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
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
|
SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, K, LDA, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DORG2R generates an m by n real matrix Q with orthonormal columns,
* which is defined as the first n columns of a product of k elementary
* reflectors of order m
*
* Q = H(1) H(2) . . . H(k)
*
* as returned by DGEQRF.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix Q. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix Q. M >= N >= 0.
*
* K (input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. N >= K >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the i-th column must contain the vector which
* defines the elementary reflector H(i), for i = 1,2,...,k, as
* returned by DGEQRF in the first k columns of its array
* argument A.
* On exit, the m-by-n matrix Q.
*
* LDA (input) INTEGER
* The first dimension of the array A. LDA >= max(1,M).
*
* TAU (input) DOUBLE PRECISION array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DGEQRF.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument has an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, L
* ..
* .. External Subroutines ..
EXTERNAL DLARF, DSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
INFO = -2
ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORG2R', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.0 )
$ RETURN
*
* Initialise columns k+1:n to columns of the unit matrix
*
DO 20 J = K + 1, N
DO 10 L = 1, M
A( L, J ) = ZERO
10 CONTINUE
A( J, J ) = ONE
20 CONTINUE
*
DO 40 I = K, 1, -1
*
* Apply H(i) to A(i:m,i:n) from the left
*
IF( I.LT.N ) THEN
A( I, I ) = ONE
CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
$ A( I, I+1 ), LDA, WORK )
END IF
IF( I.LT.M )
$ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
A( I, I ) = ONE - TAU( I )
*
* Set A(1:i-1,i) to zero
*
DO 30 L = 1, I - 1
A( L, I ) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
*
* End of DORG2R
*
END
|
