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 algebraic form as described below. More...
Public Member Functions | |
procedure | get => getInt1 |
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 algebraic form as described below.
The full integrand is defined as,
\begin{equation} f(x) = \frac{x^2}{(x^2 + 1)(x^2 + 4)} ~,~ x \in (\ms{lb}, \ms{ub}) \end{equation}
where the integration bounds could be infinities.
The indefinite integral of the integrand is,
\begin{equation} \int f(x) dx = \frac{2}{3} \tan^{-1}\bigg(\frac{x}{2}\bigg) - \frac{1}{3} \tan^{-1}(x) + \mathrm{constant} ~. \end{equation}
[in] | lb | : The input scalar of type real of kind RKH, containing the lower limit of integration.(optional, default = getInfNeg(real(0,kind(lb))) |
[in] | ub | : The input scalar of the same type and kind as lb , containing the upper limit of integration.(optional, default = getInfPos(real(0,kind(ub))) |
Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 331 of file pm_quadTest.F90.
procedure pm_quadTest::int1_type::get |
Definition at line 333 of file pm_quadTest.F90.
References pm_kind::RKH.