SUBROUTINE DGETRF_F95( A, IPIV, RCOND, NORM, INFO ) ! ! -- LAPACK95 interface driver routine (version 3.0) -- ! UNI-C, Denmark; Univ. of Tennessee, USA; NAG Ltd., UK ! September, 2000 ! ! .. USE STATEMENTS .. USE LA_PRECISION, ONLY: WP => DP USE LA_AUXMOD, ONLY: LSAME, ERINFO USE F77_LAPACK, ONLY: GETRF_F77 => LA_GETRF, LANGE_F77 => LA_LANGE, & GECON_F77 => LA_GECON ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: NORM INTEGER, INTENT(OUT), OPTIONAL :: INFO REAL(WP), INTENT( OUT ), OPTIONAL :: RCOND ! .. ARRAY ARGUMENTS .. INTEGER, INTENT( OUT ), OPTIONAL, TARGET :: IPIV( : ) REAL(WP), INTENT( INOUT ) :: A( :, : ) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_GESV computes the solution to a real or complex linear system of ! equations A*X = B, where A is a square matrix and X and B are ! rectangular matrices or vectors. Gaussian elimination with row ! interchanges is used to factor A as A = P*L*U , where P is a permutation ! matrix, L is unit lower triangular, and U is upper triangular. The ! factored form of A is then used to solve the above system. ! ! ========= ! ! SUBROUTINE LA_GESV( A, B, IPIV=ipiv, INFO=info ) ! (), INTENT(INOUT) :: A(:,:), ! INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:) ! INTEGER, INTENT(OUT), OPTIONAL :: INFO ! where ! ::= REAL | COMPLEX ! ::= KIND(1.0) | KIND(1.0D0) ! ::= B(:,:) | B(:) ! ! Arguments ! ========= ! ! A (input/output) REAL or COMPLEX square array, shape (:,:). ! On entry, the matrix A. ! On exit, the factors L and U from the factorization A = P*L*U; ! the unit diagonal elements of L are not stored. ! B (input/output) REAL or COMPLEX array, shape (:,:) with ! size(B,1) = size(A,1) or shape (:) with size(B) = size(A,1). ! On entry, the matrix B. ! On exit, the solution matrix X . ! IPIV Optional (output) INTEGER array, shape (:) with size(IPIV) = ! size(A,1). ! The pivot indices that define the permutation matrix P; row i of ! the matrix was interchanged with row IPIV(i). ! INFO Optional (output) INTEGER ! = 0 : successful exit. ! < 0 : if INFO = -i, the i-th argument has an illegal value. ! > 0 : if INFO = i, then U(i,i) = 0. The factorization has been ! completed, but the factor U is singular, so the solution could ! not be computed. ! If INFO is not present and an error occurs, then the program is ! terminated with an error message. !---------------------------------------------------------------------- ! .. PARAMETERS .. CHARACTER(LEN=8), PARAMETER :: SRNAME = 'LA_GETRF' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LNORM INTEGER :: LINFO, M, N, LD, ISTAT, ISTAT1, MINMN, LWORK, SIPIV REAL(WP) :: LANORM ! .. LOCAL POINTERS .. INTEGER, POINTER :: LIPIV(:), IWORK(:) REAL(WP), POINTER :: WORK(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC PRESENT, MAX, MIN, SIZE, TINY ! .. EXECUTABLE STATEMENTS .. M = SIZE(A,1); N = SIZE(A,2); LINFO = 0; ISTAT = 0; MINMN = MIN(M,N) LD = MAX(1,M) IF( PRESENT(IPIV) )THEN; SIPIV = SIZE(IPIV); ELSE; SIPIV = MINMN; ENDIF IF ( PRESENT(NORM) ) THEN; LNORM = NORM; ELSE; LNORM = '1'; END IF ! .. TEST THE ARGUMENTS IF( M < 0 .OR. N < 0 .OR. PRESENT(RCOND) .AND. M /= N )THEN; LINFO = -1 ELSE IF( SIPIV /= MINMN )THEN; LINFO = -2 ELSE IF( ( .NOT.PRESENT(RCOND) .AND. PRESENT(NORM) ) .OR. & ( .NOT.LSAME(LNORM,'I') .AND. .NOT.LSAME(LNORM,'O') & .AND. LNORM /= '1' ) ) THEN; LINFO = -4 ELSE IF( M > 0 .AND. N > 0 ) THEN IF( PRESENT(RCOND) .AND. M == N ) THEN ! .. COMPUTE THE NORM OF THE MATRIX A IF( LNORM == 'I' ) THEN; LWORK = MINMN; ELSE; LWORK = 1; END IF ALLOCATE( WORK(LWORK), STAT=ISTAT ) IF( ISTAT == 0 )THEN LANORM = LANGE_F77( LNORM, MINMN, MINMN, A, LD, WORK ) ELSE LINFO = -100 END IF DEALLOCATE(WORK, STAT=ISTAT1) END IF IF( LINFO == 0 ) THEN IF( PRESENT(IPIV) )THEN; LIPIV => IPIV ELSE; ALLOCATE( LIPIV( MINMN ), STAT=ISTAT ); ENDIF IF( ISTAT /= 0 )LINFO = -100 END IF IF( LINFO == 0 ) THEN ! .. COMPUTE THE LU FACTORS OF THE MATRIX A CALL GETRF_F77( M, N, A, LD, LIPIV, LINFO ) IF( .NOT. PRESENT(IPIV) )DEALLOCATE( LIPIV, STAT=ISTAT ) IF( PRESENT(RCOND) ) THEN ! .. COMPUTE THE RECIPROCAL OF THE CONDITION NUMBER OF A IF( LANORM <= TINY(1.0_WP) .OR. M /= N .OR. LINFO /= 0 ) THEN RCOND = 0.0_WP ELSE ALLOCATE(WORK(4*MINMN), IWORK(MINMN), STAT=ISTAT) IF( ISTAT == 0 )THEN CALL GECON_F77( LNORM, MINMN, A, LD, LANORM, & RCOND, WORK, IWORK, LINFO ) ELSE LINFO = -100 END IF DEALLOCATE( WORK, IWORK, STAT=ISTAT1 ) END IF END IF END IF ELSE IF( PRESENT(RCOND) ) THEN IF( M == N )THEN RCOND = 1.0_WP ELSE RCOND = 0.0_WP END IF END IF CALL ERINFO(LINFO,SRNAME,INFO,ISTAT) END SUBROUTINE DGETRF_F95