#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "Polylib.h"
#include <float.h>
#include <complex>
#include <LibUtilities/BasicConst/NektarUnivTypeDefs.hpp>

Include dependency graph for Polylib.cpp:

Namespaces
	Polylib
	The namespace associated with the the Polylib library (Polylib introduction)

Macros
#define	STOP 30
	Maximum number of iterations in polynomial defalation routine Jacobz. More...

#define	EPS 100*DBL_EPSILON
	Precision tolerance for two points to be similar. More...

#define	sign(a, b) ((b)<0 ? -fabs(a) : fabs(a))
	return the sign(b)*a More...

#define	POLYNOMIAL_DEFLATION 0
	Define whether to use polynomial deflation (1) or tridiagonal solver (0). More...

#define	jacobz(n, z, alpha, beta) Jacobz(n,z,alpha,beta)
	zero determination using Newton iteration with polynomial deflation More...

Functions
double	Polylib::optdiff (double xl, double xr)
	The following function is used to circumvent/reduce "Subtractive Cancellation" The expression 1/dz is replaced by optinvsub(.,.) Added on 26 April 2017. More...

double	Polylib::laginterp (double z, int j, const double *zj, int np)

static void	Polylib::Jacobz (const int n, double *z, const double alpha, const double beta)
	Calculate the n zeros, z, of the Jacobi polynomial, i.e. More...

static void	Polylib::TriQL (const int n, double d, double e, double **z)
	QL algorithm for symmetric tridiagonal matrix. More...

double	Polylib::gammaF (const double x)
	Calculate the Gamma function , $\Gamma(n)$ , for integer. More...

static void	Polylib::RecCoeff (const int n, double a, double b, const double alpha, const double beta)
	The routine finds the recurrence coefficients a and. More...

void	Polylib::JKMatrix (int n, double a, double b)
	Calcualtes the Jacobi-kronrod matrix by determining the. More...

void	Polylib::chri1 (int n, double a, double b, double a0, double b0, double z)
	Given a weight function through the first n+1. More...

void	Polylib::zwgj (double z, double w, const int np, const double alpha, const double beta)
	Gauss-Jacobi zeros and weights. More...

void	Polylib::zwgrjm (double z, double w, const int np, const double alpha, const double beta)
	Gauss-Radau-Jacobi zeros and weights with end point at z=-1. More...

void	Polylib::zwgrjp (double z, double w, const int np, const double alpha, const double beta)
	Gauss-Radau-Jacobi zeros and weights with end point at z=1. More...

void	Polylib::zwglj (double z, double w, const int np, const double alpha, const double beta)
	Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1. More...

void	Polylib::zwgk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Kronrod-Jacobi zeros and weights. More...

void	Polylib::zwrk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Radau-Kronrod-Jacobi zeros and weights. More...

void	Polylib::zwlk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Lobatto-Kronrod-Jacobi zeros and weights. More...

void	Polylib::Dgj (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix and its transpose associated. More...

void	Polylib::Dgrjm (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix and its transpose associated. More...

void	Polylib::Dgrjp (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix associated with the. More...

void	Polylib::Dglj (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix associated with the. More...

double	Polylib::hgj (const int i, const double z, const double *zgj, const int np, const double alpha, const double beta)
	Compute the value of the i th Lagrangian interpolant through. More...

double	Polylib::hgrjm (const int i, const double z, const double *zgrj, const int np, const double alpha, const double beta)
	Compute the value of the i th Lagrangian interpolant through the. More...

double	Polylib::hgrjp (const int i, const double z, const double *zgrj, const int np, const double alpha, const double beta)
	Compute the value of the i th Lagrangian interpolant through the. More...

double	Polylib::hglj (const int i, const double z, const double *zglj, const int np, const double alpha, const double beta)
	Compute the value of the i th Lagrangian interpolant through the. More...

void	Polylib::Imgj (double im, const double zgj, const double *zm, const int nz, const int mz, const double alpha, const double beta)
	Interpolation Operator from Gauss-Jacobi points to an. More...

void	Polylib::Imgrjm (double im, const double zgrj, const double *zm, const int nz, const int mz, const double alpha, const double beta)
	Interpolation Operator from Gauss-Radau-Jacobi points. More...

void	Polylib::Imgrjp (double im, const double zgrj, const double *zm, const int nz, const int mz, const double alpha, const double beta)
	Interpolation Operator from Gauss-Radau-Jacobi points. More...

void	Polylib::Imglj (double im, const double zglj, const double *zm, const int nz, const int mz, const double alpha, const double beta)
	Interpolation Operator from Gauss-Lobatto-Jacobi points. More...

void	Polylib::jacobfd (const int np, const double z, double poly_in, double *polyd, const int n, const double alpha, const double beta)
	Routine to calculate Jacobi polynomials, $P^{\alpha,\beta}_n(z)$ , and their first derivative, $\frac{d}{dz} P^{\alpha,\beta}_n(z)$ . More...

void	Polylib::jacobd (const int np, const double z, double polyd, const int n, const double alpha, const double beta)
	Calculate the derivative of Jacobi polynomials. More...

void	Polylib::JacZeros (const int n, double a, double b, const double alpha, const double beta)
	Zero and Weight determination through the eigenvalues and eigenvectors of a tridiagonal. More...

std::complex< Nektar::NekDouble >	Polylib::ImagBesselComp (int n, std::complex< Nektar::NekDouble > y)
	Calcualte the bessel function of the first kind with complex double input y. Taken from Numerical Recipies in C. More...