NAME¶

ZLACN2 - estimates the 1-norm of a square, complex matrix A

SYNOPSIS¶

SUBROUTINE ZLACN2(

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

INTEGER KASE, N DOUBLE PRECISION EST INTEGER ISAVE( 3 ) COMPLEX*16 V( * ), X( * )

PURPOSE¶

ZLACN2 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*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 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 ZLACN2 must be re-called with all the other parameters unchanged.

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 ZLACN2. On exit, EST is an estimate (a lower bound) for norm(A).

KASE (input/output) INTEGER

On the initial call to ZLACN2, 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 ZLACN2, KASE will again be 0.

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

ISAVE is used to save variables between calls to ZLACN2

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. Last modified: April, 1999
This is a thread safe version of ZLACON, which uses the array ISAVE in place of a SAVE statement, as follows:
ZLACON ZLACN2
JUMP ISAVE(1)
J ISAVE(2)
ITER ISAVE(3)