1DLANTR(1)           LAPACK auxiliary routine (version 3.2)           DLANTR(1)
2
3
4

NAME

6       DLANTR  -  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
9

SYNOPSIS

11       DOUBLE PRECISION FUNCTION  DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK
12                        )
13
14           CHARACTER    DIAG, NORM, UPLO
15
16           INTEGER      LDA, M, N
17
18           DOUBLE       PRECISION A( LDA, * ), WORK( * )
19

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.
24

DESCRIPTION

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

ARGUMENTS

41       NORM    (input) CHARACTER*1
42               Specifies  the  value  to  be  returned  in DLANTR as described
43               above.
44
45       UPLO    (input) CHARACTER*1
46               Specifies whether the matrix A is upper or  lower  trapezoidal.
47               = 'U':  Upper trapezoidal
48               =  'L':  Lower trapezoidal Note that A is triangular instead of
49               trapezoidal if M = N.
50
51       DIAG    (input) CHARACTER*1
52               Specifies whether or not the matrix A  has  unit  diagonal.   =
53               'N':  Non-unit diagonal
54               = 'U':  Unit diagonal
55
56       M       (input) INTEGER
57               The number of rows of the matrix A.  M >= 0, and if UPLO = 'U',
58               M <= N.  When M = 0, DLANTR is set to zero.
59
60       N       (input) INTEGER
61               The number of columns of the matrix A.  N >= 0, and if  UPLO  =
62               'L', N <= M.  When N = 0, DLANTR is set to zero.
63
64       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
65               The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
66               'U', the leading m by n upper trapezoidal part of the  array  A
67               contains  the  upper trapezoidal matrix, and the strictly lower
68               triangular part of A is not referenced.  If  UPLO  =  'L',  the
69               leading  m  by n lower trapezoidal part of the array A contains
70               the lower trapezoidal matrix, and the strictly upper triangular
71               part  of  A  is not referenced.  Note that when DIAG = 'U', the
72               diagonal elements of A are not referenced and are assumed to be
73               one.
74
75       LDA     (input) INTEGER
76               The leading dimension of the array A.  LDA >= max(M,1).
77
78       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
79               where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
80               enced.
81
82
83
84 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLANTR(1)