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 algebraic form as described below. More...

Inheritance diagram for pm_quadTest::intDoncker2_type:
Collaboration diagram for pm_quadTest::intDoncker2_type:

## Public Member Functions

procedure get => getIntDoncker2

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 algebraic form as described below.

The full integrand is defined over a finite interval as,

$$f(x) = \frac{\exp(x)}{\sqrt{-x}} ~,~ x \in (\ms{lb}, \ms{ub} < 0.) ~.$$

The integrand has the precise value,

$$\int_{\ms{lb} = -\infty}^{\ms{ub}} f(x) dx = \sqrt{\pi} \big(\mathrm{erf}(\sqrt{-\ms{lb}} - \mathrm{erf}(\sqrt{-\ms{ub}}) \big) ~.$$

This integrand is an extension of the example discussed in Doncker et al (1976), Automatic Computation of Integrals with Singular integrand.

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

Possible calling interfaces

type(intSinCos_type) :: integrand
integrand = intDoncker2_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 algebraic form as described below.
Warning
The conditions lb < ub < 0._RK must for the relevant input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
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 1589 of file pm_quadTest.F90.