pm_quadTest Module Reference

This module contains a collection of interesting or challenging integrands for testing or examining the integration routines of the ParaMonte library.
More...

Data Types
interface	get_proc
	This is the abstract interface of the get() type-bound procedure of integrand_type class whose arguments of type real are of the highest precision kind RKH, made available by the processor. More...
type	int1_type
	This is the derived type for generating test integrand objects of the algebraic form as described below. More...
type	int2_type
	This is the derived type for generating test integrand objects of algebraic form as described below. More...
type	int3_type
	This is the derived type for generating test integrand objects of algebraic form as described below. More...
type	int4_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	int5_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	int6_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	int7_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	int8_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	int9_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	intCauchy1_type
	This is the derived type for generating test integrand objects of the algebraic form as described below, whose Cauchy Principal Value is to be computed. More...
type	intCauchy2_type
	This is the derived type for generating test integrand objects of the algebraic form as described below, whose Cauchy Principal Value is to be computed. More...
type	intDoncker1_type
	This is the derived type for generating test integrand objects of algebraic form as described below. More...
type	intDoncker2_type
	This is the derived type for generating test integrand objects of algebraic form as described below. More...
type	integrand_type
	This is the base type integrand_type standing abstract integrand type to generate a variety of integration test functions. More...
type	intGamUpp_type
	This is the derived type for generating test integrand objects of the following algebraic form. More...
type	intGenExpGammaPDF_type
	This is the derived type for generating test integrand objects of the Probability Density Function of the GenExpGamma distribution. More...
type	intLogNormPDF_type
	This is the derived type for generating test integrand objects of the Probability Density Function of the Lognormal distribution. More...
type	intNormPDF_type
	This is the derived type for generating test integrand objects of the Probability Density Function of the Normal distribution. More...
type	intPentaGammaInf_type
	This is the derived type for generating test integrand objects of the sum of five Probability Density Functions of the Gamma distribution. More...
type	intSinCos_type
	This is the derived type for generating test integrand objects of the trigonometric form as described below. More...
interface	test_getQuadErr
	Run the adaptive global quadrature methods for the specified input integrand object. More...
interface	test_isFailedQuad
	Run the adaptive global quadrature methods for the specified input integrand object. More...

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

Detailed Description

This module contains a collection of interesting or challenging integrands for testing or examining the integration routines of the ParaMonte library.

The routines to be tested include but are not limited to those of

• pm_quadPack
  
• pm_quadRomb
  

All test integrands are wrapped in a derived type of the base abstract class integrand_type.

See also

pm_quadPack
pm_quadRomb

Todo:

Critical Priority: Unfortunately, gfortran 12 and older versions do not properly support the parameterized derived types (PDTs).
As such, the example generic-real-kind PDT types could not be used here.
This creates significant complexities when using the examples of these modules,
because all real kinds in this module are set to the highest precision available.
The onus is then on the end user to write wrappers that convert the relevant components and function-returns to the desired real kinds.
In addition to being ugly, error-prone and verbose, this usage of the highest-precision real kind is also highly inefficient computationally.
Fortunately, once PDTs are supported in gfortran, the conversion of the example types of this module to PDTs is straightforward and non-breaking.
The migration to PDTs must be done as soon as gfortran supports for PDTs is complete.
Note that other compilers have full support of PDTs.

Final Remarks ⛓

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If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
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.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

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, Oct 16, 2009, 11:14 AM, Michigan

Variable Documentation

MODULE_NAME

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

Definition at line 64 of file pm_quadTest.F90.