1 SUBROUTINE CGELQS( 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 COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * Compute a minimum-norm solution
20 * min || A*X - B ||
21 * using the LQ factorization
22 * A = L*Q
23 * computed by CGELQF.
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. N >= M >= 0.
33 *
34 * NRHS (input) INTEGER
35 * The number of columns of B. NRHS >= 0.
36 *
37 * A (input) COMPLEX array, dimension (LDA,N)
38 * Details of the LQ factorization of the original matrix A as
39 * returned by CGELQF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) COMPLEX array, dimension (M)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) COMPLEX 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.
50 *
51 * LDB (input) INTEGER
52 * The leading dimension of the array B. LDB >= N.
53 *
54 * WORK (workspace) COMPLEX array, dimension (LWORK)
55 *
56 * LWORK (input) INTEGER
57 * The length of the array WORK. LWORK must be at least NRHS,
58 * and should be at least NRHS*NB, where NB is the block size
59 * for this environment.
60 *
61 * INFO (output) INTEGER
62 * = 0: successful exit
63 * < 0: if INFO = -i, the i-th argument had an illegal value
64 *
65 * =====================================================================
66 *
67 * .. Parameters ..
68 COMPLEX CZERO, CONE
69 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
70 $ CONE = ( 1.0E+0, 0.0E+0 ) )
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL CLASET, CTRSM, CUNMLQ, XERBLA
74 * ..
75 * .. Intrinsic Functions ..
76 INTRINSIC MAX
77 * ..
78 * .. Executable Statements ..
79 *
80 * Test the input parameters.
81 *
82 INFO = 0
83 IF( M.LT.0 ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 .OR. M.GT.N ) 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, N ) ) 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( 'CGELQS', -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 * Solve L*X = B(1:m,:)
108 *
109 CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
110 $ CONE, A, LDA, B, LDB )
111 *
112 * Set B(m+1:n,:) to zero
113 *
114 IF( M.LT.N )
115 $ CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ),
116 $ LDB )
117 *
118 * B := Q' * B
119 *
120 CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
121 $ TAU, B, LDB, WORK, LWORK, INFO )
122 *
123 RETURN
124 *
125 * End of CGELQS
126 *
127 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 COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * Compute a minimum-norm solution
20 * min || A*X - B ||
21 * using the LQ factorization
22 * A = L*Q
23 * computed by CGELQF.
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. N >= M >= 0.
33 *
34 * NRHS (input) INTEGER
35 * The number of columns of B. NRHS >= 0.
36 *
37 * A (input) COMPLEX array, dimension (LDA,N)
38 * Details of the LQ factorization of the original matrix A as
39 * returned by CGELQF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) COMPLEX array, dimension (M)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) COMPLEX 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.
50 *
51 * LDB (input) INTEGER
52 * The leading dimension of the array B. LDB >= N.
53 *
54 * WORK (workspace) COMPLEX array, dimension (LWORK)
55 *
56 * LWORK (input) INTEGER
57 * The length of the array WORK. LWORK must be at least NRHS,
58 * and should be at least NRHS*NB, where NB is the block size
59 * for this environment.
60 *
61 * INFO (output) INTEGER
62 * = 0: successful exit
63 * < 0: if INFO = -i, the i-th argument had an illegal value
64 *
65 * =====================================================================
66 *
67 * .. Parameters ..
68 COMPLEX CZERO, CONE
69 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
70 $ CONE = ( 1.0E+0, 0.0E+0 ) )
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL CLASET, CTRSM, CUNMLQ, XERBLA
74 * ..
75 * .. Intrinsic Functions ..
76 INTRINSIC MAX
77 * ..
78 * .. Executable Statements ..
79 *
80 * Test the input parameters.
81 *
82 INFO = 0
83 IF( M.LT.0 ) THEN
84 INFO = -1
85 ELSE IF( N.LT.0 .OR. M.GT.N ) 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, N ) ) 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( 'CGELQS', -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 * Solve L*X = B(1:m,:)
108 *
109 CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
110 $ CONE, A, LDA, B, LDB )
111 *
112 * Set B(m+1:n,:) to zero
113 *
114 IF( M.LT.N )
115 $ CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ),
116 $ LDB )
117 *
118 * B := Q' * B
119 *
120 CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
121 $ TAU, B, LDB, WORK, LWORK, INFO )
122 *
123 RETURN
124 *
125 * End of CGELQS
126 *
127 END