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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 => getInt2 |
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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 | |
real(RKH) | a |
real(RKH) | b |
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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}{\sqrt{a - bx}} ~,~ x \in (0, a / b) ~,~ a > 0 ~,~ b > 0 ~, \end{equation}
where the factors \(a\) and \(b\) are any finite positive real numbers.
The integrand has a singularity at the upper bound of integration and has the precise value,
\begin{equation} \int_{\ms{lb} = 0}^{\ms{ub} = a / b} f(x) dx = -\frac{(2 \sqrt{a - bx})}{b} \bigg|_{lb}^{ub} ~. \end{equation}
[in] | a | : The input positive-valued scalar of type real of kind RKH, such that a / b represents the upper limit of integration.(optional, default = 1. ) |
[in] | b | : The input positive-valued scalar of type real of kind RKH, such that a / b represents the upper limit of integration.(optional, default = 1. ) |
Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 412 of file pm_quadTest.F90.
procedure pm_quadTest::int2_type::get |
Definition at line 415 of file pm_quadTest.F90.
References pm_kind::RKH.
real(RKH) pm_quadTest::int2_type::a |
Definition at line 413 of file pm_quadTest.F90.
real(RKH) pm_quadTest::int2_type::b |
Definition at line 413 of file pm_quadTest.F90.