subroutine zlacn2 (N, V, X, EST, KASE, ISAVE)
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.
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
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
September 2012Further 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)
Nick Higham, University of ManchesterReferences:
N.J. Higham, 'FORTRAN codes for estimating the one-norm ofDefinition at line 134 of file zlacn2.f.
a real or complex matrix, with applications to condition estimation', ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.