pm_matrixTrace::getMatMulTraceLog Interface Reference

Generate and return the natural logarithm of the multiplicative trace of an input square matrix of type integer, complex, or real of arbitrary kind.
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Detailed Description

Generate and return the natural logarithm of the multiplicative trace of an input square matrix of type integer, complex, or real of arbitrary kind.

See the documentation of pm_matrixTrace for more details.

Parameters

[in]	mat	: The input non-zero-order matrix of shape (1 : ndim * (ndim - 1) / 2 or (1:ndim, 1:ndim) of, type integer of kind any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64), type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the matrix whose natural logarithm of the multiplicative trace is to be computed. It can be of rank 1 (of shape (1 : ndim * (ndim - 1) / 2) if and only if the input argument mat is present and set to lfpack.
[in]	pack	: The input scalar that can be, the constant lfpack signifying the linear full packing of the input matrix. the constant rdpack signifying the rectangular default packing of the input matrix. the constant rfpack signifying the rectangular full packing of the input matrix. (optional, default = rdpack)
[in]	subset	: The input scalar that can be, the constant uppDia signifying the storage of the upper-diagonal subset of original matrix in the input matrix. the constant lowDia signifying the storage of the lower-diagonal subset of original matrix in the input matrix. (optional. It must be present if and only if the input argument is present and set to either lfpack or rfpack.)

Returns

logMulTrace : The output scalar of the same type and kind as the input matrix mat, containing the natural logarithm of the multiplicative trace of the input square matrix.

Possible calling interfaces ⛓

use pm_matrixTrace, only: getMatMulTraceLog
use pm_matrixTrace, only: lfpack, rdpack, rfpack, uppDia, lowDia
 
logMulTrace = getMatMulTraceLog(mat)
logMulTrace = getMatMulTraceLog(mat, pack)          ! pack = rdpack
logMulTrace = getMatMulTraceLog(mat, pack, subset)  ! pack = rdpack/lfpack, subset = uppDia/lowDia
!

Warning

The input matrix must correspond to a square matrix or a triangular subset of a non-zero-order square matrix.
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.

See also

getMatTrace
getMatMulTrace
getMatMulTraceLog
pm_matrixPack
pm_matrixSubset

Example usage ⛓

program example
 
    use iso_fortran_env, only: output_unit
    use pm_kind, only: SK, IK, LK, CK, RK
    use pm_matrixSubset, only: dia, uppDia, lowDia, uppLow, uppLowDia
    use pm_matrixCopy, only: getMatCopy, rdpack, rfpack, lfpack
    use pm_matrixTrace, only: getMatMulTraceLog
    use pm_distUnif, only: getUnifRand
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK) :: ndim, itry, ntry = 5
 
    type(display_type)  :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        integer, allocatable :: mat(:,:), rfp(:,:), lfp(:) ! all integer kinds are supported.
        do itry = 1, ntry
            call disp%skip()
            call disp%show("ndim = getUnifRand(1, 7)")
                            ndim = getUnifRand(1, 7)
            call disp%show("mat = getUnifRand(1, 9, ndim, ndim)")
                            mat = getUnifRand(1, 9, ndim, ndim)
            call disp%show("mat")
            call disp%show( mat )
            call disp%show("getMatMulTraceLog(mat)")
            call disp%show( getMatMulTraceLog(mat) )
            call disp%show("getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))")
            call disp%show( getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia)) )
            call disp%show("getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))")
            call disp%show( getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia)) )
            call disp%show("getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)")
            call disp%show( getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia) )
            call disp%skip()
        end do
    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 ⛓

 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+5
getMatMulTraceLog(mat)
+1.6094379124341003
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+1.6094379124341003
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+1.6094379124341003
getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+1.6094379124341003
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+7, +1, +4, +5, +2
+9, +1, +6, +8, +7
+8, +4, +7, +6, +4
+2, +1, +6, +6, +9
+7, +5, +1, +1, +7
getMatMulTraceLog(mat)
+7.6294899163939949
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+7.6294899163939949
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+7.6294899163939949
getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+5.5012582105447265
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+7, +3, +3, +3, +5, +7, +6
+1, +8, +8, +4, +5, +3, +5
+8, +6, +1, +2, +7, +1, +3
+6, +5, +1, +8, +9, +4, +9
+6, +9, +1, +5, +4, +1, +3
+6, +7, +6, +3, +8, +6, +7
+3, +1, +9, +6, +6, +8, +3
getMatMulTraceLog(mat)
+10.381459351431038
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+10.381459351431038
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+10.381459351431038
getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+10.904707495195588
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+1
getMatMulTraceLog(mat)
+0.0000000000000000
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+0.0000000000000000
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+0.0000000000000000
getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+0.0000000000000000
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+6, +6
+7, +1
getMatMulTraceLog(mat)
+1.7917594692280550
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+1.7917594692280550
getMatMulTraceLog(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+1.7917594692280550
getMatMulTraceLog(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+3.7376696182833680
 
 

Test:

test_pm_matrixTrace

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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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, April 23, 2017, 1:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 2769 of file pm_matrixTrace.F90.

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

• src/fortran/main/pm_matrixTrace.F90