Chi-Tech
Public Member Functions | Data Fields | Private Member Functions
chi_math::GolubFischer Class Reference

#include <GolubFischer.h>

Public Member Functions

AnglePairs & GetDiscreteScatAngles (Tvecdbl &mell)
 

Data Fields

AnglePairs xn_wn_
 
Tvecdbl alpha_
 
Tvecdbl beta_
 

Private Member Functions

void MCA (Tvecdbl &in_mell, Tvecdbl &a, Tvecdbl &b, Tvecdbl &c)
 
void RootsOrtho (int &N, Tvecdbl &in_alpha, Tvecdbl &in_beta)
 
double dOrtho (int ell, double x, Tvecdbl &in_alpha, Tvecdbl &in_beta)
 
double Ortho (int ell, double x, Tvecdbl &in_alpha, Tvecdbl &in_beta)
 

Detailed Description

Implementation of the GolubFischer Modified ChebyShev Algorithm (MCA) to find moment-preserving angles from a set of moments computed for the expansion of an angular function in Legendre polynomials.

Supply an even amount of moments to the method GetDiscreteScatAngles and it will populate its member xn_wn which is a vector of pairs, abscissae and weights. It also return a reference to xn_wn.

alpha and beta are the recusrion coefficients of the orthogonal polynomials described in [1].

Author
John Grissom (with guidance from Jan)

Definition at line 53 of file GolubFischer.h.

Member Function Documentation

◆ dOrtho()

double chi_math::GolubFischer::dOrtho ( int  ell,
double  x,
Tvecdbl &  in_alpha,
Tvecdbl &  in_beta 
)
private

Computes the derivative of the orthogonal polynomials.

Definition at line 260 of file GolubFischer.cc.

◆ GetDiscreteScatAngles()

AnglePairs & chi_math::GolubFischer::GetDiscreteScatAngles ( Tvecdbl &  mell)

Master callable function that will return a reference to the abscissae and weights of the discrete angles.

Definition at line 10 of file GolubFischer.cc.

◆ MCA()

void chi_math::GolubFischer::MCA ( Tvecdbl &  in_mell,
Tvecdbl &  a,
Tvecdbl &  b,
Tvecdbl &  c 
)
private

Applies the Modified Chebyshev Algorithm contained in [1] to find the recursion coefficients for the orthogonal polynomials.

Definition at line 64 of file GolubFischer.cc.

◆ Ortho()

double chi_math::GolubFischer::Ortho ( int  ell,
double  x,
Tvecdbl &  in_alpha,
Tvecdbl &  in_beta 
)
private

Computes the function evaluation of the orthogonal polynomials.

Definition at line 232 of file GolubFischer.cc.

◆ RootsOrtho()

void chi_math::GolubFischer::RootsOrtho ( int &  N,
Tvecdbl &  in_alpha,
Tvecdbl &  in_beta 
)
private

Finds the roots of the orthogonal polynomial.

Definition at line 122 of file GolubFischer.cc.

Field Documentation

◆ alpha_

Tvecdbl chi_math::GolubFischer::alpha_

Definition at line 57 of file GolubFischer.h.

◆ beta_

Tvecdbl chi_math::GolubFischer::beta_

Definition at line 58 of file GolubFischer.h.

◆ xn_wn_

AnglePairs chi_math::GolubFischer::xn_wn_

Definition at line 56 of file GolubFischer.h.

The documentation for this class was generated from the following files: