*> \brief \b DSYGST
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
*                         LWORK, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          JOBZ, UPLO
*       INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] ITYPE
*> \verbatim
*>          ITYPE is 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
*> \endverbatim
*>
*> \param[in] JOBZ
*> \verbatim
*>          JOBZ is CHARACTER*1
*>          = 'N':  Compute eigenvalues only;
*>          = 'V':  Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangles of A and B are stored;
*>          = 'L':  Lower triangles of A and B are stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrices A and B.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*>          W is DOUBLE PRECISION array, dimension (N)
*>          If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is 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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup doubleSYeigen
*
*  =====================================================================
      SUBROUTINE GAL_DSYGV(ITYPE,JOBZ,UPLO,N,A,LDA,B,LDB,W,WORK,
     $LWORK,INFO)
*
*  -- LAPACK driver routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTERJOBZ,UPLO
      INTEGER INFO,ITYPE,LDA,LDB,LWORK,N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),B(LDB,*),W(*),WORK(*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE
      PARAMETER (ONE=1.0D+0)
*     ..
*     .. Local Scalars ..
      LOGICAL LQUERY,UPPER,WANTZ
      CHARACTERTRANS
      INTEGER LWKMIN,LWKOPT,NB,NEIG
*     ..
*     .. External Functions ..
      LOGICAL GAL_LSAME
      INTEGER GAL_ILAENV
      EXTERNAL GAL_LSAME,GAL_ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DPOTRF,GAL_DSYEV,
     $GAL_DSYGST,GAL_DTRMM,GAL_DTRSM,GAL_XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      WANTZ=GAL_LSAME(JOBZ,'V')
      UPPER=GAL_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.GAL_LSAME(JOBZ,'N')))THEN
      INFO=-2
      ELSE IF(.NOT.(UPPER.OR.GAL_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=GAL_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 GAL_XERBLA('GAL_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 GAL_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 GAL_DSYGST(ITYPE,UPLO,N,A,LDA,B,LDB,INFO)
      CALL GAL_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)**T*y or inv(U)*y
*
      IF(UPPER)THEN
      TRANS='N'
      ELSE 
      TRANS='T'
      END IF
*
      CALL GAL_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**T*y
*
      IF(UPPER)THEN
      TRANS='T'
      ELSE 
      TRANS='N'
      END IF
*
      CALL GAL_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 
