1 SUBROUTINE ZUNGL2( 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 * ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
19 * which is defined as the first m rows of a product of k elementary
20 * reflectors of order n
21 *
22 * Q = H(k)**H . . . H(2)**H H(1)**H
23 *
24 * as returned by ZGELQF.
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 i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by ZGELQF in the first k rows of its array argument A.
43 * On exit, the m by n matrix Q.
44 *
45 * LDA (input) INTEGER
46 * The first dimension of the array A. LDA >= max(1,M).
47 *
48 * TAU (input) COMPLEX*16 array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by ZGELQF.
51 *
52 * WORK (workspace) COMPLEX*16 array, dimension (M)
53 *
54 * INFO (output) INTEGER
55 * = 0: successful exit
56 * < 0: if INFO = -i, the i-th argument has an illegal value
57 *
58 * =====================================================================
59 *
60 * .. Parameters ..
61 COMPLEX*16 ONE, ZERO
62 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
63 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I, J, L
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC DCONJG, MAX
73 * ..
74 * .. Executable Statements ..
75 *
76 * Test the input arguments
77 *
78 INFO = 0
79 IF( M.LT.0 ) THEN
80 INFO = -1
81 ELSE IF( N.LT.M ) THEN
82 INFO = -2
83 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
84 INFO = -3
85 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
86 INFO = -5
87 END IF
88 IF( INFO.NE.0 ) THEN
89 CALL XERBLA( 'ZUNGL2', -INFO )
90 RETURN
91 END IF
92 *
93 * Quick return if possible
94 *
95 IF( M.LE.0 )
96 $ RETURN
97 *
98 IF( K.LT.M ) THEN
99 *
100 * Initialise rows k+1:m to rows of the unit matrix
101 *
102 DO 20 J = 1, N
103 DO 10 L = K + 1, M
104 A( L, J ) = ZERO
105 10 CONTINUE
106 IF( J.GT.K .AND. J.LE.M )
107 $ A( J, J ) = ONE
108 20 CONTINUE
109 END IF
110 *
111 DO 40 I = K, 1, -1
112 *
113 * Apply H(i)**H to A(i:m,i:n) from the right
114 *
115 IF( I.LT.N ) THEN
116 CALL ZLACGV( N-I, A( I, I+1 ), LDA )
117 IF( I.LT.M ) THEN
118 A( I, I ) = ONE
119 CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
120 $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
121 END IF
122 CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
123 CALL ZLACGV( N-I, A( I, I+1 ), LDA )
124 END IF
125 A( I, I ) = ONE - DCONJG( TAU( I ) )
126 *
127 * Set A(i,1:i-1) to zero
128 *
129 DO 30 L = 1, I - 1
130 A( I, L ) = ZERO
131 30 CONTINUE
132 40 CONTINUE
133 RETURN
134 *
135 * End of ZUNGL2
136 *
137 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 * ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
19 * which is defined as the first m rows of a product of k elementary
20 * reflectors of order n
21 *
22 * Q = H(k)**H . . . H(2)**H H(1)**H
23 *
24 * as returned by ZGELQF.
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 i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by ZGELQF in the first k rows of its array argument A.
43 * On exit, the m by n matrix Q.
44 *
45 * LDA (input) INTEGER
46 * The first dimension of the array A. LDA >= max(1,M).
47 *
48 * TAU (input) COMPLEX*16 array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by ZGELQF.
51 *
52 * WORK (workspace) COMPLEX*16 array, dimension (M)
53 *
54 * INFO (output) INTEGER
55 * = 0: successful exit
56 * < 0: if INFO = -i, the i-th argument has an illegal value
57 *
58 * =====================================================================
59 *
60 * .. Parameters ..
61 COMPLEX*16 ONE, ZERO
62 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
63 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I, J, L
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC DCONJG, MAX
73 * ..
74 * .. Executable Statements ..
75 *
76 * Test the input arguments
77 *
78 INFO = 0
79 IF( M.LT.0 ) THEN
80 INFO = -1
81 ELSE IF( N.LT.M ) THEN
82 INFO = -2
83 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
84 INFO = -3
85 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
86 INFO = -5
87 END IF
88 IF( INFO.NE.0 ) THEN
89 CALL XERBLA( 'ZUNGL2', -INFO )
90 RETURN
91 END IF
92 *
93 * Quick return if possible
94 *
95 IF( M.LE.0 )
96 $ RETURN
97 *
98 IF( K.LT.M ) THEN
99 *
100 * Initialise rows k+1:m to rows of the unit matrix
101 *
102 DO 20 J = 1, N
103 DO 10 L = K + 1, M
104 A( L, J ) = ZERO
105 10 CONTINUE
106 IF( J.GT.K .AND. J.LE.M )
107 $ A( J, J ) = ONE
108 20 CONTINUE
109 END IF
110 *
111 DO 40 I = K, 1, -1
112 *
113 * Apply H(i)**H to A(i:m,i:n) from the right
114 *
115 IF( I.LT.N ) THEN
116 CALL ZLACGV( N-I, A( I, I+1 ), LDA )
117 IF( I.LT.M ) THEN
118 A( I, I ) = ONE
119 CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
120 $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
121 END IF
122 CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
123 CALL ZLACGV( N-I, A( I, I+1 ), LDA )
124 END IF
125 A( I, I ) = ONE - DCONJG( TAU( I ) )
126 *
127 * Set A(i,1:i-1) to zero
128 *
129 DO 30 L = 1, I - 1
130 A( I, L ) = ZERO
131 30 CONTINUE
132 40 CONTINUE
133 RETURN
134 *
135 * End of ZUNGL2
136 *
137 END