NAME¶

SLACN2 - estimates the 1-norm of a square, real matrix A

SYNOPSIS¶

SUBROUTINE SLACN2(

N, V, X, ISGN, EST, KASE, ISAVE )

INTEGER KASE, N REAL EST INTEGER ISGN( * ), ISAVE( 3 ) REAL V( * ), X( * )

PURPOSE¶

SLACN2 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) REAL array, dimension (N)

On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned).

X (input/output) REAL array, dimension (N)

On an intermediate return, X should be overwritten by A * X, if KASE=1, A' * X, if KASE=2, and SLACN2 must be re-called with all the other parameters unchanged.

ISGN (workspace) INTEGER array, dimension (N)

EST (input/output) REAL

On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to SLACN2. On exit, EST is an estimate (a lower bound) for norm(A).

KASE (input/output) INTEGER

On the initial call to SLACN2, 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 SLACN2, KASE will again be 0.

ISAVE (input/output) INTEGER array, dimension (3)

ISAVE is used to save variables between calls to SLACN2

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 SLACON, which uses the array ISAVE in place of a SAVE statement, as follows:
SLACON SLACN2
JUMP ISAVE(1)
J ISAVE(2)
ITER ISAVE(3)