{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical integration: high-order quadratures\n", "\n", "Recall some of the standard techniques for numerical integration that we covered:\n", "\n", "- Rectangle rule\n", "\n", "$$\n", "\\int_{a}^b f(x) \\, dx \\approx (b - a) \\, f\\left(\\frac{a+b}{2}\\right)~.\n", "$$\n", "\n", "\n", "\n", "\n", "- Trapezoidal rule\n", "\n", "$$\n", "\\int_{a}^b f(x) \\, dx \\approx (b-a) \\, \\frac{f(a) + f(b)}{2}~.\n", "$$\n", "\n", "\n", "\n", "- Simpson's rule\n", "\n", "$$\n", "\\int_{a}^b f(x) \\, dx \\approx \\frac{(b-a)}{6} \\, \\left[f(a) + 4 f \\left( \\frac{a+b}{2} \\right) + f(b)\\right].\n", "$$\n", "\n", "\n", "\n", "\n", "All these rules can be written in a form\n", "$$\n", "\\int_a^b f(x) \\, dx \\approx \\sum_k w_k f(x_k),\n", "$$\n", "i.e. the integral is approximated as a sum integrand evaluations at various points with various weights.\n", "In particular, we have\n", "- Rectangle rule\n", "$$\n", "x_k = \\{(a+b)/2\\}, \\qquad w_k = \\{(b-a)\\}\n", "$$\n", "\n", "- Trapezoidal rule\n", "$$\n", "x_k = \\{a,~b\\}, \\qquad w_k = \\{(b-a)/2,~(b-a)/2\\}\n", "$$\n", "\n", "- Simpson's rule\n", "$$\n", "x_k = \\{a,~(a+b)/2,~c\\}, \\qquad w_k = \\{(b-a)/6,~2(b-a)/3,~(b-a)/6\\}\n", "$$\n", "\n", "Different numerical schemes correspond to different choices of $x_k$ and $w_k$.\n", "\n", "The only real constraint is that the sum of weights should be equal \n", "$$\n", "\\sum_k w_k = (b - a),\n", "$$\n", "such that the scheme gives correct result for the integration of a constant function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## High-order quadratures\n", "\n", "There is a systematic way to derive a numerical integration scheme \n", "$$\n", "\\int_a^b f(x) dx \\approx \\sum_k w_k f(x_k),\n", "$$\n", "which will give an exact result when the integrand $f(x)$ is a polynomial up to a certain degree.\n", "\n", "Let us assume that $f(x)$ can be calculated at $N+1$ points inside the integration interval $(a,b)$.\n", "Recall that function $f(x)$ evaluated at $N+1$ distinct points can be approximated by an interpolating polynomial of order $N$:\n", "$$\n", "f(x) \\approx p_N(x) = \\sum_{k=0}^{N} f(x_k) \\, L_{N,k}(x)~.\n", "$$\n", "Here $L_{N,k}(x)$ are the Lagrange basis functions\n", "$$\n", "L_{N,k}(x) = \\prod_{j\\neq k} \\frac{x-x_j}{x_k-x_j}.\n", "$$\n", "\n", "The approximation $f(x) \\approx p_N(x)$ becomes exact when $f(x)$ is a polynomial of degree $N$.\n", "Integrating $p_N(x)$ gives the following numerical quadrature:\n", "$$\n", "\\int_a^b f(x) \\, dx \\approx \\int_a^b p_N(x) \\, dx = \\sum_{k = 0}^N w_k f(x_k),\n", "$$\n", "where\n", "$$\n", "w_k = \\int_a^b L_{N,k}(x) dx~.\n", "$$\n", "\n", "## Remapping\n", "\n", "Note that one only really needs to calculate the quadratures (the nodes and weights) once for a single interval [typically (-1.,1.)]. The corresponding $(-1,1)$ quadrature can always be mapped to any finite interval $(a,b)$ by the following tranformation\n", "$$\n", "x_k \\to \\frac{a+b}{2} + \\frac{b-a}{2} x_k~,\\\\\n", "w_k \\to \\frac{b-a}{2} w_k~.\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Generic integration using quadratures\n", "def integrate_quadrature(\n", " f, # Function to be integrated \n", " quad # A pair of lists (x,w) where x are the integration nodes and w are the weights \n", " ):\n", " ret = 0.\n", " n = len(quad[0])\n", " for k in range(n):\n", " xk = quad[0][k]\n", " wk = quad[1][k]\n", " ret += wk * f(xk)\n", " return ret" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton-Cotes quadratures\n", "\n", "The simplest assumption is to take the $x_k$ to be distributed equidistantly.\n", "This is called Newton-Cotes quadratures.\n", "The integral is approximated as\n", "$$\n", "\\int_a^b f(x) \\, dx \\approx \\int_a^b p_N(x) \\, dx = \\sum_{k=0}^N w_k f(x_k),\\\\\n", "w_k = \\int_a^b L_{N,k}(x) dx~,\n", "$$\n", "but two scenarios are possible: the points $x_k$ either (a) include the endpoints $(a,b)$ or (b) exclude the endpoint.\n", "\n", "In the case (a) we have closed Newton-Cotes quadrature\n", "$$\n", "x_k = a + h k, \\qquad k = 0\\ldots N, \\qquad h = (b-a)/N,\n", "$$\n", "while in case (b) we have open Newton-Cotes quadrature\n", "$$\n", "x_k = a + h k, \\qquad k = 1\\ldots N+1, \\qquad h = (b-a)/(N+2).\n", "$$\n", "\n", "The weights $w_k$ can be evaluated just once using e.g. one of the earlier developed methods of numerical integration.\n", "\n", "The Newton-Cotes quadratures give exact answer for the integration of polynomials up to degree $N$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Lagrange basis functions from Lecture 2\n", "def Lnj(x,j,xdata):\n", " \"\"\"Lagrange basis function.\"\"\"\n", " ret = 1.\n", " for k in range(0, len(xdata)):\n", " if (k != j):\n", " ret *= (x - xdata[k]) / (xdata[j] - xdata[k])\n", " return ret\n", "\n", "# Romberg method from previous lecture\n", "# to calculate the weights wk\n", "def romberg(\n", " f, \n", " a, \n", " b, \n", " accuracy=1e-8,\n", " max_order=16,\n", " min_order=2\n", "):\n", " R = np.zeros((max_order, max_order))\n", " h = (b - a) / 2.\n", " R[0, 0] = h * (f(a) + f(b)) # The initial trapezoidal rule \n", " for n in range(1, max_order):\n", " trapezoid = 0.0\n", " for j in range(2**(n-1)):\n", " trapezoid += f(a + (2*j+1)*h)\n", " R[n, 0] = 0.5 * R[n-1, 0] + h * trapezoid # The trapezoidal rule\n", " l = 1\n", " # The Romberg iterations\n", " for m in range(1, n+1):\n", " l *= 4\n", " R[n, m] = (l * R[n, m-1] - R[n-1, m-1]) / (l-1)\n", " # print(\"Iteration: {0:5}, I = {1:20.15f}, error estimate = {2:10.15f}\".format(n, R[n, m], abs(R[n, m] - R[n-1, m-1])))\n", " if abs(R[n, m] - R[n-1, m-1]) < accuracy and n > min_order:\n", " return R[n, m]\n", " h /= 2.\n", " print(\"Romberg method did not converge to required accuracy\")\n", " return R[-1, -1]\n", "\n", "# Calculating the weights using the Romberg method\n", "# to requested accuracy for a given set of nodes x\n", "# over the interval (a,b)\n", "def compute_weights(x, \n", " a, \n", " b, \n", " tol = 1.e-15):\n", " ret = []\n", " for k in range(0,len(x)):\n", " tx = x\n", " def f(t):\n", " return Lnj(t, k, x)\n", " ret.append(romberg(f, a, b, tol))\n", " return ret\n", "\n", "# Calculate the nodes and weights of either\n", "# closed or open Newton-Cotes quadrature\n", "# to requested accuracy\n", "def newton_cotes(n, \n", " a = -1., \n", " b = 1., \n", " isopen = False, \n", " tol = 1.e-15):\n", " x = []\n", " if (isopen):\n", " h = (b - a) / (n + 2.)\n", " x = [a + (i+1)*h for i in range(0,n+1)]\n", " else:\n", " h = (b - a) / n\n", " x = [a + i*h for i in range(0,n+1)]\n", " return x, compute_weights(x, a, b, tol)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([0.0], [np.float64(2.0)])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Open Newton-Cotes rule with N = 0 gives the rectangle rule\n", "newton_cotes(0, -1., 1., True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gauss-Legendre quadratures from Mark Newman's book" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([-1.0, 1.0], [np.float64(1.0), np.float64(1.0)])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Closed Newton-Cotes rule with N = 1 gives the trapezoidal rule\n", "newton_cotes(1, -1., 1., False)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([-1.0, 0.0, 1.0],\n", " [np.float64(0.3333333333333333),\n", " np.float64(1.3333333333333333),\n", " np.float64(0.3333333333333333)])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Closed Newton-Cotes rule with N = 2 gives the Simpson's rule\n", "newton_cotes(2, -1., 1., False)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Visualize\n", "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "# Default style parameters (feel free to modify as you see fit)\n", "params = {'legend.fontsize': 'large',\n", " 'axes.labelsize': 'x-large',\n", " 'axes.titlesize':'x-large',\n", " 'xtick.labelsize':'x-large',\n", " 'ytick.labelsize':'x-large',\n", " 'xtick.direction':'in',\n", " 'ytick.direction':'in',\n", " }\n", "plt.rcParams.update(params)\n", "\n", "accuracy = 1.e-12\n", "\n", "def quadrature_visualize(quad, a = -1., b = 1., title = \"Quadrature\"):\n", " n = len(quad[0])\n", "\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"${w_k}$\")\n", " plt.xlim(a,b)\n", " plt.title(title)\n", " for k in range(0,n):\n", " xk = quad[0][k]\n", " wk = quad[1][k]\n", " # print(xk,\" \",wk)\n", " plt.plot([xk,xk],[0.,wk], color = 'blue')\n", " plt.axhline(y = 0., color = 'black', linestyle = '--')\n", " \n", " return plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Newton-Cotes quadrature permits negative weights" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "quadrature_visualize(newton_cotes(4, -1., 1., True), -1.1, 1.1, \"Open 5-point Newton-Cotes\").show()\n", "quadrature_visualize(newton_cotes(4, -1., 1., False), -1.1, 1.1, \"Closed 5-point Newton-Cotes\").show()\n", "quadrature_visualize(newton_cotes(9, -1., 1., False), -1.1, 1.1, \"Closed 10-point Newton-Cotes\").show()\n", "quadrature_visualize(newton_cotes(14, -1., 1., False), -1.1, 1.1, \"Closed 15-point Newton-Cotes\").show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now apply Newton-Cotes quadratures to the integration of a polynomial we had before " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Take our function example from last lecture\n", "flabel = 'x^4 - 2x + 2'\n", "def f(x):\n", " return x**4 - 2*x + 2\n", "flimit_a = 0.\n", "flimit_b = 2.\n", "\n", "# Overwrite as applicable\n", "# flabel = 'x^4 - 3x + 1'\n", "# def f(x):\n", "# return x**4 - 3*x + 1\n", "# flimit_a = 0.\n", "# flimit_b = 2." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using open Newton-Cotes quadratures\n", " N I_N\n", " 0 2.0000000000000000\n", " 1 3.3580246913580254\n", " 2 6.1666666666666661\n", " 3 6.2378666666666671\n", " 4 6.4000000000000039\n", " 5 6.3999999999999986\n", " 6 6.4000000000000021\n", " 7 6.4000000000000039\n" ] } ], "source": [ "# Closed Newton-Cotes integration\n", "print(\"Computing the integral of\",flabel, \"over the interval (\",flimit_a,\",\",flimit_b,\") using open Newton-Cotes quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(0,8):\n", " quadr = newton_cotes(N, flimit_a, flimit_b, True)\n", " integral = integrate_quadrature(f, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using closed Newton-Cotes quadratures\n", " N I_N\n", " 1 16.0000000000000000\n", " 2 6.6666666666666661\n", " 3 6.5185185185185182\n", " 4 6.4000000000000004\n", " 5 6.4000000000000012\n", " 6 6.3999999999999986\n", " 7 6.4000000000000004\n" ] } ], "source": [ "# Closed Newton-Cotes integration\n", "print(\"Computing the integral of\",flabel, \"over the interval (\",flimit_a,\",\",flimit_b,\") using closed Newton-Cotes quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(1,8):\n", " quadr = newton_cotes(N, flimit_a, flimit_b, False)\n", " integral = integrate_quadrature(f, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Newton-Cotes quadratures work well when the integrand is a polynomial since in this case the interpolating polynomial approximates the integrand exactly\n", "\n", "However, issues may arise when the interpolating polynomial does not approximate the integrand well, as was in the case of Runge function" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "rungelabel = \"Runge function\"\n", "def runge(x):\n", " return 1./(25*x**2 + 1.)\n", "\n", "runge_a = -1.\n", "runge_b = 1." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of Runge function over the interval ( -1.0 , 1.0 ) using open Newton-Cotes quadratures\n", " N I_N\n", " 0 2.0000000000000000\n", " 1 0.5294117647058825\n", " 2 -0.2988505747126436\n", " 3 0.2666666666666667\n", " 4 2.0404749055585549\n", " 5 0.9320668542657328\n", " 6 -2.0045340869981669\n", " 7 -0.1816307907657775\n" ] } ], "source": [ "# Closed Newton-Cotes integration\n", "print(\"Computing the integral of\",rungelabel, \"over the interval (\",runge_a,\",\",runge_b,\") using open Newton-Cotes quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(0,8):\n", " quadr = newton_cotes(N, runge_a, runge_b, True)\n", " integral = integrate_quadrature(runge, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of Runge function over the interval ( -1.0 , 1.0 ) using closed Newton-Cotes quadratures\n", " N I_N\n", " 1 0.0769230769230769\n", " 2 1.3589743589743588\n", " 3 0.4162895927601810\n", " 4 0.4748010610079575\n", " 5 0.4615384615384615\n", " 6 0.7740897346941600\n", " 7 0.5797988819496757\n", " 8 0.3000977814255821\n", " 9 0.4797235795683667\n", " 10 0.9346601111306989\n", " 11 0.6489545880557170\n", " 12 -0.0625873031506956\n", " 13 0.3839594433665099\n", " 14 1.5799089281703083\n" ] } ], "source": [ "# Closed Newton-Cotes integration\n", "print(\"Computing the integral of\",rungelabel, \"over the interval (\",runge_a,\",\",runge_b,\") using closed Newton-Cotes quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(1,15):\n", " quadr = newton_cotes(N, runge_a, runge_b, False)\n", " integral = integrate_quadrature(runge, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Integration of Runge's function using Newton-Cotes quadratures does not give an accurate answer because high oscillations at the edges of the integration. Romberg method on the other hand gives an accurate estimate" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of Runge function over the interval ( -1.0 , 1.0 ) using Romberg method\n", "0.549360306777909\n" ] } ], "source": [ "# Romberg method\n", "print(\"Computing the integral of\",rungelabel, \"over the interval (\",runge_a,\",\",runge_b,\") using Romberg method\")\n", "print(romberg(runge, runge_a, runge_b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Newton-Cotes method can be improved by adjusting the choice of nodes. For instance, we learned that Chebyshed nodes minimize the Runge phenomenon. \n", "\n", "A quadrature based on Chebyshev nodes is called Clenshaw-Curtis quadrature. The weights of Clenshaw-Curtis quadrature can be efficiently computed using discrete cosine transform but for the present purposes we will using the straightforward numerical integration" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def chebyshev_nodes(n,a,b):\n", " return [(a+b)/2. + (b-a) / 2. * np.cos((2.*k+1.)/(2.*n+2.)*np.pi) for k in range(n+1)]\n", "\n", "def clenshaw_curtis(n, a = -1., b = 1., tol = 1.e-15):\n", " x = chebyshev_nodes(n,a,b)\n", " return x, compute_weights(x, a, b, tol)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cc10 = clenshaw_curtis(10, -1., 1.)\n", "quadrature_visualize(cc10, -1., 1., \"Open 10-point Clenshaw-Curtis\").show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of Runge function over the interval ( -1.0 , 1.0 ) using closed Clenshaw-Curtis quadratures\n", " N I_N\n", " 0 2.0000000000000000\n", " 1 0.1481481481481482\n", " 2 1.1561181434599159\n", " 3 0.3393357342937174\n", " 4 0.7366108212029662\n", " 5 0.4422623071358261\n", " 6 0.6363602552248223\n", " 7 0.4995830749190563\n", " 8 0.5839263513091471\n", " 9 0.5259711610228504\n", " 10 0.5661564732597759\n", " 11 0.5388727075897808\n", " 12 0.5562316021895978\n", " 13 0.5445109449451717\n", " 14 0.5527811219474377\n", " 15 0.5472112438100144\n", " 16 0.5507349751776419\n", " 17 0.5483645031315993\n", " 18 0.5500702958302579\n", " 19 0.5489233775473976\n", " 20 0.5496321498366131\n", " 21 0.5491557069456035\n", " 22 0.5495101923607436\n", " 23 0.5492719294992722\n", " 24 0.5494126772553229\n" ] } ], "source": [ "# Clenshaw-Curtis integration\n", "print(\"Computing the integral of\",rungelabel, \"over the interval (\",runge_a,\",\",runge_b,\") using closed Clenshaw-Curtis quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(0,25):\n", " quadr = clenshaw_curtis(N, runge_a, runge_b)\n", " integral = integrate_quadrature(runge, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Clenshaw-Curtis quadrature shows convergence, albeit a slow one" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian quadratures\n", "\n", "## Gauss-Legendre quadrature\n", "\n", "It turns out that the choice of nodes $x_k$ can be improved further upon such that an $n$-point quadrature\n", "$$\n", "\\int_a^b f(x) dx \\approx \\sum_{k=1}^n w_k f(x_k)\n", "$$\n", "gives an exact result for any polynomial of degree $2n - 1$.\n", "\n", "The derivation is a little bit tedious. \n", "First the integration range is taken as $(-1,1)$ [it always be rescaled back to $(a,b)$].\n", "The outcome is that the nodes $x_k$ correspond to the roots of the Legendre polynomial $P_n(x)$.\n", "\n", "The nodes $x_k$ can in principle be found as roots of $P_n(x)$ using the methods we developed earlier, while the weights $w_k$ are evaluated through numerical integration of Lagrange basis functions. $P_n(x)$ can itself be evaluated through a recurrence relation\n", "$$\n", "(n+1) P_{n+1}(x) = (2n+1) x P_n(x) - n P_{n-1}(x),\n", "$$\n", "starting from $P_0(x) = 1$ and $P_1(x) = x$.\n", "\n", "This method is not the most efficient one and prone to large round-off error starting from ($n \\sim 20$) (try it!).\n", "\n", "More efficient methods exists. These calculate the roots of $P_n(x)$ using analytic approximation for the initial guess and\n", " use the recursion formula directly to calculate the $P_n(x)$ at given $x$ rather than for pre-calculating the polynomial coefficients. The weights can also be shown to be equal to\n", "$$\n", "w_k = \\frac{2}{(1-x_k^2) [P'_n(x_k)]^2}~.\n", "$$\n", "\n", "An efficient implementation can be found in M. Newman \"Computational Physics\" textbook http://www-personal.umich.edu/~mejn/cp/programs/gaussxw.py" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "######################################################################\n", "#\n", "# Functions to calculate integration points and weights for Gaussian\n", "# quadrature\n", "#\n", "# x,w = gaussxw(N) returns integration points x and integration\n", "# weights w such that sum_i w[i]*f(x[i]) is the Nth-order\n", "# Gaussian approximation to the integral int_{-1}^1 f(x) dx\n", "# x,w = gaussxwab(N,a,b) returns integration points and weights\n", "# mapped to the interval [a,b], so that sum_i w[i]*f(x[i])\n", "# is the Nth-order Gaussian approximation to the integral\n", "# int_a^b f(x) dx\n", "#\n", "# This code finds the zeros of the nth Legendre polynomial using\n", "# Newton's method, starting from the approximation given in Abramowitz\n", "# and Stegun 22.16.6. The Legendre polynomial itself is evaluated\n", "# using the recurrence relation given in Abramowitz and Stegun\n", "# 22.7.10. The function has been checked against other sources for\n", "# values of N up to 1000. It is compatible with version 2 and version\n", "# 3 of Python.\n", "#\n", "# Written by Mark Newman , June 4, 2011\n", "# You may use, share, or modify this file freely\n", "#\n", "######################################################################\n", "\n", "from numpy import ones,copy,cos,tan,pi,linspace\n", "\n", "def gaussxw(N):\n", "\n", " # Initial approximation to roots of the Legendre polynomial\n", " a = linspace(3,4*N-1,N)/(4*N+2)\n", " x = cos(pi*a+1/(8*N*N*tan(a)))\n", "\n", " # Find roots using Newton's method\n", " epsilon = 1e-15\n", " delta = 1.0\n", " while delta>epsilon:\n", " p0 = ones(N,float)\n", " p1 = copy(x)\n", " for k in range(1,N):\n", " p0,p1 = p1,((2*k+1)*x*p1-k*p0)/(k+1)\n", " dp = (N+1)*(p0-x*p1)/(1-x*x)\n", " dx = p1/dp\n", " x -= dx\n", " delta = max(abs(dx))\n", "\n", " # Calculate the weights\n", " w = 2*(N+1)*(N+1)/(N*N*(1-x*x)*dp*dp)\n", "\n", " return x,w\n", "\n", "def gaussxwab(N,a,b):\n", " x,w = gaussxw(N)\n", " return 0.5*(b-a)*x+0.5*(b+a),0.5*(b-a)*w" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([-8.05825236e-16]), array([2.]))\n", "(array([ 0.57735027, -0.57735027]), array([1., 1.]))\n", "(array([ 7.74596669e-01, -8.96888137e-17, -7.74596669e-01]), array([0.55555556, 0.88888889, 0.55555556]))\n" ] } ], "source": [ "print(gaussxw(1))\n", "print(gaussxw(2))\n", "print(gaussxw(3))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "quadrature_visualize(gaussxw(5), -1., 1., \"5-point Gauss-Legendre quadrature\").show()\n", "quadrature_visualize(gaussxw(10), -1., 1., \"10-point Gauss-Legendre quadrature\").show()\n", "quadrature_visualize(gaussxw(32), -1., 1., \"32-point Gauss-Legendre quadrature\").show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using Gauss-Legendre quadratures\n", " N I_N\n", " 1 1.9999999999999969\n", " 2 6.2222222222222303\n", " 3 6.4000000000000066\n", " 4 6.4000000000000208\n", " 5 6.4000000000000190\n", " 6 6.4000000000000021\n", " 7 6.4000000000000083\n" ] } ], "source": [ "# Gauss-Legendre quadrature integration\n", "print(\"Computing the integral of\",flabel, \"over the interval (\",flimit_a,\",\",flimit_b,\") using Gauss-Legendre quadratures\")\n", "print(\"{0:>10} {1:>20}\".format(\"N\", \"I_N\"))\n", "for N in range(1,8):\n", " quadr = gaussxwab(N, flimit_a, flimit_b)\n", " integral = integrate_quadrature(f, quadr)\n", " print(\"{0:>10} {1:>20.16f}\".format(N, integral))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From $N = 3$ the result is exact to machine precision!" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing the integral of 7x^3-8x^2-3x+3 over the interval ( -1.0 , 1.0 )\n", " Trapezoidal: -10.0\n", "Clenshaw-Curtis: -2.0\n", " Gauss-Legendre: 0.6666666666666641\n" ] } ], "source": [ "# Another example, cubic function: trapezoidal rule vs 2-point gauss-legendre\n", "\n", "def f2(x):\n", " return 7. * x**3 - 8. * x**2 - 3. * x + 3.\n", "\n", "a = -1.\n", "b = 1.\n", "\n", "trapezoidal = newton_cotes(1, -1., 1., False)\n", "clenshawcurtis = clenshaw_curtis(1, -1., 1.)\n", "gaussn2 = gaussxwab(2, -1., 1.)\n", "\n", "print(\"Computing the integral of\",\"7x^3-8x^2-3x+3\", \"over the interval (\",-1.,\",\",1.,\")\")\n", "print(\" Trapezoidal:\", integrate_quadrature(f2, trapezoidal))\n", "print(\"Clenshaw-Curtis:\", integrate_quadrature(f2, clenshawcurtis))\n", "print(\" Gauss-Legendre:\", integrate_quadrature(f2, gaussn2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exact result is $2/3$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generalized Gaussian quadratures\n", "\n", "The method of Gaussian quadratures can be generalized to integrals of the following type\n", "$$\n", "\\int_a^b \\omega(x) f(x) dx \\approx \\sum_{k=1}^n w_k f(x_k)~.\n", "$$\n", "\n", "Here $a$ and $b$ need not necessarily have to correspond to a finite interval, and the integration of $f(x)$ is performed with a weight function $\\omega(x)$. In this case it is possible to construct an $n$-point quadrature which provides exact answer when $f(x)$ is a polynomial of degree up to $2n - 1$. The weights $w_k$ are given by\n", "$$\n", "w_k = \\int_a^b \\omega(x) \\, L_{{n-1},k}(x) \\, dx~.\n", "$$\n", "\n", "Here $x_k$ correspond to the roots of a polynomial $p_n(x)$ satisfying the relation\n", "$$\n", "\\int_a^b \\omega(x) \\, x^k \\, p_n(x) \\, dx = 0, \\qquad k = 0,\\ldots,n-1~.\n", "$$\n", "\n", "For $a = -1$, $b = 1$, and $\\omega(x) = 1$, $p_n(x)$ corresponds to $n$th Legendre polynomial as discussed before.\n", "\n", "Other common possibilities are\n", "- Jacobi polynomials $P_n^{(\\alpha,\\beta)}(x)$\n", " - interval $(-1,1)$\n", " - $\\omega(x) = (1-x)^\\alpha \\, (1+x)^{\\beta}$\n", "- Laguerre polynomials $L_n(x)$\n", " - interval $[0,\\infty)$\n", " - $\\omega(x) = e^{-x}$\n", "- Hermite polynomials $H_n(x)$\n", " - interval $(-\\infty, \\infty)$\n", " - $\\omega(x) = e^{-x^2}$\n", " \n", "For all these cases efficient methods exist for calculating the nodes $x_k$ and the weights $\\omega_k$ accurately. This calculation has to be done only once." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below is an example for Laguerre and Hermite polynomials using sympy" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sympy\n", "import math\n", "\n", "# Nodes and weight for n-point Gauss-Hermite quadrature\n", "def hermitexw(n):\n", " x = sympy.Symbol(\"x\")\n", " roots = sympy.Poly(sympy.hermite(n, x)).all_roots()\n", " x_i = [float(rt.evalf(20)) for rt in roots]\n", " w_i = [float(2**(n-1) * math.factorial(n) * np.sqrt(np.pi) / ((n**2) * sympy.hermite(n - 1, rt)**2).evalf(20)) for rt in roots]\n", " return x_i, w_i\n", "\n", "plt.yscale('log')\n", "quadrature_visualize(hermitexw(5), -5., 5., \"5-point Gauss-Hermite quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(hermitexw(10), -5., 5., \"10-point Gauss-Hermite quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(hermitexw(15), -5., 5., \"15-point Gauss-Hermite quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(hermitexw(20), -5., 5., \"20-point Gauss-Hermite quadrature\").show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Nodes and weight for n-point Gauss-Laguerre quadrature\n", "def laguerrexw(n):\n", " x = sympy.Symbol(\"x\")\n", " roots = sympy.Poly(sympy.laguerre(n, x)).all_roots()\n", " x_i = [float(rt.evalf(20)) for rt in roots]\n", " w_i = [float((rt / ((n + 1) * sympy.laguerre(n + 1, rt)) ** 2).evalf(20)) for rt in roots]\n", " return x_i, w_i\n", "\n", "plt.yscale('log')\n", "quadrature_visualize(laguerrexw(5), 0., 10., \"5-point Gauss-Laguerre quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(laguerrexw(10), 0., 10., \"10-point Gauss-Laguerre quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(laguerrexw(15), 0., 10., \"15-point Gauss-Laguerre quadrature\").show()\n", "plt.yscale('log')\n", "quadrature_visualize(laguerrexw(20), 0., 10., \"20-point Gauss-Laguerre quadrature\").show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Relativistic quantum distribution\n", "\n", "Let us revisit the density of a relativistic quantum gas\n", "$$\n", "n = \\frac{d T^3}{2\\pi^2} \\int_0^\\infty d \\tilde k \\, \\tilde k^2 \\, \\left[\\exp\\left\\{\\sqrt{\\tilde m^2+\\tilde k^2}-\\tilde \\mu \\right\\} + \\eta \\right ]^{-1},\n", "$$\n", "where $\\tilde m = m/T$ and $\\tilde \\mu = \\mu / T$.\n", "\n", "This expression can be cast in a form\n", "$$\n", "\\tilde n = n/T^3 = \\int_0^\\infty d x e^{-x} f(x)\n", "$$\n", "with\n", "$$\n", "f(x) = \\frac{d}{2\\pi^2} x^2 \\, e^{x} \\, \\left[\\exp\\left\\{\\sqrt{\\tilde m^2+x^2}-\\tilde \\mu \\right\\} + \\eta \\right ]^{-1}~.\n", "$$\n", "\n", "One can see that the function $f(x) \\sim x^2$ in the limit $x \\to \\infty$, thus Gauss-Laguerre should be a good choice for evaluting this type of interval.\n", "\n", "Let us do that using a 32-point Gauss-Laguerre quadrature." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# Precomute 32-point Gauss-Laguerre quadrature\n", "laguerrexw32 = laguerrexw(32)\n", "\n", "# Parameters\n", "T = 150 # MeV\n", "mu = 0 \n", "m = 138 # MeV\n", "d = 1\n", "eta = 0\n", "\n", "# Function for integration\n", "def fThermal(x):\n", " x = float(x)\n", " return d * x**2 * np.exp(x) / (2 * np.pi**2) / (np.exp(np.sqrt((m/T)**2 + x**2) - mu/T) + eta)\n", "\n", "def nIntegral(n_nodes = 32):\n", " quad = laguerrexw32\n", " if (n_nodes != 32):\n", " quad = laguerrexw(n_nodes)\n", " return integrate_quadrature(fThermal, quad)\n", "\n", "def nT3num(inT, inMu, n_nodes = 32):\n", " global T, mu\n", " T = inT\n", " mu = inMu\n", " return nIntegral(n_nodes)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Maxwell-Boltzmann integral\n", "T = 150\n", "mu = 0\n", "eta = 0\n", "n(T,mu) = 0.0847224926254013\n" ] } ], "source": [ "# Maxwell-Boltzmann\n", "\n", "T = 150 # MeV\n", "mu = 0\n", "eta = 0\n", "\n", "print(\"Computing Maxwell-Boltzmann integral\")\n", "print(\"T = \",T)\n", "print(\"mu = \",mu)\n", "print(\"eta = \",eta)\n", "print(\"n(T,mu) = \",nT3num(150,0,32))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Bose-Einstein integral\n", "T = 150\n", "mu = 0\n", "eta = -1\n", "n(T,mu) = 0.09332222578416971\n" ] } ], "source": [ "#Bose-Einstein\n", "\n", "T = 150 # MeV\n", "mu = 0\n", "eta = -1\n", "\n", "print(\"Computing Bose-Einstein integral\")\n", "print(\"T = \",T)\n", "print(\"mu = \",mu)\n", "print(\"eta = \",eta)\n", "print(\"n(T,mu) = \",nT3num(150,0,32))" ] } ], "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 2 }