*> \brief <b> DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices</b>
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
*                         LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYSV_ROOK computes the solution to a real system of linear
*> equations
*>    A * X = B,
*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
*> matrices.
*>
*> The diagonal pivoting method is used to factor A as
*>    A = U * D * U**T,  if UPLO = 'U', or
*>    A = L * D * L**T,  if UPLO = 'L',
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and D is symmetric and block diagonal with
*> 1-by-1 and 2-by-2 diagonal blocks.
*>
*> DSYTRF_ROOK is called to compute the factorization of a real
*> symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
*> pivoting method.
*>
*> The factored form of A is then used to solve the system
*> of equations A * X = B by calling DSYTRS_ROOK.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of linear equations, i.e., the order of the
*>          matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand sides, i.e., the number of columns
*>          of the matrix B.  NRHS >= 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, and the strictly lower
*>          triangular part of A is not referenced.  If UPLO = 'L', the
*>          leading N-by-N lower triangular part of A contains the lower
*>          triangular part of the matrix A, and the strictly upper
*>          triangular part of A is not referenced.
*>
*>          On exit, if INFO = 0, the block diagonal matrix D and the
*>          multipliers used to obtain the factor U or L from the
*>          factorization A = U*D*U**T or A = L*D*L**T as computed by
*>          DSYTRF_ROOK.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges and the block structure of D,
*>          as determined by DSYTRF_ROOK.
*>
*>          If UPLO = 'U':
*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
*>
*>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
*>               columns k and -IPIV(k) were interchanged and rows and
*>               columns k-1 and -IPIV(k-1) were inerchaged,
*>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
*>
*>          If UPLO = 'L':
*>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
*>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
*>
*>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
*>               columns k and -IPIV(k) were interchanged and rows and
*>               columns k+1 and -IPIV(k+1) were inerchaged,
*>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          On entry, the N-by-NRHS right hand side matrix B.
*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \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 WORK.  LWORK >= 1, and for best performance
*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
*>          DSYTRF_ROOK.
*>
*>          TRS will be done with Level 2 BLAS
*>
*>          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: if INFO = i, D(i,i) is exactly zero.  The factorization
*>               has been completed, but the block diagonal matrix D is
*>               exactly singular, so the solution could not be computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hesv_rook
*
*> \par Contributors:
*  ==================
*>
*> \verbatim
*>
*>   April 2012, Igor Kozachenko,
*>                  Computer Science Division,
*>                  University of California, Berkeley
*>
*>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
*>                  School of Mathematics,
*>                  University of Manchester
*>
*> \endverbatim
*
*  =====================================================================
      SUBROUTINE DSYSV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
     $                       WORK,
     $                  LWORK, INFO )
*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            LWKOPT
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, DSYTRF_ROOK, DSYTRS_ROOK
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( .NOT.LSAME( UPLO, 'U' ) .AND.
     $    .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
         INFO = -10
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( N.EQ.0 ) THEN
            LWKOPT = 1
         ELSE
            CALL DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
            LWKOPT = INT( WORK( 1 ) )
         END IF
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYSV_ROOK ', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
*
      CALL DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
      IF( INFO.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
*        Solve with TRS_ROOK ( Use Level 2 BLAS)
*
         CALL DSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
     $                     INFO )
*
      END IF
*
      WORK( 1 ) = LWKOPT
*
      RETURN
*
*     End of DSYSV_ROOK
*
      END
