Laguerre::ModifiedLaguerre18< T > Class Template Reference

#include <Laguerre18m.h>

Inheritance diagram for Laguerre::ModifiedLaguerre18< T >:

Public Member Functions
	ModifiedLaguerre18 ()
void	operator() (std::vector< T > &poly, std::vector< std::complex< T > > &roots, std::vector< int > &conv, int itmax) override
	Find the roots of a polynomial using Laguerre's method.

Private Member Functions
T	cross (std::vector< int > &h, std::vector< T > &a, int c, int i)
	Calculate the determinant between two points.
void	conv_hull (int n, std::vector< T > &a, std::vector< int > &h, int &c)
	Calculate the convex hull of a set of points. Dont forget to calculate Andrews alghoritm to vector a!
void	estimates (vector< T > &alpha, int deg, std::vector< std::complex< T > > &roots, std::vector< int > &conv, int &nz)
	Estimate roots of a polynomial.
void	rcheck_lag (std::vector< T > &p, vector< T > &alpha, int deg, complex< T > &b, complex< T > &c, complex< T > z, T r, int &conv, T &berr, T &cond)
	Perform Laguerre correction, compute backward error, and condition.
void	check_lag (std::vector< T > &p, std::vector< T > &alpha, int deg, std::complex< T > &b, std::complex< T > &c, std::complex< T > z, T r, int &conv, T &berr, T &cond)
	Perform Laguerre correction, compute backward error, and condition.
void	modify_lag (int deg, std::complex< T > &b, std::complex< T > &c, std::complex< T > z, int j, std::vector< std::complex< T > > &roots)
	Modify Laguerre correction based on Aberth's method.

Static Private Attributes
static constexpr T	eps = std::numeric_limits<T>::epsilon()
static constexpr T	big = std::numeric_limits<T>::max()
static constexpr T	small = std::numeric_limits<T>::min()
static constexpr T	PI = std::numbers::pi_v<T>
static constexpr T	pi2 = PI*static_cast<T>(2)

Constructor & Destructor Documentation

ModifiedLaguerre18()

template<typename T >

Laguerre::ModifiedLaguerre18< T >::ModifiedLaguerre18 ( )

inline

Member Function Documentation

check_lag()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::check_lag ( std::vector< T > & p, std::vector< T > & alpha, int deg, std::complex< T > & b, std::complex< T > & c, std::complex< T > z, T r, int & conv, T & berr, T & cond )

inlineprivate

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.

conv_hull()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::conv_hull ( int n, std::vector< T > & a, std::vector< int > & h, int & c )

inlineprivate

Calculate the convex hull of a set of points. Dont forget to calculate Andrews alghoritm to vector a!

Parameters

n	Number of points.
a	Vector of templated type T representing points coordinates.
h	Vector to store the convex hull.
c	Number of points in the convex hull.

cross()

template<typename T >

T Laguerre::ModifiedLaguerre18< T >::cross ( std::vector< int > & h, std::vector< T > & a, int c, int i )

inlineprivate

Calculate the determinant between two points.

Parameters

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

Returns

T Determinant between two points.

estimates()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::estimates ( vector< T > & alpha, int deg, std::vector< std::complex< T > > & roots, std::vector< int > & conv, int & nz )

inlineprivate

Estimate roots of a polynomial.

Parameters

alpha	Polynomial object.
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.

modify_lag()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::modify_lag ( int deg, std::complex< T > & b, std::complex< T > & c, std::complex< T > z, int j, std::vector< std::complex< T > > & roots )

inlineprivate

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.

operator()()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::operator() ( std::vector< T > & poly, std::vector< std::complex< T > > & roots, std::vector< int > & conv, int itmax )

inlineoverridevirtual

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

Parameters

poly	Polynomial object.
roots	Vector to store the roots.
conv	Vector to store convergence status of each root.
itmax	Maximum number of iterations.

Implements BaseSolver< T >.

rcheck_lag()

template<typename T >

void Laguerre::ModifiedLaguerre18< T >::rcheck_lag ( std::vector< T > & p, vector< T > & alpha, int deg, complex< T > & b, complex< T > & c, complex< T > z, T r, int & conv, T & berr, T & cond )

inlineprivate

Perform Laguerre correction, compute backward error, and condition.

Parameters

p	Polynomial object.
alpha	Vector of coefficients.
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.

Member Data Documentation

big

template<typename T >

constexpr T Laguerre::ModifiedLaguerre18< T >::big = std::numeric_limits<T>::max()

staticconstexprprivate

eps

template<typename T >

constexpr T Laguerre::ModifiedLaguerre18< T >::eps = std::numeric_limits<T>::epsilon()

staticconstexprprivate

PI

template<typename T >

constexpr T Laguerre::ModifiedLaguerre18< T >::PI = std::numbers::pi_v<T>

staticconstexprprivate

pi2

template<typename T >

constexpr T Laguerre::ModifiedLaguerre18< T >::pi2 = PI*static_cast<T>(2)

staticconstexprprivate

small

template<typename T >

constexpr T Laguerre::ModifiedLaguerre18< T >::small = std::numeric_limits<T>::min()

staticconstexprprivate

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The documentation for this class was generated from the following file:

• headers/Laguerre18m.h