zlacon(3P)

NAME

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

SYNOPSIS

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

INTEGER KASE, N

DOUBLE PRECISION EST

COMPLEX∗16 V( N ), X( N )

#include <sunperf.h>

void zlacon(int n, doublecomplex ∗v, doublecomplex ∗zx, double ∗est, int ∗kase) ;

PURPOSE

ZLACON estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. If the initial call is made with KASE equal to -255 and subsequent intermediate calls made as described below then this subroutine is MT-safe, otherwise it is not MT-safe.

ARGUMENTS

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

V (workspace) COMPLEX∗16 array, dimension (N)
On the final return, V = A∗W, where EST = norm(V)/norm(W) (W is not returned).

X (input/output) COMPLEX∗16 array, dimension (N)
On an MT-unsafe 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 ZLACON must be re-called with all the other parameters unchanged. On an MT-safe intermediate return, X should be overwritten by A ∗ X if bits 8-11 of KASE=0001, A’ ∗ X if bits 8-11 of KASE=0010, where A’ is the conjugate transpose of A, and ZLACON must be re-called with all the other parameters unchanged. The MT-safe mode is described below in the description of the KASE argument.

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

KASE (input/output) INTEGER
On the initial call to ZLACON, KASE should be 0 or -255. If KASE was supplied as 0 on the initial call then on an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A ∗ X or A’ ∗ X. If KASE was supplied as -255 on the initial call then on an intermediate return, the low 8 bits of KASE will be 0 and the next 4 bits will contain 1 or 2, indicating whether X should be overwritten by A ∗ X or A’ ∗ X. On the final return from ZLACON, KASE will again be 0. If the initial call is made with KASE equal to -255 then this subroutine is MT-safe but does not conform to the standard LAPACK calling sequence. If the initial call is made with KASE equal to 0 then it is not MT-safe, but it conforms to the standard LAPACK calling sequence.

FURTHER DETAILS

Contributed by Nick Higham, University of Manchester.
Originally named CONEST, dated 27 Jun 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.