LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zgelqs.f
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1 *> \brief \b ZGELQS
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 ZGELQS( 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*16 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 ZGELQF.
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*16 array, dimension (LDA,N)
59 *> Details of the LQ factorization of the original matrix A as
60 *> returned by ZGELQF.
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*16 array, dimension (M)
72 *> Details of the orthogonal matrix Q.
73 *> \endverbatim
74 *>
75 *> \param[in,out] B
76 *> \verbatim
77 *> B is COMPLEX*16 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*16 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 *> \date December 2016
117 *
118 *> \ingroup complex16_lin
119 *
120 * =====================================================================
121  SUBROUTINE zgelqs( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
122  $ INFO )
123 *
124 * -- LAPACK test routine (version 3.7.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * December 2016
128 *
129 * .. Scalar Arguments ..
130  INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
131 * ..
132 * .. Array Arguments ..
133  COMPLEX*16 A( lda, * ), B( ldb, * ), TAU( * ),
134  $ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  COMPLEX*16 CZERO, CONE
141  parameter( czero = ( 0.0d+0, 0.0d+0 ),
142  $ cone = ( 1.0d+0, 0.0d+0 ) )
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL xerbla, zlaset, ztrsm, zunmlq
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC max
149 * ..
150 * .. Executable Statements ..
151 *
152 * Test the input parameters.
153 *
154  info = 0
155  IF( m.LT.0 ) THEN
156  info = -1
157  ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
158  info = -2
159  ELSE IF( nrhs.LT.0 ) THEN
160  info = -3
161  ELSE IF( lda.LT.max( 1, m ) ) THEN
162  info = -5
163  ELSE IF( ldb.LT.max( 1, n ) ) THEN
164  info = -8
165  ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
166  $ THEN
167  info = -10
168  END IF
169  IF( info.NE.0 ) THEN
170  CALL xerbla( 'ZGELQS', -info )
171  RETURN
172  END IF
173 *
174 * Quick return if possible
175 *
176  IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
177  $ RETURN
178 *
179 * Solve L*X = B(1:m,:)
180 *
181  CALL ztrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
182  $ cone, a, lda, b, ldb )
183 *
184 * Set B(m+1:n,:) to zero
185 *
186  IF( m.LT.n )
187  $ CALL zlaset( 'Full', n-m, nrhs, czero, czero, b( m+1, 1 ),
188  $ ldb )
189 *
190 * B := Q' * B
191 *
192  CALL zunmlq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
193  $ tau, b, ldb, work, lwork, info )
194 *
195  RETURN
196 *
197 * End of ZGELQS
198 *
199  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
subroutine zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:169
subroutine zgelqs(M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
ZGELQS
Definition: zgelqs.f:123
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:182