LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dgelqs.f
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1*> \brief \b DGELQS
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 DGELQS( 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* DOUBLE PRECISION 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 DGELQF.
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 DOUBLE PRECISION array, dimension (LDA,N)
59*> Details of the LQ factorization of the original matrix A as
60*> returned by DGELQF.
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 DOUBLE PRECISION array, dimension (M)
72*> Details of the orthogonal matrix Q.
73*> \endverbatim
74*>
75*> \param[in,out] B
76*> \verbatim
77*> B is DOUBLE PRECISION 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 DOUBLE PRECISION 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 double_lin
117*
118* =====================================================================
119 SUBROUTINE dgelqs( 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 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
131 $ work( lwork )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 DOUBLE PRECISION ZERO, ONE
138 parameter( zero = 0.0d+0, one = 1.0d+0 )
139* ..
140* .. External Subroutines ..
141 EXTERNAL dlaset, dormlq, dtrsm, xerbla
142* ..
143* .. Intrinsic Functions ..
144 INTRINSIC max
145* ..
146* .. Executable Statements ..
147*
148* Test the input parameters.
149*
150 info = 0
151 IF( m.LT.0 ) THEN
152 info = -1
153 ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
154 info = -2
155 ELSE IF( nrhs.LT.0 ) THEN
156 info = -3
157 ELSE IF( lda.LT.max( 1, m ) ) THEN
158 info = -5
159 ELSE IF( ldb.LT.max( 1, n ) ) THEN
160 info = -8
161 ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
162 $ THEN
163 info = -10
164 END IF
165 IF( info.NE.0 ) THEN
166 CALL xerbla( 'DGELQS', -info )
167 RETURN
168 END IF
169*
170* Quick return if possible
171*
172 IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
173 $ RETURN
174*
175* Solve L*X = B(1:m,:)
176*
177 CALL dtrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
178 $ one, a, lda, b, ldb )
179*
180* Set B(m+1:n,:) to zero
181*
182 IF( m.LT.n )
183 $ CALL dlaset( 'Full', n-m, nrhs, zero, zero, b( m+1, 1 ), ldb )
184*
185* B := Q' * B
186*
187 CALL dormlq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188 $ work, lwork, info )
189*
190 RETURN
191*
192* End of DGELQS
193*
194 END
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dgelqs(M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
DGELQS
Definition: dgelqs.f:121
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:167