dlacon(3P)

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( ∗ )

#include <sunperf.h>

void dlacon(int n, double ∗v, double ∗dx, int ∗isgn, double ∗est, int ∗kase) ;

PURPOSE

DLACON estimates the 1-norm of a square, real 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) 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 MT-unsafe 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. 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, and DLACON must be re-called with all the other parameters unchanged. The MT-safe mode is described below in the description of the KASE argument.

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 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 DLACON, 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 SONEST, 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.