# zlacn2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zlacn2** (**N**, V, X, EST, KASE, ISAVE)**ZLACN2** estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

## Function/Subroutine Documentation

### subroutine zlacn2 (integer N, complex*16, dimension( * ) V, complex*16, dimension( * ) X, double precision EST, integer KASE, 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:**December 2016

**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 135 of file zlacn2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlacn2(3) is an alias of zlacn2.f(3).