LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgelqs.f
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1 *> \brief \b CGELQS
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
12 * INFO )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
16 * ..
17 * .. Array Arguments ..
18 * COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
19 * $ WORK( LWORK )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> Compute a minimum-norm solution
29 *> min || A*X - B ||
30 *> using the LQ factorization
31 *> A = L*Q
32 *> computed by CGELQF.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] M
39 *> \verbatim
40 *> M is INTEGER
41 *> The number of rows of the matrix A. M >= 0.
42 *> \endverbatim
43 *>
44 *> \param[in] N
45 *> \verbatim
46 *> N is INTEGER
47 *> The number of columns of the matrix A. N >= M >= 0.
48 *> \endverbatim
49 *>
50 *> \param[in] NRHS
51 *> \verbatim
52 *> NRHS is INTEGER
53 *> The number of columns of B. NRHS >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] A
57 *> \verbatim
58 *> A is COMPLEX array, dimension (LDA,N)
59 *> Details of the LQ factorization of the original matrix A as
60 *> returned by CGELQF.
61 *> \endverbatim
62 *>
63 *> \param[in] LDA
64 *> \verbatim
65 *> LDA is INTEGER
66 *> The leading dimension of the array A. LDA >= M.
67 *> \endverbatim
68 *>
69 *> \param[in] TAU
70 *> \verbatim
71 *> TAU is COMPLEX array, dimension (M)
72 *> Details of the orthogonal matrix Q.
73 *> \endverbatim
74 *>
75 *> \param[in,out] B
76 *> \verbatim
77 *> B is COMPLEX array, dimension (LDB,NRHS)
78 *> On entry, the m-by-nrhs right hand side matrix B.
79 *> On exit, the n-by-nrhs solution matrix X.
80 *> \endverbatim
81 *>
82 *> \param[in] LDB
83 *> \verbatim
84 *> LDB is INTEGER
85 *> The leading dimension of the array B. LDB >= N.
86 *> \endverbatim
87 *>
88 *> \param[out] WORK
89 *> \verbatim
90 *> WORK is COMPLEX array, dimension (LWORK)
91 *> \endverbatim
92 *>
93 *> \param[in] LWORK
94 *> \verbatim
95 *> LWORK is INTEGER
96 *> The length of the array WORK. LWORK must be at least NRHS,
97 *> and should be at least NRHS*NB, where NB is the block size
98 *> for this environment.
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -i, the i-th argument had an illegal value
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \ingroup complex_lin
117 *
118 * =====================================================================
119  SUBROUTINE cgelqs( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
120  $ INFO )
121 *
122 * -- LAPACK test routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
128 * ..
129 * .. Array Arguments ..
130  COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
131  $ work( lwork )
132 * ..
133 *
134 * =====================================================================
135 *
136 * .. Parameters ..
137  COMPLEX CZERO, CONE
138  parameter( czero = ( 0.0e+0, 0.0e+0 ),
139  $ cone = ( 1.0e+0, 0.0e+0 ) )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL claset, ctrsm, cunmlq, xerbla
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input parameters.
150 *
151  info = 0
152  IF( m.LT.0 ) THEN
153  info = -1
154  ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
155  info = -2
156  ELSE IF( nrhs.LT.0 ) THEN
157  info = -3
158  ELSE IF( lda.LT.max( 1, m ) ) THEN
159  info = -5
160  ELSE IF( ldb.LT.max( 1, n ) ) THEN
161  info = -8
162  ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
163  $ THEN
164  info = -10
165  END IF
166  IF( info.NE.0 ) THEN
167  CALL xerbla( 'CGELQS', -info )
168  RETURN
169  END IF
170 *
171 * Quick return if possible
172 *
173  IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
174  $ RETURN
175 *
176 * Solve L*X = B(1:m,:)
177 *
178  CALL ctrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
179  $ cone, a, lda, b, ldb )
180 *
181 * Set B(m+1:n,:) to zero
182 *
183  IF( m.LT.n )
184  $ CALL claset( 'Full', n-m, nrhs, czero, czero, b( m+1, 1 ),
185  $ ldb )
186 *
187 * B := Q' * B
188 *
189  CALL cunmlq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
190  $ tau, b, ldb, work, lwork, info )
191 *
192  RETURN
193 *
194 * End of CGELQS
195 *
196  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine cgelqs(M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
CGELQS
Definition: cgelqs.f:121
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine cunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMLQ
Definition: cunmlq.f:168