CLACON(l) — LAPACK auxiliary routine (version 2.0)

NAME

CLACON - estimate the 1-norm of a square, complex matrix A

SYNOPSIS

SUBROUTINE CLACON(
N, V, X, EST, KASE )

INTEGER KASE, N

REAL EST

COMPLEX V( N ), X( N )

PURPOSE

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

ARGUMENTS

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

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

X (input/output) COMPLEX array, dimension (N)
On an intermediate return, X should be overwritten by A ∗ X, if KASE=1, A’ ∗ X, if KASE=2, where A’ is the conjugate transpose of A, and CLACON must be re-called with all the other parameters unchanged.

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

KASE (input/output) INTEGER
On the initial call to CLACON, 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 CLACON, KASE will again be 0.

FURTHER DETAILS

Contributed by Nick Higham, University of Manchester.
Originally named CONEST, 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.