#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "Polylib.h"
#include <float.h>

Include dependency graph for Polylib.cpp:

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

Macros
#define	STOP 30
	Maximum number of iterations in polynomial defalation routine Jacobz.
#define	EPS 100*DBL_EPSILON
	Precision tolerance for two points to be similar.
#define	sign(a, b) ((b)<0 ? -fabs(a) : fabs(a))
	return the sign(b)*a
#define	POLYNOMIAL_DEFLATION 0
	Define whether to use polynomial deflation (1) or tridiagonal solver (0).
#define	jacobz(n, z, alpha, beta) Jacobz(n,z,alpha,beta)
	zero determination using Newton iteration with polynomial deflation

Functions
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.
static void	Polylib::TriQL (const int n, double d, double e, double **z)
	QL algorithm for symmetric tridiagonal matrix.
double	Polylib::gammaF (const double x)
	Calculate the Gamma function , $\Gamma(n)$ , for integer.
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.
void	Polylib::JKMatrix (int n, double a, double b)
	Calcualtes the Jacobi-kronrod matrix by determining the.
void	Polylib::chri1 (int n, double a, double b, double a0, double b0, double z)
	Given a weight function through the first n+1.
void	Polylib::zwgj (double z, double w, const int np, const double alpha, const double beta)
	Gauss-Jacobi zeros and weights.
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.
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.
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.
void	Polylib::zwgk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Kronrod-Jacobi zeros and weights.
void	Polylib::zwrk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Radau-Kronrod-Jacobi zeros and weights.
void	Polylib::zwlk (double z, double w, const int npt, const double alpha, const double beta)
	Gauss-Lobatto-Kronrod-Jacobi zeros and weights.
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.
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.
void	Polylib::Dgrjp (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix associated with the.
void	Polylib::Dglj (double D, const double z, const int np, const double alpha, const double beta)
	Compute the Derivative Matrix associated with the.
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.
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.
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.
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.
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.
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.
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.
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.
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, $\frac{d}{dz} P^{\alpha,\beta}_n(z)$ .
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.
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.