pm_distUnifPar::getUnifParLogPDF Interface Reference

Generate and return the natural logarithm of the Probability Density Function (PDF) of the MultiVariate Uniform Parallelepiped (MVUP) Distribution.
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Detailed Description

Generate and return the natural logarithm of the Probability Density Function (PDF) of the MultiVariate Uniform Parallelepiped (MVUP) Distribution.

See the documentation of pm_distUnifPar for details of the definition of the PDF.

Parameters

[in]	logLenEdge	: The input scalar or contiguous array of shape (1:ndim), of the same type and kind as the output logPDF, containing the natural logarithm of the lengths of the edges of the ndim-dimensional rectangular support of the distribution along each of the ndim axes. If logLenEdge is a scalar, the support of the distribution is assumed to be a ndim-dimensional hyper-cube. In such a case, the input optional argument ndim must be specified. If logLenEdge is a vector, the support of the distribution is assumed to be a hyper-rectangle. (optional. It must be present if and only if the input repmat is missing.)
[in]	ndim	: The input positive scalar of type integer of default kind IK, containing the number of dimensions of the domain of the distribution. (optional. It must be present if and only if the input logLenEdge is present and is a scalar.)
[in]	repmat	: The input square matrix of shape (1:ndim, 1:ndim) of the same type and kind as the output logPDF, containing the representative matrix \(M_R\) of the parallelepiped. (optional. It must be present if and only if the input logLenEdge is missing.)

Returns

logPDF : The output scalar of,

1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the natural logarithm of the PDF of the distribution.

Possible calling interfaces ⛓

use pm_distUnifPar, only: getUnifParLogPDF
 
logPDF = getUnifParLogPDF(logLenEdge, ndim)        ! Hyper-cube support
logPDF = getUnifParLogPDF(logLenEdge(1:ndim))      ! Hyper-rectangle support
logPDF = getUnifParLogPDF(repmat(1:ndim, 1:ndim))  ! Hyper-parallelepiped support
!

Warning

The condition 0 < ndim must hold for the corresponding input arguments.
The condition size(repmat, 1) == size(repmat, 2) must hold for the corresponding input arguments.
The condition \(|\ms{repmat}| \neq 0\) must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

The procedures under this generic interface are elemental when the input argument ndim is present.

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_distUnifPar, only: getUnifParLogPDF
    use pm_io, only: display_type
 
    implicit none
 
    type(display_type)      :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("1. / exp(getUnifParLogPDF(log(2.), [1, 2, 3, 4])) ! volume of the support.")
    call disp%show( 1. / exp(getUnifParLogPDF(log(2.), [1, 2, 3, 4])) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("1. / exp(getUnifParLogPDF(log([1., 2., 3., 4.]))) ! volume of the support.")
    call disp%show( 1. / exp(getUnifParLogPDF(log([1., 2., 3., 4.]))) )
    call disp%skip()
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
1. / exp(getUnifParLogPDF(log(2.), [1, 2, 3, 4])) ! volume of the support.
+2.00000000, +4.00000000, +8.00000000, +16.0000000
 
 
1. / exp(getUnifParLogPDF(log([1., 2., 3., 4.]))) ! volume of the support.
+24.0000019
 
 

Test:

test_pm_distUnifPar

Todo:

Critical Priority: The implementation of this generic interface with an input representative matrix repmat must be improved for better efficiency.
The current implementation computes the corresponding Gramian matrix which may be slower than directly computing the determinant of the representative matrix.

Final Remarks ⛓

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If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Monday March 6, 2017, 3:22 pm, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin.

Definition at line 211 of file pm_distUnifPar.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_distUnifPar.F90