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Gauss-Legendre Quadrature.ipynb
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{ | |
"nbformat": 4, | |
"nbformat_minor": 0, | |
"metadata": { | |
"colab": { | |
"name": "Gauss-Legendre Quadrature.ipynb", | |
"provenance": [], | |
"collapsed_sections": [], | |
"authorship_tag": "ABX9TyOiJgLzB9yjwxbO4fiSd+QF", | |
"include_colab_link": true | |
}, | |
"kernelspec": { | |
"name": "python3", | |
"display_name": "Python 3" | |
}, | |
"language_info": { | |
"name": "python" | |
} | |
}, | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "view-in-github", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"<a href=\"https://colab.research.google.com/gist/iampramodyadav/eab629b54c33608d2e6df5846456dc5c/gauss-legendre-quadrature.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "EztDrpdwbDDY" | |
}, | |
"source": [ | |
"\n", | |
"\n", | |
"---\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "I_IaCaxwaM7C" | |
}, | |
"source": [ | |
"# Gauss-Legendre Quadrature implementation in Python\n", | |
"\n", | |
"By: Pramod Kumar Yadav (@iampramodyadav)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "-oKr32FrbA_H" | |
}, | |
"source": [ | |
"\n", | |
"\n", | |
"---\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "C5UshuFRVk5Q" | |
}, | |
"source": [ | |
"# Legendre Polynomial (symbolic)\n", | |
"\n", | |
"[SymPy Documentation](https://docs.sympy.org/latest/tutorial/basic_operations.html)\n", | |
"\n", | |
"[Gaussian quadrature](https://en.wikipedia.org/wiki/Gaussian_quadrature)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "YlA4hfdfLgRC" | |
}, | |
"source": [ | |
"from sympy import *\n", | |
"import numpy as np" | |
], | |
"execution_count": 1, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "iS0D9PtRL_Oj" | |
}, | |
"source": [ | |
"x=symbols('x')" | |
], | |
"execution_count": 2, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "q5sq4wQDL0vJ" | |
}, | |
"source": [ | |
"def Legendre(n,x):\n", | |
" \"\"\"\n", | |
" n: Order of polynomial\n", | |
" x: Variable\n", | |
" This function print Legendre polynomial of order n\n", | |
" \"\"\"\n", | |
"\n", | |
" x=symbols('x')\n", | |
" if (n==0):\n", | |
" return x*0+1.0\n", | |
" elif (n==1):\n", | |
" return x\n", | |
" else:\n", | |
" return ((2.0*n-1.0)*x*Legendre(n-1,x)-(n-1)*Legendre(n-2,x))/n" | |
], | |
"execution_count": 3, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "yBovgMiWGtBM", | |
"outputId": "3d24b9ec-154a-4a5f-c73d-be8865241ebc" | |
}, | |
"source": [ | |
"print(Legendre.__doc__)" | |
], | |
"execution_count": 4, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"\n", | |
" n: Order of polynomial\n", | |
" x: Variable\n", | |
" This function print Legendre polynomial of order n\n", | |
" \n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 38 | |
}, | |
"id": "3wkk0fKZMI5x", | |
"outputId": "7cce352e-3fa9-4aab-c43c-4619bac14be6" | |
}, | |
"source": [ | |
"Legendre(2,x)" | |
], | |
"execution_count": 5, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/latex": "$\\displaystyle 1.5 x^{2} - 0.5$", | |
"text/plain": [ | |
"1.5*x**2 - 0.5" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 5 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "Xw-_Vlt5bUPn" | |
}, | |
"source": [ | |
"# Derivative of the Legendre polynomials" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "jZSDWnM9MVII" | |
}, | |
"source": [ | |
"def DLegendre(n,x):\n", | |
" \"\"\"\n", | |
" n: Order of polynomial\n", | |
" x: Variable\n", | |
" This function print Derivative of Legendre polynomial of order n\n", | |
" \"\"\"\n", | |
" x=symbols('x')\n", | |
" if (n==0):\n", | |
" return x*0\n", | |
" elif (n==1):\n", | |
" return x*0+1.0\n", | |
" else:\n", | |
" return (n/(x**2-1.0))*(x*Legendre(n,x)-Legendre(n-1,x))" | |
], | |
"execution_count": 6, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "T_VpnDv9HAO4", | |
"outputId": "90365f0b-c390-464c-c2b2-93676a1e6961" | |
}, | |
"source": [ | |
"print(DLegendre.__doc__)" | |
], | |
"execution_count": 7, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"\n", | |
" n: Order of polynomial\n", | |
" x: Variable\n", | |
" This function print Derivative of Legendre polynomial of order n\n", | |
" \n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 38 | |
}, | |
"id": "JTbjniKiMctA", | |
"outputId": "23a1fb32-ee65-49ba-e28f-25b9a8d2a82e" | |
}, | |
"source": [ | |
"simplify(DLegendre(2,x))" | |
], | |
"execution_count": 8, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/latex": "$\\displaystyle 3.0 x$", | |
"text/plain": [ | |
"3.0*x" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 8 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "dIli9J1fbctm" | |
}, | |
"source": [ | |
"# Plot Legendre Polynomial" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "GkzurmUAOBRN" | |
}, | |
"source": [ | |
"f=Legendre(3,x)" | |
], | |
"execution_count": 9, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 314 | |
}, | |
"id": "o_qaA6AtOVqw", | |
"outputId": "76f19884-208e-4a3a-8469-c9c2d9ea717e" | |
}, | |
"source": [ | |
"from matplotlib import style\n", | |
"style.use('ggplot')\n", | |
"plot(f,(x,-1,1),legend=True)" | |
], | |
"execution_count": 10, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"<sympy.plotting.plot.Plot at 0x7ff2bcdb2b90>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 10 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "F3Udo4BrfMVx" | |
}, | |
"source": [ | |
"f1=Legendre(1,x)\n", | |
"f2=simplify(Legendre(3,x))" | |
], | |
"execution_count": 11, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 297 | |
}, | |
"id": "mofGJ9otfict", | |
"outputId": "bc912324-6ec1-42c1-d7b8-5cccfabef667" | |
}, | |
"source": [ | |
"pl=plot(f1,f2,(x,-1,1),legend=True,show=False)\n", | |
"pl[0].line_color = 'red'\n", | |
"pl[1].line_color = 'green'\n", | |
"pl.show()" | |
], | |
"execution_count": 12, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 314 | |
}, | |
"id": "CopwiC8cQgJQ", | |
"outputId": "23306eaa-fb05-4262-9ed7-f224a5e91ab6" | |
}, | |
"source": [ | |
"plot(Legendre(1,x),Legendre(2,x),Legendre(3,x),Legendre(4,x),Legendre(5,x),(x,-1,1))" | |
], | |
"execution_count": 13, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"<sympy.plotting.plot.Plot at 0x7ff2b4835750>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 13 | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 293 | |
}, | |
"id": "--qTqR-ERl71", | |
"outputId": "30d80000-9e0c-4974-d301-ab35d5b3b526" | |
}, | |
"source": [ | |
"import seaborn as sns\n", | |
"sns.set()\n", | |
"sns.set_style(\"whitegrid\", {'grid.linestyle': '--'})\n", | |
"\n", | |
"p=plot(Legendre(1,x),Legendre(2,x),Legendre(3,x),Legendre(4,x),Legendre(5,x),(x,-1,1),title='SymPy plot example',show=False);\n", | |
"p[0].line_color = 'red'\n", | |
"p[1].line_color = 'green'\n", | |
"p[2].line_color = 'yellow'\n", | |
"p[3].line_color = ['b','r']\n", | |
"p.show()" | |
], | |
"execution_count": 14, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "C2COlaWlgxXg" | |
}, | |
"source": [ | |
"# Legedre Roots" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "kfD87rI5HrN0" | |
}, | |
"source": [ | |
"def LegendreRoots(polyorder,tolerance=1e-20):\n", | |
" \"\"\"\n", | |
" polyorder: Order of polynomial\n", | |
" tolerance: tolerance of error (default: 1e-20)\n", | |
" This function return Roots of Legendre polynomial\n", | |
" \"\"\"\n", | |
" if polyorder<2:\n", | |
" err=1 # bad polyorder no roots can be found\n", | |
" else:\n", | |
" roots=[]\n", | |
"\t\t# The polynomials are alternately even and odd functions. So we evaluate only half the number of roots. \n", | |
" for i in range(1,int((polyorder)/2) +1): \n", | |
" x1=cos(pi*(i-0.25)/(polyorder+0.5))\n", | |
" error=10*tolerance\n", | |
" iters=0\n", | |
" while (error>tolerance) and (iters<1000):\n", | |
" dx=-Legendre(polyorder,x)/DLegendre(polyorder,x)\n", | |
" dx=N(dx.subs(x,x1))\n", | |
" x1=N(x1+dx)\n", | |
" iters=iters+1\n", | |
" error=abs(dx)\n", | |
" #print(roots)\n", | |
" roots.append(x1)\n", | |
" #print(roots)\n", | |
"\t\t# Use symmetry to get the other roots\n", | |
" roots=np.array(roots)\n", | |
" if polyorder%2==0:\n", | |
" roots=np.concatenate( (-1.0*roots, roots[::-1]) )\n", | |
" else:\n", | |
" roots=np.concatenate( (-1.0*roots, [0.0], roots[::-1]) )\n", | |
" err=0 # successfully determined roots\n", | |
" return [roots, err]" | |
], | |
"execution_count": 15, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "2MIVtFHEHzkS", | |
"outputId": "290e99f7-05f7-41ee-e399-8f6010ac0187" | |
}, | |
"source": [ | |
"print(LegendreRoots.__doc__)" | |
], | |
"execution_count": 16, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"\n", | |
" polyorder: Order of polynomial\n", | |
" tolerance: tolerance of error (default: 1e-20)\n", | |
" This function return Roots of Legendre polynomial\n", | |
" \n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "bNxRGVmOIIWm", | |
"outputId": "c2ba54ba-51c8-41a4-8908-aacc4ad4dc72" | |
}, | |
"source": [ | |
"LegendreRoots(5)" | |
], | |
"execution_count": 17, | |
"outputs": [ | |
{ | |
"output_type": "execute_result", | |
"data": { | |
"text/plain": [ | |
"[array([-0.906179845938664, -0.538469310105683, 0.0, 0.538469310105683,\n", | |
" 0.906179845938664], dtype=object), 0]" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
}, | |
"execution_count": 17 | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "ZITxjIGbg3cV" | |
}, | |
"source": [ | |
"# Weight Coefficient" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"id": "rVK228HyVRJi" | |
}, | |
"source": [ | |
"def GaussLegendreWeights(polyorder):\n", | |
" \"\"\"\n", | |
" polyorder: Order of polynomial\n", | |
" This function return Weights of Legendre polynomial\n", | |
" \"\"\"\n", | |
" W=[]\n", | |
" [xis,err]=LegendreRoots(polyorder)\n", | |
" xis=list(xis)\n", | |
" if err==0:\n", | |
" for x1 in xis:\n", | |
" w=2.0/( (1.0-x**2)*(DLegendre(polyorder,x)**2) )\n", | |
" w=w.subs(x,x1)\n", | |
" W.append(w)\n", | |
" err=0\n", | |
" else:\n", | |
" err=1 # could not determine roots - so no weights\n", | |
" return [W, xis, err]" | |
], | |
"execution_count": 18, | |
"outputs": [] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "piAETldfIrcl", | |
"outputId": "d3b7e95e-f3a7-436f-d78f-9802d606fd1c" | |
}, | |
"source": [ | |
"print(GaussLegendreWeights.__doc__)" | |
], | |
"execution_count": 19, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"text": [ | |
"\n", | |
" polyorder: Order of polynomial\n", | |
" This function return Weights of Legendre polynomial\n", | |
" \n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "sVOFuHAFg_n7" | |
}, | |
"source": [ | |
"# Final Result" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 1000 | |
}, | |
"id": "lwFGgZFHVehY", | |
"outputId": "e5a35b5e-f8f5-4125-c3a3-f79a132334f1" | |
}, | |
"source": [ | |
"for Polyorder in range(2,7):\n", | |
" plot(Legendre(Polyorder,x),(x,-1,1))\n", | |
"\n", | |
" [W, xis, err]=GaussLegendreWeights(Polyorder)\n", | |
" print(\"order:\", Polyorder)\n", | |
" print(\"Weights:\", W)\n", | |
" print (\"Roots : \",xis)\n", | |
"\n", | |
" print('='*100)\n", | |
" print('\\n\\n')\n", | |
" print('='*100)" | |
], | |
"execution_count": 20, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "stream", | |
"text": [ | |
"order: 2\n", | |
"Weights: [1.00000000000000, 1.00000000000000]\n", | |
"Roots : [-0.577350269189626, 0.577350269189626]\n", | |
"====================================================================================================\n", | |
"\n", | |
"\n", | |
"\n", | |
"====================================================================================================\n" | |
], | |
"name": "stdout" | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "stream", | |
"text": [ | |
"order: 3\n", | |
"Weights: [0.555555555555556, 0.888888888888889, 0.555555555555556]\n", | |
"Roots : [-0.774596669241483, 0.0, 0.774596669241483]\n", | |
"====================================================================================================\n", | |
"\n", | |
"\n", | |
"\n", | |
"====================================================================================================\n" | |
], | |
"name": "stdout" | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "stream", | |
"text": [ | |
"order: 4\n", | |
"Weights: [0.347854845137454, 0.652145154862546, 0.652145154862546, 0.347854845137454]\n", | |
"Roots : [-0.861136311594053, -0.339981043584856, 0.339981043584856, 0.861136311594053]\n", | |
"====================================================================================================\n", | |
"\n", | |
"\n", | |
"\n", | |
"====================================================================================================\n" | |
], | |
"name": "stdout" | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "stream", | |
"text": [ | |
"order: 5\n", | |
"Weights: [0.236926885056189, 0.478628670499366, 0.568888888888889, 0.478628670499366, 0.236926885056189]\n", | |
"Roots : [-0.906179845938664, -0.538469310105683, 0.0, 0.538469310105683, 0.906179845938664]\n", | |
"====================================================================================================\n", | |
"\n", | |
"\n", | |
"\n", | |
"====================================================================================================\n" | |
], | |
"name": "stdout" | |
}, | |
{ | |
"output_type": "display_data", | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"tags": [] | |
} | |
}, | |
{ | |
"output_type": "stream", | |
"text": [ | |
"order: 6\n", | |
"Weights: [0.171324492379171, 0.360761573048138, 0.467913934572691, 0.467913934572691, 0.360761573048138, 0.171324492379171]\n", | |
"Roots : [-0.932469514203152, -0.661209386466265, -0.238619186083197, 0.238619186083197, 0.661209386466265, 0.932469514203152]\n", | |
"====================================================================================================\n", | |
"\n", | |
"\n", | |
"\n", | |
"====================================================================================================\n" | |
], | |
"name": "stdout" | |
} | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "3-_vDxaGm_Nk" | |
}, | |
"source": [ | |
"\n", | |
"\n", | |
"---\n" | |
] | |
} | |
] | |
} |
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