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

6       SLANTR  -  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 SLANTR( 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      A( LDA, * ), WORK( * )
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PURPOSE

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

26       SLANTR returns the value
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28          SLANTR = ( 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'
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36       where   norm1   denotes the  one norm of a matrix (maximum column sum),
37       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
38       normF   denotes  the  Frobenius norm of a matrix (square root of sum of
39       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
40       norm.
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ARGUMENTS

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