Defines the function \( f: \lambda \mapsto \frac{a \lambda + b}{ c \lambda + d} \). More...

#include <homographic.h>

Inheritance diagram for Homographic:

Collaboration diagram for Homographic:

Public Member Functions
	Homographic (double a_, double b_, double c_, double d_)
	Sets the default for the parameter `a`, `b`, `c`, and `d`.

virtual float	function (const float lambda_) const

virtual double	function (const double lambda_) const

virtual long double	function (const long double lambda_) const

Public Member Functions inherited from Function
virtual	~Function ()
	Default virtual destructor.

Public Attributes
double	a

double	b

double	c

double	d

Detailed Description

Defines the function \( f: \lambda \mapsto \frac{a \lambda + b}{ c \lambda + d} \).

The matrix function \( f: \mathbb{R}^{n \times n} \to \mathbb{R}^{n \times n} \) is used in

\[ \mathrm{trace} \left( f(\mathbf{A}) \right). \]

However, instead of a matrix function, the equivalent scalar function \( f: \mathbb{R} \to \mathbb{R} \) is defiend which acts on the eigenvalues of the matrix.

Definition at line 41 of file homographic.h.

Constructor & Destructor Documentation

◆ Homographic()

Homographic::Homographic	(	double	a_,
		double	b_,
		double	c_,
		double	d_
	)

Sets the default for the parameter a, b, c, and d.

Definition at line 26 of file homographic.cpp.

{
    this->a = a_;
    this->b = b_;
    this->c = c_;
    this->d = d_;
}

References a, b, c, and d.

Member Function Documentation

◆ function() [1/3]

double Homographic::function ( const double lambda_ ) const

virtual

Parameters

[in] lambda_ Eigenvalue (or singular value) of matrix.

Returns: The value of matrix function for the given eigenvalue.

Implements Function.

Definition at line 63 of file homographic.cpp.

{
    // Casting
    double a_ = static_cast<double>(this->a);
    double b_ = static_cast<double>(this->b);
    double c_ = static_cast<double>(this->c);
    double d_ = static_cast<double>(this->d);
 
    return (a_ * lambda_ + b_) / (c_ * lambda_ + d_);
}

References a, b, c, and d.

◆ function() [2/3]

float Homographic::function ( const float lambda_ ) const

virtual

Parameters

[in] lambda_ Eigenvalue (or singular value) of matrix.

Returns: The value of matrix function for the given eigenvalue.

Implements Function.

Definition at line 43 of file homographic.cpp.

{
    // Casting
    float a_ = static_cast<float>(this->a);
    float b_ = static_cast<float>(this->b);
    float c_ = static_cast<float>(this->c);
    float d_ = static_cast<float>(this->d);
 
    return (a_ * lambda_ + b_) / (c_ * lambda_ + d_);
}

References a, b, c, and d.

◆ function() [3/3]

long double Homographic::function ( const long double lambda_ ) const

virtual

Parameters

[in] lambda_ Eigenvalue (or singular value) of matrix.

Returns: The value of matrix function for the given eigenvalue.

Implements Function.

Definition at line 83 of file homographic.cpp.

{
    // Casting
    long double a_ = static_cast<long double>(this->a);
    long double b_ = static_cast<long double>(this->b);
    long double c_ = static_cast<long double>(this->c);
    long double d_ = static_cast<long double>(this->d);
 
    return (a_ * lambda_ + b_) / (c_ * lambda_ + d_);
}