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Numerical integration/Gauss-Legendre Quadrature: Difference between revisions
Numerical integration/Gauss-Legendre Quadrature (view source)
Revision as of 00:13, 22 April 2022
, 2 years agoAdded in C# version, suprised it wasnt already in as C# and Java are quite close.
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m (Added in C# version, suprised it wasnt already in as C# and Java are quite close.) |
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Actual value: 20.03574985
</pre>
=={{header|C sharp|C#}}==
Derived from the C++ and Java versions here.
<lang csharp>
using System;
//Works in .NET 6+
//Tested using https://dotnetfiddle.net because im lazy
public class Program {
public static double[][] legeCoef(int N) {
//Initialising Jagged Array
double[][] lcoef = new double[N+1][];
for (int i=0; i < lcoef.Length; ++i)
lcoef[i] = new double[N+1];
lcoef[0][0] = lcoef[1][1] = 1;
for (int n = 2; n <= N; n++) {
lcoef[n][0] = -(n - 1) * lcoef[n - 2][0] / n;
for (int i = 1; i <= n; i++)
lcoef[n][i] = ((2*n - 1) * lcoef[n-1][i-1]
- (n-1) * lcoef[n-2][i] ) / n;
}
return lcoef;
}
static double legeEval(double[][] lcoef, int N, double x) {
double s = lcoef[N][N];
for (int i = N; i > 0; --i)
s = s * x + lcoef[N][i-1];
return s;
}
static double legeDiff(double[][] lcoef, int N, double x) {
return N * (x * legeEval(lcoef, N, x) - legeEval(lcoef, N-1, x)) / (x*x - 1);
}
static void legeRoots(double[][] lcoef, int N, out double[] lroots, out double[] weight) {
lroots = new double[N];
weight = new double[N];
double x, x1;
for (int i = 1; i <= N; i++) {
x = Math.Cos(Math.PI * (i - 0.25) / (N + 0.5));
do {
x1 = x;
x -= legeEval(lcoef, N, x) / legeDiff(lcoef, N, x);
}
while (x != x1);
lroots[i-1] = x;
x1 = legeDiff(lcoef, N, x);
weight[i-1] = 2 / ((1 - x*x) * x1*x1);
}
}
static double legeInte(Func<Double, Double> f, int N, double[] weights, double[] lroots, double a, double b) {
double c1 = (b - a) / 2, c2 = (b + a) / 2, sum = 0;
for (int i = 0; i < N; i++)
sum += weights[i] * f.Invoke(c1 * lroots[i] + c2);
return c1 * sum;
}
//..................Main...............................
public static string Combine(double[] arrayD) {
return string.Join(", ", arrayD);
}
public static void Main() {
int N = 5;
var lcoeff = legeCoef(N);
double[] roots;
double[] weights;
legeRoots(lcoeff, N, out roots, out weights);
var integrateResult = legeInte(x=>Math.Exp(x), N, weights, roots, -3, 3);
Console.WriteLine("Roots: " + Combine(roots));
Console.WriteLine("Weights: " + Combine(weights)+ "\n" );
Console.WriteLine("integral: " + integrateResult );
Console.WriteLine("actual: " + (Math.Exp(3)-Math.Exp(-3)) );
}
}</lang>
{{out}}
<pre>
Roots: 0.906179845938664, 0.538469310105683, 0, -0.538469310105683, -0.906179845938664
Weights: 0.236926885056189, 0.478628670499367, 0.568888888888889, 0.478628670499367, 0.236926885056189
integral: 20.0355777183856
actual: 20.0357498548198
</pre>
=={{header|Common Lisp}}==
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