LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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sorgrq.f
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1*> \brief \b SORGRQ
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> Download SORGRQ + dependencies
9*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorgrq.f">
10*> [TGZ]</a>
11*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgrq.f">
12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgrq.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* SUBROUTINE SORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
20*
21* .. Scalar Arguments ..
22* INTEGER INFO, K, LDA, LWORK, M, N
23* ..
24* .. Array Arguments ..
25* REAL A( LDA, * ), TAU( * ), WORK( * )
26* ..
27*
28*
29*> \par Purpose:
30* =============
31*>
32*> \verbatim
33*>
34*> SORGRQ generates an M-by-N real matrix Q with orthonormal rows,
35*> which is defined as the last M rows of a product of K elementary
36*> reflectors of order N
37*>
38*> Q = H(1) H(2) . . . H(k)
39*>
40*> as returned by SGERQF.
41*> \endverbatim
42*
43* Arguments:
44* ==========
45*
46*> \param[in] M
47*> \verbatim
48*> M is INTEGER
49*> The number of rows of the matrix Q. M >= 0.
50*> \endverbatim
51*>
52*> \param[in] N
53*> \verbatim
54*> N is INTEGER
55*> The number of columns of the matrix Q. N >= M.
56*> \endverbatim
57*>
58*> \param[in] K
59*> \verbatim
60*> K is INTEGER
61*> The number of elementary reflectors whose product defines the
62*> matrix Q. M >= K >= 0.
63*> \endverbatim
64*>
65*> \param[in,out] A
66*> \verbatim
67*> A is REAL array, dimension (LDA,N)
68*> On entry, the (m-k+i)-th row must contain the vector which
69*> defines the elementary reflector H(i), for i = 1,2,...,k, as
70*> returned by SGERQF in the last k rows of its array argument
71*> A.
72*> On exit, the M-by-N matrix Q.
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*> LDA is INTEGER
78*> The first dimension of the array A. LDA >= max(1,M).
79*> \endverbatim
80*>
81*> \param[in] TAU
82*> \verbatim
83*> TAU is REAL array, dimension (K)
84*> TAU(i) must contain the scalar factor of the elementary
85*> reflector H(i), as returned by SGERQF.
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*> WORK is REAL array, dimension (MAX(1,LWORK))
91*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
92*> \endverbatim
93*>
94*> \param[in] LWORK
95*> \verbatim
96*> LWORK is INTEGER
97*> The dimension of the array WORK. LWORK >= max(1,M).
98*> For optimum performance LWORK >= M*NB, where NB is the
99*> optimal blocksize.
100*>
101*> If LWORK = -1, then a workspace query is assumed; the routine
102*> only calculates the optimal size of the WORK array, returns
103*> this value as the first entry of the WORK array, and no error
104*> message related to LWORK is issued by XERBLA.
105*> \endverbatim
106*>
107*> \param[out] INFO
108*> \verbatim
109*> INFO is INTEGER
110*> = 0: successful exit
111*> < 0: if INFO = -i, the i-th argument has an illegal value
112*> \endverbatim
113*
114* Authors:
115* ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \ingroup ungrq
123*
124* =====================================================================
125 SUBROUTINE sorgrq( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
126*
127* -- LAPACK computational routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 INTEGER INFO, K, LDA, LWORK, M, N
133* ..
134* .. Array Arguments ..
135 REAL A( LDA, * ), TAU( * ), WORK( * )
136* ..
137*
138* =====================================================================
139*
140* .. Parameters ..
141 REAL ZERO
142 parameter( zero = 0.0e+0 )
143* ..
144* .. Local Scalars ..
145 LOGICAL LQUERY
146 INTEGER I, IB, II, IINFO, IWS, J, KK, L, LDWORK,
147 $ LWKOPT, NB, NBMIN, NX
148* ..
149* .. External Subroutines ..
150 EXTERNAL slarfb, slarft, sorgr2, xerbla
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max, min
154* ..
155* .. External Functions ..
156 INTEGER ILAENV
157 REAL SROUNDUP_LWORK
158 EXTERNAL ilaenv, sroundup_lwork
159* ..
160* .. Executable Statements ..
161*
162* Test the input arguments
163*
164 info = 0
165 lquery = ( lwork.EQ.-1 )
166 IF( m.LT.0 ) THEN
167 info = -1
168 ELSE IF( n.LT.m ) THEN
169 info = -2
170 ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
171 info = -3
172 ELSE IF( lda.LT.max( 1, m ) ) THEN
173 info = -5
174 END IF
175*
176 IF( info.EQ.0 ) THEN
177 IF( m.LE.0 ) THEN
178 lwkopt = 1
179 ELSE
180 nb = ilaenv( 1, 'SORGRQ', ' ', m, n, k, -1 )
181 lwkopt = m*nb
182 END IF
183 work( 1 ) = sroundup_lwork(lwkopt)
184*
185 IF( lwork.LT.max( 1, m ) .AND. .NOT.lquery ) THEN
186 info = -8
187 END IF
188 END IF
189*
190 IF( info.NE.0 ) THEN
191 CALL xerbla( 'SORGRQ', -info )
192 RETURN
193 ELSE IF( lquery ) THEN
194 RETURN
195 END IF
196*
197* Quick return if possible
198*
199 IF( m.LE.0 ) THEN
200 RETURN
201 END IF
202*
203 nbmin = 2
204 nx = 0
205 iws = m
206 IF( nb.GT.1 .AND. nb.LT.k ) THEN
207*
208* Determine when to cross over from blocked to unblocked code.
209*
210 nx = max( 0, ilaenv( 3, 'SORGRQ', ' ', m, n, k, -1 ) )
211 IF( nx.LT.k ) THEN
212*
213* Determine if workspace is large enough for blocked code.
214*
215 ldwork = m
216 iws = ldwork*nb
217 IF( lwork.LT.iws ) THEN
218*
219* Not enough workspace to use optimal NB: reduce NB and
220* determine the minimum value of NB.
221*
222 nb = lwork / ldwork
223 nbmin = max( 2, ilaenv( 2, 'SORGRQ', ' ', m, n, k,
224 $ -1 ) )
225 END IF
226 END IF
227 END IF
228*
229 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
230*
231* Use blocked code after the first block.
232* The last kk rows are handled by the block method.
233*
234 kk = min( k, ( ( k-nx+nb-1 ) / nb )*nb )
235*
236* Set A(1:m-kk,n-kk+1:n) to zero.
237*
238 DO 20 j = n - kk + 1, n
239 DO 10 i = 1, m - kk
240 a( i, j ) = zero
241 10 CONTINUE
242 20 CONTINUE
243 ELSE
244 kk = 0
245 END IF
246*
247* Use unblocked code for the first or only block.
248*
249 CALL sorgr2( m-kk, n-kk, k-kk, a, lda, tau, work, iinfo )
250*
251 IF( kk.GT.0 ) THEN
252*
253* Use blocked code
254*
255 DO 50 i = k - kk + 1, k, nb
256 ib = min( nb, k-i+1 )
257 ii = m - k + i
258 IF( ii.GT.1 ) THEN
259*
260* Form the triangular factor of the block reflector
261* H = H(i+ib-1) . . . H(i+1) H(i)
262*
263 CALL slarft( 'Backward', 'Rowwise', n-k+i+ib-1, ib,
264 $ a( ii, 1 ), lda, tau( i ), work, ldwork )
265*
266* Apply H**T to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
267*
268 CALL slarfb( 'Right', 'Transpose', 'Backward',
269 $ 'Rowwise',
270 $ ii-1, n-k+i+ib-1, ib, a( ii, 1 ), lda, work,
271 $ ldwork, a, lda, work( ib+1 ), ldwork )
272 END IF
273*
274* Apply H**T to columns 1:n-k+i+ib-1 of current block
275*
276 CALL sorgr2( ib, n-k+i+ib-1, ib, a( ii, 1 ), lda,
277 $ tau( i ),
278 $ work, iinfo )
279*
280* Set columns n-k+i+ib:n of current block to zero
281*
282 DO 40 l = n - k + i + ib, n
283 DO 30 j = ii, ii + ib - 1
284 a( j, l ) = zero
285 30 CONTINUE
286 40 CONTINUE
287 50 CONTINUE
288 END IF
289*
290 work( 1 ) = sroundup_lwork(iws)
291 RETURN
292*
293* End of SORGRQ
294*
295 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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:195
recursive 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:162
subroutine sorgr2(m, n, k, a, lda, tau, work, info)
SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf...
Definition sorgr2.f:112
subroutine sorgrq(m, n, k, a, lda, tau, work, lwork, info)
SORGRQ
Definition sorgrq.f:126