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 trigonometric form as described below. More...

## Public Member Functions

procedure get => getIntSinCos

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

integer(IK) lf

integer(IK) uf

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 the trigonometric form as described below.

The full integrand is defined over a finite interval as,

$$f(x) = \cos(a\sin(bx)) ~,~ x \in (-\infty < \ms{lb} = \mathrm{lf} * \pi, \ms{ub} = \mathrm{uf} * \pi < +\infty)$$

where the factors $$a$$ and $$b$$ are any finite real numbers and $$(\mathrm{lf}, \mathrm{uf})$$ are whole numbers (integer-valued).
The definite integral of the integrand is,

$$\int_{\ms{lb}}^{\ms{ub}} f(x) dx = (\ms{ub} - \ms{lb}) J_0(a) ~,$$

where $$J_0$$ is the Modified Bessel function of the zeroth kind.

Parameters
 [in] lf : The input scalar of type integer of default kind IK, standing for Lower Factor, such that lb = lf * pi is the lower bound of integration. (optional, default = -1.) [in] uf : The input scalar of type integer of default kind IK, standing for Upper Factor, such that ub = uf * pi is the upper bound of integration. (optional, default = +1.) [in] a : The input scalar of type real of kind RKH. (optional, default = 10.) [in] b : The input scalar of the same type and kind as a. (optional, default = +1.)

Possible calling interfaces

type(intSinCos_type) :: integrand
integrand = intSinCos_type(lb = lb, ub = ub, 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 the trigonometric form as described...
integrand_type
Test:

Final Remarks

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1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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

Definition at line 1111 of file pm_quadTest.F90.

## ◆ get()

Definition at line 1115 of file pm_quadTest.F90.

References pm_kind::RKH.

## ◆ a

Definition at line 1113 of file pm_quadTest.F90.

## ◆ b

Definition at line 1113 of file pm_quadTest.F90.