pm_distUnifElls::getUnifEllsLogPDF Interface Reference

Generate and return the natural logarithm of an approximation of the Probability Density Function (PDF) of the Multiple MultiVariate Uniformly Ellipsoidal (MMVUE) Distribution.
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Detailed Description

Generate and return the natural logarithm of an approximation of the Probability Density Function (PDF) of the Multiple MultiVariate Uniformly Ellipsoidal (MMVUE) Distribution.

See the documentation of pm_distUnifElls 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]	invmul	: The input vector of shape (1:nsam) of the same type and kind as the output logPDF, each element of which represents the inverse of the number of ellipsoids within which the corresponding sampled random vector falls.
[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 argument nell is also present and chol is missing.)
[in]	nell	: The input positive scalar of type integer of default kind IK, containing the number of ellpisoids in the distribution. (optional. It must be present if and only if the input argument ndim is also present and chol is missing.)
[in]	chol	: The input contiguous array of shape (1:ndim, 1:ndim, 1:nell) whose specified triangular subset contains the Cholesky Factorization of the Gramian matrix of the MMVUE distribution. (optional, the default is the Identity matrix of rank ndim. It must be present if and only if the input argument subset and invGram are also present.)

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_distUnifElls, only: getUnifEllsLogPDF
 
logPDF = getUnifEllsLogPDF(chol, invmul)
!

Warning

The condition 0 < ndim must hold for the corresponding input arguments.
The condition 0 < nell must hold for the corresponding input arguments.
The condition all(invmul <= 1) must hold for the corresponding input arguments.
The condition size(chol, 1) == size(chol, 2) 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
getUnifEllsRand
setUnifEllsRand

Example usage ⛓

program example
 
    use pm_kind, only: SK
    use pm_kind, only: IK, LK
    use pm_io, only: display_type
    use pm_arrayResize, only: setResized
    use pm_distUnif, only: getUnifRand, rngf_type
    use pm_matrixChol, only: getMatChol, uppDia, lowDia
    use pm_distUnifElls, only: getUnifEllsLogPDF
    use pm_distUnifElls, only: setUnifEllsRand
    use pm_distChol, only: getCholRand, uppDia
    use pm_matrixInv, only: getMatInv, choUpp
    use pm_io, only: getErrTableWrite, trans
 
    implicit none
 
    integer(IK) :: ndim, iell, nell, nsam
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        use pm_kind, only: TKG => RKD
        real(TKG), allocatable :: logPDF, mean(:,:), invGram(:, :, :), chol(:, :, :), rand(:, :), mahalSq(:, :), invmul(:)
 
        call disp%skip()
        call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
        call disp%show("! Random vectors from Multiple Multivariate Uniform Balls with particular means.")
        call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
        call disp%skip()
 
        call disp%skip()
        call disp%show("ndim = 2; nell = getUnifRand(5, 10); nsam = 2000")
                        ndim = 2; nell = getUnifRand(5, 10); nsam = 2000
        call disp%show("[ndim, nell, nsam]")
        call disp%show( [ndim, nell, nsam] )
        call disp%show("mean = getUnifRand(-5._TKG, +5._TKG, ndim, nell)")
                        mean = getUnifRand(-5._TKG, +5._TKG, ndim, nell)
        call disp%show("mean")
        call disp%show( mean )
        call disp%show("call setResized(mahalSq, [nell, nsam])")
                        call setResized(mahalSq, [nell, nsam])
        call disp%show("call setResized(rand, [ndim, nsam])")
                        call setResized(rand, [ndim, nsam])
        call disp%show("call setResized(invmul, nsam)")
                        call setResized(invmul, nsam)
        call disp%show("call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean)")
                        call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean)
        call disp%show("logPDF = getUnifEllsLogPDF(invmul, ndim, nell)")
                        logPDF = getUnifEllsLogPDF(invmul, ndim, nell)
        call disp%show("logPDF")
        call disp%show( logPDF )
        call disp%skip()
 
        call disp%skip()
        call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
        call disp%show("! Random vectors from Multiple Multivariate Uniform Ellipsoids with particular means.")
        call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
        call disp%skip()
 
        call disp%show("call setResized(chol, [ndim, ndim, nell])")
                        call setResized(chol, [ndim, ndim, nell])
        call disp%show("call setResized(invGram, [ndim, ndim, nell])")
                        call setResized(invGram, [ndim, ndim, nell])
        call disp%show("do iell = 1, nell; chol(:, :, iell) = getCholRand(0._TKG, ndim, uppDia); invGram(:, :, iell) = getMatInv(chol(:, :, iell), choUpp); end do")
                        do iell = 1, nell; chol(:, :, iell) = getCholRand(0._TKG, ndim, uppDia); invGram(:, :, iell) = getMatInv(chol(:, :, iell), choUpp); end do
        call disp%show("call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean, chol, uppDia, invGram)")
                        call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean, chol, uppDia, invGram)
        call disp%show("logPDF = getUnifEllsLogPDF(invmul, chol)")
                        logPDF = getUnifEllsLogPDF(invmul, chol)
        call disp%show("logPDF")
        call disp%show( logPDF )
        call disp%skip()
 
    end block
 
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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Random vectors from Multiple Multivariate Uniform Balls with particular means.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
ndim = 2; nell = getUnifRand(5, 10); nsam = 2000
[ndim, nell, nsam]
+2, +5, +2000
mean = getUnifRand(-5._TKG, +5._TKG, ndim, nell)
mean
-2.4796979686571250, -2.2324086859414072, -4.0794108705286831, -1.2752456501913321, +0.57284736041570739
-2.0766337185785764, -3.9676085517739494, +2.5868455192286666, -2.5524757020556645, -3.4448758874187000
call setResized(mahalSq, [nell, nsam])
call setResized(rand, [ndim, nsam])
call setResized(invmul, nsam)
call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean)
logPDF = getUnifEllsLogPDF(invmul, ndim, nell)
logPDF
-5.6926746249475704
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Random vectors from Multiple Multivariate Uniform Ellipsoids with particular means.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
call setResized(chol, [ndim, ndim, nell])
call setResized(invGram, [ndim, ndim, nell])
do iell = 1, nell; chol(:, :, iell) = getCholRand(0._TKG, ndim, uppDia); invGram(:, :, iell) = getMatInv(chol(:, :, iell), choUpp); end do
call setUnifEllsRand(rngf_type(), rand, mahalSq, invmul, mean, chol, uppDia, invGram)
logPDF = getUnifEllsLogPDF(invmul, chol)
logPDF
-1.4631085299078808
 
 

Test:

test_pm_distUnifElls

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.

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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This software is available to the public under a highly permissive license.
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 278 of file pm_distUnifElls.F90.

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

• src/fortran/main/pm_distUnifElls.F90