MomentBasedGaussianPolynomial< mp_real > Class Template Reference

#include <ql/math/integrals/momentbasedgaussianpolynomial.hpp>

Inheritance diagram for MomentBasedGaussianPolynomial< mp_real >:

Collaboration diagram for MomentBasedGaussianPolynomial< mp_real >:

Public Member Functions
	MomentBasedGaussianPolynomial ()
Real	mu_0 () const override
Real	alpha (Size i) const override
Real	beta (Size i) const override
virtual mp_real	moment (Size i) const =0
Real	alpha (Size u) const
Real	beta (Size u) const
Real	mu_0 () const
Public Member Functions inherited from GaussianOrthogonalPolynomial
virtual	~GaussianOrthogonalPolynomial ()=default
virtual Real	mu_0 () const =0
virtual Real	alpha (Size i) const =0
virtual Real	beta (Size i) const =0
virtual Real	w (Real x) const =0
Real	value (Size i, Real x) const
Real	weightedValue (Size i, Real x) const

Private Member Functions
mp_real	alpha_ (Size i) const
mp_real	beta_ (Size i) const
mp_real	z (Integer k, Integer i) const

Private Attributes
std::vector< mp_real >	b_
std::vector< mp_real >	c_
std::vector< std::vector< mp_real > >	z_

Detailed Description

template<class mp_real>
class QuantLib::MomentBasedGaussianPolynomial< mp_real >

References: Gauss quadratures and orthogonal polynomials

G.H. Gloub and J.H. Welsch: Calculation of Gauss quadrature rule. Math. Comput. 23 (1986), 221-230, http://web.stanford.edu/class/cme335/spr11/S0025-5718-69-99647-1.pdf

M. Morandi Cecchi and M. Redivo Zaglia, Computing the coefficients of a recurrence formula for numerical integration by moments and modified moments. http://ac.els-cdn.com/0377042793901522/1-s2.0-0377042793901522-main.pdf?_tid=643d5dca-a05d-11e6-9a56-00000aab0f27&acdnat=1478023545_cf7c87cba4cc9e37a136e68a2564d411

Definition at line 48 of file momentbasedgaussianpolynomial.hpp.

Constructor & Destructor Documentation

MomentBasedGaussianPolynomial()

MomentBasedGaussianPolynomial

Definition at line 70 of file momentbasedgaussianpolynomial.hpp.

Member Function Documentation

mu_0() [1/2]

Real mu_0

overridevirtual

Implements GaussianOrthogonalPolynomial.

Definition at line 167 of file momentbasedgaussianpolynomial.hpp.

alpha() [1/2]

Real alpha ( Size  i ) const

overridevirtual

Implements GaussianOrthogonalPolynomial.

Definition at line 143 of file momentbasedgaussianpolynomial.hpp.

beta() [1/2]

Real beta ( Size  i ) const

overridevirtual

Implements GaussianOrthogonalPolynomial.

Definition at line 153 of file momentbasedgaussianpolynomial.hpp.

moment()

virtual mp_real moment ( Size  i ) const

pure virtual

Implemented in GaussNonCentralChiSquaredPolynomial, GaussLaguerreCosinePolynomial< mp_real >, and GaussLaguerreSinePolynomial< mp_real >.

alpha_()

mp_real alpha_ ( Size  i ) const

private

Definition at line 103 of file momentbasedgaussianpolynomial.hpp.

beta_()

mp_real beta_ ( Size  i ) const

private

Definition at line 122 of file momentbasedgaussianpolynomial.hpp.

z()

mp_real z ( Integer  k, Integer  i  ) const

private

Definition at line 74 of file momentbasedgaussianpolynomial.hpp.

alpha() [2/2]

Real alpha ( Size  u ) const

virtual

Implements GaussianOrthogonalPolynomial.

Definition at line 138 of file momentbasedgaussianpolynomial.hpp.

beta() [2/2]

Real beta ( Size  u ) const

virtual

Implements GaussianOrthogonalPolynomial.

Definition at line 148 of file momentbasedgaussianpolynomial.hpp.

mu_0() [2/2]

Real mu_0 ( ) const

virtual

Implements GaussianOrthogonalPolynomial.

Definition at line 159 of file momentbasedgaussianpolynomial.hpp.

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Member Data Documentation

b_

std::vector<mp_real> b_

mutableprivate

Definition at line 65 of file momentbasedgaussianpolynomial.hpp.

c_

std::vector<mp_real> c_

private

Definition at line 65 of file momentbasedgaussianpolynomial.hpp.

z_

std::vector<std::vector<mp_real> > z_

mutableprivate

Definition at line 66 of file momentbasedgaussianpolynomial.hpp.