1 SUBROUTINE ZGEQRS( 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*16 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 QR factorization
22 * A = Q*R
23 * computed by ZGEQRF.
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) COMPLEX*16 array, dimension (LDA,N)
38 * Details of the QR factorization of the original matrix A as
39 * returned by ZGEQRF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) COMPLEX*16 array, dimension (N)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) COMPLEX*16 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 >= M.
53 *
54 * WORK (workspace) COMPLEX*16 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*16 ONE
69 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL XERBLA, ZTRSM, ZUNMQR
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX
76 * ..
77 * .. Executable Statements ..
78 *
79 * Test the input arguments.
80 *
81 INFO = 0
82 IF( M.LT.0 ) THEN
83 INFO = -1
84 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
85 INFO = -2
86 ELSE IF( NRHS.LT.0 ) THEN
87 INFO = -3
88 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
89 INFO = -5
90 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
91 INFO = -8
92 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
93 $ THEN
94 INFO = -10
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'ZGEQRS', -INFO )
98 RETURN
99 END IF
100 *
101 * Quick return if possible
102 *
103 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
104 $ RETURN
105 *
106 * B := Q' * B
107 *
108 CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
109 $ TAU, B, LDB, WORK, LWORK, INFO )
110 *
111 * Solve R*X = B(1:n,:)
112 *
113 CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
114 $ ONE, A, LDA, B, LDB )
115 *
116 RETURN
117 *
118 * End of ZGEQRS
119 *
120 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*16 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 QR factorization
22 * A = Q*R
23 * computed by ZGEQRF.
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) COMPLEX*16 array, dimension (LDA,N)
38 * Details of the QR factorization of the original matrix A as
39 * returned by ZGEQRF.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= M.
43 *
44 * TAU (input) COMPLEX*16 array, dimension (N)
45 * Details of the orthogonal matrix Q.
46 *
47 * B (input/output) COMPLEX*16 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 >= M.
53 *
54 * WORK (workspace) COMPLEX*16 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*16 ONE
69 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL XERBLA, ZTRSM, ZUNMQR
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX
76 * ..
77 * .. Executable Statements ..
78 *
79 * Test the input arguments.
80 *
81 INFO = 0
82 IF( M.LT.0 ) THEN
83 INFO = -1
84 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
85 INFO = -2
86 ELSE IF( NRHS.LT.0 ) THEN
87 INFO = -3
88 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
89 INFO = -5
90 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
91 INFO = -8
92 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
93 $ THEN
94 INFO = -10
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'ZGEQRS', -INFO )
98 RETURN
99 END IF
100 *
101 * Quick return if possible
102 *
103 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
104 $ RETURN
105 *
106 * B := Q' * B
107 *
108 CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
109 $ TAU, B, LDB, WORK, LWORK, INFO )
110 *
111 * Solve R*X = B(1:n,:)
112 *
113 CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
114 $ ONE, A, LDA, B, LDB )
115 *
116 RETURN
117 *
118 * End of ZGEQRS
119 *
120 END