1SLACN2(1)           LAPACK auxiliary routine (version 3.1)           SLACN2(1)
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NAME

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

9       SUBROUTINE SLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
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11           INTEGER        KASE, N
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13           REAL           EST
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15           INTEGER        ISGN( * ), ISAVE( 3 )
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17           REAL           V( * ), X( * )
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PURPOSE

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

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

54       Contributed by Nick Higham, University of Manchester.
55       Originally named SONEST, dated March 16, 1988.
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57       Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a
58       real or complex matrix, with applications to condition estimation", ACM
59       Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
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61       This is a thread safe version of SLACON, which uses the array ISAVE  in
62       place of a SAVE statement, as follows:
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64          SLACON     SLACN2
65           JUMP     ISAVE(1)
66           J        ISAVE(2)
67           ITER     ISAVE(3)
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72 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLACN2(1)
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