ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
This is the derived type for generating test integrand objects of the following algebraic form. More...
Public Member Functions | |
procedure | get => getInt9 |
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... | |
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) = \begin{cases} \frac{\log\big( |(1 - x^2)(1 - 2x^2)| \big) - 4\log(x)}{x^5} &, x \in (\frac{1}{3}, +\infty) \\ \frac{1}{\pi\sqrt{-(9 + x)(10 + x)}} &, x \in (-10, -9) \\ 0 &, \text{otherwise} \end{cases} \end{equation}
with an integral of \(53.7407483834714449977291997202299809\).
The integrand has singularities and break points at break = [-10, -9, 1 / sqrt(2), 1]
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Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 929 of file pm_quadTest.F90.
procedure pm_quadTest::int9_type::get |
Definition at line 931 of file pm_quadTest.F90.
References pm_kind::RKH.