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 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 |
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 trigonometric form as described below.
The full integrand is defined over a finite interval as,
\begin{equation} f(x) = \cos(a\sin(bx)) ~,~ x \in (-\infty < \ms{lb} = \mathrm{lf} * \pi, \ms{ub} = \mathrm{uf} * \pi < +\infty) \end{equation}
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,
\begin{equation} \int_{\ms{lb}}^{\ms{ub}} f(x) dx = (\ms{ub} - \ms{lb}) J_0(a) ~, \end{equation}
where \(J_0\) is the Modified Bessel function of the zeroth kind.
[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 ⛓
Final Remarks ⛓
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Definition at line 1111 of file pm_quadTest.F90.
procedure pm_quadTest::intSinCos_type::get |
Definition at line 1115 of file pm_quadTest.F90.
References pm_kind::RKH.
real(RKH) pm_quadTest::intSinCos_type::a |
Definition at line 1113 of file pm_quadTest.F90.
real(RKH) pm_quadTest::intSinCos_type::b |
Definition at line 1113 of file pm_quadTest.F90.
integer(IK) pm_quadTest::intSinCos_type::lf |
Definition at line 1112 of file pm_quadTest.F90.
integer(IK) pm_quadTest::intSinCos_type::uf |
Definition at line 1112 of file pm_quadTest.F90.