PolynomialQuadrature::SmolyakGrid Class Reference

Smolyak sparse grid. More...

#include <PolynomialQuadrature.h>

Inheritance diagram for PolynomialQuadrature::SmolyakGrid:

Public Member Functions
	SmolyakGrid (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 Member Functions
unsigned int	gridIndex (const unsigned int n) const
	Helper function to find which quadrature product to use.

Private Attributes
const unsigned int	_ndim
std::vector< std::size_t >	_npoints
	Cumulative number of points for each quadrature product.
std::vector< int >	_coeff
	Modification of quadrature weight based on polynomial order.
std::vector< std::unique_ptr< const StochasticTools::WeightedCartesianProduct< Real, Real > > >	_quad
	Container for all the combinations of quadrature products.

Detailed Description

Smolyak sparse grid.

Definition at line 181 of file PolynomialQuadrature.h.

Constructor & Destructor Documentation

SmolyakGrid()

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

Definition at line 449 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);
 
  _npoints.push_back(0);
  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);
      _coeff.push_back(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]->gaussQuadrature(dorder[d], qpoints_1D[d], qweights_1D[d]);
 
      _quad.push_back(std::make_unique<const StochasticTools::WeightedCartesianProduct<Real, Real>>(
          qpoints_1D, qweights_1D));
      _npoints.push_back(_npoints.back() + _quad.back()->numRows());
    }
  }
}

Member Function Documentation

gridIndex()

unsigned int PolynomialQuadrature::SmolyakGrid::gridIndex ( const unsigned int  n ) const

private

Helper function to find which quadrature product to use.

Definition at line 510 of file PolynomialQuadrature.C.

{
  for (unsigned int i = 0; i < _npoints.size() - 1; ++i)
    if (_npoints[i + 1] > n)
      return i;
 
  ::mooseError("Point index requested is greater than number of points.");
 
  return 0;
}

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

nDim()

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

inlineoverridevirtual

Inputted number of dimensions.

Implements PolynomialQuadrature::Quadrature.

Definition at line 187 of file PolynomialQuadrature.h.

{ return _ndim; }

nPoints()

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

inlineoverridevirtual

Resulting number of quadrature points in grid.

Implements PolynomialQuadrature::Quadrature.

Definition at line 186 of file PolynomialQuadrature.h.

{ return _npoints.back(); }

quadraturePoint() [1/2]

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

overridevirtual

Quadrature point n.

Implements PolynomialQuadrature::Quadrature.

Definition at line 489 of file PolynomialQuadrature.C.

{
  unsigned int ind = gridIndex(n);
  return _quad[ind]->computeRow(n - _npoints[ind]);
}

quadraturePoint() [2/2]

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

overridevirtual

Quadrature point n for dimension dim.

Implements PolynomialQuadrature::Quadrature.

Definition at line 496 of file PolynomialQuadrature.C.

{
  unsigned int ind = gridIndex(n);
  return _quad[ind]->computeValue(n - _npoints[ind], dim);
}

quadratureWeight()

Real PolynomialQuadrature::SmolyakGrid::quadratureWeight ( const unsigned int  n ) const

overridevirtual

Weight for quadrature point n.

Implements PolynomialQuadrature::Quadrature.

Definition at line 503 of file PolynomialQuadrature.C.

{
  unsigned int ind = gridIndex(n);
  return static_cast<Real>(_coeff[ind]) * _quad[ind]->computeWeight(n - _npoints[ind]);
}

Member Data Documentation

_coeff

std::vector<int> PolynomialQuadrature::SmolyakGrid::_coeff

private

Modification of quadrature weight based on polynomial order.

Definition at line 200 of file PolynomialQuadrature.h.

Referenced by quadratureWeight(), and SmolyakGrid().

_ndim

const unsigned int PolynomialQuadrature::SmolyakGrid::_ndim

private

Definition at line 196 of file PolynomialQuadrature.h.

Referenced by nDim(), and SmolyakGrid().

_npoints

std::vector<std::size_t> PolynomialQuadrature::SmolyakGrid::_npoints

private

Cumulative number of points for each quadrature product.

Definition at line 198 of file PolynomialQuadrature.h.

Referenced by gridIndex(), nPoints(), quadraturePoint(), quadraturePoint(), quadratureWeight(), and SmolyakGrid().

_quad

std::vector<std::unique_ptr<const StochasticTools::WeightedCartesianProduct<Real, Real> > > PolynomialQuadrature::SmolyakGrid::_quad

private

Container for all the combinations of quadrature products.

Definition at line 202 of file PolynomialQuadrature.h.

Referenced by quadraturePoint(), quadraturePoint(), quadratureWeight(), and SmolyakGrid().

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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