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

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine cunmqr ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( ldc, * )  C,
integer  LDC,
complex, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

CUNMQR

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Purpose:
 CUNMQR overwrites the general complex M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'C':      Q**H * C       C * Q**H

 where Q is a complex unitary matrix defined as the product of k
 elementary reflectors

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

 as returned by CGEQRF. 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**H from the Left;
          = 'R': apply Q or Q**H from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.
[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 COMPLEX array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CGEQRF in the first k columns of its array argument A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).
[in]TAU
          TAU is COMPLEX array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CGEQRF.
[in,out]C
          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
          WORK is COMPLEX 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 172 of file cunmqr.f.

172 *
173 * -- LAPACK computational routine (version 3.4.0) --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 * November 2011
177 *
178 * .. Scalar Arguments ..
179  CHARACTER side, trans
180  INTEGER info, k, lda, ldc, lwork, m, n
181 * ..
182 * .. Array Arguments ..
183  COMPLEX a( lda, * ), c( ldc, * ), tau( * ),
184  $ work( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * .. Parameters ..
190  INTEGER nbmax, ldt
191  parameter( nbmax = 64, ldt = nbmax+1 )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL left, lquery, notran
195  INTEGER i, i1, i2, i3, ib, ic, iinfo, iws, jc, ldwork,
196  $ lwkopt, mi, nb, nbmin, ni, nq, nw
197 * ..
198 * .. Local Arrays ..
199  COMPLEX t( ldt, nbmax )
200 * ..
201 * .. External Functions ..
202  LOGICAL lsame
203  INTEGER ilaenv
204  EXTERNAL lsame, ilaenv
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL clarfb, clarft, cunm2r, xerbla
208 * ..
209 * .. Intrinsic Functions ..
210  INTRINSIC max, min
211 * ..
212 * .. Executable Statements ..
213 *
214 * Test the input arguments
215 *
216  info = 0
217  left = lsame( side, 'L' )
218  notran = lsame( trans, 'N' )
219  lquery = ( lwork.EQ.-1 )
220 *
221 * NQ is the order of Q and NW is the minimum dimension of WORK
222 *
223  IF( left ) THEN
224  nq = m
225  nw = n
226  ELSE
227  nq = n
228  nw = m
229  END IF
230  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
231  info = -1
232  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
233  info = -2
234  ELSE IF( m.LT.0 ) THEN
235  info = -3
236  ELSE IF( n.LT.0 ) THEN
237  info = -4
238  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
239  info = -5
240  ELSE IF( lda.LT.max( 1, nq ) ) THEN
241  info = -7
242  ELSE IF( ldc.LT.max( 1, m ) ) THEN
243  info = -10
244  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
245  info = -12
246  END IF
247 *
248  IF( info.EQ.0 ) THEN
249 *
250 * Determine the block size. NB may be at most NBMAX, where NBMAX
251 * is used to define the local array T.
252 *
253  nb = min( nbmax, ilaenv( 1, 'CUNMQR', side // trans, m, n, k,
254  $ -1 ) )
255  lwkopt = max( 1, nw )*nb
256  work( 1 ) = lwkopt
257  END IF
258 *
259  IF( info.NE.0 ) THEN
260  CALL xerbla( 'CUNMQR', -info )
261  RETURN
262  ELSE IF( lquery ) THEN
263  RETURN
264  END IF
265 *
266 * Quick return if possible
267 *
268  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
269  work( 1 ) = 1
270  RETURN
271  END IF
272 *
273  nbmin = 2
274  ldwork = nw
275  IF( nb.GT.1 .AND. nb.LT.k ) THEN
276  iws = nw*nb
277  IF( lwork.LT.iws ) THEN
278  nb = lwork / ldwork
279  nbmin = max( 2, ilaenv( 2, 'CUNMQR', side // trans, m, n, k,
280  $ -1 ) )
281  END IF
282  ELSE
283  iws = nw
284  END IF
285 *
286  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
287 *
288 * Use unblocked code
289 *
290  CALL cunm2r( side, trans, m, n, k, a, lda, tau, c, ldc, work,
291  $ iinfo )
292  ELSE
293 *
294 * Use blocked code
295 *
296  IF( ( left .AND. .NOT.notran ) .OR.
297  $ ( .NOT.left .AND. notran ) ) THEN
298  i1 = 1
299  i2 = k
300  i3 = nb
301  ELSE
302  i1 = ( ( k-1 ) / nb )*nb + 1
303  i2 = 1
304  i3 = -nb
305  END IF
306 *
307  IF( left ) THEN
308  ni = n
309  jc = 1
310  ELSE
311  mi = m
312  ic = 1
313  END IF
314 *
315  DO 10 i = i1, i2, i3
316  ib = min( nb, k-i+1 )
317 *
318 * Form the triangular factor of the block reflector
319 * H = H(i) H(i+1) . . . H(i+ib-1)
320 *
321  CALL clarft( 'Forward', 'Columnwise', nq-i+1, ib, a( i, i ),
322  $ lda, tau( i ), t, ldt )
323  IF( left ) THEN
324 *
325 * H or H**H is applied to C(i:m,1:n)
326 *
327  mi = m - i + 1
328  ic = i
329  ELSE
330 *
331 * H or H**H is applied to C(1:m,i:n)
332 *
333  ni = n - i + 1
334  jc = i
335  END IF
336 *
337 * Apply H or H**H
338 *
339  CALL clarfb( side, trans, 'Forward', 'Columnwise', mi, ni,
340  $ ib, a( i, i ), lda, t, ldt, c( ic, jc ), ldc,
341  $ work, ldwork )
342  10 CONTINUE
343  END IF
344  work( 1 ) = lwkopt
345  RETURN
346 *
347 * End of CUNMQR
348 *
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: clarfb.f:197
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine clarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: clarft.f:165
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
subroutine cunm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf...
Definition: cunm2r.f:161

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