SmoothStep Class Reference

Defines the function. More...

#include <smoothstep.h>

Inheritance diagram for SmoothStep:

Collaboration diagram for SmoothStep:

Public Member Functions
	SmoothStep (double alpha_)
	Sets the default for the parameter alpha to 1.0. More...
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. More...

Public Attributes
double	alpha

Detailed Description

Defines the function.

\[ f: \lambda \mapsto \frac{1}{2} \left( 1 + \mathrm{tanh}(\alpha \lambda) \right) \]

where \( \alpha \) is a scale parameter and should be set by this->alpha member.

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.

Note

The smooth step function defined here should not be confused with a conventionally used function of the same name using cubic polynomial.

Definition at line 50 of file smoothstep.h.

Constructor & Destructor Documentation

SmoothStep()

SmoothStep::SmoothStep

(

double

alpha_

)

Sets the default for the parameter alpha to 1.0.

Definition at line 27 of file smoothstep.cpp.

{
    this->alpha = alpha_;
}

References alpha.

Member Function Documentation

function() [1/3]

double SmoothStep::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 55 of file smoothstep.cpp.

{
    return 0.5 * (1.0 + tanh(this->alpha * lambda_));
}

References alpha.

function() [2/3]

float SmoothStep::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 41 of file smoothstep.cpp.

{
    return 0.5 * (1.0 + tanh(static_cast<float>(this->alpha) * lambda_));
}

References alpha.

function() [3/3]

long double SmoothStep::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 69 of file smoothstep.cpp.

{
    return 0.5 * (1.0 + tanh(static_cast<long double>(this->alpha) * lambda_));
}

References alpha.

Member Data Documentation

alpha

double SmoothStep::alpha

Definition at line 57 of file smoothstep.h.

Referenced by function(), and SmoothStep().

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

• /home/runner/work/imate/imate/imate/functions/smoothstep.h
• /home/runner/work/imate/imate/imate/functions/smoothstep.cpp