LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dormql.f
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1*> \brief \b DORMQL
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormql.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormql.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DORMQL( 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*> DORMQL 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(k) . . . H(2) H(1)
48*>
49*> as returned by DGEQLF. 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 (LDA,K)
94*> The i-th column must contain the vector which defines the
95*> elementary reflector H(i), for i = 1,2,...,k, as returned by
96*> DGEQLF in the last k columns of its array argument A.
97*> \endverbatim
98*>
99*> \param[in] LDA
100*> \verbatim
101*> LDA is INTEGER
102*> The leading dimension of the array A.
103*> If SIDE = 'L', LDA >= max(1,M);
104*> if SIDE = 'R', LDA >= max(1,N).
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 DGEQLF.
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 unmql
163*
164* =====================================================================
165 SUBROUTINE dormql( 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 INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
190 \$ mi, nb, nbmin, ni, nq, nw
191* ..
192* .. External Functions ..
193 LOGICAL LSAME
194 INTEGER ILAENV
195 EXTERNAL lsame, ilaenv
196* ..
197* .. External Subroutines ..
198 EXTERNAL dlarfb, dlarft, dorm2l, xerbla
199* ..
200* .. Intrinsic Functions ..
201 INTRINSIC max, min
202* ..
203* .. Executable Statements ..
204*
205* Test the input arguments
206*
207 info = 0
208 left = lsame( side, 'L' )
209 notran = lsame( trans, 'N' )
210 lquery = ( lwork.EQ.-1 )
211*
212* NQ is the order of Q and NW is the minimum dimension of WORK
213*
214 IF( left ) THEN
215 nq = m
216 nw = max( 1, n )
217 ELSE
218 nq = n
219 nw = max( 1, m )
220 END IF
221 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
222 info = -1
223 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
224 info = -2
225 ELSE IF( m.LT.0 ) THEN
226 info = -3
227 ELSE IF( n.LT.0 ) THEN
228 info = -4
229 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
230 info = -5
231 ELSE IF( lda.LT.max( 1, nq ) ) THEN
232 info = -7
233 ELSE IF( ldc.LT.max( 1, m ) ) THEN
234 info = -10
235 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
236 info = -12
237 END IF
238*
239 IF( info.EQ.0 ) THEN
240*
241* Compute the workspace requirements
242*
243 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
244 lwkopt = 1
245 ELSE
246 nb = min( nbmax, ilaenv( 1, 'DORMQL', side // trans, m, n,
247 \$ k, -1 ) )
248 lwkopt = nw*nb + tsize
249 END IF
250 work( 1 ) = lwkopt
251 END IF
252*
253 IF( info.NE.0 ) THEN
254 CALL xerbla( 'DORMQL', -info )
255 RETURN
256 ELSE IF( lquery ) THEN
257 RETURN
258 END IF
259*
260* Quick return if possible
261*
262 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
263 RETURN
264 END IF
265*
266 nbmin = 2
267 ldwork = nw
268 IF( nb.GT.1 .AND. nb.LT.k ) THEN
269 IF( lwork.LT.lwkopt ) THEN
270 nb = (lwork-tsize) / ldwork
271 nbmin = max( 2, ilaenv( 2, 'DORMQL', side // trans, m, n, k,
272 \$ -1 ) )
273 END IF
274 END IF
275*
276 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
277*
278* Use unblocked code
279*
280 CALL dorm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
281 \$ iinfo )
282 ELSE
283*
284* Use blocked code
285*
286 iwt = 1 + nw*nb
287 IF( ( left .AND. notran ) .OR.
288 \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
289 i1 = 1
290 i2 = k
291 i3 = nb
292 ELSE
293 i1 = ( ( k-1 ) / nb )*nb + 1
294 i2 = 1
295 i3 = -nb
296 END IF
297*
298 IF( left ) THEN
299 ni = n
300 ELSE
301 mi = m
302 END IF
303*
304 DO 10 i = i1, i2, i3
305 ib = min( nb, k-i+1 )
306*
307* Form the triangular factor of the block reflector
308* H = H(i+ib-1) . . . H(i+1) H(i)
309*
310 CALL dlarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
311 \$ a( 1, i ), lda, tau( i ), work( iwt ), ldt )
312 IF( left ) THEN
313*
314* H or H**T is applied to C(1:m-k+i+ib-1,1:n)
315*
316 mi = m - k + i + ib - 1
317 ELSE
318*
319* H or H**T is applied to C(1:m,1:n-k+i+ib-1)
320*
321 ni = n - k + i + ib - 1
322 END IF
323*
324* Apply H or H**T
325*
326 CALL dlarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
327 \$ ib, a( 1, i ), lda, work( iwt ), ldt, c, ldc,
328 \$ work, ldwork )
329 10 CONTINUE
330 END IF
331 work( 1 ) = lwkopt
332 RETURN
333*
334* End of DORMQL
335*
336 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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 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 dorm2l(side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sge...
Definition dorm2l.f:159
subroutine dormql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
Definition dormql.f:167