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slacon

 NAME
      SLACON - estimate the 1-norm of a square, real matrix A

 SYNOPSIS
      SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE )

          INTEGER        KASE, N

          REAL           EST

          INTEGER        ISGN( * )

          REAL           V( * ), X( * )

 PURPOSE
      SLACON estimates the 1-norm of a square, real matrix A.
      Reverse communication is used for evaluating matrix-vector
      products.

 ARGUMENTS
      N      (input) INTEGER
             The order of the matrix.  N >= 1.

      V      (workspace) REAL array, dimension (N)
             On the final return, V = A*W,  where  EST =
             norm(V)/norm(W) (W is not returned).

      X      (input/output) REAL array, dimension (N)
             On an intermediate return, X should be overwritten by
             A * X,   if KASE=1, A' * X,  if KASE=2, and SLACON
             must be re-called with all the other parameters
             unchanged.

      ISGN   (workspace) INTEGER array, dimension (N)

      EST    (output) REAL
             An estimate (a lower bound) for norm(A).

      KASE   (input/output) INTEGER
             On the initial call to SLACON, KASE should be 0.  On
             an intermediate return, KASE will be 1 or 2, indicat-
             ing whether X should be overwritten by A * X  or A' *
             X.  On the final return from SLACON, KASE will again
             be 0.

 FURTHER DETAILS
      Contributed by Nick Higham, University of Manchester.
      Originally named SONEST, dated March 16, 1988.

      Reference: N.J. Higham, "FORTRAN codes for estimating the
      one-norm of a real or complex matrix, with applications to

      condition estimation", ACM Trans. Math. Soft., vol. 14, no.
      4, pp. 381-396, December 1988.