# zlacn2.f man page

zlacn2.f —

## Synopsis

### Functions/Subroutines

subroutinezlacn2(N, V, X, EST, KASE, ISAVE)ZLACN2estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

## Function/Subroutine Documentation

### subroutine zlacn2 (integerN, complex*16, dimension( * )V, complex*16, dimension( * )X, double precisionEST, integerKASE, integer, dimension( 3 )ISAVE)

**ZLACN2** estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

**Purpose:**

```
ZLACN2 estimates the 1-norm of a square, complex matrix A.
Reverse communication is used for evaluating matrix-vector products.
```

**Parameters:**

*N*

```
N is INTEGER
The order of the matrix. N >= 1.
```

*V*

```
V is COMPLEX*16 array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned).
```

*X*

```
X is COMPLEX*16 array, dimension (N)
On an intermediate return, X should be overwritten by
A * X, if KASE=1,
A**H * X, if KASE=2,
where A**H is the conjugate transpose of A, and ZLACN2 must be
re-called with all the other parameters unchanged.
```

*EST*

```
EST is 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*

```
KASE is 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**H * X.
On the final return from ZLACN2, KASE will again be 0.
```

*ISAVE*

```
ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to ZLACN2
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Further Details:**

```
Originally named CONEST, dated March 16, 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)
```

**Contributors:**

Nick Higham, University of Manchester

**References:**

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.

Definition at line 134 of file zlacn2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlacn2(3) is an alias of zlacn2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK