SundanceFeketeBrickQuadrature.cpp

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//                             Sundance
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#include "SundanceFeketeBrickQuadrature.hpp"
#include "SundanceOut.hpp"
#include "SundanceGaussLobatto1D.hpp"
#include "PlayaTabs.hpp"

using namespace Sundance;
using namespace Teuchos;

void FeketeBrickQuadrature::getPoints(int order, Array<double>& wgt, Array<
    double>& x, Array<double>& y, Array<double>& z)
{
  int p = order + 3;
  p = p + (p % 2);
  int nNodes = p / 2;
  GaussLobatto1D rule(nNodes, 0.0, 1.0);
  Array<double> d1 = rule.nodes();
  Array<double> d2 = d1;
  Array<double> d3 = d1;
  Array<double> w = rule.weights();
  int n = rule.nPoints();

  wgt.resize(n * n * n);
  x.resize(n * n * n);
  y.resize(n * n * n);
  z.resize(n * n * n);

  int k = 0;
  for (int i = 0; i < n; i++)
  {
    double p = d1[i];
    for (int j = 0; j < n; j++)
    {
      double q = d2[j]; //similar to the p value, caz we have quad
      for (int l = 0; l < n; l++, k++)
      {
        double r = d3[l];
        x[k] = p;
        y[k] = q;
        z[k] = r;
        wgt[k] = w[i] * w[j] * w[l];
      }
    }
  }
}

bool FeketeBrickQuadrature::test(int p)
{
  Array<double> w;
  Array<double> x;
  Array<double> y;
  Array<double> z;

  getPoints(p, w, x, y, z);
  bool pass = true;
  for (int a = 0; a <= p; a++)
  {
    int bMax = p - a;
    for (int b = 0; b <= bMax; b++)
    {
      int cMax = bMax - b;
      for (int c = 0; c <= cMax; c++)
      {
        double sum = 0.0;
        for (int q = 0; q < w.length(); q++)
        {
          sum += w[q] * pow(x[q], (double) a) * pow(y[q], (double) b)
              * pow(z[q], (double) c);
        }
        double err = fabs(sum - exact(a, b, c));
        bool localPass = err < 1.0e-14;
        pass = pass && localPass;
        if (!localPass)
        {
          fprintf(
              stderr,
              "order=%d m (%d, %d, %d) q=%22.15g exact=%22.15g\n",
              p, a, b, c, sum, exact(a, b, c));
          std::cerr << "error = " << err << std::endl;
        }
      }
    }
  }
  return pass;
}

double FeketeBrickQuadrature::exact(int a, int b, int c)
{
  return 1.0 / (a + 1) / (b + 1) / (c + 1);
}