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# dlacon

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

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

INTEGER        KASE, N

DOUBLE         PRECISION EST

INTEGER        ISGN( * )

DOUBLE         PRECISION V( * ), X( * )

PURPOSE
DLACON 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) DOUBLE PRECISION array, dimension (N)
On the final return, V = A*W,  where  EST =
norm(V)/norm(W) (W is not returned).

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

ISGN   (workspace) INTEGER array, dimension (N)

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

KASE   (input/output) INTEGER
On the initial call to DLACON, 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 DLACON, 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.
```