Normal distributions use Hermite polynomials. More...
#include <PolynomialQuadrature.h>
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! More... | |
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}. More... | |
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) More... | |
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 |
Normal distributions use Hermite polynomials.
Definition at line 96 of file PolynomialQuadrature.h.
Definition at line 240 of file PolynomialQuadrature.C.
|
virtualinherited |
Reimplemented in PolynomialQuadrature::Legendre.
Definition at line 81 of file PolynomialQuadrature.C.
|
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.
|
overridevirtual |
Compute derivative of Hermite polynomial P'n = nP{n-1}.
Reimplemented from PolynomialQuadrature::Polynomial.
Definition at line 275 of file PolynomialQuadrature.C.
|
overridevirtual |
Gauss-Hermite quadrature: sum(weights) = sqrt(2)
Implements PolynomialQuadrature::Polynomial.
Definition at line 289 of file PolynomialQuadrature.C.
Implements PolynomialQuadrature::Polynomial.
Definition at line 243 of file PolynomialQuadrature.C.
Referenced by compute().
|
inherited |
Definition at line 89 of file PolynomialQuadrature.C.
|
overridevirtual |
Reimplemented from PolynomialQuadrature::Polynomial.
Definition at line 249 of file PolynomialQuadrature.C.
|
overridevirtual |
Reimplemented from PolynomialQuadrature::Polynomial.
Definition at line 258 of file PolynomialQuadrature.C.
|
private |
Definition at line 119 of file PolynomialQuadrature.h.
Referenced by compute(), computeDerivative(), gaussQuadrature(), and store().
|
private |
Definition at line 120 of file PolynomialQuadrature.h.
Referenced by compute(), computeDerivative(), gaussQuadrature(), and store().