LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dgemlqt.f
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1*> \brief \b DGEMLQT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgemlqt.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgemlqt.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgemlqt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
22* C, LDC, WORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> DGEMLQT overwrites the general real M-by-N matrix C with
39*>
40*> SIDE = 'L' SIDE = 'R'
41*> TRANS = 'N': Q C C Q
42*> TRANS = 'T': Q**T C C Q**T
43*>
44*> where Q is a real orthogonal matrix defined as the product of K
45*> elementary reflectors:
46*>
47*> Q = H(1) H(2) . . . H(K) = I - V T V**T
48*>
49*> generated using the compact WY representation as returned by DGELQT.
50*>
51*> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
52*> \endverbatim
53*
54* Arguments:
55* ==========
56*
57*> \param[in] SIDE
58*> \verbatim
59*> SIDE is CHARACTER*1
60*> = 'L': apply Q or Q**T from the Left;
61*> = 'R': apply Q or Q**T from the Right.
62*> \endverbatim
63*>
64*> \param[in] TRANS
65*> \verbatim
66*> TRANS is CHARACTER*1
67*> = 'N': No transpose, apply Q;
68*> = 'C': Transpose, apply Q**T.
69*> \endverbatim
70*>
71*> \param[in] M
72*> \verbatim
73*> M is INTEGER
74*> The number of rows of the matrix C. M >= 0.
75*> \endverbatim
76*>
77*> \param[in] N
78*> \verbatim
79*> N is INTEGER
80*> The number of columns of the matrix C. N >= 0.
81*> \endverbatim
82*>
83*> \param[in] K
84*> \verbatim
85*> K is INTEGER
86*> The number of elementary reflectors whose product defines
87*> the matrix Q.
88*> If SIDE = 'L', M >= K >= 0;
89*> if SIDE = 'R', N >= K >= 0.
90*> \endverbatim
91*>
92*> \param[in] MB
93*> \verbatim
94*> MB is INTEGER
95*> The block size used for the storage of T. K >= MB >= 1.
96*> This must be the same value of MB used to generate T
97*> in DGELQT.
98*> \endverbatim
99*>
100*> \param[in] V
101*> \verbatim
102*> V is DOUBLE PRECISION array, dimension
103*> (LDV,M) if SIDE = 'L',
104*> (LDV,N) if SIDE = 'R'
105*> The i-th row must contain the vector which defines the
106*> elementary reflector H(i), for i = 1,2,...,k, as returned by
107*> DGELQT in the first K rows of its array argument A.
108*> \endverbatim
109*>
110*> \param[in] LDV
111*> \verbatim
112*> LDV is INTEGER
113*> The leading dimension of the array V. LDV >= max(1,K).
114*> \endverbatim
115*>
116*> \param[in] T
117*> \verbatim
118*> T is DOUBLE PRECISION array, dimension (LDT,K)
119*> The upper triangular factors of the block reflectors
120*> as returned by DGELQT, stored as a MB-by-K matrix.
121*> \endverbatim
122*>
123*> \param[in] LDT
124*> \verbatim
125*> LDT is INTEGER
126*> The leading dimension of the array T. LDT >= MB.
127*> \endverbatim
128*>
129*> \param[in,out] C
130*> \verbatim
131*> C is DOUBLE PRECISION array, dimension (LDC,N)
132*> On entry, the M-by-N matrix C.
133*> On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
134*> \endverbatim
135*>
136*> \param[in] LDC
137*> \verbatim
138*> LDC is INTEGER
139*> The leading dimension of the array C. LDC >= max(1,M).
140*> \endverbatim
141*>
142*> \param[out] WORK
143*> \verbatim
144*> WORK is DOUBLE PRECISION array. The dimension of
145*> WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
146*> \endverbatim
147*>
148*> \param[out] INFO
149*> \verbatim
150*> INFO is INTEGER
151*> = 0: successful exit
152*> < 0: if INFO = -i, the i-th argument had an illegal value
153*> \endverbatim
154*
155* Authors:
156* ========
157*
158*> \author Univ. of Tennessee
159*> \author Univ. of California Berkeley
160*> \author Univ. of Colorado Denver
161*> \author NAG Ltd.
162*
163*> \ingroup gemlqt
164*
165* =====================================================================
166 SUBROUTINE dgemlqt( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
167 \$ C, LDC, WORK, INFO )
168*
169* -- LAPACK computational routine --
170* -- LAPACK is a software package provided by Univ. of Tennessee, --
171* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172*
173* .. Scalar Arguments ..
174 CHARACTER SIDE, TRANS
175 INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
176* ..
177* .. Array Arguments ..
178 DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
179* ..
180*
181* =====================================================================
182*
183* ..
184* .. Local Scalars ..
185 LOGICAL LEFT, RIGHT, TRAN, NOTRAN
186 INTEGER I, IB, LDWORK, KF, Q
187* ..
188* .. External Functions ..
189 LOGICAL LSAME
190 EXTERNAL lsame
191* ..
192* .. External Subroutines ..
193 EXTERNAL xerbla, dlarfb
194* ..
195* .. Intrinsic Functions ..
196 INTRINSIC max, min
197* ..
198* .. Executable Statements ..
199*
200* .. Test the input arguments ..
201*
202 info = 0
203 left = lsame( side, 'L' )
204 right = lsame( side, 'R' )
205 tran = lsame( trans, 'T' )
206 notran = lsame( trans, 'N' )
207*
208 IF( left ) THEN
209 ldwork = max( 1, n )
210 q = m
211 ELSE IF ( right ) THEN
212 ldwork = max( 1, m )
213 q = n
214 END IF
215 IF( .NOT.left .AND. .NOT.right ) THEN
216 info = -1
217 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
218 info = -2
219 ELSE IF( m.LT.0 ) THEN
220 info = -3
221 ELSE IF( n.LT.0 ) THEN
222 info = -4
223 ELSE IF( k.LT.0 .OR. k.GT.q ) THEN
224 info = -5
225 ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
226 info = -6
227 ELSE IF( ldv.LT.max( 1, k ) ) THEN
228 info = -8
229 ELSE IF( ldt.LT.mb ) THEN
230 info = -10
231 ELSE IF( ldc.LT.max( 1, m ) ) THEN
232 info = -12
233 END IF
234*
235 IF( info.NE.0 ) THEN
236 CALL xerbla( 'DGEMLQT', -info )
237 RETURN
238 END IF
239*
240* .. Quick return if possible ..
241*
242 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
243*
244 IF( left .AND. notran ) THEN
245*
246 DO i = 1, k, mb
247 ib = min( mb, k-i+1 )
248 CALL dlarfb( 'L', 'T', 'F', 'R', m-i+1, n, ib,
249 \$ v( i, i ), ldv, t( 1, i ), ldt,
250 \$ c( i, 1 ), ldc, work, ldwork )
251 END DO
252*
253 ELSE IF( right .AND. tran ) THEN
254*
255 DO i = 1, k, mb
256 ib = min( mb, k-i+1 )
257 CALL dlarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
258 \$ v( i, i ), ldv, t( 1, i ), ldt,
259 \$ c( 1, i ), ldc, work, ldwork )
260 END DO
261*
262 ELSE IF( left .AND. tran ) THEN
263*
264 kf = ((k-1)/mb)*mb+1
265 DO i = kf, 1, -mb
266 ib = min( mb, k-i+1 )
267 CALL dlarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
268 \$ v( i, i ), ldv, t( 1, i ), ldt,
269 \$ c( i, 1 ), ldc, work, ldwork )
270 END DO
271*
272 ELSE IF( right .AND. notran ) THEN
273*
274 kf = ((k-1)/mb)*mb+1
275 DO i = kf, 1, -mb
276 ib = min( mb, k-i+1 )
277 CALL dlarfb( 'R', 'T', 'F', 'R', m, n-i+1, ib,
278 \$ v( i, i ), ldv, t( 1, i ), ldt,
279 \$ c( 1, i ), ldc, work, ldwork )
280 END DO
281*
282 END IF
283*
284 RETURN
285*
286* End of DGEMLQT
287*
288 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
DGEMLQT
Definition dgemlqt.f:168
subroutine dlarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition dlarfb.f:197