L18_or.h File Reference

#include <complex>
#include <vector>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <limits>
#include "ExtendedFunctions.h"

Go to the source code of this file.

Functions
double	cross (std::vector< int > &h, std::vector< double > &a, int c, int i)
	Calculate the determinant between two points.
void	conv_hull (int n, std::vector< double > &a, std::vector< int > &h, int &c)
	Calculate the convex hull of a set of points.
void	estimates (std::vector< double > &alpha, int deg, std::vector< std::complex< double > > &roots, std::vector< int > &conv, int &nz)
	Estimate roots of a polynomial.
bool	check_nan_inf (std::complex< double > a)
	Check if a complex number contains NaN or Inf values.
void	rcheck_lag (std::vector< double > &p, std::vector< double > &alpha, int deg, std::complex< double > &b, std::complex< double > &c, std::complex< double > z, double r, int &conv, double &berr, double &cond)
	Perform Laguerre correction, compute backward error, and condition.
void	check_lag (std::vector< double > &p, std::vector< double > &alpha, int deg, std::complex< double > &b, std::complex< double > &c, std::complex< double > z, double r, int &conv, double &berr, double &cond)
	Perform Laguerre correction, compute backward error, and condition.
void	modify_lag (int deg, std::complex< double > &b, std::complex< double > &c, std::complex< double > z, int j, std::vector< std::complex< double > > &roots)
	Modify Laguerre correction based on Aberth's method.
void	laguerre (std::vector< double > &poly, int deg, std::vector< std::complex< double > > &roots, std::vector< int > &conv, int itmax)
	Find the roots of a polynomial using Laguerre's method.

Variables
const double	eps = std::numeric_limits<double>::epsilon()
const double	big = std::numeric_limits<double>::max()
const double	small = std::numeric_limits<double>::min()

Function Documentation

check_lag()

void check_lag	(	std::vector< double > &	p,
		std::vector< double > &	alpha,
		int	deg,
		std::complex< double > &	b,
		std::complex< double > &	c,
		std::complex< double >	z,
		double	r,
		int &	conv,
		double &	berr,
		double &	cond )

Perform Laguerre correction, compute backward error, and condition.

Parameters

p	Vector of polynomial coefficients.
alpha	Vector of coefficients.
deg	Degree of the polynomial.
b	Output complex number representing root.
c	Output complex number representing correction.
z	Complex number used for correction.
r	Value used for correction.
conv	Output value indicating convergence status.
berr	Output backward error.
cond	Output condition number.

check_nan_inf()

bool check_nan_inf

(

std::complex< double >

a

)

Check if a complex number contains NaN or Inf values.

Parameters

a	Complex number to check.

Returns

bool True if NaN or Inf is found, false otherwise.

conv_hull()

void conv_hull	(	int	n,
		std::vector< double > &	a,
		std::vector< int > &	h,
		int &	c )

Calculate the convex hull of a set of points.

Parameters

n	Number of points.
a	Vector of doubles representing points' coordinates.
h	Vector to store the convex hull.
c	Number of points in the convex hull.

cross()

double cross	(	std::vector< int > &	h,
		std::vector< double > &	a,
		int	c,
		int	i )

Calculate the determinant between two points.

Parameters

h	Vector of integers representing points.
a	Vector of doubles representing points' coordinates.
c	Index for the current point.
i	Index for the next point.

Returns

double Determinant between two points.

estimates()

void estimates	(	std::vector< double > &	alpha,
		int	deg,
		std::vector< std::complex< double > > &	roots,
		std::vector< int > &	conv,
		int &	nz )

Estimate roots of a polynomial.

Parameters

alpha	Vector of coefficients.
deg	Degree of the polynomial.
roots	Vector to store the estimated roots.
conv	Vector to store convergence status of each root.
nz	Number of zeros.

laguerre()

void laguerre	(	std::vector< double > &	poly,
		int	deg,
		std::vector< std::complex< double > > &	roots,
		std::vector< int > &	conv,
		int	itmax )

Find the roots of a polynomial using Laguerre's method.

Parameters

poly	Vector of polynomial coefficients.
deg	Degree of the polynomial.
roots	Vector to store the roots.
berr	Vector to store the backward errors.
cond	Vector to store the condition numbers.
conv	Vector to store convergence status of each root.
itmax	Maximum number of iterations.

modify_lag()

void modify_lag	(	int	deg,
		std::complex< double > &	b,
		std::complex< double > &	c,
		std::complex< double >	z,
		int	j,
		std::vector< std::complex< double > > &	roots )

Modify Laguerre correction based on Aberth's method.

Parameters

deg	Degree of the polynomial.
b	Complex number representing root.
c	Complex number representing correction.
z	Complex number used for correction.
j	Index of the root to modify.
roots	Vector of estimated roots.

rcheck_lag()

void rcheck_lag	(	std::vector< double > &	p,
		std::vector< double > &	alpha,
		int	deg,
		std::complex< double > &	b,
		std::complex< double > &	c,
		std::complex< double >	z,
		double	r,
		int &	conv,
		double &	berr,
		double &	cond )

Perform Laguerre correction, compute backward error, and condition.

Parameters

p	Vector of polynomial coefficients.
alpha	Vector of coefficients.
deg	Degree of the polynomial.
b	Output complex number representing root.
c	Output complex number representing correction.
z	Complex number used for correction.
r	Value used for correction.
conv	Output value indicating convergence status.
berr	Output backward error.
cond	Output condition number.

Variable Documentation

big

const double big = std::numeric_limits<double>::max()

eps

const double eps = std::numeric_limits<double>::epsilon()

small

const double small = std::numeric_limits<double>::min()