public static double[] ortho2eva0(int mmax, double[] z)
//****************************************************************************80
//
// Purpose:
//
// ORTHO2EVA0 evaluates the orthonormal polynomials on the triangle.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 30 June 2014
//
// Author:
//
// Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
// C++ version by John Burkardt.
//
// Reference:
//
// Hong Xiao, Zydrunas Gimbutas,
// A numerical algorithm for the construction of efficient quadrature
// rules in two and higher dimensions,
// Computers and Mathematics with Applications,
// Volume 59, 2010, pages 663-676.
//
// Parameters:
//
// Input, int MMAX, the maximum order to which the polynomials are
// to be evaluated.
//
// Input, double Z[2], the coordinates of the evaluation point.
//
// Output, double ORTHO2EVA0[(mmax+1)*(mmax+2)/2], the orthogonal
// polynomials evaluated at the point Z.
//
{
int m;
int npols = (mmax + 1) * (mmax + 2) / 2;
double[] pols = new double[npols];
const double zero = 0.0;
double sqrt3 = Math.Sqrt(3.0);
const double r11 = -1.0 / 3.0;
double r12 = -1.0 / sqrt3;
const double r21 = -1.0 / 3.0;
double r22 = 2.0 / sqrt3;
double a = z[0];
double b = z[1];
//
// Map the reference triangle to the right
// triangle with the vertices (-1,-1), (1,-1), (-1,1)
//
double x = r11 + r12 * b + a;
double y = r21 + r22 * b;
//
// Evaluate the Koornwinder's polynomials via the three term recursion.
//
double par1 = (2.0 * x + 1.0 + y) / 2.0;
double par2 = (1.0 - y) / 2.0;
double[] f1 = LegendreScaled.klegeypols(par1, par2, mmax);
double[] f2 = new double[(mmax + 1) * (mmax + 1)];
for (m = 0; m <= mmax; m++)
{
par1 = 2 * m + 1;
Jacobi.kjacopols(y, par1, zero, mmax - m, ref f2, polsIndex: +m * (mmax + 1));
}
int kk = 0;
for (m = 0; m <= mmax; m++)
{
int n;
for (n = 0; n <= m; n++)
{
//
// Evaluate the polynomial (m-n, n)
//
pols[kk] = f1[m - n] * f2[n + (m - n) * (mmax + 1)];
//
// Normalize.
//
double scale = Math.Sqrt
((1 + (m - n) + n) * (1 + (m - n) + (m - n)) / sqrt3
);
pols[kk] *= scale;
kk += 1;
}
}
return(pols);
}
