SLACON (3lapack)

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, indicating 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.