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

6       DLANTR  -  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       DOUBLE PRECISION FUNCTION  DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK
12                        )
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14           CHARACTER    DIAG, NORM, UPLO
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16           INTEGER      LDA, M, N
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18           DOUBLE       PRECISION A( LDA, * ), WORK( * )
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PURPOSE

21       DLANTR  returns the value of the one norm,  or the Frobenius  norm,  or
22       the   infinity  norm,  or the  element of  largest absolute value  of a
23       trapezoidal or triangular matrix A.
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DESCRIPTION

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

45       NORM    (input) CHARACTER*1
46               Specifies the value to  be  returned  in  DLANTR  as  described
47               above.
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49       UPLO    (input) CHARACTER*1
50               Specifies  whether  the matrix A is upper or lower trapezoidal.
51               = 'U':  Upper trapezoidal
52               = 'L':  Lower trapezoidal Note that A is triangular instead  of
53               trapezoidal if M = N.
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55       DIAG    (input) CHARACTER*1
56               Specifies  whether  or  not  the matrix A has unit diagonal.  =
57               'N':  Non-unit diagonal
58               = 'U':  Unit diagonal
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60       M       (input) INTEGER
61               The number of rows of the matrix A.  M >= 0, and if UPLO = 'U',
62               M <= N.  When M = 0, DLANTR is set to zero.
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64       N       (input) INTEGER
65               The  number  of columns of the matrix A.  N >= 0, and if UPLO =
66               'L', N <= M.  When N = 0, DLANTR is set to zero.
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68       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
69               The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
70               'U',  the  leading m by n upper trapezoidal part of the array A
71               contains the upper trapezoidal matrix, and the  strictly  lower
72               triangular  part  of  A  is not referenced.  If UPLO = 'L', the
73               leading m by n lower trapezoidal part of the array  A  contains
74               the lower trapezoidal matrix, and the strictly upper triangular
75               part of A is not referenced.  Note that when DIAG  =  'U',  the
76               diagonal elements of A are not referenced and are assumed to be
77               one.
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79       LDA     (input) INTEGER
80               The leading dimension of the array A.  LDA >= max(M,1).
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82       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
83               where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
84               enced.
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88 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLANTR(1)