1 SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
2 *
3 * -- LAPACK routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
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 * ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
19 * which is defined as the first n columns of a product of k elementary
20 * reflectors of order m
21 *
22 * Q = H(1) H(2) . . . H(k)
23 *
24 * as returned by ZGEQRF.
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. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the i-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGEQRF in the first k columns of its array
43 * argument 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 ZGEQRF.
52 *
53 * WORK (workspace) COMPLEX*16 array, dimension (N)
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, J, L
68 * ..
69 * .. External Subroutines ..
70 EXTERNAL XERBLA, ZLARF, ZSCAL
71 * ..
72 * .. Intrinsic Functions ..
73 INTRINSIC 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.0 .OR. N.GT.M ) THEN
83 INFO = -2
84 ELSE IF( K.LT.0 .OR. K.GT.N ) 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( 'ZUNG2R', -INFO )
91 RETURN
92 END IF
93 *
94 * Quick return if possible
95 *
96 IF( N.LE.0 )
97 $ RETURN
98 *
99 * Initialise columns k+1:n to columns of the unit matrix
100 *
101 DO 20 J = K + 1, N
102 DO 10 L = 1, M
103 A( L, J ) = ZERO
104 10 CONTINUE
105 A( J, J ) = ONE
106 20 CONTINUE
107 *
108 DO 40 I = K, 1, -1
109 *
110 * Apply H(i) to A(i:m,i:n) from the left
111 *
112 IF( I.LT.N ) THEN
113 A( I, I ) = ONE
114 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
115 $ A( I, I+1 ), LDA, WORK )
116 END IF
117 IF( I.LT.M )
118 $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
119 A( I, I ) = ONE - TAU( I )
120 *
121 * Set A(1:i-1,i) to zero
122 *
123 DO 30 L = 1, I - 1
124 A( L, I ) = ZERO
125 30 CONTINUE
126 40 CONTINUE
127 RETURN
128 *
129 * End of ZUNG2R
130 *
131 END
2 *
3 * -- LAPACK routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
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 * ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
19 * which is defined as the first n columns of a product of k elementary
20 * reflectors of order m
21 *
22 * Q = H(1) H(2) . . . H(k)
23 *
24 * as returned by ZGEQRF.
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. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the i-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGEQRF in the first k columns of its array
43 * argument 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 ZGEQRF.
52 *
53 * WORK (workspace) COMPLEX*16 array, dimension (N)
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, J, L
68 * ..
69 * .. External Subroutines ..
70 EXTERNAL XERBLA, ZLARF, ZSCAL
71 * ..
72 * .. Intrinsic Functions ..
73 INTRINSIC 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.0 .OR. N.GT.M ) THEN
83 INFO = -2
84 ELSE IF( K.LT.0 .OR. K.GT.N ) 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( 'ZUNG2R', -INFO )
91 RETURN
92 END IF
93 *
94 * Quick return if possible
95 *
96 IF( N.LE.0 )
97 $ RETURN
98 *
99 * Initialise columns k+1:n to columns of the unit matrix
100 *
101 DO 20 J = K + 1, N
102 DO 10 L = 1, M
103 A( L, J ) = ZERO
104 10 CONTINUE
105 A( J, J ) = ONE
106 20 CONTINUE
107 *
108 DO 40 I = K, 1, -1
109 *
110 * Apply H(i) to A(i:m,i:n) from the left
111 *
112 IF( I.LT.N ) THEN
113 A( I, I ) = ONE
114 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
115 $ A( I, I+1 ), LDA, WORK )
116 END IF
117 IF( I.LT.M )
118 $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
119 A( I, I ) = ONE - TAU( I )
120 *
121 * Set A(1:i-1,i) to zero
122 *
123 DO 30 L = 1, I - 1
124 A( L, I ) = ZERO
125 30 CONTINUE
126 40 CONTINUE
127 RETURN
128 *
129 * End of ZUNG2R
130 *
131 END