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
104
105
106
|
SUBROUTINE MB04OX( N, A, LDA, X, INCX )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To perform the QR factorization
C
C (U ) = Q*(R),
C (x') (0)
C
C where U and R are n-by-n upper triangular matrices, x is an
C n element vector and Q is an (n+1)-by-(n+1) orthogonal matrix.
C
C U must be supplied in the n-by-n upper triangular part of the
C array A and this is overwritten by R.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The number of elements of X and the order of the square
C matrix A. N >= 0.
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
C On entry, the leading N-by-N upper triangular part of this
C array must contain the upper triangular matrix U.
C On exit, the leading N-by-N upper triangular part of this
C array contains the upper triangular matrix R.
C The strict lower triangle of A is not referenced.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= max(1,N).
C
C X (input/output) DOUBLE PRECISION array, dimension
C (1+(N-1)*INCX)
C On entry, the incremented array X must contain the
C vector x. On exit, the content of X is changed.
C
C INCX (input) INTEGER.
C Specifies the increment for the elements of X. INCX > 0.
C
C METHOD
C
C The matrix Q is formed as a sequence of plane rotations in planes
C (1, n+1), (2, n+1), ..., (n, n+1), the rotation in the (j, n+1)th
C plane, Q(j), being chosen to annihilate the jth element of x.
C
C CONTRIBUTOR
C
C A. Varga, German Aerospace Center,
C DLR Oberpfaffenhofen, July 1998.
C Based on the RASP routine DUTUPD.
C
C REVISIONS
C
C Nov. 1998, V. Sima, Research Institute for Informatics, Bucharest.
C
C ******************************************************************
C
C .. Scalar Arguments ..
INTEGER INCX, LDA, N
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), X(*)
C .. Local Scalars ..
DOUBLE PRECISION CI, SI, TEMP
INTEGER I, IX
C .. External Subroutines ..
EXTERNAL DLARTG, DROT
C
C .. Executable Statements ..
C
C For efficiency reasons, the parameters are not checked.
C
IX = 1
C
DO 20 I = 1, N - 1
CALL DLARTG( A(I,I), X(IX), CI, SI, TEMP )
A(I,I) = TEMP
IX = IX + INCX
CALL DROT( N-I, A(I,I+1), LDA, X(IX), INCX, CI, SI )
20 CONTINUE
C
CALL DLARTG( A(N,N), X(IX), CI, SI, TEMP )
A(N,N) = TEMP
C
RETURN
C *** Last line of MB04OX ***
END
|
