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
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
|
.TH SLANTB l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
SLANTB - 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 triangular band matrix A, with ( k + 1 ) diagonals
.SH SYNOPSIS
.TP 14
REAL FUNCTION
SLANTB( NORM, UPLO, DIAG, N, K, AB,
LDAB, WORK )
.TP 14
.ti +4
CHARACTER
DIAG, NORM, UPLO
.TP 14
.ti +4
INTEGER
K, LDAB, N
.TP 14
.ti +4
REAL
AB( LDAB, * ), WORK( * )
.SH PURPOSE
SLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.
.SH DESCRIPTION
SLANTB returns the value
.br
SLANTB = ( 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 SLANTB as described
above.
.TP 8
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
.br
= 'L': Lower triangular
.TP 8
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
.br
= 'U': Unit triangular
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANTB is
set to zero.
.TP 8
K (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals of the matrix A if UPLO = 'L'.
K >= 0.
.TP 8
AB (input) REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first k+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
Note that when DIAG = 'U', the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= K+1.
.TP 8
WORK (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
|
