pm_mathGammaAM Module Reference

This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma functions. More...

Data Types
interface	getGammaIncLowAM
	Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter ( \(\kappa\)) and upper limit of the integral x. More...
interface	getGammaIncUppAM
	Generate and return the regularized Upper Incomplete Gamma function for the specified shape parameter ( \(\kappa\)) and lower limit of the integral x. More...
interface	setGammaIncLowAM
	Return the regularized Lower Incomplete Gamma function for the specified shape parameter ( \(\kappa\)) and upper limit of the integral x. More...
interface	setGammaIncUppAM
	Return the regularized Upper Incomplete Gamma function for the specified shape parameter ( \(\kappa\)) and lower limit of the integral x. More...

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_mathGammaAM"

Detailed Description

This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma functions.

This module provides multiple function and subroutine procedures for computing the Lower and Upper Incomplete Gamma functions. These routines mostly differ only in terms of performance and usage convenience.

1. If performance is important, use the subroutine interface setGammaIncLowAM to compute the Lower Incomplete Gamma function.
   
2. If ease of use matters more than performance, use the function interfaces getGammaIncLowAM to compute the Lower Incomplete Gamma function.
   

Warning

Although all generic interfaces of this module are available for all processor real kinds, the accuracy and performance of the implemented algorithms are optimized for IEEE double precision.
In particular, the algorithms may not accurately compute the lower incomplete gamma function in extended precision (e.g., 128 bits) mode corresponding to RKH kind type parameter.

Note

The computations of this module are explicitly based on the proposed approach by:
Abergel and Moisan, 2020, Algorithm 1006: Fast and Accurate Evaluation

See also

pm_mathGamma for detailed description of the (Regularized Incomplete) Gamma Function.

Test:

test_pm_mathGammaAM

Todo:

Critical Priority: The implementation of the algorithms of this module must be properly changed to allow reliable extended-precision computations of the incomplete Gamma function.
This would require significant investment in making the original algorithms of Gil et al. kind-agnostic.

Final Remarks ⛓

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
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This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, July 22, 2024, 11:45 AM, NASA Goddard Space Flight Center, Washington, D.C.

Variable Documentation

MODULE_NAME

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

Definition at line 63 of file pm_mathGammaAM.F90.