private static QuadratureRule MakeGaussianQuadrature_1Point()
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = 1;
GQ.wi = new double[1];
GQ.Xi = new double[1];
GQ.wi[0] = 2.0D;
GQ.Xi[0] = 0.0D;
return(GQ);
}
private static QuadratureRule MakeGaussianQuadrature_NPoint(int NumberOfPoints)
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = NumberOfPoints;
GQ.wi = new double[NumberOfPoints];
GQ.Xi = new double[NumberOfPoints];
//Adapted from Numerical Recipes: 10/25/12
const double EPS = 1.0E-14;
double x1, x2;
x1 = -1.0D;
x2 = 1.0D;
double z1, z, xm, xl, pp, p3, p2, p1;
int n = NumberOfPoints;
int m = (n + 1) / 2;
xm = 0.5D * (x2 + x1);
xl = 0.5D * (x2 - x1);
double Rn = Convert.ToDouble(n);
for (int i = 0; i < m; i++)
{
double Ri = Convert.ToDouble(i);
z = Math.Cos(Math.PI * (Ri + 0.75D) / (Rn + 0.5D));
do
{
p1 = 1.0D;
p2 = 0.0D;
for (int j = 0; j < n; j++)
{
double Rj = Convert.ToDouble(j);
p3 = p2;
p2 = p1;
p1 = ((2.0D * Rj + 1.0D) * z * p2 - Rj * p3) / (Rj + 1.0D);
}
pp = Rn * (z * p1 - p2) / (z * z - 1.0D);
z1 = z;
z = z1 - p1 / pp;
} while (Math.Abs(z - z1) > EPS);
GQ.Xi[i] = xm - xl * z;
GQ.Xi[n - 1 - i] = xm + xl * z;
GQ.wi[i] = 2.0D * xl / ((1.0D - z * z) * pp * pp);
GQ.wi[n - 1 - i] = GQ.wi[i];
}
return(GQ);
}
private static QuadratureRule MakeGaussianQuadrature_2Point()
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = 2;
GQ.wi = new double[2];
GQ.Xi = new double[2];
GQ.wi[0] = 1.0D;
GQ.wi[1] = 1.0D;
GQ.Xi[0] = -1.0D / Math.Sqrt(3.0D);
GQ.Xi[1] = -GQ.Xi[0];
return(GQ);
}
private static QuadratureRule MakeGaussianQuadrature_3Point()
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = 3;
GQ.wi = new double[3];
GQ.Xi = new double[3];
GQ.wi[0] = 8.0D / 9.0D;
GQ.wi[1] = 5.0D / 9.0D;
GQ.wi[2] = GQ.wi[1];
GQ.Xi[0] = 0.0D;
GQ.Xi[1] = -Math.Sqrt(3.0D / 5.0D);
GQ.Xi[2] = -GQ.Xi[1];
return(GQ);
}
private static QuadratureRule MakeGaussianQuadrature_4Point()
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = 4;
GQ.wi = new double[4];
GQ.Xi = new double[4];
GQ.wi[0] = (18.0D + Math.Sqrt(30.0D)) / 36.0D;
GQ.wi[1] = GQ.wi[0];
GQ.wi[2] = (18.0D - Math.Sqrt(30.0D)) / 36.0D;
GQ.wi[3] = GQ.wi[2];
GQ.Xi[0] = -Math.Sqrt((3.0D - 2.0D * Math.Sqrt(6.0D / 5.0D)) / 7.0D);
GQ.Xi[1] = -GQ.Xi[0];
GQ.Xi[2] = -Math.Sqrt((3.0D + 2.0D * Math.Sqrt(6.0D / 5.0D)) / 7.0D);
GQ.Xi[3] = -GQ.Xi[2];
return(GQ);
}
private static QuadratureRule MakeGaussianQuadrature_5Point()
{
QuadratureRule GQ = new QuadratureRule();
GQ.NIP = 5;
GQ.wi = new double[5];
GQ.Xi = new double[5];
GQ.wi[0] = 128.0D / 225.0D;
GQ.wi[1] = (322.0D + 13.0D * Math.Sqrt(70.0D)) / 900.0D;
GQ.wi[2] = GQ.wi[1];
GQ.wi[3] = (322.0D - 13.0D * Math.Sqrt(70.0D)) / 900.0D;
GQ.wi[4] = GQ.wi[3];
GQ.Xi[0] = 0.0D;
GQ.Xi[1] = -Math.Sqrt(5.0D - 2.0D * Math.Sqrt(10.0D / 7.0D)) / 3.0D;
GQ.Xi[2] = -GQ.Xi[1];
GQ.Xi[3] = -Math.Sqrt(5.0D + 2.0D * Math.Sqrt(10.0D / 7.0D)) / 3.0D;
GQ.Xi[4] = -GQ.Xi[3];
return(GQ);
}
public Integrator_Quadrature(QuadratureRule qRule)
{
QRule = qRule;
}
