1SLACN2(1)           LAPACK auxiliary routine (version 3.2)           SLACN2(1)
2
3
4

NAME

6       SLACN2 - estimates the 1-norm of a square, real matrix A
7

SYNOPSIS

9       SUBROUTINE SLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
10
11           INTEGER        KASE, N
12
13           REAL           EST
14
15           INTEGER        ISGN( * ), ISAVE( 3 )
16
17           REAL           V( * ), X( * )
18

PURPOSE

20       SLACN2 estimates the 1-norm of a square, real matrix A.  Reverse commu‐
21       nication is used for evaluating matrix-vector products.
22

ARGUMENTS

24       N      (input) INTEGER
25              The order of the matrix.  N >= 1.
26
27       V      (workspace) REAL array, dimension (N)
28              On the final return, V = A*W,  where  EST =  norm(V)/norm(W)  (W
29              is not returned).
30
31       X      (input/output) REAL array, dimension (N)
32              On  an  intermediate  return,  X should be overwritten by A * X,
33              if KASE=1, A' * X,  if KASE=2, and SLACN2 must be re-called with
34              all the other parameters unchanged.
35
36       ISGN   (workspace) INTEGER array, dimension (N)
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 SLACN2.  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 SLACN2, 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              SLACN2, 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 SONEST, dated March 16, 1988.
55       Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a
56       real or complex matrix, with applications to condition estimation", ACM
57       Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December  1988.   This
58       is a thread safe version of SLACON, which uses the array ISAVE in place
59       of a SAVE statement, as follows:
60          SLACON     SLACN2
61           JUMP     ISAVE(1)
62           J        ISAVE(2)
63           ITER     ISAVE(3)
64
65
66
67 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLACN2(1)