LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dormrq.f
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1*> \brief \b DORMRQ
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DORMRQ + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormrq.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormrq.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormrq.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22* WORK, LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER INFO, K, LDA, LDC, LWORK, M, N
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> DORMRQ 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)
48*>
49*> as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N
50*> if SIDE = 'R'.
51*> \endverbatim
52*
53* Arguments:
54* ==========
55*
56*> \param[in] SIDE
57*> \verbatim
58*> SIDE is CHARACTER*1
59*> = 'L': apply Q or Q**T from the Left;
60*> = 'R': apply Q or Q**T from the Right.
61*> \endverbatim
62*>
63*> \param[in] TRANS
64*> \verbatim
65*> TRANS is CHARACTER*1
66*> = 'N': No transpose, apply Q;
67*> = 'T': Transpose, apply Q**T.
68*> \endverbatim
69*>
70*> \param[in] M
71*> \verbatim
72*> M is INTEGER
73*> The number of rows of the matrix C. M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*> N is INTEGER
79*> The number of columns of the matrix C. N >= 0.
80*> \endverbatim
81*>
82*> \param[in] K
83*> \verbatim
84*> K is INTEGER
85*> The number of elementary reflectors whose product defines
86*> the matrix Q.
87*> If SIDE = 'L', M >= K >= 0;
88*> if SIDE = 'R', N >= K >= 0.
89*> \endverbatim
90*>
91*> \param[in] A
92*> \verbatim
93*> A is DOUBLE PRECISION array, dimension
94*> (LDA,M) if SIDE = 'L',
95*> (LDA,N) if SIDE = 'R'
96*> The i-th row must contain the vector which defines the
97*> elementary reflector H(i), for i = 1,2,...,k, as returned by
98*> DGERQF in the last k rows of its array argument A.
99*> \endverbatim
100*>
101*> \param[in] LDA
102*> \verbatim
103*> LDA is INTEGER
104*> The leading dimension of the array A. LDA >= max(1,K).
105*> \endverbatim
106*>
107*> \param[in] TAU
108*> \verbatim
109*> TAU is DOUBLE PRECISION array, dimension (K)
110*> TAU(i) must contain the scalar factor of the elementary
111*> reflector H(i), as returned by DGERQF.
112*> \endverbatim
113*>
114*> \param[in,out] C
115*> \verbatim
116*> C is DOUBLE PRECISION array, dimension (LDC,N)
117*> On entry, the M-by-N matrix C.
118*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
119*> \endverbatim
120*>
121*> \param[in] LDC
122*> \verbatim
123*> LDC is INTEGER
124*> The leading dimension of the array C. LDC >= max(1,M).
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
130*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
131*> \endverbatim
132*>
133*> \param[in] LWORK
134*> \verbatim
135*> LWORK is INTEGER
136*> The dimension of the array WORK.
137*> If SIDE = 'L', LWORK >= max(1,N);
138*> if SIDE = 'R', LWORK >= max(1,M).
139*> For good performance, LWORK should generally be larger.
140*>
141*> If LWORK = -1, then a workspace query is assumed; the routine
142*> only calculates the optimal size of the WORK array, returns
143*> this value as the first entry of the WORK array, and no error
144*> message related to LWORK is issued by XERBLA.
145*> \endverbatim
146*>
147*> \param[out] INFO
148*> \verbatim
149*> INFO is INTEGER
150*> = 0: successful exit
151*> < 0: if INFO = -i, the i-th argument had an illegal value
152*> \endverbatim
153*
154* Authors:
155* ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \ingroup doubleOTHERcomputational
163*
164* =====================================================================
165 SUBROUTINE dormrq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
166 $ WORK, LWORK, INFO )
167*
168* -- LAPACK computational routine --
169* -- LAPACK is a software package provided by Univ. of Tennessee, --
170* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172* .. Scalar Arguments ..
173 CHARACTER SIDE, TRANS
174 INTEGER INFO, K, LDA, LDC, LWORK, M, N
175* ..
176* .. Array Arguments ..
177 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
178* ..
179*
180* =====================================================================
181*
182* .. Parameters ..
183 INTEGER NBMAX, LDT, TSIZE
184 parameter( nbmax = 64, ldt = nbmax+1,
185 $ tsize = ldt*nbmax )
186* ..
187* .. Local Scalars ..
188 LOGICAL LEFT, LQUERY, NOTRAN
189 CHARACTER TRANST
190 INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
191 $ mi, nb, nbmin, ni, nq, nw
192* ..
193* .. External Functions ..
194 LOGICAL LSAME
195 INTEGER ILAENV
196 EXTERNAL lsame, ilaenv
197* ..
198* .. External Subroutines ..
199 EXTERNAL dlarfb, dlarft, dormr2, xerbla
200* ..
201* .. Intrinsic Functions ..
202 INTRINSIC max, min
203* ..
204* .. Executable Statements ..
205*
206* Test the input arguments
207*
208 info = 0
209 left = lsame( side, 'L' )
210 notran = lsame( trans, 'N' )
211 lquery = ( lwork.EQ.-1 )
212*
213* NQ is the order of Q and NW is the minimum dimension of WORK
214*
215 IF( left ) THEN
216 nq = m
217 nw = max( 1, n )
218 ELSE
219 nq = n
220 nw = max( 1, m )
221 END IF
222 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223 info = -1
224 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225 info = -2
226 ELSE IF( m.LT.0 ) THEN
227 info = -3
228 ELSE IF( n.LT.0 ) THEN
229 info = -4
230 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231 info = -5
232 ELSE IF( lda.LT.max( 1, k ) ) THEN
233 info = -7
234 ELSE IF( ldc.LT.max( 1, m ) ) THEN
235 info = -10
236 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
237 info = -12
238 END IF
239*
240 IF( info.EQ.0 ) THEN
241*
242* Compute the workspace requirements
243*
244 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
245 lwkopt = 1
246 ELSE
247 nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
248 $ k, -1 ) )
249 lwkopt = nw*nb + tsize
250 END IF
251 work( 1 ) = lwkopt
252 END IF
253*
254 IF( info.NE.0 ) THEN
255 CALL xerbla( 'DORMRQ', -info )
256 RETURN
257 ELSE IF( lquery ) THEN
258 RETURN
259 END IF
260*
261* Quick return if possible
262*
263 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
264 RETURN
265 END IF
266*
267 nbmin = 2
268 ldwork = nw
269 IF( nb.GT.1 .AND. nb.LT.k ) THEN
270 IF( lwork.LT.lwkopt ) THEN
271 nb = (lwork-tsize) / ldwork
272 nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
273 $ -1 ) )
274 END IF
275 END IF
276*
277 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
278*
279* Use unblocked code
280*
281 CALL dormr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
282 $ iinfo )
283 ELSE
284*
285* Use blocked code
286*
287 iwt = 1 + nw*nb
288 IF( ( left .AND. .NOT.notran ) .OR.
289 $ ( .NOT.left .AND. notran ) ) THEN
290 i1 = 1
291 i2 = k
292 i3 = nb
293 ELSE
294 i1 = ( ( k-1 ) / nb )*nb + 1
295 i2 = 1
296 i3 = -nb
297 END IF
298*
299 IF( left ) THEN
300 ni = n
301 ELSE
302 mi = m
303 END IF
304*
305 IF( notran ) THEN
306 transt = 'T'
307 ELSE
308 transt = 'N'
309 END IF
310*
311 DO 10 i = i1, i2, i3
312 ib = min( nb, k-i+1 )
313*
314* Form the triangular factor of the block reflector
315* H = H(i+ib-1) . . . H(i+1) H(i)
316*
317 CALL dlarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
318 $ a( i, 1 ), lda, tau( i ), work( iwt ), ldt )
319 IF( left ) THEN
320*
321* H or H**T is applied to C(1:m-k+i+ib-1,1:n)
322*
323 mi = m - k + i + ib - 1
324 ELSE
325*
326* H or H**T is applied to C(1:m,1:n-k+i+ib-1)
327*
328 ni = n - k + i + ib - 1
329 END IF
330*
331* Apply H or H**T
332*
333 CALL dlarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
334 $ ib, a( i, 1 ), lda, work( iwt ), ldt, c, ldc,
335 $ work, ldwork )
336 10 CONTINUE
337 END IF
338 work( 1 ) = lwkopt
339 RETURN
340*
341* End of DORMRQ
342*
343 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: dlarft.f:163
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
subroutine dormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMRQ
Definition: dormrq.f:167
subroutine dormr2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sge...
Definition: dormr2.f:159