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

Go to the source code of this file.

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine cunmlq ( 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 
)

CUNMLQ

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

Purpose:
 CUNMLQ 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(k)**H . . . H(2)**H H(1)**H

 as returned by CGELQF. 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,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
          CGELQF in the first 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 COMPLEX array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CGELQF.
[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 cunmlq.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  CHARACTER transt
196  INTEGER i, i1, i2, i3, ib, ic, iinfo, iws, jc, ldwork,
197  $ lwkopt, mi, nb, nbmin, ni, nq, nw
198 * ..
199 * .. Local Arrays ..
200  COMPLEX t( ldt, nbmax )
201 * ..
202 * .. External Functions ..
203  LOGICAL lsame
204  INTEGER ilaenv
205  EXTERNAL lsame, ilaenv
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL clarfb, clarft, cunml2, xerbla
209 * ..
210 * .. Intrinsic Functions ..
211  INTRINSIC max, min
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input arguments
216 *
217  info = 0
218  left = lsame( side, 'L' )
219  notran = lsame( trans, 'N' )
220  lquery = ( lwork.EQ.-1 )
221 *
222 * NQ is the order of Q and NW is the minimum dimension of WORK
223 *
224  IF( left ) THEN
225  nq = m
226  nw = n
227  ELSE
228  nq = n
229  nw = m
230  END IF
231  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
232  info = -1
233  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
234  info = -2
235  ELSE IF( m.LT.0 ) THEN
236  info = -3
237  ELSE IF( n.LT.0 ) THEN
238  info = -4
239  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
240  info = -5
241  ELSE IF( lda.LT.max( 1, k ) ) THEN
242  info = -7
243  ELSE IF( ldc.LT.max( 1, m ) ) THEN
244  info = -10
245  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
246  info = -12
247  END IF
248 *
249  IF( info.EQ.0 ) THEN
250 *
251 * Determine the block size. NB may be at most NBMAX, where NBMAX
252 * is used to define the local array T.
253 *
254  nb = min( nbmax, ilaenv( 1, 'CUNMLQ', side // trans, m, n, k,
255  $ -1 ) )
256  lwkopt = max( 1, nw )*nb
257  work( 1 ) = lwkopt
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'CUNMLQ', -info )
262  RETURN
263  ELSE IF( lquery ) THEN
264  RETURN
265  END IF
266 *
267 * Quick return if possible
268 *
269  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
270  work( 1 ) = 1
271  RETURN
272  END IF
273 *
274  nbmin = 2
275  ldwork = nw
276  IF( nb.GT.1 .AND. nb.LT.k ) THEN
277  iws = nw*nb
278  IF( lwork.LT.iws ) THEN
279  nb = lwork / ldwork
280  nbmin = max( 2, ilaenv( 2, 'CUNMLQ', side // trans, m, n, k,
281  $ -1 ) )
282  END IF
283  ELSE
284  iws = nw
285  END IF
286 *
287  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
288 *
289 * Use unblocked code
290 *
291  CALL cunml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
292  $ iinfo )
293  ELSE
294 *
295 * Use blocked code
296 *
297  IF( ( left .AND. notran ) .OR.
298  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
299  i1 = 1
300  i2 = k
301  i3 = nb
302  ELSE
303  i1 = ( ( k-1 ) / nb )*nb + 1
304  i2 = 1
305  i3 = -nb
306  END IF
307 *
308  IF( left ) THEN
309  ni = n
310  jc = 1
311  ELSE
312  mi = m
313  ic = 1
314  END IF
315 *
316  IF( notran ) THEN
317  transt = 'C'
318  ELSE
319  transt = 'N'
320  END IF
321 *
322  DO 10 i = i1, i2, i3
323  ib = min( nb, k-i+1 )
324 *
325 * Form the triangular factor of the block reflector
326 * H = H(i) H(i+1) . . . H(i+ib-1)
327 *
328  CALL clarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
329  $ lda, tau( i ), t, ldt )
330  IF( left ) THEN
331 *
332 * H or H**H is applied to C(i:m,1:n)
333 *
334  mi = m - i + 1
335  ic = i
336  ELSE
337 *
338 * H or H**H is applied to C(1:m,i:n)
339 *
340  ni = n - i + 1
341  jc = i
342  END IF
343 *
344 * Apply H or H**H
345 *
346  CALL clarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
347  $ a( i, i ), lda, t, ldt, c( ic, jc ), ldc, work,
348  $ ldwork )
349  10 CONTINUE
350  END IF
351  work( 1 ) = lwkopt
352  RETURN
353 *
354 * End of CUNMLQ
355 *
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
subroutine cunml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf...
Definition: cunml2.f:161
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83

Here is the call graph for this function:

Here is the caller graph for this function: