*> \brief \b DSYTRI_ROOK
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYTRI_ROOK computes the inverse of a real symmetric
*> matrix A using the factorization A = U*D*U**T or A = L*D*L**T
*> computed by DSYTRF_ROOK.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the details of the factorization are stored
*>          as an upper or lower triangular matrix.
*>          = 'U':  Upper triangular, form is A = U*D*U**T;
*>          = 'L':  Lower triangular, form is A = L*D*L**T.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the block diagonal matrix D and the multipliers
*>          used to obtain the factor U or L as computed by DSYTRF_ROOK.
*>
*>          On exit, if INFO = 0, the (symmetric) inverse of the original
*>          matrix.  If UPLO = 'U', the upper triangular part of the
*>          inverse is formed and the part of A below the diagonal is not
*>          referenced; if UPLO = 'L' the lower triangular part of the
*>          inverse is formed and the part of A above the diagonal is
*>          not referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges and the block structure of D
*>          as determined by DSYTRF_ROOK.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (N)
*> \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) = 0; the matrix is singular and its
*>               inverse could not be computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleSYcomputational
*
*> \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 DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
*  -- LAPACK computational 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, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            K, KP, KSTEP
      DOUBLE PRECISION   AK, AKKP1, AKP1, D, T, TEMP
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DDOT
      EXTERNAL           LSAME, DDOT
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DSWAP, DSYMV, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYTRI_ROOK', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Check that the diagonal matrix D is nonsingular.
*
      IF( UPPER ) THEN
*
*        Upper triangular storage: examine D from bottom to top
*
         DO 10 INFO = N, 1, -1
            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
     $         RETURN
   10    CONTINUE
      ELSE
*
*        Lower triangular storage: examine D from top to bottom.
*
         DO 20 INFO = 1, N
            IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
     $         RETURN
   20    CONTINUE
      END IF
      INFO = 0
*
      IF( UPPER ) THEN
*
*        Compute inv(A) from the factorization A = U*D*U**T.
*
*        K is the main loop index, increasing from 1 to N in steps of
*        1 or 2, depending on the size of the diagonal blocks.
*
         K = 1
   30    CONTINUE
*
*        If K > N, exit from loop.
*
         IF( K.GT.N )
     $      GO TO 40
*
         IF( IPIV( K ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
            A( K, K ) = ONE / A( K, K )
*
*           Compute column K of the inverse.
*
            IF( K.GT.1 ) THEN
               CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
     $                     A( 1, K ), 1 )
               A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
     $                     1 )
            END IF
            KSTEP = 1
         ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
            T = ABS( A( K, K+1 ) )
            AK = A( K, K ) / T
            AKP1 = A( K+1, K+1 ) / T
            AKKP1 = A( K, K+1 ) / T
            D = T*( AK*AKP1-ONE )
            A( K, K ) = AKP1 / D
            A( K+1, K+1 ) = AK / D
            A( K, K+1 ) = -AKKP1 / D
*
*           Compute columns K and K+1 of the inverse.
*
            IF( K.GT.1 ) THEN
               CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
     $                     A( 1, K ), 1 )
               A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
     $                     1 )
               A( K, K+1 ) = A( K, K+1 ) -
     $                       DDOT( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
               CALL DCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
               CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
     $                     A( 1, K+1 ), 1 )
               A( K+1, K+1 ) = A( K+1, K+1 ) -
     $                         DDOT( K-1, WORK, 1, A( 1, K+1 ), 1 )
            END IF
            KSTEP = 2
         END IF
*
         IF( KSTEP.EQ.1 ) THEN
*
*           Interchange rows and columns K and IPIV(K) in the leading
*           submatrix A(1:k+1,1:k+1)
*
            KP = IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.GT.1 )
     $             CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
            END IF
         ELSE
*
*           Interchange rows and columns K and K+1 with -IPIV(K) and
*           -IPIV(K+1)in the leading submatrix A(1:k+1,1:k+1)
*
            KP = -IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.GT.1 )
     $            CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
*
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
               TEMP = A( K, K+1 )
               A( K, K+1 ) = A( KP, K+1 )
               A( KP, K+1 ) = TEMP
            END IF
*
            K = K + 1
            KP = -IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.GT.1 )
     $            CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
               CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
            END IF
         END IF
*
         K = K + 1
         GO TO 30
   40    CONTINUE
*
      ELSE
*
*        Compute inv(A) from the factorization A = L*D*L**T.
*
*        K is the main loop index, increasing from 1 to N in steps of
*        1 or 2, depending on the size of the diagonal blocks.
*
         K = N
   50    CONTINUE
*
*        If K < 1, exit from loop.
*
         IF( K.LT.1 )
     $      GO TO 60
*
         IF( IPIV( K ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
            A( K, K ) = ONE / A( K, K )
*
*           Compute column K of the inverse.
*
            IF( K.LT.N ) THEN
               CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
     $                     ZERO, A( K+1, K ), 1 )
               A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
     $                     1 )
            END IF
            KSTEP = 1
         ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
            T = ABS( A( K, K-1 ) )
            AK = A( K-1, K-1 ) / T
            AKP1 = A( K, K ) / T
            AKKP1 = A( K, K-1 ) / T
            D = T*( AK*AKP1-ONE )
            A( K-1, K-1 ) = AKP1 / D
            A( K, K ) = AK / D
            A( K, K-1 ) = -AKKP1 / D
*
*           Compute columns K-1 and K of the inverse.
*
            IF( K.LT.N ) THEN
               CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
     $                     ZERO, A( K+1, K ), 1 )
               A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
     $                     1 )
               A( K, K-1 ) = A( K, K-1 ) -
     $                       DDOT( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
     $                       1 )
               CALL DCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
               CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
     $                     ZERO, A( K+1, K-1 ), 1 )
               A( K-1, K-1 ) = A( K-1, K-1 ) -
     $                         DDOT( N-K, WORK, 1, A( K+1, K-1 ), 1 )
            END IF
            KSTEP = 2
         END IF
*
         IF( KSTEP.EQ.1 ) THEN
*
*           Interchange rows and columns K and IPIV(K) in the trailing
*           submatrix A(k-1:n,k-1:n)
*
            KP = IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.LT.N )
     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
            END IF
         ELSE
*
*           Interchange rows and columns K and K-1 with -IPIV(K) and
*           -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
*
            KP = -IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.LT.N )
     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
*
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
               TEMP = A( K, K-1 )
               A( K, K-1 ) = A( KP, K-1 )
               A( KP, K-1 ) = TEMP
            END IF
*
            K = K - 1
            KP = -IPIV( K )
            IF( KP.NE.K ) THEN
               IF( KP.LT.N )
     $            CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
               CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
               TEMP = A( K, K )
               A( K, K ) = A( KP, KP )
               A( KP, KP ) = TEMP
            END IF
         END IF
*
         K = K - 1
         GO TO 50
   60    CONTINUE
      END IF
*
      RETURN
*
*     End of DSYTRI_ROOK
*
      END