/usr/include/trilinos/ROL_GaussChebyshev3Quadrature.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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#ifndef ROL_GAUSSCHEBYSHEV3QUADRATURE_HPP
#define ROL_GAUSSCHEBYSHEV3QUADRATURE_HPP
#include "ROL_Quadrature1D.hpp"
#include <cmath>
namespace ROL {
template<class Real>
class GaussChebyshev3Quadrature : public Quadrature1D<Real> {
private:
const int nQuad_;
public:
GaussChebyshev3Quadrature(const int nQuad) : nQuad_(nQuad) {
// Check inputs
std::vector<Real> pts, wts;
buildQuadrature(pts,wts);
Quadrature1D<Real>::set(pts,wts);
}
std::vector<std::vector<Real> > test(const bool printToStream = true,
std::ostream &outStream = std::cout) const {
const int deg = 2*nQuad_-1;
const Real pi(M_PI), two(2), three(3), half(0.5), C(4.0/M_PI);
std::vector<Real> tmp(4);
std::vector<std::vector<Real> > out(deg+1,tmp);
std::vector<Real> pts, wts;
Quadrature1D<Real>::get(pts,wts);
for (int i = 0; i < deg+1; ++i) {
if (printToStream) {
if (i==0) {
outStream << std::right
<< std::setw(20) << "Poly order"
<< std::setw(20) << "integral"
<< std::setw(20) << "quad approx"
<< std::setw(20) << "abs error"
<< std::endl;
}
}
out[i][0] = static_cast<Real>(i);
if ( i == 0 ) {
out[i][1] = static_cast<Real>(2);
}
else {
out[i][1] = C*std::sqrt(pi)*std::tgamma(out[i][0]+half*three)
/std::tgamma(out[i][0]+two);
}
for (int j = 0; j < nQuad_; ++j) {
out[i][2] += wts[j]*std::pow(pts[j],out[i][0]);
}
out[i][3] = std::abs(out[i][2] - out[i][1]);
if (printToStream) {
outStream << std::fixed << std::setprecision(0) << std::right
<< std::setw(20) << out[i][0]
<< std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << out[i][1]
<< std::setw(20) << out[i][2]
<< std::setw(20) << out[i][3]
<< std::endl;
}
}
return out;
}
private:
void buildQuadrature(std::vector<Real> &pts, std::vector<Real> &wts) const {
pts.resize(nQuad_); wts.resize(nQuad_);
Real sum(0), pi(M_PI), two(2), one(1), half(0.5), n = static_cast<Real>(nQuad_);
for (int i = 0; i < nQuad_; ++i) {
pts[i] = std::pow(std::cos(half*pi*(two*static_cast<Real>(i+1)-one)/(two*n+one)),two);
wts[i] = two*pi/(two*n+one) * pts[i];
sum += wts[i];
}
for (int i = 0; i < nQuad_; ++i) {
wts[i] *= two/sum;
}
}
};
}
#endif
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