1DLACN2(1)           LAPACK auxiliary routine (version 3.2)           DLACN2(1)
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NAME

6       DLACN2 - estimates the 1-norm of a square, real matrix A
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SYNOPSIS

9       SUBROUTINE DLACN2( N, V, X, ISGN, 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        ISGN( * ), ISAVE( 3 )
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17           DOUBLE         PRECISION V( * ), X( * )
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PURPOSE

20       DLACN2 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

24       N      (input) INTEGER
25              The order of the matrix.  N >= 1.
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27       V      (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DLACN2 must be re-called with
34              all the other parameters unchanged.
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36       ISGN   (workspace) INTEGER array, dimension (N)
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38       EST    (input/output) DOUBLE PRECISION
39              On  entry  with  KASE  =  1 or 2 and ISAVE(1) = 3, EST should be
40              unchanged from the previous call to DLACN2.  On exit, EST is  an
41              estimate (a lower bound) for norm(A).
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43       KASE   (input/output) INTEGER
44              On the initial call to DLACN2, 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              DLACN2, KASE will again be 0.
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49       ISAVE  (input/output) INTEGER array, dimension (3)
50              ISAVE is used to save variables between calls to DLACN2
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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 DLACON, which uses the array ISAVE in place
59       of a SAVE statement, as follows:
60          DLACON     DLACN2
61           JUMP     ISAVE(1)
62           J        ISAVE(2)
63           ITER     ISAVE(3)
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67 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLACN2(1)