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## man page of LAPACK-3

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

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## 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 ZLACN2FURTHER 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. 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) LAPACK auxiliary routine (versionMarch 2011 LAPACK-3(3)

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