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 sum of five Probability Density Functions of the Gamma distribution. More...
Public Member Functions | |
procedure | get => getIntPentaGammaInf |
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 sum of five Probability Density Functions of the Gamma distribution.
The full integrand is defined as,
\begin{eqnarray} f(x) &=& \pi_\mathcal{G}(x + 9; 0.7, 1) \\ \nonumber &+& \pi_\mathcal{G}(x + 5; 0.7, 1) \\ \nonumber &+& \pi_\mathcal{G}(x - 5; 0.7, 1) \\ \nonumber &+& \pi_\mathcal{G}(2 - x; 0.7, 1) \\ \nonumber &+& \pi_\mathcal{G}(7 - x; 0.7, 1) \\ \nonumber &,& x \in (-\infty, +\infty) \end{eqnarray}
where \(\pi_\mathcal{G}\) represents the PDF of the Gamma distribution computed via getGammaLogPDF.
The integrand has five singularities and break points at \(\ms{break} = [-9, -5, 2, 5, 7]\).
By definition, the integral of the integrand over the entire fully-infinite integration range is 5.
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Possible calling interfaces ⛓
Final Remarks ⛓
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Definition at line 1428 of file pm_quadTest.F90.
procedure pm_quadTest::intPentaGammaInf_type::get |
Definition at line 1430 of file pm_quadTest.F90.
References pm_kind::RKH.