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!
! Copyright (C) 2016 Quantum ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
MODULE matrix_inversion
IMPLICIT NONE
PRIVATE
PUBLIC :: invmat
INTERFACE invmat
MODULE PROCEDURE invmat_r, invmat_c
END INTERFACE
CONTAINS
SUBROUTINE invmat_r (n, a, a_inv, da)
!-----------------------------------------------------------------------
! computes the inverse of a n*n real matrix "a" using LAPACK routines
! if "a_inv" is not present, "a" contains the inverse on output
! if "a_inv" is present, it contains the inverse on output, "a" is unchanged
! if "da" is specified and if the matrix is dimensioned 3x3,
! it also returns the determinant in "da"
!
USE kinds, ONLY : DP
IMPLICIT NONE
INTEGER, INTENT(in) :: n
REAL(DP), DIMENSION (n,n), INTENT(inout) :: a
REAL(DP), DIMENSION (n,n), INTENT(out), OPTIONAL :: a_inv
REAL(DP), OPTIONAL, INTENT(out) :: da
!
INTEGER :: info, lda, lwork
! info=0: inversion was successful
! lda : leading dimension (the same as n)
INTEGER, ALLOCATABLE :: ipiv (:)
! ipiv : work space for pivoting
REAL(DP), ALLOCATABLE :: work (:)
! more work space
INTEGER, SAVE :: lworkfact = 64
!
IF ( PRESENT(da) ) THEN
IF ( n == 3 ) THEN
da = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) + &
a(1,2)*(a(2,3)*a(3,1)-a(2,1)*a(3,3)) + &
a(1,3)*(a(2,1)*a(3,2)-a(3,1)*a(2,2))
IF (abs(da) < 1.d-10) CALL errore(' invmat ',' singular matrix ', 1)
ELSE
da = 0.0_dp
ENDIF
ENDIF
!
lda = n
lwork=64*n
ALLOCATE(ipiv(n), work(lwork) )
!
IF ( PRESENT(a_inv) ) THEN
a_inv(:,:) = a(:,:)
CALL dgetrf (n, n, a_inv, lda, ipiv, info)
ELSE
CALL dgetrf (n, n, a, lda, ipiv, info)
END IF
CALL errore ('invmat', 'error in DGETRF', abs (info) )
IF ( PRESENT(a_inv) ) THEN
CALL dgetri (n, a_inv, lda, ipiv, work, lwork, info)
ELSE
CALL dgetri (n, a, lda, ipiv, work, lwork, info)
END IF
CALL errore ('invmat', 'error in DGETRI', abs (info) )
!
lworkfact = INT (work(1)/n)
DEALLOCATE ( work, ipiv )
END SUBROUTINE invmat_r
SUBROUTINE invmat_c (n, a, a_inv, da)
!-----------------------------------------------------------------------
! as invmat_r, for a complex matrix
!
USE kinds, ONLY : DP
IMPLICIT NONE
INTEGER, INTENT(IN) :: n
COMPLEX (DP), DIMENSION (n,n), INTENT(INOUT) :: a
COMPLEX (DP), OPTIONAL, DIMENSION (n,n), INTENT(OUT) :: a_inv
COMPLEX (DP), OPTIONAL, INTENT(OUT) :: da
!
INTEGER :: info, lda, lwork
! info=0: inversion was successful
! lda : leading dimension (the same as n)
INTEGER, ALLOCATABLE :: ipiv (:)
! ipiv : work space for pivoting
COMPLEX(DP), ALLOCATABLE :: work (:)
! more work space
INTEGER, SAVE :: lworkfact = 64
!
IF ( PRESENT(da) ) THEN
IF (n == 3) THEN
da = a(1,1)*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) + &
a(1,2)*(a(2,3)*a(3,1)-a(2,1)*a(3,3)) + &
a(1,3)*(a(2,1)*a(3,2)-a(3,1)*a(2,2))
IF (abs(da) < 1.d-10) CALL errore(' invmat ',' singular matrix ', 1)
ELSE
da = (0.d0,0.d0)
ENDIF
ENDIF
!
lda = n
lwork=64*n
ALLOCATE(ipiv(n), work(lwork) )
!
IF ( PRESENT(a_inv) ) THEN
a_inv(:,:) = a(:,:)
CALL zgetrf (n, n, a_inv, lda, ipiv, info)
ELSE
CALL zgetrf (n, n, a, lda, ipiv, info)
END IF
CALL errore ('invmat', 'error in ZGETRF', abs (info) )
IF ( PRESENT(a_inv) ) THEN
CALL zgetri (n, a_inv, lda, ipiv, work, lwork, info)
ELSE
CALL zgetri (n, a, lda, ipiv, work, lwork, info)
END IF
CALL errore ('invmat', 'error in ZGETRI', abs (info) )
!
lworkfact = INT (work(1)/n)
DEALLOCATE ( work, ipiv )
!
END SUBROUTINE invmat_c
END MODULE matrix_inversion
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