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

6       ZLANTR  -  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       DOUBLE PRECISION FUNCTION  ZLANTR( 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 WORK( * )
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20           COMPLEX*16   A( LDA, * )
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PURPOSE

23       ZLANTR  returns the value of the one norm,  or the Frobenius  norm,  or
24       the   infinity  norm,  or the  element of  largest absolute value  of a
25       trapezoidal or triangular matrix A.
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DESCRIPTION

28       ZLANTR returns the value
29          ZLANTR = ( 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'  where
36       norm1   denotes  the   one norm of a matrix (maximum column sum), normI
37       denotes the  infinity norm  of a matrix  (maximum row  sum)  and  normF
38       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

43       NORM    (input) CHARACTER*1
44               Specifies  the  value  to  be  returned  in ZLANTR as described
45               above.
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47       UPLO    (input) CHARACTER*1
48               Specifies whether the matrix A is upper or  lower  trapezoidal.
49               = 'U':  Upper trapezoidal
50               =  'L':  Lower trapezoidal Note that A is triangular instead of
51               trapezoidal if M = N.
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53       DIAG    (input) CHARACTER*1
54               Specifies whether or not the matrix A  has  unit  diagonal.   =
55               'N':  Non-unit diagonal
56               = 'U':  Unit diagonal
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58       M       (input) INTEGER
59               The number of rows of the matrix A.  M >= 0, and if UPLO = 'U',
60               M <= N.  When M = 0, ZLANTR is set to zero.
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62       N       (input) INTEGER
63               The number of columns of the matrix A.  N >= 0, and if  UPLO  =
64               'L', N <= M.  When N = 0, ZLANTR is set to zero.
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66       A       (input) COMPLEX*16 array, dimension (LDA,N)
67               The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
68               'U', the leading m by n upper trapezoidal part of the  array  A
69               contains  the  upper trapezoidal matrix, and the strictly lower
70               triangular part of A is not referenced.  If  UPLO  =  'L',  the
71               leading  m  by n lower trapezoidal part of the array A contains
72               the lower trapezoidal matrix, and the strictly upper triangular
73               part  of  A  is not referenced.  Note that when DIAG = 'U', the
74               diagonal elements of A are not referenced and are assumed to be
75               one.
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77       LDA     (input) INTEGER
78               The leading dimension of the array A.  LDA >= max(M,1).
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80       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
81               where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
82               enced.
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86 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLANTR(1)