{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "instrumental-peace",
   "metadata": {},
   "source": [
    "# Least-squares Fitting to Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dietary-concentration",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Chapter 4 *Least Squares* of [Sauer](../frontmatter/references.html#Sauer), Sections 1 and 2.\n",
    "- Section 8.1 *Discrete Least Squares Approximation* of [Burden&Faires](../frontmatter/references.html#Burden-Faires)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "another-saying",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib.pyplot import figure, plot, title, legend, grid, loglog\n",
    "from numpy.random import random\n",
    "from numerical_methods import solvelinearsystem\n",
    "from numerical_methods import evaluatepolynomial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "romance-premises",
   "metadata": {},
   "source": [
    "We have seen that when trying to fit a curve to a large collection of data points, fitting a single polynomial to all of them can be a bad approach.\n",
    "This is even more so if the data itself is inaccurate, due for example to measurement error.\n",
    "\n",
    "Thus an important approach is to find a function of some simple form that is close to the given points but not necesarily fitting them exactly:\n",
    "given $N$ points\n",
    "\n",
    "$$(x_i, y_i),\\; 1 \\leq i \\leq N \\quad \\text{ (or $0 \\leq i < N$ with Python!)}$$\n",
    "\n",
    "we seek a function $f(x)$ so that the errors at each point,\n",
    "\n",
    "$$e_i = y_i - f(x_i),$$\n",
    "\n",
    "are \"small\" overall, in some sense.\n",
    "\n",
    "Two important choices for the function $f(x)$ are\n",
    "\n",
    "(a) polynomials of low degree, and\n",
    "\n",
    "(b) periodic sinusidal functions;\n",
    "\n",
    "we will start with the simplest case of fitting a straight line."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pressing-garbage",
   "metadata": {},
   "source": [
    "## Measuring \"goodness of fit\": several options\n",
    "\n",
    "The first decision to be made is how to measure the overall error in the fit, since the error is now a vector of values $e = \\{e_i\\}$, not a single number.\n",
    "Two approaches are widely used:\n",
    "\n",
    "* *Min-Max*: minimize the maximum of the absolute errors at each point,\n",
    "$\\displaystyle \\|e\\|_{max} \\text{ or } \\|e\\|_\\infty, = \\max_{1 \\leq i \\leq n} |e_i|$\n",
    "\n",
    "* *Least Squares*: Minimize the sum of the squares of the errors,\n",
    "$\\displaystyle \\sum_1^n e_i^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungarian-taiwan",
   "metadata": {},
   "source": [
    "## What doesn't work\n",
    "\n",
    "Another seemingly natural approach is:\n",
    "\n",
    "* Minimize the sum of the absolute errors,\n",
    "$\\displaystyle \\|e\\|_1 = \\sum_1^n |e_i|$\n",
    "\n",
    "but this often fails completely.\n",
    "In the following example, all three lines minimize this measure of error, along with infinitely many others: any line that passes below half of the points and above the other half."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "early-wesley",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdata = [1., 2., 3., 4.]\n",
    "ydata = [0., 3., 2., 5.]\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "plot(xdata, ydata, 'b*', label=\"Data\")\n",
    "xplot = np.linspace(0.,5.)\n",
    "ylow = xplot -0.5\n",
    "yhigh = xplot + 0.5\n",
    "yflat = 2.5*np.ones_like(xplot)\n",
    "plot(xplot, ylow, label=\"low\")\n",
    "plot(xplot, yhigh, label=\"high\")\n",
    "plot(xplot, yflat, label=\"flat\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "environmental-saturday",
   "metadata": {},
   "source": [
    "The Min-Max method is important and useful, but computationally difficult.\n",
    "One hint is the presence of absolute values in the formula, which get in the way of using calculus to get equations for the minimum.\n",
    "\n",
    "Thus the easiest and most common approach is **Least Squares**, or equivalently, minimizing the root-mean-square error, which is just the Euclidean length $\\|e\\|_2$ of the error vector $e$.\n",
    "That \"geometrical\" interpretation of the goal can be useful.\n",
    "So we start with that."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "material-monitor",
   "metadata": {},
   "source": [
    "## Linear least squares\n",
    "\n",
    "The simplest approach is to seek the straight line $y = f(x) = c_0 + c_1x$ that minimizes the total square sum error,\n",
    "\n",
    "$$E(c_0, c_1) = \\sum_i e_i^2 = \\sum_i (c_0 + c_1x_i - y_i)^2.$$\n",
    "\n",
    "Note well that the unknowns here are just the two values $c_0$ and $c_1$, and\n",
    "$E$ is s fairly simple polynomial function of them.\n",
    "The minimum error must occur at a critical point of this function, where both partial derivatives are zero:\n",
    "\n",
    "$$\\frac{\\partial E}{\\partial c_0} = 2 \\sum_i (c_0 + c_1x_i - y_i) = 0,$$\n",
    "\n",
    "$$\\frac{\\partial E}{\\partial c_1} = 2 \\sum_i (c_0 + c_1x_i - y_i) x_i = 0.$$\n",
    "\n",
    "These are just simultaneous linear equations, which is the secret of why the least squares approach is so much easier than any alternative.\n",
    "The equations are:\n",
    "\n",
    "$$\n",
    "\\left[\\begin{array}{cc} \\sum_i 1 & \\sum_i x_i \\\\ \\sum_i x_i & \\sum_i x_i^2 \\end{array}\\right]\n",
    "\\left[\\begin{array}{c} c_0 \\\\ c_1 \\end{array}\\right]\n",
    "=\n",
    "\\left[\\begin{array}{c} \\sum_i y_i \\\\ \\sum_i x_iy_i \\end{array}\\right]\n",
    "$$\n",
    "\n",
    "where of course $\\sum_i 1$ is just $N$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "necessary-fluid",
   "metadata": {},
   "source": [
    "It will help later to introduce the notation\n",
    "\n",
    "$$m_j = \\sum_i x_i^j, \\quad p_j = \\sum_i x_i^j y_i$$\n",
    "\n",
    "so that the equations are\n",
    "\n",
    "$$M c = p$$\n",
    "\n",
    "with\n",
    "\n",
    "$$\n",
    "M = \\left[\\begin{array}{cc} m_0 & m_1 \\\\ m_1 & m_2\\end{array}\\right],\n",
    "p = \\left[\\begin{array}{c} p_0 \\\\ p_1 \\end{array}\\right],\n",
    "c = \\left[\\begin{array}{c} c_0 \\\\ c_1 \\end{array}\\right].\n",
    "$$\n",
    "\n",
    "(0-based indexing wins this time.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d42ab0a2-36d3-42ab-88fd-6e46d53bdeff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linefit(x, y):\n",
    "    m0 = len(x)\n",
    "    m1 = sum(x)\n",
    "    m2 = sum(x**2)\n",
    "    M = np.array([[m0, m1], [m1, m2]])\n",
    "    p = np.array([sum(y), sum(x*y)])\n",
    "    c = solvelinearsystem(M, p)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "brief-edward",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [3.09084524 1.83019038]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "x = np.linspace(-1, 1, N)\n",
    "# Emulate a straight line with measurement errors:\n",
    "# random(N) gives N values uniformly distributed in the range [0,1],\n",
    "# and so with mean 0.5.\n",
    "# Thus subtracting 1/2 simulates more symmetric \"errors\", of mean zero.\n",
    "yline = 2*x + 3\n",
    "y = yline + (random(N) - 0.5)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "plot(x, yline, 'g', label=\"The original line\")\n",
    "plot(x, y, '*', label=\"Data\")\n",
    "c = linefit(x, y)\n",
    "print(\"The coefficients are\", c)\n",
    "xplot = np.linspace(-1, 1, 100)\n",
    "plot(xplot, evaluatepolynomial(xplot, c), 'r', label=\"Linear least squares fit\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "streaming-defendant",
   "metadata": {},
   "source": [
    "## Least squares fiting to higher degree polynomials\n",
    "\n",
    "The method above extends to finding a polynomial\n",
    "\n",
    "$$p(x) = c_0 + c_1 x + \\cdots + c_n x^n$$\n",
    "\n",
    "that gives the best least squares fit to data\n",
    "\n",
    "$$(x_1, y_1), \\dots (x_N, y_N)$$\n",
    "\n",
    "in that the coefficients $c_k$ given the minimum of\n",
    "\n",
    "$$\n",
    "E(c_0, \\dots c_n) = \\sum_i(p(x_i) - y_i)^2\n",
    "= \\sum_i \\left( y_i - \\sum_k c_k x_i^k \\right)^2\n",
    "$$\n",
    "\n",
    "Note that when $N=n+1$, the solution is the interpolating polynomial, with error zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "colored-sweet",
   "metadata": {},
   "source": [
    "The necessary conditions for a minimum are that all $n+1$ partial derivatives of $E$ are zero:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial c_j} = 2 \\sum_i \\left( y_i - \\sum_k c_k x_i^k\\right) x_i^j = 0,\n",
    "\\; 0 \\leq j \\leq n.\n",
    "$$\n",
    "\n",
    "This gives\n",
    "\n",
    "$$\n",
    "\\sum_i \\sum_k \\left( c_k x_i^{j+k} \\right) = \\sum_k \\left( \\sum_i x_i^{j+k} \\right) c_k = \\sum_i y_i x_i^j, \\; 0 \\leq j \\leq n,\n",
    "$$\n",
    "\n",
    "or with the notation $m_k = \\sum_i x_i^k$, $p_k = \\sum_i x_i^k y_i$ introduced above,\n",
    "\n",
    "$$\n",
    "\\sum_k m_{j+k} c_k = p_j,\\; 0 \\leq j \\leq n.\n",
    "$$\n",
    "\n",
    "That is, the equations are again $Mc = p$, but now with\n",
    "\n",
    "$$\n",
    "M = \\left[\\begin{array}{cccc}\n",
    "m_0 & m_1 & \\dots & m_n \\\\\n",
    "m_1 & m_2 & \\dots & m_{n+1} \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "m_n & m_{n+1} & \\dots & m_{2n}\n",
    "\\end{array}\\right],\n",
    "\\quad\n",
    "p = \\left[\\begin{array}{c} p_0 \\\\ p_1 \\\\ \\vdots \\\\ p_n \\end{array}\\right],\n",
    "\\quad\n",
    "c = \\left[\\begin{array}{c} c_0 \\\\ c_1 \\\\ \\vdots  \\\\ c_n \\end{array}\\right].\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c1277ec-7905-4003-8125-d87ef0e8811c",
   "metadata": {},
   "source": [
    "**Note:**\n",
    "The next section {doc}`least-squares-fitting-appendix-geometrical-approach` presents another way to derive this result,\n",
    "using geometry and linear algebra instead of calculus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ec6ba21c-b9c6-41a1-87e5-153495d8232e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitpolynomialleastsquares(x, y, n):\n",
    "    \"\"\"Compute the coeffients c_i of the polynomial of degree n that give the best least squares fit to data (x[i], y[i]).\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    m = np.zeros(2*n+1)\n",
    "    for k in range(2*n+1):\n",
    "        m[k] = sum(x**k)\n",
    "    M = np.zeros([n+1,n+1])\n",
    "    for i in range(n+1):\n",
    "        for j in range(n+1):\n",
    "             M[i, j] = m[i+j]\n",
    "    p = np.zeros(n+1)\n",
    "    for k in range(n+1):\n",
    "        p[k] = sum(x**k * y)\n",
    "    c = solvelinearsystem(M, p)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "armed-baghdad",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [-0.00108728  1.02381733 -0.06859178 -0.11328717]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10\n",
    "n = 3\n",
    "xdata = np.linspace(0, np.pi/2, N)\n",
    "ydata = np.sin(xdata)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plot(xdata, ydata, 'b*', label=\"sin(x) data\")\n",
    "xplot = np.linspace(-0.5, np.pi/2 + 0.5, 100)\n",
    "plot(xplot, np.sin(xplot), 'b', label=\"sin(x) curve\")\n",
    "c = fitpolynomialleastsquares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluatepolynomial(xplot, c), 'r', label=\"Cubic least squares fit\")\n",
    "legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "informed-failing",
   "metadata": {},
   "source": [
    "The discrepancy between the original function $\\sin(x)$ and this cubic is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "excess-there",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[14,5])\n",
    "plot(xplot, np.sin(xplot) - evaluatepolynomial(xplot, c))\n",
    "title(\"errors fitting at N = 10 points\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advanced-january",
   "metadata": {},
   "source": [
    "What if we fit at more points?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "proud-token",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficients are [-0.00200789  1.02647568 -0.06970463 -0.1137182 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 50\n",
    "xdata = np.linspace(0, np.pi/2, N)\n",
    "ydata = np.sin(xdata)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plot(xdata, ydata, 'b.', label=\"sin(x) data\")\n",
    "plot(xplot, np.sin(xplot), 'b', label=\"sin(x) curve\")\n",
    "c = fitpolynomialleastsquares(xdata, ydata, n)\n",
    "print(\"The coefficients are\", c)\n",
    "plot(xplot, evaluatepolynomial(xplot, c), 'r', label=\"Cubic least squares fit\")\n",
    "legend(loc=\"best\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "accepted-laundry",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[14,5])\n",
    "plot(xplot, np.sin(xplot) - evaluatepolynomial(xplot, c))\n",
    "title(\"errors fitting at N = 50 points\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compatible-republican",
   "metadata": {},
   "source": [
    "Not much changes!\n",
    "\n",
    "This hints at another use of least squares fitting:\n",
    "fitting a simpler curve (like a cubic) to a function (like $\\sin(x)$), rather than to discrete data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "musical-illness",
   "metadata": {},
   "source": [
    "## Nonlinear fitting: power-law relationships\n",
    "\n",
    "When data $(x_i, y_i)$ is inherently positive, it is often natural to seek an approximate power law relationship\n",
    "\n",
    "$$ y_i \\approx c x_i^p$$\n",
    "\n",
    "That is, one seeks the power $p$ and scale factor $c$ that minimizes error in some sense.\n",
    "\n",
    "When the magnitudes and the data $y_i$ vary greatly, it is often appropriate to look at the relative errors\n",
    "\n",
    "$$ e_i = \\left| \\frac{c x_i^p - y_i}{y_i} \\right| $$\n",
    "\n",
    "and this can be shown to be very close to looking at the absolute errors of the logarithms\n",
    "\n",
    "$$ |\\ln(c x_i^p) - \\ln(y_i)| = |\\ln(c) + p \\ln(x_i) - \\ln(y_i)| $$\n",
    "\n",
    "Introducing the new variables $X_i = \\ln(x_i)$, $Y_i = \\ln(Y_i)$ and $C = \\ln(c)$,\n",
    "this becomes the familiar problem of finding a linear approxation of the data $Y_i$ by $C + p X_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "conditional-cream",
   "metadata": {},
   "source": [
    "## A simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "rural-arlington",
   "metadata": {},
   "outputs": [],
   "source": [
    "cexact = 2.0\n",
    "pexact = 1.5\n",
    "x = np.logspace(0.01, 2.0, 10)\n",
    "xplot = np.logspace(0.01, 2.0)  # For graphs later\n",
    "yexact = cexact * x**pexact\n",
    "y = yexact * (1.0 + (random(len(yexact))- 0.5)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "determined-compromise",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(x, yexact, '.', label='exact')\n",
    "plot(x, y, '*', label='noisy')\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "constitutional-realtor",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "loglog(x, yexact, '.', label='exact')\n",
    "loglog(x, y, '*', label='noisy')\n",
    "legend()\n",
    "grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "interim-montgomery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C=1.6511541516041683, p=1.5555120311948827\n"
     ]
    }
   ],
   "source": [
    "X = np.log(x)\n",
    "Y = np.log(y)\n",
    "Cp = fitpolynomialleastsquares(X, Y, 1)\n",
    "C = np.exp(Cp[0])\n",
    "p = Cp[1]\n",
    "print(f\"{C=}, {p=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "clinical-accused",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "plot(x, yexact, '.', label='exact')\n",
    "plot(x, y, '*', label='noisy')\n",
    "plot(xplot, C * xplot**p)\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "institutional-shame",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "loglog(x, yexact, '.', label='exact')\n",
    "loglog(x, y, '*', label='noisy')\n",
    "loglog(xplot, C * xplot**p)\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "noble-lewis",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
