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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: estimates the 1-norm of a square, complex matrix A

```NAME
LAPACK-3 - 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.
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)

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
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