GaussianInt Class Reference

Defines the integral of the normal probability density function by. More...

#include <gaussian_int.h>

Inheritance diagram for GaussianInt:

Collaboration diagram for GaussianInt:

Public Member Functions
	GaussianInt (double mu_, double sigma_)
	Sets the default for the parameter mu to 0.0 and for the parameter sigma to 1.0.
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	mu
double	sigma

Detailed Description

Defines the integral of the normal probability density function by.

\[ f: \lambda \mapsto \frac{1}{2} \operatorname{erf} \left(\frac{x}{\sqrt{2}} \right), \]

where

\[ x = \frac{\lambda - \mu}{\sigma}, \]

and \( \mu \) and \( \sigma \) parameters are the mean and standard deviation of the Gaussian function and should be set by this->mu and this->sigma members, respectively. This function essentialy defines the cumulative distribution function of the normal distribution.

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 53 of file gaussian_int.h.

Constructor & Destructor Documentation

GaussianInt()

GaussianInt::GaussianInt	(	double	mu_,
		double	sigma_
	)

Sets the default for the parameter mu to 0.0 and for the parameter sigma to 1.0.

Definition at line 34 of file gaussian_int.cpp.

{
    this->mu = mu_;
    this->sigma = sigma_;
}

References mu, and sigma.

Member Function Documentation

function() [1/3]

double GaussianInt::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 71 of file gaussian_int.cpp.

{
    double x = (lambda_ - this->mu) / this->sigma;
 
    // C++11 and later
    #if __cplusplus >= 201103L
        return 0.5 * (1.0 + std::erf(x * M_SQRT1_2));
    #else
        return 0.5 * (1.0 + erf(x * M_SQRT1_2));
    #endif
}

References mu, and sigma.

function() [2/3]

float GaussianInt::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 48 of file gaussian_int.cpp.

{
    float mu_ = static_cast<float>(this->mu);
    float sigma_ = static_cast<float>(this->sigma);
    float x = (lambda_ - mu_) / sigma_;
 
    // C++11 and later
    #if __cplusplus >= 201103L
        return 0.5f * (1.0f + std::erf(x * M_SQRT1_2));
    #else
        return 0.5f * (1.0f + static_cast<float>(erf(x * M_SQRT1_2)));
    #endif
}

References mu, and sigma.

function() [3/3]

long double GaussianInt::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 92 of file gaussian_int.cpp.

{
    long double mu_ = static_cast<long double>(this->mu);
    long double sigma_ = static_cast<long double>(this->sigma);
    long double x = (lambda_ - mu_) / sigma_;
 
    // C++11 and later
    #if __cplusplus >= 201103L
        return 0.5l * (1.0l + std::erf(x * M_SQRT1_2));
    #else
        return 0.5l * (1.0l + static_cast<long double>(erf(x * M_SQRT1_2)));
    #endif
}

References mu, and sigma.

Member Data Documentation

mu

double GaussianInt::mu

Definition at line 60 of file gaussian_int.h.

Referenced by function(), function(), function(), and GaussianInt().

sigma

double GaussianInt::sigma

Definition at line 61 of file gaussian_int.h.

Referenced by function(), function(), function(), and GaussianInt().

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

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