# dlacn2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlacn2.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlacn2 (N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

## Function/Subroutine Documentation

### subroutine dlacn2 (integer N, double precision, dimension( * ) V, double precision, dimension( * ) X, integer, dimension( * ) ISGN, double precision EST, integer KASE, integer, dimension( 3 ) ISAVE)

DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

``` DLACN2 estimates the 1-norm of a square, real 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 DOUBLE PRECISION array, dimension (N)
On the final return, V = A*W,  where  EST = norm(V)/norm(W)
(W is not returned).
```

X

```          X is DOUBLE PRECISION array, dimension (N)
On an intermediate return, X should be overwritten by
A * X,   if KASE=1,
A**T * X,  if KASE=2,
and DLACN2 must be re-called with all the other parameters
unchanged.
```

ISGN

```          ISGN is INTEGER array, dimension (N)
```

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 DLACN2.
On exit, EST is an estimate (a lower bound) for norm(A).
```

KASE

```          KASE is INTEGER
On the initial call to DLACN2, 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**T * X.
On the final return from DLACN2, KASE will again be 0.
```

ISAVE

```          ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to DLACN2
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Further Details:

```  Originally named SONEST, dated March 16, 1988.

This is a thread safe version of DLACON, which uses the array ISAVE
in place of a SAVE statement, as follows:

DLACON     DLACN2
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 138 of file dlacn2.f.

## Author

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