pm_quadTest::intDoncker2_type Type Reference

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,

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

The integrand has the precise value,

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

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 ⛓

use pm_quadTest, only: intDoncker2_type
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)

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.

See also

integrand_type

Test:

test_pm_quadPack

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

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

Definition at line 1589 of file pm_quadTest.F90.

Member Function/Subroutine Documentation

get()

procedure pm_quadTest::intDoncker2_type::get

Definition at line 1591 of file pm_quadTest.F90.

References pm_kind::RKH.

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

• src/fortran/main/pm_quadTest.F90