ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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pm_distEggBox Module Reference

This module contains classes and procedures for computing various statistical quantities related to the mathematical EggBox density function. More...

Data Types

interface  getEggBoxLogUDF
 Generate and return the natural logarithm of the EggBox density function at the specified input point X. More...
 

Variables

character(*, SK), parameter MODULE_NAME = "@pm_distEggBox"
 

Detailed Description

This module contains classes and procedures for computing various statistical quantities related to the mathematical EggBox density function.

The EggBox density function is frequently used in testing the efficiency of optimization and sampling algorithms.
Given a value \(x\in\mathbb{R}^n\), the EggBox function with the (intercept, location, scale, shape) parameters \((\zeta, \mu, \sigma, \alpha)\) is defined as,

\begin{equation} f(x) = \exp\left( \left[ \zeta + \prod_{i = 1}^{i = n} \cos\left(\pi\frac{x_i - \mu_i}{\sigma_i}\right)\right]^\alpha \right) ~, \end{equation}

where \(\pi\) in the right-hand-side expression is the number \(\ms{Pi}\).

Test:
test_pm_distEggBox


Final Remarks


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Author:
Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Variable Documentation

◆ MODULE_NAME

character(*, SK), parameter pm_distEggBox::MODULE_NAME = "@pm_distEggBox"

Definition at line 43 of file pm_distEggBox.F90.