pm_distUnifEll::getUnifEllLogPDF Interface Reference

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

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

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

Note

Note that the procedures of this generic interface do not require an input X value representing a location within the domain of the density function.
This is fine and intentional by design because the PDF is uniform across the entire support of the PDF.

Parameters

[in]	logChoDia	: The input scalar or contiguous vector of shape (1:ndim) of the same type and kind as the output logPDF. If logChoDia is scalar, it must contain the natural logarithm of the radius of the corresponding hyper-spherical support of the distribution. If logChoDia is vector, it must contain the natural logarithm of the diagonal elements of the Cholesky Factorization of the symmetric positive-definite representative Gramian matrix \(\gramian_\ell\) of the corresponding hyper-spherical support of the distribution. (optional. It must be present if and only if the input gramian is missing.)
[in]	ndim	: The input positive scalar of type integer of default kind IK, containing the number of dimensions of the distribution. (optional. It must be present if and only if the input logChoDia is present and is a scalar.)
[in]	gramian	: The input square matrix of shape (1:ndim, 1:ndim) of the same type and kind as the output logPDF, containing the upper triangle and diagonal elements of the representative Gramian matrix \(\gramian_\ell\) of the ellipsoid. (optional. It must be present if and only if the input logChoDia 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_distUnifEll, only: getUnifEllLogPDF
 
logPDF = getUnifEllLogPDF(logChoDia, ndim)         ! Hyper-sphere support
logPDF = getUnifEllLogPDF(logChoDia(1:ndim))       ! Hyper-ellipsoid support
logPDF = getUnifEllLogPDF(gramian(1:ndim, 1:ndim)) ! Hyper-ellipsoid support
!

Warning

The condition 0 < ndim must hold for the corresponding input arguments.
The condition size(gramian, 1) == size(gramian, 2) must hold for the corresponding input arguments.
The condition \(0 < |\ms{gramian}|\) 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.

See also

pm_ellipsoid
getUnifEllRand
setUnifEllRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_matrixInit, only: uppLowDia, getMatInit
    use pm_distUnifEll, only: getUnifEllLogPDF
    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(getUnifEllLogPDF(log(1.), [1, 2, 3, 4])) ! volume of the spherical support with unit radius.")
    call disp%show( 1. / exp(getUnifEllLogPDF(log(1.), [1, 2, 3, 4])) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("1. / exp(getUnifEllLogPDF(log([1., 1., 1., 1.]))) ! volume of the support.")
    call disp%show( 1. / exp(getUnifEllLogPDF(log([1., 1., 1., 1.]))) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.5, 0.5, 1.))) ! volume of the support.")
    call disp%show( 1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.5, 0.5, 1.))) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.99, 0.99, 1.))) ! volume of the support.")
    call disp%show( 1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.99, 0.99, 1.))) )
    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(getUnifEllLogPDF(log(1.), [1, 2, 3, 4])) ! volume of the spherical support with unit radius.
+2.00000024, +3.14159274, +4.18879032, +4.93480301
 
 
1. / exp(getUnifEllLogPDF(log([1., 1., 1., 1.]))) ! volume of the support.
+4.93480301
 
 
1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.5, 0.5, 1.))) ! volume of the support.
+2.72069931
 
 
1. / exp(getUnifEllLogPDF(getMatInit([2, 2], uppLowDia, 0.99, 0.99, 1.))) ! volume of the support.
+0.443175852
 
 

Test:

test_pm_distUnifEll

Final Remarks ⛓

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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.

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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 271 of file pm_distUnifEll.F90.

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

• src/fortran/main/pm_distUnifEll.F90