orthogonal.h File Reference

Orthogonal polynomial bases. More...

#include "./polynomial.h"
#include "../optimization/roots.h"
#include <functional>

Go to the source code of this file.

Namespaces
namespace	theoretica
	Main namespace of the library which contains all functions and objects.

Typedefs
using	theoretica::polyn_recurr_formula = std::function< polynomial< real >(polynomial< real >, polynomial< real >, unsigned int)>
	Polynomial sequence recurrence formula type Used for computing orthogonal polynomial basis elements.

Functions
polynomial< real >	theoretica::gen_polyn_recurr (polynomial< real > P0, polynomial< real > P1, polyn_recurr_formula f, unsigned int n)
	Generate a polynomial basis using a recursion formula.
polynomial< real >	theoretica::legendre_polyn_recurr (polynomial< real > P0, polynomial< real > P1, unsigned int l)
	Recursion formula for Legendre polynomials.
polynomial< real >	theoretica::legendre_polynomial (unsigned int n)
	Compute the nth Legendre polynomial.
real	theoretica::legendre_polyn_normalization (unsigned int n)
	Normalization constant for the nth Legendre polynomial.
polynomial< real >	theoretica::laguerre_polyn_recurr (polynomial< real > L0, polynomial< real > L1, unsigned int i)
	Recursion formula for Laguerre polynomials.
polynomial< real >	theoretica::laguerre_polynomial (unsigned int n)
	Compute the nth Laguerre polynomial.
polynomial< real >	theoretica::general_laguerre_polyn_recurr (polynomial< real > L0, polynomial< real > L1, real alpha, unsigned int i)
	Recursion formula for Generalized Laguerre polynomials.
polynomial< real >	theoretica::general_laguerre_polynomial (real alpha, unsigned int n)
	Compute the nth Laguerre polynomial.
polynomial< real >	theoretica::hermite_polyn_recurr (polynomial< real > H0, polynomial< real > H1, unsigned int i)
	Recursion formula for Hermite polynomials.
polynomial< real >	theoretica::hermite_polynomial (unsigned int n)
	Compute the nth Hermite polynomial.
real	theoretica::hermite_polyn_normalization (unsigned int n)
	Normalization constant for the nth Hermite polynomial.
polynomial< real >	theoretica::chebyshev_polyn_recurr (polynomial< real > T0, polynomial< real > T1, unsigned int i)
	Recursion formula for Chebyshev polynomials The formula is the same for first and second kind polynomials.
polynomial< real >	theoretica::chebyshev1_polynomial (unsigned int n)
	Compute the nth Chebyshev polynomial of the first kind.
polynomial< real >	theoretica::chebyshev2_polynomial (unsigned int n)
	Compute the nth Chebyshev polynomial of the second kind.
std::vector< real >	theoretica::legendre_roots (unsigned int n)
	Roots of the n-th Legendre polynomial.
std::vector< real >	theoretica::legendre_weights (const std::vector< real > &roots)
	Legendre weights for Gauss-Legendre quadrature of n-th order.
std::vector< real >	theoretica::laguerre_weights (const std::vector< real > &roots)
	Laguerre weights for Gauss-Laguerre quadrature of n-th order.
std::vector< real >	theoretica::hermite_weights (const std::vector< real > &roots)
	Hermite weights for Gauss-Hermite quadrature of n-th order.

Detailed Description

Orthogonal polynomial bases.