{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Collocation (Interpolation/Extrapolation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 3.1 *Data and Interpolating Functions* in {cite}`Sauer`.\n",
    "- Section 3.1 *Interpolation and the Lagrange Polynomial* in {cite}`Burden-Faires`.\n",
    "- Section 4.1 in {cite}`Chenney-Kincaid`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Numerical methods for dealing with functions require describing them, at least approximately, using a finite list of numbers, and the most basic approach is to approximate by a polynomial.\n",
    "(Other important choices are rational functions and \"trigonometric polynomials\": sums of multiples of sines and cosines.)\n",
    "Such polynomials can then be used to approximate derivatives and integrals.\n",
    "\n",
    "The simplest idea for approximating $f(x)$ on domain $[a, b]$ is to start with a finite collection of **node** values $x_i \\in [a, b]$, $0 \\leq i \\leq n$ and then seek a polynomial $p$ which **collocates** with $f$ at those values: $p(x_i) = f(x_i)$ for $0 \\leq i \\leq n$.\n",
    "Actually, we can put the function aside for now, and simply seek a polynomial that passes through a list of points $(x_i, y_i)$; later we will achieve collocation with $f$ by choosing $y_i = f(x_i)$.\n",
    "\n",
    "In fact there are infinitely many such polynomials: given one, add to it any polynomial with zeros at all of the $n+1$ notes.\n",
    "So to make the problem well-posed, we seek the collocating polynomial of *lowest degree*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} Existence and uniqueness of a collocating polynomial\n",
    ":label: theorem-collocation\n",
    "\n",
    "Given $n+1$ distinct values $x_i$, $0 \\leq i \\leq n$, and corresponding $y$-values $y_i$,\n",
    "there is a unique polynomial $P$ of degree at most $n$ with $P(x_i) = y_i$ for $0 \\leq i \\leq n$.\n",
    "```\n",
    "(*Note:* although the degree is typically $n$, it can be less; as an extreme example, if all $y_i$ are equal to $c$, then $P(x)$ is that constant $c$.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Historically there are several methods for finding $P_n$ and proving its uniqueness, in particular, the *divided difference* method introduced by Newton and the *Lagrange polynomial* method.\n",
    "However for our purposes, and for most modern needs, a different method is easiest, and it also introduces a strategy that will be of repeated use later in this course: the **Method of Undertermined Coefficients** or **MUC**.\n",
    "\n",
    "In general, this method starts by assuming that the function wanted is a sum of unknown multiples of a collection of known functions.\n",
    "Here, $P(x) = c_n x^n + c_{n-1} x^{n-1} + \\cdots+ c_1 x + c_0 = \\sum_{j=0}^n c_j x^j$.\n",
    "<br>\n",
    "(*Note:* any of the $c_i$ could be zero, including $c_n$, in which case the degree is less than $n$.)\n",
    "<br>\n",
    "The unknown factors ($c_0 \\cdots c_n$) are the *undetermined coefficients.*\n",
    "\n",
    "Next one states the problem as a system of equations for these undetermined coefficients, and solves them.\n",
    "<br>\n",
    "Here, we have $n+1$ conditions to be met:\n",
    "\n",
    "$$P(x_i) = \\sum_{j=0}^n c_j x_i^j = y_i, \\quad 0 \\leq i \\leq n$$\n",
    "\n",
    "This is a system if $n+1$ simultaneous linear equations in $n+1$ iunknowns, so the question of existence and uniqueness is exactly the question of whether the corresponding matrix is singular,\n",
    "and so is equivalent to the case of all $y_i = 0$ having *only* the solution with all\n",
    "$c_i = 0$.\n",
    "\n",
    "Back in terms of polynomials, this is the claim that the only polynomial of degree at most $n$ with distinct zeros $x_0 \\dots x_n$ is the zero function.\n",
    "And this is true, because any non-trivial polynomial with those $n+1$ distinct roots is of degree at least $n+1$, so the only \"degree n\" polynomial fitting this data is $P(x) \\equiv 0$.\n",
    "The theorem is proven."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The proof of this theorem is completely constructive; it gives the only numerical method we need, and which is the one implemented in Numpy through the pair of functions `numpy.polyfit` and `numpy.polyval`.\n",
    "(Aside: here as in many places, Numpy mimics the names and functionality of corresponding Matlab tools.)\n",
    "\n",
    "Briefly, the algorithm is this (indexing from 0 !)\n",
    "- Create the $n+1 \\times n+1$ matrix $V$ with elements\n",
    "\n",
    "$$v_{i,j} = x_i^j,\\; 0 \\leq i \\leq n, \\, 0 \\leq j \\leq n$$\n",
    "\n",
    "and the $n+1$-element column vector $y$ with elements $y_i$ as above.\n",
    "- Solve $V c = y$ for the vector of coefficients $c_j$ as above.\n",
    "\n",
    "I use the name $V$ because this is called the **Vandermonde Matrix.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import array, linspace, zeros, zeros_like, exp\n",
    "from  matplotlib.pyplot import figure, plot, title, grid, legend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example}\n",
    ":label: interpolation-example-1\n",
    "\n",
    "As usual, I concoct a first example with known correct answer, by using a polynomial as $f$:\n",
    "\n",
    "$$ f(x) = 4 + 7x -2x^2 - 5x^3 + 2x^4 $$\n",
    "\n",
    "using the nodes $x_0 = 1$, $x_1 = 2$, $x_2= 0$, $x_3 = 3.3$ and $x_4 = 4$  (They do not need to be in order.)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 4 + 7*x - 2*x**2 -5*x**3 + 3*x**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The x nodes 'x_i' are [1. 2. 7. 5. 4.]\n",
      "The y values at the nodes are [   7.   18. 5443. 1239.  448.]\n"
     ]
    }
   ],
   "source": [
    "xnodes = array([1., 2., 7., 5., 4.])  # They do not need to be in order\n",
    "nnodes = len(xnodes)\n",
    "n = nnodes-1\n",
    "print(f\"The x nodes 'x_i' are {xnodes}\")\n",
    "ynodes = zeros_like(xnodes)\n",
    "for i in range(nnodes):\n",
    "    ynodes[i] = f(xnodes[i])\n",
    "print(f\"The y values at the nodes are {ynodes}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Vandermonde matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "V = zeros([nnodes, nnodes])\n",
    "for i in range(nnodes):\n",
    "    for j in range(nnodes):\n",
    "        V[i,j] = xnodes[i]**j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve, using our functions seen in earlier sections and gathered in {doc}`numericalMethods`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from numericalMethods import rowReduce, backwardSubstitution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients of P are [ 4.  7. -2. -5.  3.]\n"
     ]
    }
   ],
   "source": [
    "(U, z) = rowReduce(V, ynodes)\n",
    "c = backwardSubstitution(U, z)\n",
    "print(f\"The coefficients of P are {c}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also check the resulting values of the polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = c[0] + c[1]*xnodes + c[2]*xnodes**2 + c[3]*xnodes**3 + c[4]*xnodes**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(1.0) should be 7.0; it is 7.0\n",
      "P(2.0) should be 18.0; it is 18.0\n",
      "P(7.0) should be 5443.0; it is 5443.0\n",
      "P(5.0) should be 1239.0; it is 1239.0\n",
      "P(4.0) should be 448.0; it is 448.0\n"
     ]
    }
   ],
   "source": [
    "for (x, y, P_i) in zip(xnodes, ynodes, P):\n",
    "    print(f\"P({x}) should be {y}; it is {P_i}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions for computing the coefficients and evaluating the polynomials\n",
    "\n",
    "We will use this procedure several times, so it time to put it into a functions —\n",
    "and add a pretty printer for polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitPolynomial(x, y):\n",
    "    \"\"\"Compute the coefficients c_i of the polynomial of lowest degree that collocates the points (x[i], y[i]).\n",
    "    These are returned in an array c of the same length as x and y, even if the degree is less than the normal length(x)-1,\n",
    "    in which case the array has some trailing zeroes.\n",
    "    The polynomial is thus p(x) = c[0] + c[1]x + ... c[d] x^d where n =length(x)-1, the nominal degree.\n",
    "    \"\"\"\n",
    "    nnodes = len(x)\n",
    "    n = nnodes - 1\n",
    "    V = zeros([nnodes, nnodes])\n",
    "    for i in range(nnodes):\n",
    "        for j in range(nnodes):\n",
    "             V[i,j] = x[i]**j\n",
    "    (U, z) = rowReduce(V, y)\n",
    "    c = backwardSubstitution(U, z)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluatePolynomial(x, coeffs):\n",
    "    # Evaluate the polynomial with coefficients in coeffs  at the points in x.\n",
    "    npoints = len(x)\n",
    "    ncoeffs = len(coeffs)\n",
    "    n = ncoeffs - 1\n",
    "    powers = linspace(0, n, n+1)\n",
    "    y = zeros_like(x)\n",
    "    for i in range(npoints):\n",
    "        y[i] = sum(coeffs * x[i]**powers)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def showPolynomial(c):\n",
    "    print(\"P(x) = \", end=\"\")\n",
    "    n = len(c)-1\n",
    "    print(f\"{c[0]:.4}\", end=\"\")\n",
    "    if n > 0:\n",
    "        coeff = c[1]\n",
    "        if coeff > 0:\n",
    "            print(f\" + {coeff:.4}x\", end=\"\")\n",
    "        elif coeff < 0:\n",
    "            print(f\" - {-coeff:.4}x\", end=\"\")\n",
    "    if n > 1:\n",
    "        for j in range(2, len(c)):\n",
    "            coeff = c[j]\n",
    "            if coeff > 0:\n",
    "                print(f\" + {coeff:.4}x^{j}\", end=\"\")\n",
    "            elif coeff < 0:\n",
    "                print(f\" - {-coeff:.4}x^{j}\", end=\"\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While debugging, redo the first example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.  7. -2. -5.  3.]\n"
     ]
    }
   ],
   "source": [
    "c_new = fitPolynomial(xnodes, ynodes)\n",
    "print(c_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   7.   18. 5443. 1239.  448.]\n"
     ]
    }
   ],
   "source": [
    "P_i_new = evaluatePolynomial(xnodes, c_new)\n",
    "\n",
    "print(P_i_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The values of P(x_i) are [   7.   18. 5443. 1239.  448.]\n"
     ]
    }
   ],
   "source": [
    "print(f\"The values of P(x_i) are {P_i_new}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(x) = 4.0 + 7.0x - 2.0x^2 - 5.0x^3 + 3.0x^4\n"
     ]
    }
   ],
   "source": [
    "showPolynomial(c_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $f(x)$ not a polynomial of degree $\\leq n$\n",
    ":label: interpolation-example-2\n",
    "\n",
    "Make an exact fit impossible by using the same function but using only four nodes and reducing the degree of the interpolating $P$ to three:\n",
    "$x_0 = 1$, $x_1 = 2$, $x_2 = 3$ and $x_3 = 4$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n is now 3, the nodes are now [-2.  0.  1.  2.], with f(x_i) values [70.  4.  7. 18.]\n",
      "The coefficients of P are now [ 4. -5. 10. -2.]\n",
      "P(x) = 4.0 - 5.0x + 10.0x^2 - 2.0x^3\n",
      "The values of P at the nodes are now [70.  4.  7. 18.]\n"
     ]
    }
   ],
   "source": [
    "# Reduce the degree of $P$ to at most 3:\n",
    "n = 3\n",
    "xnodes = array([-2.0, 0., 1.0, 2.])\n",
    "ynodes = zeros_like(xnodes)\n",
    "for i in range(len(xnodes)):\n",
    "    ynodes[i] = f(xnodes[i])\n",
    "print(f\"n is now {n}, the nodes are now {xnodes}, with f(x_i) values {ynodes}\")\n",
    "c = fitPolynomial(xnodes, ynodes)\n",
    "print(f\"The coefficients of P are now {c}\")\n",
    "showPolynomial(c)\n",
    "print(f\"The values of P at the nodes are now {evaluatePolynomial(xnodes, c)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several ways to assess the accuracy of this fit; we start graphically, and later consider the maximum and root-mean-square (RMS) errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = linspace(min(xnodes), max(xnodes))  # defaulting to 50 points, for graphing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(x, f(x), label=\"y=f(x)\")\n",
    "plot(xnodes, ynodes, \"*\", label=\"nodes\")\n",
    "P_n_x = evaluatePolynomial(x, c)\n",
    "plot(x, P_n_x, label=\"y = P_n(x)\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_error = f(x) - P_n_x\n",
    "figure(figsize=[12,6])\n",
    "title(\"Error in P_n(x)\")\n",
    "plot(x, P_error, label=\"y=f(x)\")\n",
    "plot(xnodes, zeros_like(xnodes), \"*\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $f(x)$ not a polynomial at all\n",
    ":label: interpolation-example-3\n",
    "\n",
    "$f(x) = e^x$ with five nodes, equally spaced from $-1$ to $1$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x): return exp(x)\n",
    "a_g = -1.0\n",
    "b_g = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=3\n",
      "node x values [-1.         -0.33333333  0.33333333  1.        ]\n",
      "node y values [0.36787944 0.71653131 1.39561243 2.71828183]\n",
      "The coefficients of P are [0.99519577 0.99904923 0.54788486 0.17615196]\n",
      "P(x) = 0.9952 + 0.999x + 0.5479x^2 + 0.1762x^3\n",
      "The values of P(x_i) are [-0.01593727 -0.00316622 -0.91810613 -1.04290824]\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "xnodes_g = linspace(a_g, b_g, n+1)\n",
    "ynodes_g = zeros_like(xnodes_g)\n",
    "for i in range(len(xnodes_g)):\n",
    "    ynodes_g[i] = g(xnodes_g[i])\n",
    "print(f\"{n=}\")\n",
    "print(f\"node x values {xnodes_g}\")\n",
    "print(f\"node y values {ynodes_g}\")\n",
    "c_g = fitPolynomial(xnodes_g, ynodes_g)\n",
    "print(f\"The coefficients of P are {c_g}\")\n",
    "showPolynomial(c_g)\n",
    "P_values = evaluatePolynomial(c_g, xnodes_g)\n",
    "print(f\"The values of P(x_i) are {P_values}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several ways to assess the accuracy of this fit.\n",
    "We start graphically, and later consider the maximum and root-mean-square (RMS) errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_g = linspace(a_g - 0.25, b_g + 0.25)  # Go a bit beyond the nodes in each direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[14,10])\n",
    "title(\"With $g(x) = e^x$\")\n",
    "plot(x_g, g(x_g), label=\"y = $g(x)$\")\n",
    "plot(xnodes_g, ynodes_g, \"*\", label=\"nodes\")\n",
    "P_g = evaluatePolynomial(x_g, c_g)\n",
    "plot(x_g, P_g, label=f\"y = $P_{n}(x)$\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_error = g(x_g) - P_g\n",
    "figure(figsize=[14,10])\n",
    "title(f\"Error in $P_{n}(x)$ for $g(x) = e^x$\")\n",
    "plot(x_g, P_error)\n",
    "plot(xnodes_g, zeros_like(xnodes_g), \"*\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
