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 => getInt5 |
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) = x^3 \log(\big|(x^2 - 1) (x^2 - 2.)\big|) ~,~ x \in (\ms{lb}, \ms{ub}) \end{equation}
with four possible singularities depending on the choice of integration range: \( [ -\sqrt{2}, -1, 1, \sqrt{2} ] \)
The integral is of the form,
\begin{equation} \int_{\ms{lb}}^{\ms{lb}} f(x) dx = 0.25 \bigg[ x^4 \log( \big|(x^2 - 1) (x^2 - 2)\big| ) ) - 4\log(x^2 - 2) - \log(x^2 - 1) - 3x^2 - x^4 \bigg] \bigg|_{\ms{lb}}^{\ms{ub}} \end{equation}
This integrand is inspired by and extends the examples of John Burkardt test suite for QAGWS routine of QuadPack.
[in] | lb | : The input scalar of type real of kind RKH, containing the lower limit of integration.(optional, default = 0 ) |
[in] | ub | : The input scalar of the same type and kind as lb , containing the upper limit of integration.(optional, default = 3. ) |
Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 637 of file pm_quadTest.F90.
procedure pm_quadTest::int5_type::get |
Definition at line 639 of file pm_quadTest.F90.
References pm_kind::RKH.