topic mkl -- inverse square matrix -- transpose in Intel® oneAPI Math Kernel Library

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 10:29:41 GMT

hi every one,

I would like to find the inverse and after that of a square matrix. The matrix it is n x n with n very small, max n = 20-30.
I would like to use the mkl libraries in intel fortran 95\\2003.
what libraries could I use ?
How shall I do?
thanks

mkl -- inverse square matrix -- transpose

Gennady_F_Intel — Fri, 19 Aug 2011 12:37:44 GMT

Diedro,

Please see the MKL Manual Documentation - Lapack\Computations routines\Routines for Matrix Inversion.

also see the MKL Linker Adviser - to select what MKL'slibraries are recommended for linking ...

--Gennady

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 13:42:25 GMT

hi,

thank you very much but it seems very comlicate.

I found the functio that are:

[bash]    call GETRF(CoeffMat,ipiv)
    call GETRI(CoeffMat,ipiv) [/bash]

and I try to compile as:

[bash]ifort -L$MKLPATH -lmkl_lapack -mkl -lpthread *.f90
[/bash]

but I get the following error:

[bash]quadraturepoints.f90(86): error #6285: There is no matching specific subroutine for this generic subroutine call.   [GETRF]
    call GETRF(CoeffMat,ipiv)
---------^
quadraturepoints.f90(87): error #6285: There is no matching specific subroutine for this generic subroutine call.   [GETRI]
[/bash]

could you please what it is wrong?

thank you very much

mkl -- inverse square matrix -- transpose

TimP — Fri, 19 Aug 2011 15:02:47 GMT

The combination of array data types and rank declarations must match one of the original BLAS functions. The source code for the lapack use modules is provided in your installation, in case that will help you see what are the supported specific subroutines. You could post a complete small example if you want further advice.

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 16:09:38 GMT

hi,

thank you again very much.

the function defined in

[bash]/opt/intel/composerxe-2011.0.084/mkl/interfaces/lapack95/source/[/bash]

that I want to use to "computes an LU factorization of a nxm genelral matrix A" (first step to invert a matrix) is:

[bash]DGETRF[/bash]

and in dgetrf.f90 the subroutine is:

[bash]PURE SUBROUTINE DGETRF_F95(A,IPIV,INFO)

USE F77_LAPACK, ONLY: F77_GETRF, F77_XERBLA
    ! <<< ENTRY point >>>
    ENTRY DGETRF_MKL95(A,IPIV,INFO)
    ! <<< Implicit statement >>>
    IMPLICIT NONE

...
...
...
END SUBROUTINE DGETRF_F95[/bash]

[bash]
[/bash]

As you can see it need only three arguments:

1) the matrix to invert A(nxn)

2) an array dim(n)

3) a flag

I compile as:

[bash]-L$MKLPATH -lmkl_lapack95 -mkl  *.f90 
[/bash]

It runs but I have the following error:

[bash]SIGSEGV, segmentation fault occurred
Image              PC                Routine            Line        Source             
libmkl_intel_lp64  00007FBDAD0B37D3  Unknown               Unknown  Unknown
[/bash]

and here my code:

[bash]SUBROUTINE quadraturepoints
USE precisionpc
USE basic_funtions_modal_2D
USE comuni
IMPLICIT NONE

....
....
REAL    (DBL),  DIMENSION(nGP1D,nGP1D) :: CoeffMat
REAL    (DBL),  DIMENSION(nGP1D)       :: IPIV

...
...
CALL DGETRF(CoeffMat,ipiv,info)

...
...
...
[/bash]

If I try to callDGETRF_F95 I have an errot

I don't know if the problem is in the link between my code and lapack95 or in the input in the subroutineDGETRF_F95

thank you very much you are my lifesaver

mkl -- inverse square matrix -- transpose

TimP — Fri, 19 Aug 2011 18:24:34 GMT

You must first resolve the compile time problem. The message you quoted before refers to the list of specific versions of getrf, dgetri, which you will see in lapack/interfaces.f90. Fortran looks at the list of alternatives there and gives you the error when none of the alternate specific subroutines match your data types.
IPIV is not a flag; it's an array of default integers to record interchanges. If you don't get that right, that would give rise to the error. If you supply it as an array of double precision, as you appear to have done, that also will give rise to the rejection. Likewise, INFO, which you may call a flag, must be typed integer (rank 0).
The integer types would be default integer, unless you choose the ilp libraries, in which case they would be integer(kind=8).

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 19:41:37 GMT

Hi really really thank you,

A is amatrix andIPIV an array:

[bash]REAL    (DBL),  DIMENSION(nGP1D)       :: IPIV[/bash]

info is an integer, not standard I suppose, what do you mean forilp libraries.

AboutDGETRI_f95, it seems to be inDGETRI.f90 where it calls some F77 subroutine (ex.F77_GETRF)I suppose using lapack_interfaces.f90.

How can I use it? How shall compile with mkl?

I will use DGETRIeacuse it os double , is it right?

thank again

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 20:25:03 GMT

Hi,

I tried also to set all the variables and mlk again:

[bash]./mklvars.sh intel64
[/bash]

and I have:

[bash]./mklvars.sh: 12: Bad substitution
diego@diedro:/opt/intel/composerxe-2011/mkl/bin$ 
[/bash]

Is this the problem?

mkl -- inverse square matrix -- transpose

TimP — Fri, 19 Aug 2011 22:02:37 GMT

I guess you're not using the ilp (64-bit integer) libraries, but you haven't given us that information. You don't need to change anything in the source code for the MKL .mod files; I just referred you to it to point out where the data type mismatch is (evidently, your wrong data type for IPIV, possibly others).

mkl -- inverse square matrix -- transpose

diedro — Fri, 19 Aug 2011 23:19:03 GMT

hi,

now I can compile, I hope correctely:

[bash]ifort *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread
[/bash]

But there is a problem:

If I use:

[bash]SUBROUTINE quadraturepoints
USE precisionpc
USE basic_funtions_modal_2D
USE mkl95_LAPACK[/bash]

Fortran compile without any problem, it recognize also:

[bash]CALL DGETRF_F95 (Inv,IPIV,INFO)[/bash]

however the program is non able to run to the end. I have check, the subroutine

[bash]DGETRF_F95[/bash]

seems to not work.

If I choose also

[bash]USE LAPACK95[/bash]

and I compile as

[bash] ifort *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread -llapack95
[/bash]

I have the following errors:

[bash]error #6633: The type of the actual argument differs from the type of the dummy argument.   [INV]
   CALL DGETRF_F95 (Inv,IPIV,INFO)
--------------------^
quadraturepoints.f90(91): error #6633: The type of the actual argument differs from the type of the dummy argument.   [IPIV]
   CALL DGETRF_F95 (Inv,IPIV,INFO)
------------------------^
quadraturepoints.f90(91): error #6633: The type of the actual argument differs from the type of the dummy argument.   [INFO]
   CALL DGETRF_F95 (Inv,IPIV,INFO)
-----------------------------^
compilation aborted for quadraturepoints.f90 (code 1)
diego@diedro:~/Desktop/dottorato/src/fortran_src/cgk2D_gauss_n$ 
[/bash]

why?

mkl -- inverse square matrix -- transpose

diedro — Sun, 21 Aug 2011 11:20:38 GMT

hi,

now I try ti summurized what is going on.

I am using composerxe2011.0.084

First of all I compile my program as:

[bash] ifort *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread
[/bash]

After that I wrote a program to test the inversion of a matrix using mkl libraries:

[bash]program inversion
use f95_precision
use lapack95
implicit none
    
    integer(sp)   :: I, N,info
    integer(sp)  ,  dimension(:)   , allocatable:: IPIV
    real   (sp)  ,  dimension(:,:) , allocatable:: A, AA
    
    N = 3
    
    allocate( IPIV(N) )
    allocate( A(N,N), AA(N,N) )
    
    AA(1,1) = 1.0d0; AA(1,2) = 3.0d0; AA(1,3) = 1.0d0
    AA(2,1) = 1.0d0; AA(2,2) = 1.0d0; AA(2,3) = 2.0d0
    AA(3,1) = 2.0d0; AA(3,2) = 3.0d0; AA(3,3) = 4.0d0

    A = AA

    write(*,*) 'The Matrix A is:'
    do I = 1,N
        write(*,*) AA(I,:)
    end do

    write(*,*) 'The First Step is to Factorise A'
    call GETRF( A, IPIV)


    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do
!     
    write(*,*) 'IPIV',IPIV
    write(*,*) 'The Second Step is to Invert A'
    call GETRI(A, IPIV )
! 
    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do

end program inversion[/bash]

and this are the results:

[bash] The Matrix A is:
   1.000000       3.000000       1.000000    
   1.000000       1.000000       2.000000    
   2.000000       3.000000       4.000000    
 The First Step is to Factorise A
 The Inverted Matrix is:
   2.000000       3.000000       4.000000    
  0.5000000       1.500000      -1.000000    
  0.5000000     -0.3333333     -0.3333333    
 info           0
 IPIV           3           3           3
 The Second Step is to Invert A
forrtl: severe (174): SIGSEGV, segmentation fault occurred
[/bash]

why Do I have a segmentation fault with the GETRI call?

I am not able to understand,GETRF seems to work correctely but notGETRI, and the belong to the same family functions

mkl -- inverse square matrix -- transpose

diedro — Sun, 21 Aug 2011 11:20:48 GMT

hi,

now I try ti summurized what is going on.

First of all I compile my program as:

[bash] ifort *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread
[/bash]

After that I wrote a program to test the inversion of a matrix using mkl libraries:

[bash]program inversion
use f95_precision
use lapack95
implicit none
    
    integer(sp)   :: I, N,info
    integer(sp)  ,  dimension(:)   , allocatable:: IPIV
    real   (sp)  ,  dimension(:,:) , allocatable:: A, AA
    
    N = 3
    
    allocate( IPIV(N) )
    allocate( A(N,N), AA(N,N) )
    
    AA(1,1) = 1.0d0; AA(1,2) = 3.0d0; AA(1,3) = 1.0d0
    AA(2,1) = 1.0d0; AA(2,2) = 1.0d0; AA(2,3) = 2.0d0
    AA(3,1) = 2.0d0; AA(3,2) = 3.0d0; AA(3,3) = 4.0d0

    A = AA

    write(*,*) 'The Matrix A is:'
    do I = 1,N
        write(*,*) AA(I,:)
    end do

    write(*,*) 'The First Step is to Factorise A'
    call GETRF( A, IPIV)


    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do
!     
    write(*,*) 'IPIV',IPIV
    write(*,*) 'The Second Step is to Invert A'
    call GETRI(A, IPIV )
! 
    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do

end program inversion[/bash]

and this are the results:

[bash] The Matrix A is:
   1.000000       3.000000       1.000000    
   1.000000       1.000000       2.000000    
   2.000000       3.000000       4.000000    
 The First Step is to Factorise A
 The Inverted Matrix is:
   2.000000       3.000000       4.000000    
  0.5000000       1.500000      -1.000000    
  0.5000000     -0.3333333     -0.3333333    
 info           0
 IPIV           3           3           3
 The Second Step is to Invert A
forrtl: severe (174): SIGSEGV, segmentation fault occurred
[/bash]

why Do I have a segmentation fault with the GETRI call?

I am not able to understand,GETRF seems to work correctely but notGETRI, and the belong to the same family functions

mkl -- inverse square matrix -- transpose

barragan_villanueva_ — Sun, 21 Aug 2011 15:17:43 GMT

Hi,

You need to link with LP64 MKL libraries if yourprogram uses default INTEGERs.
Otherwise please try adding -i8 option for ifort to use INTEGER*8to correspond to ILP64 MKL libraries.
Intel MKL Link Line Advisorwill help you too.

mkl -- inverse square matrix -- transpose

diedro — Sun, 21 Aug 2011 22:49:18 GMT

hi,

it seems that does not work.

I'm using ubuntu 11.04 and this is my bash.bashrc (now I have include also the ilp64 to compile also the integer in 64 bit):

[bash]PATH="/opt/intel/compilerpro-12.0.0.084/bin/intel64$PATH"
source /opt/intel/compilerpro-12.0.0.084/bin/ifortvars.sh intel64
export LD_LIBRARY_PATH=/opt/intel/compilerpro-12.0.0.084/debugger/lib/intel64:$LD_LIBRARY_PATH
export PATH
###################################################################################################
source /opt/intel/composerxe-2011.0.084/mkl/bin/mklvars.sh intel64 mod ilp64
export PATH[/bash]

I have use the Intel MKL Link Line Advisorand here is the result:

[bash]-L$(MKLROOT)/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread[/bash]

so I compile as:

[bash]~/Desktop/prova/prova3$ ifort *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread[/bash]

after that I run the same program, all in single precision, so I use the:

[bash]call GETRF( A, IPIV,info)

and

call GETRI( A, IPIV,info)[/bash]

but I get the same problem:

[bash] The Matrix A is:
   1.000000       3.000000       1.000000    
   1.000000       1.000000       2.000000    
   2.000000       3.000000       4.000000    
 The First Step is to Factorise A
 The Inverted Matrix is:
   2.000000       3.000000       4.000000    
  0.5000000       1.500000      -1.000000    
  0.5000000     -0.3333333     -0.3333333    
 info           0
 IPIV           3           3           3
 The Second Step is to Invert A
forrtl: severe (174): SIGSEGV, segmentation fault occured[/bash]

mkl -- inverse square matrix -- transpose

diedro — Sun, 21 Aug 2011 22:56:04 GMT

GETRF works but not GETRI

Have I done something wrong?

do I have to update my compiler? (compilerpro-12.0.0.084)

mkl -- inverse square matrix -- transpose

diedro — Mon, 22 Aug 2011 00:22:56 GMT

hi,

now it seems to work

the code:

[bash]program inversion
use f95_precision
use lapack95
implicit none
!ifort -i8 *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core 
    integer(dp)   :: I, N,info
    integer(dp)  ,  dimension(:)   , allocatable:: IPIV
    real   (dp)  ,  dimension(:,:) , allocatable:: A, AA
    
    N = 3
    
    allocate( IPIV(N) )
    allocate( A(N,N), AA(N,N) )
    
    AA(1,1) = 1.0d0; AA(1,2) = 3.0d0; AA(1,3) = 1.0d0
    AA(2,1) = 1.0d0; AA(2,2) = 1.0d0; AA(2,3) = 2.0d0
    AA(3,1) = 2.0d0; AA(3,2) = 3.0d0; AA(3,3) = 4.0d0

    A = AA

    write(*,*) 'The Matrix A is:'
    do I = 1,N
        write(*,*) AA(I,:)
    end do

    write(*,*) 'The First Step is to Factorise A'
    call GETRF( A, IPIV,info)


    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do
!    
    write(*,*) 'info',info 
    write(*,*) 'IPIV',IPIV
    write(*,*) 'The Second Step is to Invert A'
    call GETRI(A, IPIV,info)
! 
    write(*,*) 'The Inverted Matrix is:'
    do I = 1,N
        write(*,*) A(I,:)
    end do
end program inversion[/bash]

and I compile as:

[bash] ifort -i8 *.f90 -L$MKLPATH/lib/em64t  -lmkl_blas95_ilp64 -lmkl_lapack95_ilp64 -lmkl_intel_ilp64 -lmkl_sequential -lmkl_core -lpthread[/bash]

now I have a new question:

If I want to compile inQuadruple precision?

what are the difference between GETRi e DGETRI, because when I compile with DGETRI?

mkl -- inverse square matrix -- transpose

TimP — Mon, 22 Aug 2011 00:43:34 GMT

There's no MKL support for quad precision, in part because quad precision (e.g. ifort REAL(KIND=16)) doesn't allow for the optimizations typical of MKL, including vectorization. You could build the netlib functions using ifort quad precision, if you chose.
The lapack95 getri is simply a way of letting the compiler choose among the f77 ?getri functions, supplying the additional arguments automatically.

mkl -- inverse square matrix -- transpose

diedro — Mon, 22 Aug 2011 06:48:11 GMT

hi,

ok, I get it.

However, DGETRI does not work, I have a segmetation fault error.

mkl -- inverse square matrix -- transpose

diedro — Mon, 22 Aug 2011 22:00:49 GMT

hi,

do you know why?

This is just to understand better.

Everything is working now:

[bash]CALL GETRF(Inv,IPIV,info)
CALL GETRI(Inv,IPIV,info)

Coeff1D = TRANSPOSE(Inv)
        DO i=1,nCP1D
          DO j=1,nCP1D
              Coeff1D(i,j) = REAL(Coeff1D(i,j),R16P)
          ENDDO
        ENDDO[/bash]

in this way I get also the quadruple precision