{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "instrumental-peace",
   "metadata": {},
   "source": [
    "# Least-squares Fitting to Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6fe15e-a215-40b1-bab6-d06b76e2b752",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Chapter 4 *Least Squares* of {cite}`Sauer`, sections 1 and 2.\n",
    "- Section 8.1 *Discrete Least Squares Approximation* of {cite}`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": "code",
   "execution_count": 1,
   "id": "e31e3991-b3bf-4eba-be46-cfbe227e266c",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (numerical_methods.py, line 1223)",
     "output_type": "error",
     "traceback": [
      "Traceback \u001b[0;36m(most recent call last)\u001b[0m:\n",
      "  File \u001b[1;32m/Applications/anaconda3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3398\u001b[0m in \u001b[1;35mrun_code\u001b[0m\n    exec(code_obj, self.user_global_ns, self.user_ns)\n",
      "\u001b[0;36m  Input \u001b[0;32mIn [1]\u001b[0;36m in \u001b[0;35m<cell line: 1>\u001b[0;36m\u001b[0m\n\u001b[0;31m    import numerical_methods as nm\u001b[0m\n",
      "\u001b[0;36m  File \u001b[0;32m~/Library/CloudStorage/OneDrive-CollegeofCharleston/numerical-methods-and-analysis/numerical-methods-and-analysis-python/docs/numerical_methods.py:1223\u001b[0;36m\u001b[0m\n\u001b[0;31m    else\u001b[0m\n\u001b[0m        ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "import numerical_methods as nm"
   ]
  },
  {
   "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 [2.9889185  2.09016102]\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": "b1a06227-f597-4646-b387-2caab92b629c",
   "metadata": {},
   "source": [
    "```{prf:remark} Alternative geometrical derivation\n",
    ":label: geometrical-derivation-of-least-squares\n",
    "\n",
    "In the next section {doc}`least-squares-fitting-appendix-geometrical-approach`,\n",
    "another way to derive this result is given, using geometry and linear algebra instead of calculus.\n",
    "```"
   ]
  },
  {
   "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=2.0553131465671295, p=1.4657222019447553\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);"
   ]
  }
 ],
 "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
}
