DLACN2(1) LAPACK auxiliary routine (version 3.2) DLACN2(1)NAME
DLACN2 - estimates the 1-norm of a square, real matrix A
SYNOPSIS
SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
INTEGER KASE, N
DOUBLE PRECISION EST
INTEGER ISGN( * ), ISAVE( 3 )
DOUBLE PRECISION V( * ), X( * )
PURPOSE
DLACN2 estimates the 1-norm of a square, real matrix A. Reverse commu‐
nication 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 DLACN2 must be re-called with
all the other parameters unchanged.
ISGN (workspace) INTEGER array, dimension (N)
EST (input/output) DOUBLE PRECISION
On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
unchanged from the previous call to DLACN2. On exit, EST is an
estimate (a lower bound) for norm(A).
KASE (input/output) INTEGER
On the initial call to DLACN2, KASE should be 0. On an interme‐
diate return, KASE will be 1 or 2, indicating whether X should
be overwritten by A * X or A' * X. On the final return from
DLACN2, KASE will again be 0.
ISAVE (input/output) INTEGER array, dimension (3)
ISAVE is used to save variables between calls to DLACN2
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. This
is a thread safe version of DLACON, which uses the array ISAVE in place
of a SAVE statement, as follows:
DLACON DLACN2
JUMP ISAVE(1)
J ISAVE(2)
ITER ISAVE(3)
LAPACK auxiliary routine (versioNovember 2008 DLACN2(1)
