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 algebraic form as described below, whose Cauchy Principal Value is to be computed. More...

Public Member Functions

procedure get => getIntCauchy1

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...

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 algebraic form as described below, whose Cauchy Principal Value is to be computed.

The full integrand is defined as,

$$f(x) = \frac{1}{(x - c)} ~,~ x \in (\ms{lb}, \ms{ub}) ~,~ \ms{lb} < 0 < \ms{ub}$$

where the integration bounds are finite values.
The Cauchy Principal value of the integrand is $$\log\bigg(\frac{\ms{ub} - \ms{cs}}{\ms{lb} - \ms{cs}}\bigg)$$.

Parameters
 [in] lb : The input scalar of type real of kind RKH, containing the lower limit of integration. (optional, default = -2.) [in] ub : The input scalar of the same type and kind as lb, containing the upper limit of integration. (optional, default = +3.) [in] cs : The input scalar of the same type and kind as lb, containing the Cauchy singularity of the integrand. (optional, default = +1.)

Possible calling interfaces

type(intCauchy1_type) :: integrand
integrand = intCauchy1_type(lb = lb, ub = ub, cs = cs)
print *, "description: ", integrand%desc
print *, "lower limit: ", integrand%lb
print *, "upper limit: ", integrand%ub
print *, "singularity: ", integrand%cs
print *, "Example integrand value: ", integrand%get(x)
print *, "Example integrand value without the Cauchy weight: ", integrand%getWeighted(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 algebraic form as described bel...
integrand_type
Test:

Final Remarks

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

Definition at line 1665 of file pm_quadTest.F90.

◆ get()

Definition at line 1667 of file pm_quadTest.F90.

References pm_kind::RKH.

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