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.

          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.

          N is INTEGER
          The order of the matrix A.  N >= 0.

          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.

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by DSYTRF_ROOK.

          WORK is DOUBLE PRECISION array, dimension (N)

          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.

   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