ParaMonte Fortran 2.0.0 Parallel Monte Carlo and Machine Learning LibrarySee the latest version documentation.
pm_quadTest::int9_type Type Reference

This is the derived type for generating test integrand objects of the following algebraic form. More...

Inheritance diagram for pm_quadTest::int9_type:
Collaboration diagram for pm_quadTest::int9_type:

## Public Member Functions

procedure get => getInt9

Public Member Functions inherited from pm_quadTest::integrand_type
procedure(get_proc), deferred get
The function member returning the value of the unweighted integrand (whether Cauchy/sin/cos/algebraically types of weights) at a specified input point x. More...

## Additional Inherited Members

Public Attributes inherited from pm_quadTest::integrand_type
real(RKH) lb
The scalar of type real of the highest kind supported by the library RKH, containing the lower limit of integration. More...

real(RKH) ub
The scalar of type real of the highest kind supported by the library RKH, containing the upper limit of integration. More...

real(RKH) integral
The scalar of type real of the highest kind supported by the library RKH, containing the true result of integration. More...

real(RKH), dimension(:), allocatable break
The scalar of type real of the highest kind supported by the library RKH, containing the points of difficulties of integration. More...

type(wcauchy_type), allocatable wcauchy
The scalar of type wcauchy_type, containing the Cauchy singularity of the integrand. More...

character(:, SK), allocatable desc
The scalar allocatable character of default kind SK containing a description of the integrand and integration limits and difficulties. More...

## Detailed Description

This is the derived type for generating test integrand objects of the following algebraic form.

The full integrand is defined as,

$$f(x) = \begin{cases} \frac{\log\big( |(1 - x^2)(1 - 2x^2)| \big) - 4\log(x)}{x^5} &, x \in (\frac{1}{3}, +\infty) \\ \frac{1}{\pi\sqrt{-(9 + x)(10 + x)}} &, x \in (-10, -9) \\ 0 &, \text{otherwise} \end{cases}$$

with an integral of $$53.7407483834714449977291997202299809$$.
The integrand has singularities and break points at break = [-10, -9, 1 / sqrt(2), 1].

Possible calling interfaces

type(int9_type) :: integrand
integrand = int9_type()
print *, "description: ", integrand%desc
print *, "lower limit: ", integrand%lb
print *, "upper limit: ", integrand%ub
print *, "Example integrand value: ", integrand%get(x)
This module contains a collection of interesting or challenging integrands for testing or examining t...
Definition: pm_quadTest.F90:54
This is the derived type for generating test integrand objects of the following algebraic form.
Remarks
This integrand is a transformation of int7_type mixed with the PDF of the Beta distribution for the shape parameters $$(0.5, 0.5)$$.
See also
integrand_type
Test:
test_pm_quadPack

Final Remarks

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.

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

Definition at line 929 of file pm_quadTest.F90.

## ◆ get()

 procedure pm_quadTest::int9_type::get

Definition at line 931 of file pm_quadTest.F90.

References pm_kind::RKH.

The documentation for this type was generated from the following file: