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

6       CLANTR  -  the  value  of  the  one norm, or the Frobenius norm, or the
7       infinity norm, or the element of largest absolute  value  of  a  trape‐
8       zoidal or triangular matrix A
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SYNOPSIS

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

22       CLANTR   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       trapezoidal or triangular matrix A.
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DESCRIPTION

28       CLANTR returns the value
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30          CLANTR = ( 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 CLANTR as described
48               above.
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50       UPLO    (input) CHARACTER*1
51               Specifies whether the matrix A is upper or  lower  trapezoidal.
52               = 'U':  Upper trapezoidal
53               =  'L':  Lower trapezoidal Note that A is triangular instead of
54               trapezoidal if M = N.
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56       DIAG    (input) CHARACTER*1
57               Specifies whether or not the matrix A  has  unit  diagonal.   =
58               'N':  Non-unit diagonal
59               = 'U':  Unit diagonal
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61       M       (input) INTEGER
62               The number of rows of the matrix A.  M >= 0, and if UPLO = 'U',
63               M <= N.  When M = 0, CLANTR is set to zero.
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65       N       (input) INTEGER
66               The number of columns of the matrix A.  N >= 0, and if  UPLO  =
67               'L', N <= M.  When N = 0, CLANTR is set to zero.
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69       A       (input) COMPLEX array, dimension (LDA,N)
70               The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
71               'U', the leading m by n upper trapezoidal part of the  array  A
72               contains  the  upper trapezoidal matrix, and the strictly lower
73               triangular part of A is not referenced.  If  UPLO  =  'L',  the
74               leading  m  by n lower trapezoidal part of the array A contains
75               the lower trapezoidal matrix, and the strictly upper triangular
76               part  of  A  is not referenced.  Note that when DIAG = 'U', the
77               diagonal elements of A are not referenced and are assumed to be
78               one.
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80       LDA     (input) INTEGER
81               The leading dimension of the array A.  LDA >= max(M,1).
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83       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
84               where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
85               enced.
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89 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLANTR(1)