Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - estimates the 1-norm of a square, real matrix A

**SYNOPSIS**

SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) INTEGER KASE, N DOUBLE PRECISION EST INTEGER ISGN( * ), ISAVE( 3 ) DOUBLE PRECISION V( * ), X( * )

**PURPOSE**

DLACN2 estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products.

**ARGUMENTS**

N (input) INTEGER The order of the matrix. N >= 1. V (workspace) DOUBLE PRECISION array, dimension (N) On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned). X (input/output) 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 (workspace) INTEGER array, dimension (N) 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 DLACN2. On exit, EST is an estimate (a lower bound) for norm(A). KASE (input/output) 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 (input/output) INTEGER array, dimension (3) ISAVE is used to save variables between calls to DLACN2

**FURTHER** **DETAILS**

Contributed by Nick Higham, University of Manchester. Originally named SONEST, 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 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) LAPACK auxiliary routine (version 3.2) April 2011 DLACN2(3lapack)