SundanceQuadQuadrature.cpp

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//                             Sundance
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#include "SundanceQuadQuadrature.hpp"
#include "SundanceOut.hpp"
#include "SundanceGauss1D.hpp"
#include "PlayaTabs.hpp"

using namespace Sundance;
using namespace Teuchos;

void QuadQuadrature::getPoints(int order, Array<double>& wgt, Array<double>& x,
    Array<double>& y)
{
  int p = order + 1;
  p = p + (p % 2);
  int nNodes = p / 2;
  Gauss1D rule(nNodes, 0.0, 1.0);
  Array<double> s = rule.nodes();
  Array<double> t = s;
  Array<double> w = rule.weights();
  int n = rule.nPoints();

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

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

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

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

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