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
130
131
132
133
134
135
136
137
|
SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, K, LDA, M, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
* which is defined as the first m rows of a product of k elementary
* reflectors of order n
*
* Q = H(k)**H . . . H(2)**H H(1)**H
*
* as returned by CGELQF.
*
* 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. N >= M.
*
* K (input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. M >= K >= 0.
*
* A (input/output) COMPLEX array, dimension (LDA,N)
* On entry, the i-th row must contain the vector which defines
* the elementary reflector H(i), for i = 1,2,...,k, as returned
* by CGELQF in the first k rows 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 array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by CGELQF.
*
* WORK (workspace) COMPLEX array, dimension (M)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument has an illegal value
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, J, L
* ..
* .. External Subroutines ..
EXTERNAL CLACGV, CLARF, CSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.M ) THEN
INFO = -2
ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CUNGL2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 )
$ RETURN
*
IF( K.LT.M ) THEN
*
* Initialise rows k+1:m to rows of the unit matrix
*
DO 20 J = 1, N
DO 10 L = K + 1, M
A( L, J ) = ZERO
10 CONTINUE
IF( J.GT.K .AND. J.LE.M )
$ A( J, J ) = ONE
20 CONTINUE
END IF
*
DO 40 I = K, 1, -1
*
* Apply H(i)**H to A(i:m,i:n) from the right
*
IF( I.LT.N ) THEN
CALL CLACGV( N-I, A( I, I+1 ), LDA )
IF( I.LT.M ) THEN
A( I, I ) = ONE
CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
$ CONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
END IF
CALL CSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
CALL CLACGV( N-I, A( I, I+1 ), LDA )
END IF
A( I, I ) = ONE - CONJG( TAU( I ) )
*
* Set A(i,1:i-1,i) to zero
*
DO 30 L = 1, I - 1
A( I, L ) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
*
* End of CUNGL2
*
END
|
