LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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 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 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
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