pm_matrixTrace::getMatTrace Interface Reference

Generate and return the 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 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 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

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

Possible calling interfaces ⛓

use pm_matrixTrace, only: getMatTrace
use pm_matrixTrace, only: lfpack, rdpack, rfpack, uppDia, lowDia
 
trace = getMatTrace(mat)
trace = getMatTrace(mat, pack)          ! pack = rdpack
trace = getMatTrace(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: getMatTrace
    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("getMatTrace(mat)")
            call disp%show( getMatTrace(mat) )
            call disp%show("getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))")
            call disp%show( getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia)) )
            call disp%show("getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))")
            call disp%show( getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia)) )
            call disp%show("getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)")
            call disp%show( getMatTrace(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
+6, +9, +2, +1, +6, +7, +3
+2, +8, +9, +6, +1, +1, +6
+8, +6, +5, +8, +3, +9, +2
+3, +2, +6, +3, +5, +9, +6
+4, +8, +5, +2, +6, +2, +6
+6, +2, +7, +4, +2, +1, +5
+4, +5, +9, +7, +4, +4, +6
getMatTrace(mat)
+35
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+35
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+35
getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+39
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+8, +7, +1, +5, +7, +9
+1, +3, +5, +6, +5, +6
+4, +6, +5, +2, +9, +6
+6, +2, +5, +1, +3, +7
+4, +8, +8, +8, +5, +6
+5, +1, +5, +5, +4, +7
getMatTrace(mat)
+29
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+29
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+29
getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+28
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+8, +3, +9
+7, +3, +3
+9, +3, +5
getMatTrace(mat)
+16
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+16
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+16
getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+20
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+8, +2, +5, +9
+3, +9, +6, +2
+4, +8, +5, +2
+3, +4, +4, +3
getMatTrace(mat)
+25
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+25
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+25
getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+19
 
 
ndim = getUnifRand(1, 7)
mat = getUnifRand(1, 9, ndim, ndim)
mat
+9, +3, +7, +7, +5, +2
+5, +9, +6, +6, +9, +2
+3, +3, +9, +9, +7, +1
+7, +7, +7, +7, +1, +7
+4, +3, +9, +5, +5, +4
+5, +4, +5, +6, +4, +7
getMatTrace(mat)
+46
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = uppDia))
+46
getMatTrace(getMatCopy(rdpack, mat, rdpack, subset = lowDia))
+46
getMatTrace(getMatCopy(lfpack, mat, rdpack, lowDia), lfpack, lowDia)
+33
 
 

Test:

test_pm_matrixTrace

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

Definition at line 161 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