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
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
|
.TH DGBBRD l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
.SH SYNOPSIS
.TP 19
SUBROUTINE DGBBRD(
VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
LDQ, PT, LDPT, C, LDC, WORK, INFO )
.TP 19
.ti +4
CHARACTER
VECT
.TP 19
.ti +4
INTEGER
INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
.TP 19
.ti +4
DOUBLE
PRECISION AB( LDAB, * ), C( LDC, * ), D( * ), E( * ),
PT( LDPT, * ), Q( LDQ, * ), WORK( * )
.SH PURPOSE
DGBBRD reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
The routine computes B, and optionally forms Q or P', or computes
Q'*C for a given matrix C.
.br
.SH ARGUMENTS
.TP 8
VECT (input) CHARACTER*1
Specifies whether or not the matrices Q and P' are to be
formed.
= 'N': do not form Q or P';
.br
= 'Q': form Q only;
.br
= 'P': form P' only;
.br
= 'B': form both.
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
NCC (input) INTEGER
The number of columns of the matrix C. NCC >= 0.
.TP 8
KL (input) INTEGER
The number of subdiagonals of the matrix A. KL >= 0.
.TP 8
KU (input) INTEGER
The number of superdiagonals of the matrix A. KU >= 0.
.TP 8
AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the m-by-n 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(m,j+kl).
On exit, A is overwritten by values generated during the
reduction.
.TP 8
LDAB (input) INTEGER
The leading dimension of the array A. LDAB >= KL+KU+1.
.TP 8
D (output) DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
.TP 8
E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
The superdiagonal elements of the bidiagonal matrix B.
.TP 8
Q (output) DOUBLE PRECISION array, dimension (LDQ,M)
If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.
If VECT = 'N' or 'P', the array Q is not referenced.
.TP 8
LDQ (input) INTEGER
The leading dimension of the array Q.
LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
.TP 8
PT (output) DOUBLE PRECISION array, dimension (LDPT,N)
If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.
If VECT = 'N' or 'Q', the array PT is not referenced.
.TP 8
LDPT (input) INTEGER
The leading dimension of the array PT.
LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
.TP 8
C (input/output) DOUBLE PRECISION array, dimension (LDC,NCC)
On entry, an m-by-ncc matrix C.
On exit, C is overwritten by Q'*C.
C is not referenced if NCC = 0.
.TP 8
LDC (input) INTEGER
The leading dimension of the array C.
LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
.TP 8
WORK (workspace) DOUBLE PRECISION array, dimension (2*max(M,N))
.TP 8
INFO (output) INTEGER
= 0: successful exit.
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
|
