PolynomialQuadrature::Hermite Class Reference

Normal distributions use Hermite polynomials. More...

#include <PolynomialQuadrature.h>

Inheritance diagram for PolynomialQuadrature::Hermite:

Public Member Functions
	Hermite (const Real mu, const Real sig)
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
	Hermite polynomial using static function then scales by <P_n^2> = n!
virtual Real	computeDerivative (const unsigned int order, const Real x, const unsigned int m=1) const override
	Compute derivative of Hermite polynomial P'n = nP{n-1}.
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-Hermite quadrature: sum(weights) = sqrt(2\pi)
virtual void	clenshawQuadrature (const unsigned int order, std::vector< Real > &points, std::vector< Real > &weights) const
Real	productIntegral (const std::vector< unsigned int > order) const

Private Attributes
const Real	_mu
const Real	_sig

Detailed Description

Normal distributions use Hermite polynomials.

Definition at line 96 of file PolynomialQuadrature.h.

Constructor & Destructor Documentation

Hermite()

PolynomialQuadrature::Hermite::Hermite	(	const Real	mu,
		const Real	sig
	)

Definition at line 240 of file PolynomialQuadrature.C.

: Polynomial(), _mu(mu), _sig(sig) {}

Member Function Documentation

clenshawQuadrature()

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

virtualinherited

Reimplemented in PolynomialQuadrature::Legendre.

Definition at line 81 of file PolynomialQuadrature.C.

{
  ::mooseError("Clenshaw quadrature has not been implemented for this polynomial type.");
}

compute()

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

overridevirtual

Hermite polynomial using static function then scales by <P_n^2> = n!

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 266 of file PolynomialQuadrature.C.

{
  Real val = hermite(order, x, _mu, _sig);
  if (normalize)
    val /= innerProduct(order);
  return val;
}

computeDerivative()

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

overridevirtual

Compute derivative of Hermite polynomial P'n = nP{n-1}.

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 275 of file PolynomialQuadrature.C.

{
  if (m > order)
    return 0.0;
 
  Real xref = (x - _mu) / _sig;
  Real val = hermite(order - m, xref);
  for (unsigned int i = 0; i < m; ++i)
    val *= static_cast<Real>(order - i) / _sig;
 
  return val;
}

gaussQuadrature()

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

overridevirtual

Gauss-Hermite quadrature: sum(weights) = sqrt(2\pi)

Implements PolynomialQuadrature::Polynomial.

Definition at line 289 of file PolynomialQuadrature.C.

{
  gauss_hermite(order, points, weights, _mu, _sig);
}

innerProduct()

Real PolynomialQuadrature::Hermite::innerProduct ( const unsigned int  order ) const

overridevirtual

Implements PolynomialQuadrature::Polynomial.

Definition at line 243 of file PolynomialQuadrature.C.

{
  return (Real)Utility::factorial(order);
}

Referenced by compute().

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 PolynomialQuadrature::Hermite::store ( nlohmann::json &  json ) const

overridevirtual

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 258 of file PolynomialQuadrature.C.

{
  json["type"] = "Hermite";
  json["mu"] = _mu;
  json["sig"] = _sig;
}

store() [2/2]

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

overridevirtual

Reimplemented from PolynomialQuadrature::Polynomial.

Definition at line 249 of file PolynomialQuadrature.C.

{
  std::string type = "Hermite";
  dataStore(stream, type, context);
  dataStore(stream, _mu, context);
  dataStore(stream, _sig, context);
}

Member Data Documentation

_mu

const Real PolynomialQuadrature::Hermite::_mu

private

Definition at line 119 of file PolynomialQuadrature.h.

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

_sig

const Real PolynomialQuadrature::Hermite::_sig

private

Definition at line 120 of file PolynomialQuadrature.h.

Referenced by compute(), computeDerivative(), gaussQuadrature(), store(), 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