1CLACN2(1)           LAPACK auxiliary routine (version 3.1)           CLACN2(1)
2
3
4

NAME

6       CLACN2 - the 1-norm of a square, complex matrix A
7

SYNOPSIS

9       SUBROUTINE CLACN2( N, V, X, EST, KASE, ISAVE )
10
11           INTEGER        KASE, N
12
13           REAL           EST
14
15           INTEGER        ISAVE( 3 )
16
17           COMPLEX        V( * ), X( * )
18

PURPOSE

20       CLACN2  estimates  the  1-norm  of a square, complex matrix A.  Reverse
21       communication is used for evaluating matrix-vector products.
22
23

ARGUMENTS

25       N      (input) INTEGER
26              The order of the matrix.  N >= 1.
27
28       V      (workspace) COMPLEX array, dimension (N)
29              On the final return, V = A*W,  where  EST =  norm(V)/norm(W)  (W
30              is not returned).
31
32       X      (input/output) COMPLEX array, dimension (N)
33              On  an  intermediate  return,  X should be overwritten by A * X,
34              if KASE=1, A' * X,  if KASE=2, where A' is the conjugate  trans‐
35              pose  of  A,  and  CLACN2  must  be re-called with all the other
36              parameters unchanged.
37
38       EST    (input/output) REAL
39              On entry with KASE = 1 or 2 and ISAVE(1)  =  3,  EST  should  be
40              unchanged  from the previous call to CLACN2.  On exit, EST is an
41              estimate (a lower bound) for norm(A).
42
43       KASE   (input/output) INTEGER
44              On the initial call to CLACN2, KASE should be 0.  On an interme‐
45              diate  return,  KASE will be 1 or 2, indicating whether X should
46              be overwritten by A * X  or A' * X.  On the  final  return  from
47              CLACN2, KASE will again be 0.
48
49       ISAVE  (input/output) INTEGER array, dimension (3)
50              ISAVE is used to save variables between calls to SLACN2
51

FURTHER DETAILS

53       Contributed by Nick Higham, University of Manchester.
54       Originally named CONEST, dated March 16, 1988.
55
56       Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a
57       real or complex matrix, with applications to condition estimation", ACM
58       Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
59
60       Last modified:  April, 1999
61
62       This  is a thread safe version of CLACON, which uses the array ISAVE in
63       place of a SAVE statement, as follows:
64
65          CLACON     CLACN2
66           JUMP     ISAVE(1)
67           J        ISAVE(2)
68           ITER     ISAVE(3)
69
70
71
72
73 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLACN2(1)