LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sgerqs.f
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1*> \brief \b SGERQS
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 SGERQS( 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* REAL 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 RQ factorization
31*> A = R*Q
32*> computed by SGERQF.
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 REAL array, dimension (LDA,N)
59*> Details of the RQ factorization of the original matrix A as
60*> returned by SGERQF.
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 REAL array, dimension (M)
72*> Details of the orthogonal matrix Q.
73*> \endverbatim
74*>
75*> \param[in,out] B
76*> \verbatim
77*> B is REAL array, dimension (LDB,NRHS)
78*> On entry, the right hand side vectors for the linear system.
79*> On exit, the solution vectors X. Each solution vector
80*> is contained in rows 1:N of a column of B.
81*> \endverbatim
82*>
83*> \param[in] LDB
84*> \verbatim
85*> LDB is INTEGER
86*> The leading dimension of the array B. LDB >= max(1,N).
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*> WORK is REAL array, dimension (LWORK)
92*> \endverbatim
93*>
94*> \param[in] LWORK
95*> \verbatim
96*> LWORK is INTEGER
97*> The length of the array WORK. LWORK must be at least NRHS,
98*> and should be at least NRHS*NB, where NB is the block size
99*> for this environment.
100*> \endverbatim
101*>
102*> \param[out] INFO
103*> \verbatim
104*> INFO is INTEGER
105*> = 0: successful exit
106*> < 0: if INFO = -i, the i-th argument had an illegal value
107*> \endverbatim
108*
109* Authors:
110* ========
111*
112*> \author Univ. of Tennessee
113*> \author Univ. of California Berkeley
114*> \author Univ. of Colorado Denver
115*> \author NAG Ltd.
116*
117*> \ingroup single_lin
118*
119* =====================================================================
120 SUBROUTINE sgerqs( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
121 \$ INFO )
122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
129* ..
130* .. Array Arguments ..
131 REAL A( LDA, * ), B( LDB, * ), TAU( * ),
132 \$ work( lwork )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ZERO, ONE
139 parameter( zero = 0.0e+0, one = 1.0e+0 )
140* ..
141* .. External Subroutines ..
142 EXTERNAL slaset, sormrq, strsm, 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( 'SGERQS', -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 R*X = B(n-m+1:n,:)
177*
178 CALL strsm( 'Left', 'Upper', 'No transpose', 'Non-unit', m, nrhs,
179 \$ one, a( 1, n-m+1 ), lda, b( n-m+1, 1 ), ldb )
180*
181* Set B(1:n-m,:) to zero
182*
183 CALL slaset( 'Full', n-m, nrhs, zero, zero, b, ldb )
184*
185* B := Q' * B
186*
187 CALL sormrq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188 \$ work, lwork, info )
189*
190 RETURN
191*
192* End of SGERQS
193*
194 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
subroutine strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
Definition strsm.f:181
subroutine sormrq(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMRQ
Definition sormrq.f:168
subroutine sgerqs(m, n, nrhs, a, lda, tau, b, ldb, work, lwork, info)
SGERQS
Definition sgerqs.f:122