ParaMonte Fortran 2.0.0 Parallel Monte Carlo and Machine Learning LibrarySee the latest version documentation.

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

Inheritance diagram for pm_quadTest::int5_type:
Collaboration diagram for pm_quadTest::int5_type:

## Public Member Functions

procedure get => getInt5

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,

$$f(x) = x^3 \log(\big|(x^2 - 1) (x^2 - 2.)\big|) ~,~ x \in (\ms{lb}, \ms{ub})$$

with four possible singularities depending on the choice of integration range: $$[ -\sqrt{2}, -1, 1, \sqrt{2} ]$$
The integral is of the form,

$$\int_{\ms{lb}}^{\ms{lb}} f(x) dx = 0.25 \bigg[ x^4 \log( \big|(x^2 - 1) (x^2 - 2)\big| ) ) - 4\log(x^2 - 2) - \log(x^2 - 1) - 3x^2 - x^4 \bigg] \bigg|_{\ms{lb}}^{\ms{ub}}$$

This integrand is inspired by and extends the examples of John Burkardt test suite for QAGWS routine of QuadPack.

Parameters
 [in] lb : The input scalar of type real of kind RKH, containing the lower limit of integration. (optional, default = 0) [in] ub : The input scalar of the same type and kind as lb, containing the upper limit of integration. (optional, default = 3.)

Possible calling interfaces

type(int5_type) :: integrand
integrand = int5_type(lb = lb, ub = ub)
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...
This is the derived type for generating test integrand objects of the following algebraic form.
integrand_type
Test:

Final Remarks

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For details on the naming conventions, see this page.

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

Definition at line 637 of file pm_quadTest.F90.