PolynomialQuadrature::ClenshawCurtisGrid Class Reference

Clenshaw-Curtis sparse grid. More...

#include <PolynomialQuadrature.h>

Inheritance diagram for PolynomialQuadrature::ClenshawCurtisGrid:

Public Member Functions
	ClenshawCurtisGrid (const unsigned int max_order, std::vector< std::unique_ptr< const Polynomial > > &poly)
virtual unsigned int	nPoints () const override
	Resulting number of quadrature points in grid.
virtual unsigned int	nDim () const override
	Inputted number of dimensions.
virtual std::vector< Real >	quadraturePoint (const unsigned int n) const override
	Quadrature point n.
virtual Real	quadraturePoint (const unsigned int n, const unsigned int dim) const override
	Quadrature point n for dimension dim.
virtual Real	quadratureWeight (const unsigned int n) const override
	Weight for quadrature point n.

Private Attributes
const unsigned int	_ndim
std::vector< std::pair< std::vector< Real >, Real > >	_quadrature

Detailed Description

Clenshaw-Curtis sparse grid.

Definition at line 208 of file PolynomialQuadrature.h.

Constructor & Destructor Documentation

ClenshawCurtisGrid()

PolynomialQuadrature::ClenshawCurtisGrid::ClenshawCurtisGrid	(	const unsigned int	max_order,
		std::vector< std::unique_ptr< const Polynomial > > &	poly
	)

Definition at line 521 of file PolynomialQuadrature.C.

  : _ndim(poly.size())
{
  // Compute full tensor tuple
  std::vector<std::vector<unsigned int>> tuple_1d(_ndim);
  for (unsigned int d = 0; d < _ndim; ++d)
  {
    tuple_1d[d].resize(max_order);
    for (unsigned int i = 0; i < max_order; ++i)
      tuple_1d[d][i] = i;
  }
  StochasticTools::CartesianProduct<unsigned int> tensor_tuple(tuple_1d);
 
  // Curtis clenshaw has a lot of nested points,
  // so it behooves us to avoid duplicate points
  std::map<std::vector<Real>, Real> quad_map;
  unsigned int maxq = max_order - 1;
  unsigned int minq = (max_order > _ndim ? max_order - _ndim : 0);
  for (std::size_t p = 0; p < tensor_tuple.numRows(); ++p)
  {
    std::vector<unsigned int> dorder = tensor_tuple.computeRow(p);
    unsigned int q = std::accumulate(dorder.begin(), dorder.end(), 0);
    if (q <= maxq && q >= minq)
    {
      int sgn = ((max_order - q - 1) % 2 == 0 ? 1 : -1);
      Real coeff = static_cast<Real>(sgn * Utility::binomial(_ndim - 1, _ndim + q - max_order));
 
      std::vector<std::vector<Real>> qpoints_1D(_ndim);
      std::vector<std::vector<Real>> qweights_1D(_ndim);
      for (unsigned int d = 0; d < poly.size(); ++d)
        poly[d]->clenshawQuadrature(dorder[d], qpoints_1D[d], qweights_1D[d]);
 
      StochasticTools::WeightedCartesianProduct<Real, Real> quad(qpoints_1D, qweights_1D);
 
      for (unsigned int i = 0; i < quad.numRows(); ++i)
        quad_map[quad.computeRow(i)] += coeff * quad.computeWeight(i);
    }
  }
 
  _quadrature.reserve(quad_map.size());
  for (const auto & it : quad_map)
    _quadrature.push_back(it);
}

Member Function Documentation

nDim()

virtual unsigned int PolynomialQuadrature::ClenshawCurtisGrid::nDim ( ) const

inlineoverridevirtual

Inputted number of dimensions.

Implements PolynomialQuadrature::Quadrature.

Definition at line 215 of file PolynomialQuadrature.h.

{ return _ndim; }

nPoints()

virtual unsigned int PolynomialQuadrature::ClenshawCurtisGrid::nPoints ( ) const

inlineoverridevirtual

Resulting number of quadrature points in grid.

Implements PolynomialQuadrature::Quadrature.

Definition at line 214 of file PolynomialQuadrature.h.

{ return _quadrature.size(); }

quadraturePoint() [1/2]

virtual std::vector< Real > PolynomialQuadrature::ClenshawCurtisGrid::quadraturePoint ( const unsigned int  n ) const

inlineoverridevirtual

Quadrature point n.

Implements PolynomialQuadrature::Quadrature.

Definition at line 217 of file PolynomialQuadrature.h.

  {
    return _quadrature[n].first;
  }

quadraturePoint() [2/2]

virtual Real PolynomialQuadrature::ClenshawCurtisGrid::quadraturePoint ( const unsigned int  n, const unsigned int  dim  ) const

inlineoverridevirtual

Quadrature point n for dimension dim.

Implements PolynomialQuadrature::Quadrature.

Definition at line 221 of file PolynomialQuadrature.h.

  {
    return _quadrature[n].first[dim];
  }

quadratureWeight()

virtual Real PolynomialQuadrature::ClenshawCurtisGrid::quadratureWeight ( const unsigned int  n ) const

inlineoverridevirtual

Weight for quadrature point n.

Implements PolynomialQuadrature::Quadrature.

Definition at line 225 of file PolynomialQuadrature.h.

  {
    return _quadrature[n].second;
  }

Member Data Documentation

_ndim

const unsigned int PolynomialQuadrature::ClenshawCurtisGrid::_ndim

private

Definition at line 231 of file PolynomialQuadrature.h.

Referenced by ClenshawCurtisGrid(), and nDim().

_quadrature

std::vector<std::pair<std::vector<Real>, Real> > PolynomialQuadrature::ClenshawCurtisGrid::_quadrature

private

Definition at line 232 of file PolynomialQuadrature.h.

Referenced by ClenshawCurtisGrid(), nPoints(), quadraturePoint(), quadraturePoint(), and quadratureWeight().

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The documentation for this class was generated from the following files:

• stochastic_tools/include/utils/PolynomialQuadrature.h
• stochastic_tools/src/utils/PolynomialQuadrature.C