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

6       CLANTR  -  returns the value of the one norm, or the Frobenius norm, or
7       the 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

27       CLANTR returns the value
28          CLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29                   (
30                   ( norm1(A),         NORM = '1', 'O' or 'o'
31                   (
32                   ( normI(A),         NORM = 'I' or 'i'
33                   (
34                   (  normF(A),          NORM  =  'F',  'f',  'E' or 'e' where
35       norm1  denotes the  one norm of a matrix (maximum  column  sum),  normI
36       denotes  the   infinity  norm  of a matrix  (maximum row sum) and normF
37       denotes the  Frobenius  norm  of  a  matrix  (square  root  of  sum  of
38       squares).   Note  that   max(abs(A(i,j)))   is  not a consistent matrix
39       norm.
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ARGUMENTS

42       NORM    (input) CHARACTER*1
43               Specifies the value to  be  returned  in  CLANTR  as  described
44               above.
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46       UPLO    (input) CHARACTER*1
47               Specifies  whether  the matrix A is upper or lower trapezoidal.
48               = 'U':  Upper trapezoidal
49               = 'L':  Lower trapezoidal Note that A is triangular instead  of
50               trapezoidal if M = N.
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52       DIAG    (input) CHARACTER*1
53               Specifies  whether  or  not  the matrix A has unit diagonal.  =
54               'N':  Non-unit diagonal
55               = 'U':  Unit diagonal
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57       M       (input) INTEGER
58               The number of rows of the matrix A.  M >= 0, and if UPLO = 'U',
59               M <= N.  When M = 0, CLANTR is set to zero.
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61       N       (input) INTEGER
62               The  number  of columns of the matrix A.  N >= 0, and if UPLO =
63               'L', N <= M.  When N = 0, CLANTR is set to zero.
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65       A       (input) COMPLEX array, dimension (LDA,N)
66               The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
67               'U',  the  leading m by n upper trapezoidal part of the array A
68               contains the upper trapezoidal matrix, and the  strictly  lower
69               triangular  part  of  A  is not referenced.  If UPLO = 'L', the
70               leading m by n lower trapezoidal part of the array  A  contains
71               the lower trapezoidal matrix, and the strictly upper triangular
72               part of A is not referenced.  Note that when DIAG  =  'U',  the
73               diagonal elements of A are not referenced and are assumed to be
74               one.
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76       LDA     (input) INTEGER
77               The leading dimension of the array A.  LDA >= max(M,1).
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79       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
80               where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
81               enced.
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85 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLANTR(1)