1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
.TH DLANGB l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
.SH SYNOPSIS
.TP 17
DOUBLE PRECISION
FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
WORK )
.TP 17
.ti +4
CHARACTER
NORM
.TP 17
.ti +4
INTEGER
KL, KU, LDAB, N
.TP 17
.ti +4
DOUBLE
PRECISION AB( LDAB, * ), WORK( * )
.SH PURPOSE
DLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
.SH DESCRIPTION
DLANGB returns the value
.br
DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
.br
(
.br
( norm1(A), NORM = '1', 'O' or 'o'
.br
(
.br
( normI(A), NORM = 'I' or 'i'
.br
(
.br
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
.SH ARGUMENTS
.TP 8
NORM (input) CHARACTER*1
Specifies the value to be returned in DLANGB as described
above.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANGB is
set to zero.
.TP 8
KL (input) INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.
.TP 8
KU (input) INTEGER
The number of super-diagonals of the matrix A. KU >= 0.
.TP 8
AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th
column of A is stored in the j-th column of the array AB as
follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
.TP 8
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
|
