dsygv.f

          SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
         $                  LWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, UPLO
          INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DSYGV computes all the eigenvalues, and optionally, the eigenvectors
    *  of a real generalized symmetric-definite eigenproblem, of the form
    *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
    *  Here A and B are assumed to be symmetric and B is also
    *  positive definite.
    *
    *  Arguments
    *  =========
    *
    *  ITYPE   (input) INTEGER
    *          Specifies the problem type to be solved:
    *          = 1:  A*x = (lambda)*B*x
    *          = 2:  A*B*x = (lambda)*x
    *          = 3:  B*A*x = (lambda)*x
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangles of A and B are stored;
    *          = 'L':  Lower triangles of A and B are stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrices A and B.  N >= 0.
    *
    *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
    *          On entry, the symmetric matrix A.  If UPLO = 'U', the
    *          leading N-by-N upper triangular part of A contains the
    *          upper triangular part of the matrix A.  If UPLO = 'L',
    *          the leading N-by-N lower triangular part of A contains
    *          the lower triangular part of the matrix A.
    *
    *          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
    *          matrix Z of eigenvectors.  The eigenvectors are normalized
    *          as follows:
    *          if ITYPE = 1 or 2, Z**T*B*Z = I;
    *          if ITYPE = 3, Z**T*inv(B)*Z = I.
    *          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
    *          or the lower triangle (if UPLO='L') of A, including the
    *          diagonal, is destroyed.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
    *          On entry, the symmetric positive definite matrix B.
    *          If UPLO = 'U', the leading N-by-N upper triangular part of B
    *          contains the upper triangular part of the matrix B.
    *          If UPLO = 'L', the leading N-by-N lower triangular part of B
    *          contains the lower triangular part of the matrix B.
    *
    *          On exit, if INFO <= N, the part of B containing the matrix is
    *          overwritten by the triangular factor U or L from the Cholesky
    *          factorization B = U**T*U or B = L*L**T.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,N).
    *
    *  W       (output) DOUBLE PRECISION array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The length of the array WORK.  LWORK >= max(1,3*N-1).
    *          For optimal efficiency, LWORK >= (NB+2)*N,
    *          where NB is the blocksize for DSYTRD returned by ILAENV.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  DPOTRF or DSYEV returned an error code:
    *             <= N:  if INFO = i, DSYEV failed to converge;
    *                    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 definite.
    *                    The factorization of B could not be completed and
    *                    no eigenvalues or eigenvectors were computed.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE
          PARAMETER          ( ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, UPPER, WANTZ
          CHARACTER          TRANS
          INTEGER            LWKMIN, LWKOPT, NB, NEIG
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          WANTZ = LSAME( JOBZ, 'V' )
          UPPER = LSAME( UPLO, 'U' )
          LQUERY = ( LWORK.EQ.-1 )
    *
          INFO = 0
          IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
             INFO = -1
          ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
             INFO = -2
          ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
             INFO = -3
          ELSE IF( N.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -6
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -8
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             LWKMIN = MAX( 1, 3*N - 1 )
             NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
             LWKOPT = MAX( LWKMIN, ( NB + 2 )*N )
             WORK( 1 ) = LWKOPT
    *
             IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
                INFO = -11
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DSYGV ', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Form a Cholesky factorization of B.
    *
          CALL DPOTRF( UPLO, N, B, LDB, INFO )
          IF( INFO.NE.0 ) THEN
             INFO = N + INFO
             RETURN
          END IF
    *
    *     Transform problem to standard eigenvalue problem and solve.
    *
          CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
          CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
    *
          IF( WANTZ ) THEN
    *
    *        Backtransform eigenvectors to the original problem.
    *
             NEIG = N
             IF( INFO.GT.0 )
         $      NEIG = INFO - 1
             IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
    *
    *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
    *           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
    *
                IF( UPPER ) THEN
                   TRANS = 'N'
                ELSE
                   TRANS = 'T'
                END IF
    *
                CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
         $                  B, LDB, A, LDA )
    *
             ELSE IF( ITYPE.EQ.3 ) THEN
    *
    *           For B*A*x=(lambda)*x;
    *           backtransform eigenvectors: x = L*y or U'*y
    *
                IF( UPPER ) THEN
                   TRANS = 'T'
                ELSE
                   TRANS = 'N'
                END IF
    *
                CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
         $                  B, LDB, A, LDA )
             END IF
          END IF
    *
          WORK( 1 ) = LWKOPT
          RETURN
    *
    *     End of DSYGV
    *
          END