LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ dormrq()

subroutine dormrq ( character  side,
character  trans,
integer  m,
integer  n,
integer  k,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( * )  tau,
double precision, dimension( ldc, * )  c,
integer  ldc,
double precision, dimension( * )  work,
integer  lwork,
integer  info 
)

DORMRQ

Download DORMRQ + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DORMRQ overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'T':      Q**T * C       C * Q**T

 where Q is a real orthogonal matrix defined as the product of k
 elementary reflectors

       Q = H(1) H(2) . . . H(k)

 as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N
 if SIDE = 'R'.
Parameters
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.
[in]M
          M is INTEGER
          The number of rows of the matrix C. M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix C. N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          DGERQF in the last k rows of its array argument A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGERQF.
[in,out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).
          For good performance, LWORK should generally be larger.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 165 of file dormrq.f.

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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
ilaenv
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
dlarfb
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
dlarft
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
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dormr2
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
Here is the call graph for this function:
Here is the caller graph for this function: