LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
dgemlq.f
Go to the documentation of this file.
1*> \brief \b DGEMLQ
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T,
7* $ TSIZE, C, LDC, WORK, LWORK, INFO )
8*
9*
10* .. Scalar Arguments ..
11* CHARACTER SIDE, TRANS
12* INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
13* ..
14* .. Array Arguments ..
15* DOUBLE PRECISION A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
16* ..
17*
18*> \par Purpose:
19* =============
20*>
21*> \verbatim
22*>
23*> DGEMLQ overwrites the general real M-by-N matrix C with
24*>
25*> SIDE = 'L' SIDE = 'R'
26*> TRANS = 'N': Q * C C * Q
27*> TRANS = 'T': Q**T * C C * Q**T
28*> where Q is a real orthogonal matrix defined as the product
29*> of blocked elementary reflectors computed by short wide LQ
30*> factorization (DGELQ)
31*>
32*> \endverbatim
33*
34* Arguments:
35* ==========
36*
37*> \param[in] SIDE
38*> \verbatim
39*> SIDE is CHARACTER*1
40*> = 'L': apply Q or Q**T from the Left;
41*> = 'R': apply Q or Q**T from the Right.
42*> \endverbatim
43*>
44*> \param[in] TRANS
45*> \verbatim
46*> TRANS is CHARACTER*1
47*> = 'N': No transpose, apply Q;
48*> = 'T': Transpose, apply Q**T.
49*> \endverbatim
50*>
51*> \param[in] M
52*> \verbatim
53*> M is INTEGER
54*> The number of rows of the matrix A. M >=0.
55*> \endverbatim
56*>
57*> \param[in] N
58*> \verbatim
59*> N is INTEGER
60*> The number of columns of the matrix C. N >= 0.
61*> \endverbatim
62*>
63*> \param[in] K
64*> \verbatim
65*> K is INTEGER
66*> The number of elementary reflectors whose product defines
67*> the matrix Q.
68*> If SIDE = 'L', M >= K >= 0;
69*> if SIDE = 'R', N >= K >= 0.
70*>
71*> \endverbatim
72*>
73*> \param[in] A
74*> \verbatim
75*> A is DOUBLE PRECISION array, dimension
76*> (LDA,M) if SIDE = 'L',
77*> (LDA,N) if SIDE = 'R'
78*> Part of the data structure to represent Q as returned by DGELQ.
79*> \endverbatim
80*>
81*> \param[in] LDA
82*> \verbatim
83*> LDA is INTEGER
84*> The leading dimension of the array A. LDA >= max(1,K).
85*> \endverbatim
86*>
87*> \param[in] T
88*> \verbatim
89*> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
90*> Part of the data structure to represent Q as returned by DGELQ.
91*> \endverbatim
92*>
93*> \param[in] TSIZE
94*> \verbatim
95*> TSIZE is INTEGER
96*> The dimension of the array T. TSIZE >= 5.
97*> \endverbatim
98*>
99*> \param[in,out] C
100*> \verbatim
101*> C is DOUBLE PRECISION array, dimension (LDC,N)
102*> On entry, the M-by-N matrix C.
103*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
104*> \endverbatim
105*>
106*> \param[in] LDC
107*> \verbatim
108*> LDC is INTEGER
109*> The leading dimension of the array C. LDC >= max(1,M).
110*> \endverbatim
111*>
112*> \param[out] WORK
113*> \verbatim
114*> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
115*> \endverbatim
116*>
117*> \param[in] LWORK
118*> \verbatim
119*> LWORK is INTEGER
120*> The dimension of the array WORK.
121*> If LWORK = -1, then a workspace query is assumed. The routine
122*> only calculates the size of the WORK array, returns this
123*> value as WORK(1), and no error message related to WORK
124*> is issued by XERBLA.
125*> \endverbatim
126*>
127*> \param[out] INFO
128*> \verbatim
129*> INFO is INTEGER
130*> = 0: successful exit
131*> < 0: if INFO = -i, the i-th argument had an illegal value
132*> \endverbatim
133*
134* Authors:
135* ========
136*
137*> \author Univ. of Tennessee
138*> \author Univ. of California Berkeley
139*> \author Univ. of Colorado Denver
140*> \author NAG Ltd.
141*
142*> \par Further Details
143* ====================
144*>
145*> \verbatim
146*>
147*> These details are particular for this LAPACK implementation. Users should not
148*> take them for granted. These details may change in the future, and are not likely
149*> true for another LAPACK implementation. These details are relevant if one wants
150*> to try to understand the code. They are not part of the interface.
151*>
152*> In this version,
153*>
154*> T(2): row block size (MB)
155*> T(3): column block size (NB)
156*> T(6:TSIZE): data structure needed for Q, computed by
157*> DLASWLQ or DGELQT
158*>
159*> Depending on the matrix dimensions M and N, and row and column
160*> block sizes MB and NB returned by ILAENV, DGELQ will use either
161*> DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
162*> the LQ factorization.
163*> This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
164*> multiply matrix Q by another matrix.
165*> Further Details in DLAMSWLQ or DGEMLQT.
166*> \endverbatim
167*>
168* =====================================================================
169 SUBROUTINE dgemlq( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
170 $ C, LDC, WORK, LWORK, INFO )
171*
172* -- LAPACK computational routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER SIDE, TRANS
178 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
179* ..
180* .. Array Arguments ..
181 DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
182* ..
183*
184* =====================================================================
185*
186* ..
187* .. Local Scalars ..
188 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
189 INTEGER MB, NB, LW, NBLCKS, MN
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 EXTERNAL lsame
194* ..
195* .. External Subroutines ..
196 EXTERNAL dlamswlq, dgemlqt, xerbla
197* ..
198* .. Intrinsic Functions ..
199 INTRINSIC int, max, min, mod
200* ..
201* .. Executable Statements ..
202*
203* Test the input arguments
204*
205 lquery = lwork.EQ.-1
206 notran = lsame( trans, 'N' )
207 tran = lsame( trans, 'T' )
208 left = lsame( side, 'L' )
209 right = lsame( side, 'R' )
210*
211 mb = int( t( 2 ) )
212 nb = int( t( 3 ) )
213 IF( left ) THEN
214 lw = n * mb
215 mn = m
216 ELSE
217 lw = m * mb
218 mn = n
219 END IF
220*
221 IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
222 IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
223 nblcks = ( mn - k ) / ( nb - k )
224 ELSE
225 nblcks = ( mn - k ) / ( nb - k ) + 1
226 END IF
227 ELSE
228 nblcks = 1
229 END IF
230*
231 info = 0
232 IF( .NOT.left .AND. .NOT.right ) THEN
233 info = -1
234 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
235 info = -2
236 ELSE IF( m.LT.0 ) THEN
237 info = -3
238 ELSE IF( n.LT.0 ) THEN
239 info = -4
240 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
241 info = -5
242 ELSE IF( lda.LT.max( 1, k ) ) THEN
243 info = -7
244 ELSE IF( tsize.LT.5 ) THEN
245 info = -9
246 ELSE IF( ldc.LT.max( 1, m ) ) THEN
247 info = -11
248 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
249 info = -13
250 END IF
251*
252 IF( info.EQ.0 ) THEN
253 work( 1 ) = lw
254 END IF
255*
256 IF( info.NE.0 ) THEN
257 CALL xerbla( 'DGEMLQ', -info )
258 RETURN
259 ELSE IF( lquery ) THEN
260 RETURN
261 END IF
262*
263* Quick return if possible
264*
265 IF( min( m, n, k ).EQ.0 ) THEN
266 RETURN
267 END IF
268*
269 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
270 $ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
271 CALL dgemlqt( side, trans, m, n, k, mb, a, lda,
272 $ t( 6 ), mb, c, ldc, work, info )
273 ELSE
274 CALL dlamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
275 $ mb, c, ldc, work, lwork, info )
276 END IF
277*
278 work( 1 ) = lw
279*
280 RETURN
281*
282* End of DGEMLQ
283*
284 END
subroutine dgemlq(SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
DGEMLQ
Definition: dgemlq.f:171
subroutine dlamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
DLAMSWLQ
Definition: dlamswlq.f:195
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMLQT
Definition: dgemlqt.f:168