1 SUBROUTINE DORGL2( 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 * DORGL2 generates an m by n real 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(2) H(1)
23 *
24 * as returned by DGELQF.
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 i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by DGELQF 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) DOUBLE PRECISION array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by DGELQF.
51 *
52 * WORK (workspace) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
62 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
63 * ..
64 * .. Local Scalars ..
65 INTEGER I, J, L
66 * ..
67 * .. External Subroutines ..
68 EXTERNAL DLARF, DSCAL, XERBLA
69 * ..
70 * .. Intrinsic Functions ..
71 INTRINSIC MAX
72 * ..
73 * .. Executable Statements ..
74 *
75 * Test the input arguments
76 *
77 INFO = 0
78 IF( M.LT.0 ) THEN
79 INFO = -1
80 ELSE IF( N.LT.M ) THEN
81 INFO = -2
82 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
83 INFO = -3
84 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
85 INFO = -5
86 END IF
87 IF( INFO.NE.0 ) THEN
88 CALL XERBLA( 'DORGL2', -INFO )
89 RETURN
90 END IF
91 *
92 * Quick return if possible
93 *
94 IF( M.LE.0 )
95 $ RETURN
96 *
97 IF( K.LT.M ) THEN
98 *
99 * Initialise rows k+1:m to rows of the unit matrix
100 *
101 DO 20 J = 1, N
102 DO 10 L = K + 1, M
103 A( L, J ) = ZERO
104 10 CONTINUE
105 IF( J.GT.K .AND. J.LE.M )
106 $ A( J, J ) = ONE
107 20 CONTINUE
108 END IF
109 *
110 DO 40 I = K, 1, -1
111 *
112 * Apply H(i) to A(i:m,i:n) from the right
113 *
114 IF( I.LT.N ) THEN
115 IF( I.LT.M ) THEN
116 A( I, I ) = ONE
117 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
118 $ TAU( I ), A( I+1, I ), LDA, WORK )
119 END IF
120 CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
121 END IF
122 A( I, I ) = ONE - TAU( I )
123 *
124 * Set A(i,1:i-1) to zero
125 *
126 DO 30 L = 1, I - 1
127 A( I, L ) = ZERO
128 30 CONTINUE
129 40 CONTINUE
130 RETURN
131 *
132 * End of DORGL2
133 *
134 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 * DORGL2 generates an m by n real 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(2) H(1)
23 *
24 * as returned by DGELQF.
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 i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by DGELQF 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) DOUBLE PRECISION array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by DGELQF.
51 *
52 * WORK (workspace) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
62 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
63 * ..
64 * .. Local Scalars ..
65 INTEGER I, J, L
66 * ..
67 * .. External Subroutines ..
68 EXTERNAL DLARF, DSCAL, XERBLA
69 * ..
70 * .. Intrinsic Functions ..
71 INTRINSIC MAX
72 * ..
73 * .. Executable Statements ..
74 *
75 * Test the input arguments
76 *
77 INFO = 0
78 IF( M.LT.0 ) THEN
79 INFO = -1
80 ELSE IF( N.LT.M ) THEN
81 INFO = -2
82 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
83 INFO = -3
84 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
85 INFO = -5
86 END IF
87 IF( INFO.NE.0 ) THEN
88 CALL XERBLA( 'DORGL2', -INFO )
89 RETURN
90 END IF
91 *
92 * Quick return if possible
93 *
94 IF( M.LE.0 )
95 $ RETURN
96 *
97 IF( K.LT.M ) THEN
98 *
99 * Initialise rows k+1:m to rows of the unit matrix
100 *
101 DO 20 J = 1, N
102 DO 10 L = K + 1, M
103 A( L, J ) = ZERO
104 10 CONTINUE
105 IF( J.GT.K .AND. J.LE.M )
106 $ A( J, J ) = ONE
107 20 CONTINUE
108 END IF
109 *
110 DO 40 I = K, 1, -1
111 *
112 * Apply H(i) to A(i:m,i:n) from the right
113 *
114 IF( I.LT.N ) THEN
115 IF( I.LT.M ) THEN
116 A( I, I ) = ONE
117 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
118 $ TAU( I ), A( I+1, I ), LDA, WORK )
119 END IF
120 CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
121 END IF
122 A( I, I ) = ONE - TAU( I )
123 *
124 * Set A(i,1:i-1) to zero
125 *
126 DO 30 L = 1, I - 1
127 A( I, L ) = ZERO
128 30 CONTINUE
129 40 CONTINUE
130 RETURN
131 *
132 * End of DORGL2
133 *
134 END