LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
dormrq.f File Reference

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Functions/Subroutines

subroutine dormrq (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
 DORMRQ More...
 

Function/Subroutine Documentation

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

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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 optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
          blocksize.

          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.
Date
November 2011

Definition at line 171 of file dormrq.f.

171 *
172 * -- LAPACK computational routine (version 3.4.0) --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 * November 2011
176 *
177 * .. Scalar Arguments ..
178  CHARACTER side, trans
179  INTEGER info, k, lda, ldc, lwork, m, n
180 * ..
181 * .. Array Arguments ..
182  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  INTEGER nbmax, ldt
189  parameter( nbmax = 64, ldt = nbmax+1 )
190 * ..
191 * .. Local Scalars ..
192  LOGICAL left, lquery, notran
193  CHARACTER transt
194  INTEGER i, i1, i2, i3, ib, iinfo, iws, ldwork, lwkopt,
195  $ mi, nb, nbmin, ni, nq, nw
196 * ..
197 * .. Local Arrays ..
198  DOUBLE PRECISION t( ldt, nbmax )
199 * ..
200 * .. External Functions ..
201  LOGICAL lsame
202  INTEGER ilaenv
203  EXTERNAL lsame, ilaenv
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL dlarfb, dlarft, dormr2, xerbla
207 * ..
208 * .. Intrinsic Functions ..
209  INTRINSIC max, min
210 * ..
211 * .. Executable Statements ..
212 *
213 * Test the input arguments
214 *
215  info = 0
216  left = lsame( side, 'L' )
217  notran = lsame( trans, 'N' )
218  lquery = ( lwork.EQ.-1 )
219 *
220 * NQ is the order of Q and NW is the minimum dimension of WORK
221 *
222  IF( left ) THEN
223  nq = m
224  nw = max( 1, n )
225  ELSE
226  nq = n
227  nw = max( 1, m )
228  END IF
229  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
230  info = -1
231  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
232  info = -2
233  ELSE IF( m.LT.0 ) THEN
234  info = -3
235  ELSE IF( n.LT.0 ) THEN
236  info = -4
237  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
238  info = -5
239  ELSE IF( lda.LT.max( 1, k ) ) THEN
240  info = -7
241  ELSE IF( ldc.LT.max( 1, m ) ) THEN
242  info = -10
243  END IF
244 *
245  IF( info.EQ.0 ) THEN
246  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
247  lwkopt = 1
248  ELSE
249 *
250 * Determine the block size. NB may be at most NBMAX, where
251 * NBMAX is used to define the local array T.
252 *
253  nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
254  $ k, -1 ) )
255  lwkopt = nw*nb
256  END IF
257  work( 1 ) = lwkopt
258 *
259  IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
260  info = -12
261  END IF
262  END IF
263 *
264  IF( info.NE.0 ) THEN
265  CALL xerbla( 'DORMRQ', -info )
266  RETURN
267  ELSE IF( lquery ) THEN
268  RETURN
269  END IF
270 *
271 * Quick return if possible
272 *
273  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
274  RETURN
275  END IF
276 *
277  nbmin = 2
278  ldwork = nw
279  IF( nb.GT.1 .AND. nb.LT.k ) THEN
280  iws = nw*nb
281  IF( lwork.LT.iws ) THEN
282  nb = lwork / ldwork
283  nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
284  $ -1 ) )
285  END IF
286  ELSE
287  iws = nw
288  END IF
289 *
290  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
291 *
292 * Use unblocked code
293 *
294  CALL dormr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
295  $ iinfo )
296  ELSE
297 *
298 * Use blocked code
299 *
300  IF( ( left .AND. .NOT.notran ) .OR.
301  $ ( .NOT.left .AND. notran ) ) THEN
302  i1 = 1
303  i2 = k
304  i3 = nb
305  ELSE
306  i1 = ( ( k-1 ) / nb )*nb + 1
307  i2 = 1
308  i3 = -nb
309  END IF
310 *
311  IF( left ) THEN
312  ni = n
313  ELSE
314  mi = m
315  END IF
316 *
317  IF( notran ) THEN
318  transt = 'T'
319  ELSE
320  transt = 'N'
321  END IF
322 *
323  DO 10 i = i1, i2, i3
324  ib = min( nb, k-i+1 )
325 *
326 * Form the triangular factor of the block reflector
327 * H = H(i+ib-1) . . . H(i+1) H(i)
328 *
329  CALL dlarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
330  $ a( i, 1 ), lda, tau( i ), t, ldt )
331  IF( left ) THEN
332 *
333 * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
334 *
335  mi = m - k + i + ib - 1
336  ELSE
337 *
338 * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
339 *
340  ni = n - k + i + ib - 1
341  END IF
342 *
343 * Apply H or H**T
344 *
345  CALL dlarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
346  $ ib, a( i, 1 ), lda, t, ldt, c, ldc, work,
347  $ ldwork )
348  10 CONTINUE
349  END IF
350  work( 1 ) = lwkopt
351  RETURN
352 *
353 * End of DORMRQ
354 *
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:165
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 xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
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:161

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