SUBROUTINE DSYGV_F95( A, B, W, ITYPE, JOBZ, UPLO, 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: ERINFO, LSAME USE F77_LAPACK, ONLY: SYGV_F77 => LA_SYGV, ILAENV_F77 => ILAENV ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: JOBZ, UPLO INTEGER, INTENT(IN), OPTIONAL :: ITYPE INTEGER, INTENT(OUT), OPTIONAL :: INFO ! .. ARRAY ARGUMENTS .. REAL(WP), INTENT(INOUT) :: A(:,:), B(:,:) REAL(WP), INTENT(OUT) :: W(:) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_SYGV, LA_SYGVD, LA_HEGV and LA_HEGVD compute all eigenvalues ! and, optionally, all eigenvectors of generalized eigenvalue problems of ! the form A*z = lambda*B*z, A*B*z = lambda*z, and B*A*z = lambda*z, ! where A and B are real symmetric in the cases of LA_SYGV and LA_SYGVD ! and complex Hermitian in the cases of LA_HEGV and LA_HEGVD. In all four ! cases B is positive deffinite. ! LA_SYGVD and LA_HEGVD use a divide and conquer algorithm. If ! eigenvectors are desired, they can be much faster than LA_SYGV and ! LA_HEGV for large matrices but use more workspace. ! ! ========= ! ! SUBROUTINE LA_SYGV / LA_SYGVD / LA_HEGV / LA_HEGVD( A, B, & ! W, ITYPE=itype, JOBZ=jobz, UPLO=uplo, INFO=info ) ! (), INTENT(INOUT) :: A(:,:), B(:,:) ! REAL(), INTENT(OUT) :: W(:) ! INTEGER, INTENT(IN), OPTIONAL :: ITYPE ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: JOBZ, UPLO ! INTEGER, INTENT(OUT), OPTIONAL :: INFO ! where ! ::= REAL | COMPLEX ! ::= KIND(1.0) | KIND(1.0D0) ! ! Arguments ! ========= ! ! A (input/output) REAL or COMPLEX square array, shape (:,:). ! On entry, the matrix A. ! If UPLO = 'U', the upper triangular part of A contains the ! upper triangular part of matrix A. If UPLO = 'L', the lower ! triangular part of A contains the lower triangular part of ! matrix A. ! On exit, if JOBZ = 'V', then the columns of A contain the ! eigenvectors, normalized as follows: ! if ITYPE = 1 or 2: Z^H*B*Z = I , ! if ITYPE = 3: Z^H*B^-1*Z = I . ! If JOBZ = 'N', then the upper triangle (if UPLO = 'U') or the ! lower triangle (if UPLO = 'L') of A, including the diagonal, ! is destroyed. ! B (input/output) REAL or COMPLEX square array, shape (:,:) with ! size(B,1) = size(A,1). ! On entry, the matrix B. If UPLO = 'U', the upper triangular ! part of B contains the upper triangular part of matrix B. If ! UPLO = 'L', the lower triangular part of B contains the lower ! triangular part of matrix B. ! On exit, if the part of B containing the matrix is overwritten ! by the triangular factor U or L of the Cholesky factorization ! B = U^H*U or B = L*L^H , respectively. ! W (output) REAL array, shape (:) with size(W) = size(A,1). ! The eigenvalues in ascending order. ! ITYPE Optional (input) INTEGER. ! Specifies the problem type to be solved: ! = 1: A*z = lambda*B*z ! = 2: A*B*z = lambda*z ! = 3: B*A*z = lambda*z ! Default value: 1. ! JOBZ Optional (input) CHARACTER(LEN=1). ! = 'N': Compute eigenvalues only; ! = 'V': Compute eigenvalues and eigenvectors. ! Default value: 'N'. ! UPLO Optional (input) CHARACTER(LEN=1). ! = 'U': Upper triangles of A and B are stored; ! = 'L': Lower triangles of A and B are stored. ! Default value: 'U'. ! INFO Optional (output) INTEGER. ! = 0: successful exit. ! < 0: if INFO = -i, the i-th argument had an illegal value. ! > 0: the algorithm failed to converge or matrix B is not ! positive deffinite: ! <= n: if INFO = i, i off-diagonal elements of an ! intermediate tridiagonal form did not converge to ! zero. ! > n: if INFO = n+i, for 1 <= i <= n, then the leading minor ! of order i of B is not positive deffinite. The ! factorization of B could not be completed and no ! eigenvalues or eigenvectors were computed. ! n is the order of A. ! If INFO is not present and an error occurs, then the program is ! terminated with an error message. !------------------------------------------------------------------------ ! .. LOCAL PARAMETERS .. CHARACTER(LEN=7), PARAMETER :: SRNAME = 'LA_SYGV' CHARACTER(LEN=6), PARAMETER :: BSNAME = 'DSYTRD' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LJOBZ, LUPLO INTEGER :: LINFO, N, LD, LITYPE, LWORK, NB, ISTAT, ISTAT1 ! .. LOCAL ARRAYS .. REAL(WP), POINTER :: WORK(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC SIZE, MAX, PRESENT ! .. EXECUTABLE STATEMENTS .. LINFO = 0; N = SIZE(A,1); LD = MAX(1,N); ISTAT = 0 IF( PRESENT(ITYPE) )THEN LITYPE = ITYPE ELSE LITYPE = 1 END IF IF( PRESENT(JOBZ) ) THEN LJOBZ = JOBZ ELSE LJOBZ = 'N' END IF IF( PRESENT(UPLO) ) THEN LUPLO = UPLO ELSE LUPLO = 'U' END IF ! .. TEST THE ARGUMENTS IF( SIZE( A, 2 ) /= N .OR. N < 0 )THEN LINFO = -1 ELSE IF( SIZE( B, 1 ) /= N .OR. SIZE( B, 2 ) /= N )THEN LINFO = -2 ELSE IF( SIZE( W ) /= N )THEN LINFO = -3 ELSE IF( LITYPE < 1 .OR. LITYPE > 3 )THEN LINFO = -4 ELSE IF( .NOT.LSAME(LJOBZ,'N') .AND. .NOT.LSAME(LJOBZ,'V') )THEN LINFO = -5 ELSE IF( .NOT.LSAME(LUPLO,'U') .AND. .NOT.LSAME(LUPLO,'L') )THEN LINFO = -6 ELSE IF( N > 0 )THEN ! .. DETERMINE THE WORKSPACE NB = ILAENV_F77( 1, BSNAME, LUPLO, N, -1, -1, -1 ) IF( NB <= 1 .OR. NB >= N )THEN NB = 1 ENDIF LWORK = N*(2+NB) ALLOCATE(WORK(LWORK), STAT=ISTAT) IF( ISTAT /= 0 )THEN DEALLOCATE(WORK, STAT=ISTAT1) LWORK = N*3-1 ALLOCATE(WORK(LWORK), STAT=ISTAT) IF( ISTAT /= 0 ) THEN LINFO = - 100 ELSE CALL ERINFO( -200, SRNAME, LINFO ) ENDIF ENDIF IF( LINFO == 0 .OR. LINFO <= -200 )THEN ! .. CALL LAPACK77 ROUTINE CALL SYGV_F77( LITYPE, LJOBZ, LUPLO, N, A, LD, B, LD, W, & WORK, LWORK, LINFO ) END IF DEALLOCATE(WORK, STAT=ISTAT1) ENDIF CALL ERINFO(LINFO, SRNAME, INFO, ISTAT) END SUBROUTINE DSYGV_F95