1 SUBROUTINE ZUNGR2( M, N, K, A, LDA, TAU, WORK, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
19 * which is defined as the last m rows of a product of k elementary
20 * reflectors of order n
21 *
22 * Q = H(1)**H H(2)**H . . . H(k)**H
23 *
24 * as returned by ZGERQF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. N >= M.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. M >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the (m-k+i)-th row must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGERQF in the last k rows of its array argument
43 * A.
44 * On exit, the m-by-n matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) COMPLEX*16 array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by ZGERQF.
52 *
53 * WORK (workspace) COMPLEX*16 array, dimension (M)
54 *
55 * INFO (output) INTEGER
56 * = 0: successful exit
57 * < 0: if INFO = -i, the i-th argument has an illegal value
58 *
59 * =====================================================================
60 *
61 * .. Parameters ..
62 COMPLEX*16 ONE, ZERO
63 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
64 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
65 * ..
66 * .. Local Scalars ..
67 INTEGER I, II, J, L
68 * ..
69 * .. External Subroutines ..
70 EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
71 * ..
72 * .. Intrinsic Functions ..
73 INTRINSIC DCONJG, MAX
74 * ..
75 * .. Executable Statements ..
76 *
77 * Test the input arguments
78 *
79 INFO = 0
80 IF( M.LT.0 ) THEN
81 INFO = -1
82 ELSE IF( N.LT.M ) THEN
83 INFO = -2
84 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
85 INFO = -3
86 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
87 INFO = -5
88 END IF
89 IF( INFO.NE.0 ) THEN
90 CALL XERBLA( 'ZUNGR2', -INFO )
91 RETURN
92 END IF
93 *
94 * Quick return if possible
95 *
96 IF( M.LE.0 )
97 $ RETURN
98 *
99 IF( K.LT.M ) THEN
100 *
101 * Initialise rows 1:m-k to rows of the unit matrix
102 *
103 DO 20 J = 1, N
104 DO 10 L = 1, M - K
105 A( L, J ) = ZERO
106 10 CONTINUE
107 IF( J.GT.N-M .AND. J.LE.N-K )
108 $ A( M-N+J, J ) = ONE
109 20 CONTINUE
110 END IF
111 *
112 DO 40 I = 1, K
113 II = M - K + I
114 *
115 * Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
116 *
117 CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
118 A( II, N-M+II ) = ONE
119 CALL ZLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA,
120 $ DCONJG( TAU( I ) ), A, LDA, WORK )
121 CALL ZSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
122 CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
123 A( II, N-M+II ) = ONE - DCONJG( TAU( I ) )
124 *
125 * Set A(m-k+i,n-k+i+1:n) to zero
126 *
127 DO 30 L = N - M + II + 1, N
128 A( II, L ) = ZERO
129 30 CONTINUE
130 40 CONTINUE
131 RETURN
132 *
133 * End of ZUNGR2
134 *
135 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
19 * which is defined as the last m rows of a product of k elementary
20 * reflectors of order n
21 *
22 * Q = H(1)**H H(2)**H . . . H(k)**H
23 *
24 * as returned by ZGERQF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. N >= M.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. M >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the (m-k+i)-th row must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGERQF in the last k rows of its array argument
43 * A.
44 * On exit, the m-by-n matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) COMPLEX*16 array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by ZGERQF.
52 *
53 * WORK (workspace) COMPLEX*16 array, dimension (M)
54 *
55 * INFO (output) INTEGER
56 * = 0: successful exit
57 * < 0: if INFO = -i, the i-th argument has an illegal value
58 *
59 * =====================================================================
60 *
61 * .. Parameters ..
62 COMPLEX*16 ONE, ZERO
63 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
64 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
65 * ..
66 * .. Local Scalars ..
67 INTEGER I, II, J, L
68 * ..
69 * .. External Subroutines ..
70 EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
71 * ..
72 * .. Intrinsic Functions ..
73 INTRINSIC DCONJG, MAX
74 * ..
75 * .. Executable Statements ..
76 *
77 * Test the input arguments
78 *
79 INFO = 0
80 IF( M.LT.0 ) THEN
81 INFO = -1
82 ELSE IF( N.LT.M ) THEN
83 INFO = -2
84 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
85 INFO = -3
86 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
87 INFO = -5
88 END IF
89 IF( INFO.NE.0 ) THEN
90 CALL XERBLA( 'ZUNGR2', -INFO )
91 RETURN
92 END IF
93 *
94 * Quick return if possible
95 *
96 IF( M.LE.0 )
97 $ RETURN
98 *
99 IF( K.LT.M ) THEN
100 *
101 * Initialise rows 1:m-k to rows of the unit matrix
102 *
103 DO 20 J = 1, N
104 DO 10 L = 1, M - K
105 A( L, J ) = ZERO
106 10 CONTINUE
107 IF( J.GT.N-M .AND. J.LE.N-K )
108 $ A( M-N+J, J ) = ONE
109 20 CONTINUE
110 END IF
111 *
112 DO 40 I = 1, K
113 II = M - K + I
114 *
115 * Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
116 *
117 CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
118 A( II, N-M+II ) = ONE
119 CALL ZLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA,
120 $ DCONJG( TAU( I ) ), A, LDA, WORK )
121 CALL ZSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
122 CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
123 A( II, N-M+II ) = ONE - DCONJG( TAU( I ) )
124 *
125 * Set A(m-k+i,n-k+i+1:n) to zero
126 *
127 DO 30 L = N - M + II + 1, N
128 A( II, L ) = ZERO
129 30 CONTINUE
130 40 CONTINUE
131 RETURN
132 *
133 * End of ZUNGR2
134 *
135 END