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
|
SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, K, LDA, M, N
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
* which is defined as the last n columns of a product of k elementary
* reflectors of order m
*
* Q = H(k) . . . H(2) H(1)
*
* as returned by ZGEQLF.
*
* 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) COMPLEX*16 array, dimension (LDA,N)
* On entry, the (n-k+i)-th column must contain the vector which
* defines the elementary reflector H(i), for i = 1,2,...,k, as
* returned by ZGEQLF in the last 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) COMPLEX*16 array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by ZGEQLF.
*
* WORK (workspace) COMPLEX*16 array, dimension (N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument has an illegal value
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE, ZERO
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, II, J, L
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLARF, ZSCAL
* ..
* .. 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( 'ZUNG2L', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.0 )
$ RETURN
*
* Initialise columns 1:n-k to columns of the unit matrix
*
DO 20 J = 1, N - K
DO 10 L = 1, M
A( L, J ) = ZERO
10 CONTINUE
A( M-N+J, J ) = ONE
20 CONTINUE
*
DO 40 I = 1, K
II = N - K + I
*
* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
*
A( M-N+II, II ) = ONE
CALL ZLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
$ LDA, WORK )
CALL ZSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
A( M-N+II, II ) = ONE - TAU( I )
*
* Set A(m-k+i+1:m,n-k+i) to zero
*
DO 30 L = M - N + II + 1, M
A( L, II ) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
*
* End of ZUNG2L
*
END
|
