1 SUBROUTINE DGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
2 $ INFO )
3 *
4 * -- LAPACK routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * Solve the least squares problem
20 * min || A*X - B ||
21 * using the QL factorization
22 * A = Q*L
23 * computed by DGEQLF.
24 *
25 * Arguments
26 * =========
27 *
28 * M (input) INTEGER
29 * The number of rows of the matrix A. M >= 0.
30 *
31 * N (input) INTEGER
32 * The number of columns of the matrix A. M >= N >= 0.
33 *
34 * NRHS (input) INTEGER
35 * The number of columns of B. NRHS >= 0.
36 *
37 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
38 * Details of the QL factorization of the original matrix A as
39 * returned by DGEQLF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) DOUBLE PRECISION array, dimension (N)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
48 * On entry, the m-by-nrhs right hand side matrix B.
49 * On exit, the n-by-nrhs solution matrix X, stored in rows
50 * m-n+1:m.
51 *
52 * LDB (input) INTEGER
53 * The leading dimension of the array B. LDB >= M.
54 *
55 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
56 *
57 * LWORK (input) INTEGER
58 * The length of the array WORK. LWORK must be at least NRHS,
59 * and should be at least NRHS*NB, where NB is the block size
60 * for this environment.
61 *
62 * INFO (output) INTEGER
63 * = 0: successful exit
64 * < 0: if INFO = -i, the i-th argument had an illegal value
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 DOUBLE PRECISION ONE
70 PARAMETER ( ONE = 1.0D+0 )
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL DORMQL, DTRSM, XERBLA
74 * ..
75 * .. Intrinsic Functions ..
76 INTRINSIC MAX
77 * ..
78 * .. Executable Statements ..
79 *
80 * Test the input arguments.
81 *
82 INFO = 0
83 IF( M.LT.0 ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
86 INFO = -2
87 ELSE IF( NRHS.LT.0 ) THEN
88 INFO = -3
89 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
90 INFO = -5
91 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
92 INFO = -8
93 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
94 $ THEN
95 INFO = -10
96 END IF
97 IF( INFO.NE.0 ) THEN
98 CALL XERBLA( 'DGEQLS', -INFO )
99 RETURN
100 END IF
101 *
102 * Quick return if possible
103 *
104 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
105 $ RETURN
106 *
107 * B := Q' * B
108 *
109 CALL DORMQL( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB,
110 $ WORK, LWORK, INFO )
111 *
112 * Solve L*X = B(m-n+1:m,:)
113 *
114 CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, NRHS,
115 $ ONE, A( M-N+1, 1 ), LDA, B( M-N+1, 1 ), LDB )
116 *
117 RETURN
118 *
119 * End of DGEQLS
120 *
121 END
2 $ INFO )
3 *
4 * -- LAPACK routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * Solve the least squares problem
20 * min || A*X - B ||
21 * using the QL factorization
22 * A = Q*L
23 * computed by DGEQLF.
24 *
25 * Arguments
26 * =========
27 *
28 * M (input) INTEGER
29 * The number of rows of the matrix A. M >= 0.
30 *
31 * N (input) INTEGER
32 * The number of columns of the matrix A. M >= N >= 0.
33 *
34 * NRHS (input) INTEGER
35 * The number of columns of B. NRHS >= 0.
36 *
37 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
38 * Details of the QL factorization of the original matrix A as
39 * returned by DGEQLF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) DOUBLE PRECISION array, dimension (N)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
48 * On entry, the m-by-nrhs right hand side matrix B.
49 * On exit, the n-by-nrhs solution matrix X, stored in rows
50 * m-n+1:m.
51 *
52 * LDB (input) INTEGER
53 * The leading dimension of the array B. LDB >= M.
54 *
55 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
56 *
57 * LWORK (input) INTEGER
58 * The length of the array WORK. LWORK must be at least NRHS,
59 * and should be at least NRHS*NB, where NB is the block size
60 * for this environment.
61 *
62 * INFO (output) INTEGER
63 * = 0: successful exit
64 * < 0: if INFO = -i, the i-th argument had an illegal value
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 DOUBLE PRECISION ONE
70 PARAMETER ( ONE = 1.0D+0 )
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL DORMQL, DTRSM, XERBLA
74 * ..
75 * .. Intrinsic Functions ..
76 INTRINSIC MAX
77 * ..
78 * .. Executable Statements ..
79 *
80 * Test the input arguments.
81 *
82 INFO = 0
83 IF( M.LT.0 ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
86 INFO = -2
87 ELSE IF( NRHS.LT.0 ) THEN
88 INFO = -3
89 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
90 INFO = -5
91 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
92 INFO = -8
93 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
94 $ THEN
95 INFO = -10
96 END IF
97 IF( INFO.NE.0 ) THEN
98 CALL XERBLA( 'DGEQLS', -INFO )
99 RETURN
100 END IF
101 *
102 * Quick return if possible
103 *
104 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
105 $ RETURN
106 *
107 * B := Q' * B
108 *
109 CALL DORMQL( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB,
110 $ WORK, LWORK, INFO )
111 *
112 * Solve L*X = B(m-n+1:m,:)
113 *
114 CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, NRHS,
115 $ ONE, A( M-N+1, 1 ), LDA, B( M-N+1, 1 ), LDB )
116 *
117 RETURN
118 *
119 * End of DGEQLS
120 *
121 END