1 SUBROUTINE DORG2L( 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 * DORG2L generates an m by n real matrix Q with orthonormal columns,
19 * which is defined as the last n columns of a product of k elementary
20 * reflectors of order m
21 *
22 * Q = H(k) . . . H(2) H(1)
23 *
24 * as returned by DGEQLF.
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) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the (n-k+i)-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by DGEQLF in the last 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) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGEQLF.
52 *
53 * WORK (workspace) DOUBLE PRECISION 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 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.0 .OR. N.GT.M ) THEN
82 INFO = -2
83 ELSE IF( K.LT.0 .OR. K.GT.N ) 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( 'DORG2L', -INFO )
90 RETURN
91 END IF
92 *
93 * Quick return if possible
94 *
95 IF( N.LE.0 )
96 $ RETURN
97 *
98 * Initialise columns 1:n-k to columns of the unit matrix
99 *
100 DO 20 J = 1, N - K
101 DO 10 L = 1, M
102 A( L, J ) = ZERO
103 10 CONTINUE
104 A( M-N+J, J ) = ONE
105 20 CONTINUE
106 *
107 DO 40 I = 1, K
108 II = N - K + I
109 *
110 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
111 *
112 A( M-N+II, II ) = ONE
113 CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
114 $ LDA, WORK )
115 CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
116 A( M-N+II, II ) = ONE - TAU( I )
117 *
118 * Set A(m-k+i+1:m,n-k+i) to zero
119 *
120 DO 30 L = M - N + II + 1, M
121 A( L, II ) = ZERO
122 30 CONTINUE
123 40 CONTINUE
124 RETURN
125 *
126 * End of DORG2L
127 *
128 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 * DORG2L generates an m by n real matrix Q with orthonormal columns,
19 * which is defined as the last n columns of a product of k elementary
20 * reflectors of order m
21 *
22 * Q = H(k) . . . H(2) H(1)
23 *
24 * as returned by DGEQLF.
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) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the (n-k+i)-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by DGEQLF in the last 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) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGEQLF.
52 *
53 * WORK (workspace) DOUBLE PRECISION 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 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.0 .OR. N.GT.M ) THEN
82 INFO = -2
83 ELSE IF( K.LT.0 .OR. K.GT.N ) 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( 'DORG2L', -INFO )
90 RETURN
91 END IF
92 *
93 * Quick return if possible
94 *
95 IF( N.LE.0 )
96 $ RETURN
97 *
98 * Initialise columns 1:n-k to columns of the unit matrix
99 *
100 DO 20 J = 1, N - K
101 DO 10 L = 1, M
102 A( L, J ) = ZERO
103 10 CONTINUE
104 A( M-N+J, J ) = ONE
105 20 CONTINUE
106 *
107 DO 40 I = 1, K
108 II = N - K + I
109 *
110 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
111 *
112 A( M-N+II, II ) = ONE
113 CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
114 $ LDA, WORK )
115 CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
116 A( M-N+II, II ) = ONE - TAU( I )
117 *
118 * Set A(m-k+i+1:m,n-k+i) to zero
119 *
120 DO 30 L = M - N + II + 1, M
121 A( L, II ) = ZERO
122 30 CONTINUE
123 40 CONTINUE
124 RETURN
125 *
126 * End of DORG2L
127 *
128 END