PolynomialQuadrature::Legendre Class Reference

Uniform distributions use Legendre polynomials. More...

#include <PolynomialQuadrature.h>

Inheritance diagram for PolynomialQuadrature::Legendre:

Public Member Functions
	Legendre (const Real lower_bound, const Real upper_bound)
virtual void	store (std::ostream &stream, void *context) const override
virtual void	store (nlohmann::json &json) const override
virtual Real	compute (const unsigned int order, const Real x, const bool normalize=true) const override
	Legendre polynomial using static function then scales by <P_n^2> = 1 / (2n+1) More...
virtual Real	computeDerivative (const unsigned int order, const Real x, const unsigned int m=1) const override
	Compute derivative of Legendre polynomial Recursive algorithm: d^m/dx^m P_n = (n + m - 1)d^(m-1)/dx^(m-1) P_{n-1} + xd^m/dx^m P_{n-1}. More...
Real	computeDerivativeRef (const unsigned int order, const Real x, const unsigned int m=1) const
virtual Real	innerProduct (const unsigned int order) const override
virtual void	gaussQuadrature (const unsigned int order, std::vector< Real > &points, std::vector< Real > &weights) const override
	Gauss-Legendre quadrature: sum(weights) = 2. More...
virtual void	clenshawQuadrature (const unsigned int order, std::vector< Real > &points, std::vector< Real > &weights) const override
	Just normal Clenshaw Curtis with shifted points. More...
Real	productIntegral (const std::vector< unsigned int > order) const

Private Attributes
const Real	_lower_bound
const Real	_upper_bound

Detailed Description

Uniform distributions use Legendre polynomials.

Definition at line 58 of file PolynomialQuadrature.h.

Constructor & Destructor Documentation

Legendre()

Legendre::Legendre	(	const Real	lower_bound,
		const Real	upper_bound
	)

Definition at line 117 of file PolynomialQuadrature.C.

  : Polynomial(), _lower_bound(lower_bound), _upper_bound(upper_bound)
{
}

Member Function Documentation

clenshawQuadrature()

void Legendre::clenshawQuadrature ( const unsigned int  order, std::vector< Real > &  points, std::vector< Real > &  weights  ) const

overridevirtual

Just normal Clenshaw Curtis with shifted points.

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 188 of file PolynomialQuadrature.C.

{
  clenshaw_curtis(order, points, weights);
  Real dx = (_upper_bound - _lower_bound) / 2.0;
  Real xav = (_upper_bound + _lower_bound) / 2.0;
  for (unsigned int i = 0; i < points.size(); ++i)
    points[i] = points[i] * dx + xav;
}

compute()

Real Legendre::compute ( const unsigned int  order, const Real  x, const bool  normalize = true  ) const

overridevirtual

Legendre polynomial using static function then scales by <P_n^2> = 1 / (2n+1)

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 140 of file PolynomialQuadrature.C.

{
  if ((x < _lower_bound) || (x > _upper_bound))
    ::mooseError("The requested polynomial point is outside of distribution bounds.");

  Real val = legendre(order, x, _lower_bound, _upper_bound);
  if (normalize)
    val /= innerProduct(order);

  return val;
}

computeDerivative()

Real Legendre::computeDerivative ( const unsigned int  order, const Real  x, const unsigned int  m = 1  ) const

overridevirtual

Compute derivative of Legendre polynomial Recursive algorithm: d^m/dx^m P_n = (n + m - 1)d^(m-1)/dx^(m-1) P_{n-1} + xd^m/dx^m P_{n-1}.

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 153 of file PolynomialQuadrature.C.

{
  if ((x < _lower_bound) || (x > _upper_bound))
    ::mooseError("The requested polynomial point is outside of distribution bounds.");

  Real xref = 2.0 / (_upper_bound - _lower_bound) * (x - (_upper_bound + _lower_bound) / 2.0);
  Real Jac = pow(2.0 / (_upper_bound - _lower_bound), m);
  return Jac * computeDerivativeRef(order, xref, m);
}

computeDerivativeRef()

Real Legendre::computeDerivativeRef	(	const unsigned int	order,
		const Real	x,
		const unsigned int	m = 1
	)		const

Definition at line 164 of file PolynomialQuadrature.C.

Referenced by computeDerivative().

{
  if (m == 0)
    return legendre(order, xref);
  else if (m > order)
    return 0.0;
  else if (order == 1)
    return 1.0;
  else
    return static_cast<Real>(order + m - 1) * computeDerivativeRef(order - 1, xref, m - 1) +
           xref * computeDerivativeRef(order - 1, xref, m);
}

gaussQuadrature()

void Legendre::gaussQuadrature ( const unsigned int  order, std::vector< Real > &  points, std::vector< Real > &  weights  ) const

overridevirtual

Gauss-Legendre quadrature: sum(weights) = 2.

Implements PolynomialQuadrature::Polynomial.

Definition at line 180 of file PolynomialQuadrature.C.

{
  gauss_legendre(order, points, weights, _lower_bound, _upper_bound);
}

innerProduct()

Real Legendre::innerProduct ( const unsigned int  order ) const

overridevirtual

Implements PolynomialQuadrature::Polynomial.

Definition at line 200 of file PolynomialQuadrature.C.

Referenced by compute().

{
  return 1. / (2. * static_cast<Real>(order) + 1.);
}

productIntegral()

Real PolynomialQuadrature::Polynomial::productIntegral ( const std::vector< unsigned int >  order ) const

inherited

Definition at line 89 of file PolynomialQuadrature.C.

{
  const unsigned int nprod = order.size();

  if (nprod == 1)
    return (order[0] == 0 ? 1.0 : 0.0);
  else if (nprod == 2)
    return (order[0] == order[1] ? innerProduct(order[0]) : 0.0);

  unsigned int poly_order = std::accumulate(order.begin(), order.end(), 0);
  unsigned int quad_order = (poly_order % 2 == 0 ? poly_order : poly_order - 1) / 2;

  std::vector<Real> xq;
  std::vector<Real> wq;
  gaussQuadrature(quad_order, xq, wq);

  Real val = 0.0;
  for (unsigned int q = 0; q < xq.size(); ++q)
  {
    Real prod = wq[q];
    for (unsigned int i = 0; i < nprod; ++i)
      prod *= compute(order[i], xq[q], false);
    val += prod;
  }

  return val / std::accumulate(wq.begin(), wq.end(), 0.0);
}

store() [1/2]

void Legendre::store ( std::ostream &  stream, void *  context  ) const

overridevirtual

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 123 of file PolynomialQuadrature.C.

{
  std::string type = "Legendre";
  dataStore(stream, type, context);
  dataStore(stream, _lower_bound, context);
  dataStore(stream, _upper_bound, context);
}

store() [2/2]

void Legendre::store ( nlohmann::json &  json ) const

overridevirtual

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 132 of file PolynomialQuadrature.C.

{
  json["type"] = "Legendre";
  json["lower_bound"] = _lower_bound;
  json["upper_bound"] = _upper_bound;
}

Member Data Documentation

_lower_bound

const Real PolynomialQuadrature::Legendre::_lower_bound

private

Definition at line 89 of file PolynomialQuadrature.h.

Referenced by clenshawQuadrature(), compute(), computeDerivative(), gaussQuadrature(), and store().

_upper_bound

const Real PolynomialQuadrature::Legendre::_upper_bound

private

Definition at line 90 of file PolynomialQuadrature.h.

Referenced by clenshawQuadrature(), compute(), computeDerivative(), gaussQuadrature(), and store().

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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