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Polylib.cpp File Reference
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "Polylib.h"
#include <float.h>
Include dependency graph for Polylib.cpp:

Go to the source code of this file.

## 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

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 , , 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)

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, , and their first derivative, . 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...

## Macro Definition Documentation

 #define EPS   100*DBL_EPSILON

Precision tolerance for two points to be similar.

Definition at line 18 of file Polylib.cpp.

Referenced by Polylib::hgj(), Polylib::hglj(), Polylib::hgrjm(), Polylib::hgrjp(), and Polylib::Jacobz().

 #define jacobz ( n, z, alpha, beta ) Jacobz(n,z,alpha,beta)

zero determination using Newton iteration with polynomial deflation

Definition at line 40 of file Polylib.cpp.

Referenced by Polylib::zwgj(), Polylib::zwglj(), Polylib::zwgrjm(), and Polylib::zwgrjp().

 #define POLYNOMIAL_DEFLATION   0

Define whether to use polynomial deflation (1) or tridiagonal solver (0).

Definition at line 32 of file Polylib.cpp.

 #define STOP   30

Maximum number of iterations in polynomial defalation routine Jacobz.

Definition at line 14 of file Polylib.cpp.

Referenced by Polylib::Jacobz(), and Polylib::TriQL().