```      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

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