LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
sormlq.f
Go to the documentation of this file.
1*> \brief \b SORMLQ
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/sormlq.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormlq.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormlq.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORMLQ( 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* REAL A( LDA, * ), C( LDC, * ), TAU( * ),
30* \$ WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SORMLQ overwrites the general real M-by-N matrix C with
40*>
41*> SIDE = 'L' SIDE = 'R'
42*> TRANS = 'N': Q * C C * Q
43*> TRANS = 'T': Q**T * C C * Q**T
44*>
45*> where Q is a real orthogonal matrix defined as the product of k
46*> elementary reflectors
47*>
48*> Q = H(k) . . . H(2) H(1)
49*>
50*> as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
51*> 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*> = 'T': 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] A
93*> \verbatim
94*> A is REAL array, dimension
95*> (LDA,M) if SIDE = 'L',
96*> (LDA,N) if SIDE = 'R'
97*> The i-th row must contain the vector which defines the
98*> elementary reflector H(i), for i = 1,2,...,k, as returned by
99*> SGELQF in the first k rows of its array argument A.
100*> \endverbatim
101*>
102*> \param[in] LDA
103*> \verbatim
104*> LDA is INTEGER
105*> The leading dimension of the array A. LDA >= max(1,K).
106*> \endverbatim
107*>
108*> \param[in] TAU
109*> \verbatim
110*> TAU is REAL array, dimension (K)
111*> TAU(i) must contain the scalar factor of the elementary
112*> reflector H(i), as returned by SGELQF.
113*> \endverbatim
114*>
115*> \param[in,out] C
116*> \verbatim
117*> C is REAL array, dimension (LDC,N)
118*> On entry, the M-by-N matrix C.
119*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
120*> \endverbatim
121*>
122*> \param[in] LDC
123*> \verbatim
124*> LDC is INTEGER
125*> The leading dimension of the array C. LDC >= max(1,M).
126*> \endverbatim
127*>
128*> \param[out] WORK
129*> \verbatim
130*> WORK is REAL array, dimension (MAX(1,LWORK))
131*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132*> \endverbatim
133*>
134*> \param[in] LWORK
135*> \verbatim
136*> LWORK is INTEGER
137*> The dimension of the array WORK.
138*> If SIDE = 'L', LWORK >= max(1,N);
139*> if SIDE = 'R', LWORK >= max(1,M).
140*> For good performance, LWORK should generally be larger.
141*>
142*> If LWORK = -1, then a workspace query is assumed; the routine
143*> only calculates the optimal size of the WORK array, returns
144*> this value as the first entry of the WORK array, and no error
145*> message related to LWORK is issued by XERBLA.
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 realOTHERcomputational
164*
165* =====================================================================
166 SUBROUTINE sormlq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
167 \$ WORK, LWORK, 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, LDA, LDC, LWORK, M, N
176* ..
177* .. Array Arguments ..
178 REAL A( LDA, * ), C( LDC, * ), TAU( * ),
179 \$ work( * )
180* ..
181*
182* =====================================================================
183*
184* .. Parameters ..
185 INTEGER NBMAX, LDT, TSIZE
186 parameter( nbmax = 64, ldt = nbmax+1,
187 \$ tsize = ldt*nbmax )
188* ..
189* .. Local Scalars ..
190 LOGICAL LEFT, LQUERY, NOTRAN
191 CHARACTER TRANST
192 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
193 \$ lwkopt, mi, nb, nbmin, ni, nq, nw
194* ..
195* .. External Functions ..
196 LOGICAL LSAME
197 INTEGER ILAENV
198 EXTERNAL lsame, ilaenv
199* ..
200* .. External Subroutines ..
201 EXTERNAL slarfb, slarft, sorml2, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC max, min
205* ..
206* .. Executable Statements ..
207*
208* Test the input arguments
209*
210 info = 0
211 left = lsame( side, 'L' )
212 notran = lsame( trans, 'N' )
213 lquery = ( lwork.EQ.-1 )
214*
215* NQ is the order of Q and NW is the minimum dimension of WORK
216*
217 IF( left ) THEN
218 nq = m
219 nw = max( 1, n )
220 ELSE
221 nq = n
222 nw = max( 1, m )
223 END IF
224 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
225 info = -1
226 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
227 info = -2
228 ELSE IF( m.LT.0 ) THEN
229 info = -3
230 ELSE IF( n.LT.0 ) THEN
231 info = -4
232 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
233 info = -5
234 ELSE IF( lda.LT.max( 1, k ) ) THEN
235 info = -7
236 ELSE IF( ldc.LT.max( 1, m ) ) THEN
237 info = -10
238 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
239 info = -12
240 END IF
241*
242 IF( info.EQ.0 ) THEN
243*
244* Compute the workspace requirements
245*
246 nb = min( nbmax, ilaenv( 1, 'SORMLQ', side // trans, m, n, k,
247 \$ -1 ) )
248 lwkopt = nw*nb + tsize
249 work( 1 ) = lwkopt
250 END IF
251*
252 IF( info.NE.0 ) THEN
253 CALL xerbla( 'SORMLQ', -info )
254 RETURN
255 ELSE IF( lquery ) THEN
256 RETURN
257 END IF
258*
259* Quick return if possible
260*
261 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
262 work( 1 ) = 1
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, 'SORMLQ', 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 sorml2( 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 jc = 1
301 ELSE
302 mi = m
303 ic = 1
304 END IF
305*
306 IF( notran ) THEN
307 transt = 'T'
308 ELSE
309 transt = 'N'
310 END IF
311*
312 DO 10 i = i1, i2, i3
313 ib = min( nb, k-i+1 )
314*
315* Form the triangular factor of the block reflector
316* H = H(i) H(i+1) . . . H(i+ib-1)
317*
318 CALL slarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
319 \$ lda, tau( i ), work( iwt ), ldt )
320 IF( left ) THEN
321*
322* H or H**T is applied to C(i:m,1:n)
323*
324 mi = m - i + 1
325 ic = i
326 ELSE
327*
328* H or H**T is applied to C(1:m,i:n)
329*
330 ni = n - i + 1
331 jc = i
332 END IF
333*
334* Apply H or H**T
335*
336 CALL slarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
337 \$ a( i, i ), lda, work( iwt ), ldt,
338 \$ c( ic, jc ), ldc, work, ldwork )
339 10 CONTINUE
340 END IF
341 work( 1 ) = lwkopt
342 RETURN
343*
344* End of SORMLQ
345*
346 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: slarfb.f:197
subroutine slarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: slarft.f:163
subroutine sorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
Definition: sorml2.f:159
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:168