1 SUBROUTINE DORGR2( 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 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DORGR2 generates an m by n real 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(2) . . . H(k)
23 *
24 * as returned by DGERQF.
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) DOUBLE PRECISION 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 DGERQF 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) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGERQF.
52 *
53 * WORK (workspace) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I, II, J, L
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL DLARF, DSCAL, XERBLA
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC 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( 'DORGR2', -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 1:m-k to rows of the unit matrix
101 *
102 DO 20 J = 1, N
103 DO 10 L = 1, M - K
104 A( L, J ) = ZERO
105 10 CONTINUE
106 IF( J.GT.N-M .AND. J.LE.N-K )
107 $ A( M-N+J, J ) = ONE
108 20 CONTINUE
109 END IF
110 *
111 DO 40 I = 1, K
112 II = M - K + I
113 *
114 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
115 *
116 A( II, N-M+II ) = ONE
117 CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
118 $ A, LDA, WORK )
119 CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
120 A( II, N-M+II ) = ONE - TAU( I )
121 *
122 * Set A(m-k+i,n-k+i+1:n) to zero
123 *
124 DO 30 L = N - M + II + 1, N
125 A( II, L ) = ZERO
126 30 CONTINUE
127 40 CONTINUE
128 RETURN
129 *
130 * End of DORGR2
131 *
132 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 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DORGR2 generates an m by n real 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(2) . . . H(k)
23 *
24 * as returned by DGERQF.
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) DOUBLE PRECISION 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 DGERQF 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) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGERQF.
52 *
53 * WORK (workspace) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I, II, J, L
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL DLARF, DSCAL, XERBLA
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC 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( 'DORGR2', -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 1:m-k to rows of the unit matrix
101 *
102 DO 20 J = 1, N
103 DO 10 L = 1, M - K
104 A( L, J ) = ZERO
105 10 CONTINUE
106 IF( J.GT.N-M .AND. J.LE.N-K )
107 $ A( M-N+J, J ) = ONE
108 20 CONTINUE
109 END IF
110 *
111 DO 40 I = 1, K
112 II = M - K + I
113 *
114 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
115 *
116 A( II, N-M+II ) = ONE
117 CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
118 $ A, LDA, WORK )
119 CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
120 A( II, N-M+II ) = ONE - TAU( I )
121 *
122 * Set A(m-k+i,n-k+i+1:n) to zero
123 *
124 DO 30 L = N - M + II + 1, N
125 A( II, L ) = ZERO
126 30 CONTINUE
127 40 CONTINUE
128 RETURN
129 *
130 * End of DORGR2
131 *
132 END