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 algebraic form as described below. More...
Public Member Functions | |
procedure | get => getIntDoncker1 |
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 algebraic form as described below.
The full integrand is defined over a finite interval as,
\begin{equation} f(x) = \frac{1}{(1 + x)\sqrt{x}} ~,~ x \in (0 < \ms{lb}, \ms{ub}) ~. \end{equation}
The integrand has the precise value,
\begin{equation} \int_{\ms{lb}}^{\ms{ub}} f(x) dx = 2 ( \mathrm{atan}(\sqrt{\ms{ub}}) - \mathrm{atan}(\sqrt{\ms{lb}}) ) ~. \end{equation}
This integrand is an extension of the example discussed in Doncker et al (1976), Automatic Computation of Integrals with Singular integrand.
[in] | lb | : The input negative scalar of type real of kind RKH, containing the lower limit of integration.(optional, default = 0._RK ) |
[in] | ub | : The input positive scalar of the same type and kind as lb , containing the upper limit of integration.(optional, default = getInfPos(0._RKG)) |
Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 1506 of file pm_quadTest.F90.
procedure pm_quadTest::intDoncker1_type::get |
Definition at line 1508 of file pm_quadTest.F90.
References pm_kind::RKH.