           linecolor = :red,\n",
    "           linewidth = 2,\n",
    "           legend = nothing,\n",
    "           title = \"the sine function\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"y\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolate\n",
    "\n",
    "The next cell calls on `cubic_spline_interpolation()` to create the \"look-up\" table (more precisely, create an interpolation object). \n",
    "\n",
    "To use a cubic spline it is required that the $x_i$ grid is *uniformly spaced* (for instance, 0.1,0.2,...). Actually, it has to be a `range`. The case of a non-uniformly spaced $x$ grid is discussed later.\n",
    "\n",
    "The option `extrapolation_bc=...` determines how extrapolation beyond the range of the $x_i$ grid is done.\n",
    "\n",
    "The second cell interpolates and extrapolates $y$ at some specific $x$ values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "itp = cubic_spline_interpolation(xGrid,yGrid,extrapolation_bc=Flat());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                x   interpolated y           true y\n",
      "            0.250            0.247            0.247\n",
      "            0.750            0.682            0.682\n",
      "            1.250            0.949            0.949\n",
      "\n",
      "               x2   extrapolated y\n",
      "            3.242            0.141\n",
      "            3.642            0.141\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x  = [0.25,0.75,1.25]                          #to interpolate the y values at\n",
    "\n",
    "y_interpolated = itp(x)\n",
    "printmat([x y_interpolated sin.(x)],colNames=[\"x\",\"interpolated y\",\"true y\"],width=17)\n",
    "\n",
    "x2             = [pi+0.1,pi+0.5]                 #to extrapolate the y values at\n",
    "y_extrapolated = itp(x2)  \n",
    "                                                \n",
    "printmat([x2 y_extrapolated],colNames=[\"x2\",\"extrapolated y\"],width=17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( xGrid,yGrid,\n",
    "           linecolor = :red,\n",
    "           linewidth = 2,\n",
    "           label = \"sine function\",\n",
    "           title = \"the sine function\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"y\" )\n",
    "scatter!(x,y_interpolated,markercolor=:magenta,markersize=5,marker=:square,label=\"interpolated\")\n",
    "scatter!(x2,y_extrapolated,markercolor=:blue,markersize=8,label=\"extrapolated\")\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interpolation of y = f(x) for General x Vectors\n",
    "\n",
    "That is, when we cannot guarantee that the look-up table of $y_i=f(x_i)$ is from uniformly spaced $x_i$ values (the grid is irregular). This is useful, for instance, when we have empirical data on $(x_i,y_i)$.\n",
    "\n",
    "The approach works similar to before, except that the `cubic_spline_interpolation` must be replaced by `linear_interpolation`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xGrid2 = deleteat!(collect(xGrid),55:60)         #non-uniformly spaced grid\n",
    "yGrid2 = sin.(xGrid2)\n",
    "\n",
    "p1 = scatter( xGrid2,yGrid2,\n",
    "              linecolor = :red,\n",
    "              legend = false,\n",
    "              title = \"y\",\n",
    "              xlabel = \"x\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                x   interpolated y           true y\n",
      "            0.250            0.241            0.247\n",
      "            0.750            0.681            0.682\n",
      "            1.250            0.949            0.949\n",
      "\n",
      "               x2   extrapolated y\n",
      "            3.242            0.141\n",
      "            3.642            0.141\n",
      "\n"
     ]
    }
   ],
   "source": [
    "itp2 = linear_interpolation(xGrid2,yGrid2,extrapolation_bc=Flat())\n",
    "\n",
    "y_interpolated = itp2(x)\n",
    "printmat([x y_interpolated sin.(x)],colNames=[\"x\",\"interpolated y\",\"true y\"],width=17)\n",
    "\n",
    "y_extrapolated = itp2(x2)\n",
    "printmat([x2 y_extrapolated],colNames=[\"x2\",\"extrapolated y\"],width=17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.10.3",
   "language": "julia",
   "name": "julia-1.10"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.10.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}