1ZLACN2(1)           LAPACK auxiliary routine (version 3.2)           ZLACN2(1)
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NAME

6       ZLACN2 - estimates the 1-norm of a square, complex matrix A
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SYNOPSIS

9       SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
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11           INTEGER        KASE, N
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13           DOUBLE         PRECISION EST
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15           INTEGER        ISAVE( 3 )
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17           COMPLEX*16     V( * ), X( * )
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PURPOSE

20       ZLACN2  estimates  the  1-norm  of a square, complex matrix A.  Reverse
21       communication is used for evaluating matrix-vector products.
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ARGUMENTS

24       N      (input) INTEGER
25              The order of the matrix.  N >= 1.
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27       V      (workspace) COMPLEX*16 array, dimension (N)
28              On the final return, V = A*W,  where  EST =  norm(V)/norm(W)  (W
29              is not returned).
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31       X      (input/output) COMPLEX*16 array, dimension (N)
32              On  an  intermediate  return,  X should be overwritten by A * X,
33              if KASE=1, A' * X,  if KASE=2, where A' is the conjugate  trans‐
34              pose  of  A,  and  ZLACN2  must  be re-called with all the other
35              parameters unchanged.
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37       EST    (input/output) DOUBLE PRECISION
38              On entry with KASE = 1 or 2 and ISAVE(1)  =  3,  EST  should  be
39              unchanged  from the previous call to ZLACN2.  On exit, EST is an
40              estimate (a lower bound) for norm(A).
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42       KASE   (input/output) INTEGER
43              On the initial call to ZLACN2, KASE should be 0.  On an interme‐
44              diate  return,  KASE will be 1 or 2, indicating whether X should
45              be overwritten by A * X  or A' * X.  On the  final  return  from
46              ZLACN2, KASE will again be 0.
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48       ISAVE  (input/output) INTEGER array, dimension (3)
49              ISAVE is used to save variables between calls to ZLACN2
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FURTHER DETAILS

52       Contributed by Nick Higham, University of Manchester.
53       Originally named CONEST, dated March 16, 1988.
54       Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a
55       real or complex matrix, with applications to condition estimation", ACM
56       Trans.  Math.  Soft., vol. 14, no. 4, pp. 381-396, December 1988.  Last
57       modified:  April, 1999
58       This is a thread safe version of ZLACON, which uses the array ISAVE  in
59       place of a SAVE statement, as follows:
60          ZLACON     ZLACN2
61           JUMP     ISAVE(1)
62           J        ISAVE(2)
63           ITER     ISAVE(3)
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67 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLACN2(1)