pm_quadTest::int7_type Type Reference

This is the derived type for generating test integrand objects of the following algebraic form. More...

Inheritance diagram for pm_quadTest::int7_type:

Collaboration diagram for pm_quadTest::int7_type:

Public Member Functions
procedure	get => getInt7
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 the following algebraic form.

The full integrand is defined as,

\begin{equation} f(x) = \frac{\log\big( |(1 - x^2)(1 - 2x^2)| \big) - 4\log(x)}{x^5} , x \in (\frac{1}{3}, +\infty) \end{equation}

with an integral of \(52.7407483834714449977291997202299809\).
The integrand has singularities and break points at break = [1 / sqrt(2), 1].

Possible calling interfaces ⛓

use pm_quadTest, only: int7_type
type(int7_type) :: integrand
 
integrand = int7_type()
print *, "description: ", integrand%desc
print *, "lower limit: ", integrand%lb
print *, "upper limit: ", integrand%ub
print *, "Example integrand value: ", integrand%get(x)

Remarks

This integrand is a transformation of int5_type such that the integral of int5_typeget(1/x) / x**2 over (0, 3) equals the integral of int7_typeget(x) over (1/3, +Inf).

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 779 of file pm_quadTest.F90.

Member Function/Subroutine Documentation

get()

procedure pm_quadTest::int7_type::get

Definition at line 781 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