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

6       CLANHS  -  the  value  of  the  one norm, or the Frobenius norm, or the
7       infinity norm, or the element of largest absolute value of a Hessenberg
8       matrix A
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SYNOPSIS

11       REAL FUNCTION CLANHS( NORM, N, A, LDA, WORK )
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13           CHARACTER NORM
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15           INTEGER   LDA, N
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17           REAL      WORK( * )
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19           COMPLEX   A( LDA, * )
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PURPOSE

22       CLANHS   returns  the value of the one norm,  or the Frobenius norm, or
23       the  infinity norm,  or the  element of  largest absolute value   of  a
24       Hessenberg matrix A.
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DESCRIPTION

28       CLANHS returns the value
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30          CLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
31                   (
32                   ( norm1(A),         NORM = '1', 'O' or 'o'
33                   (
34                   ( normI(A),         NORM = 'I' or 'i'
35                   (
36                   ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
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38       where   norm1   denotes the  one norm of a matrix (maximum column sum),
39       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
40       normF   denotes  the  Frobenius norm of a matrix (square root of sum of
41       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
42       norm.
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ARGUMENTS

46       NORM    (input) CHARACTER*1
47               Specifies  the  value  to  be  returned  in CLANHS as described
48               above.
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50       N       (input) INTEGER
51               The order of the matrix A.  N >= 0.  When N = 0, CLANHS is  set
52               to zero.
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54       A       (input) COMPLEX array, dimension (LDA,N)
55               The  n  by n upper Hessenberg matrix A; the part of A below the
56               first sub-diagonal is not referenced.
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58       LDA     (input) INTEGER
59               The leading dimension of the array A.  LDA >= max(N,1).
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61       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
62               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
63               enced.
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67 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLANHS(1)