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...

## Public Member Functions

procedure get => getInt2

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...

## Public Attributes

real(RKH) a

real(RKH) b

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,

$$f(x) = \frac{1}{\sqrt{a - bx}} ~,~ x \in (0, a / b) ~,~ a > 0 ~,~ b > 0 ~,$$

where the factors $$a$$ and $$b$$ are any finite positive real numbers.
The integrand has a singularity at the upper bound of integration and has the precise value,

$$\int_{\ms{lb} = 0}^{\ms{ub} = a / b} f(x) dx = -\frac{(2 \sqrt{a - bx})}{b} \bigg|_{lb}^{ub} ~.$$

Parameters
 [in] a : The input positive-valued scalar of type real of kind RKH, such that a / b represents the upper limit of integration. (optional, default = 1.) [in] b : The input positive-valued scalar of type real of kind RKH, such that a / b represents the upper limit of integration. (optional, default = 1.)

Possible calling interfaces

type(intSinCos_type) :: integrand
integrand = int2_type(a = a, b = b)
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.
integrand_type
Test:

Final Remarks

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

Definition at line 412 of file pm_quadTest.F90.

## ◆ get()

Definition at line 415 of file pm_quadTest.F90.

References pm_kind::RKH.