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

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine cunmql ( 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 
)

CUNMQL

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Purpose:
 CUNMQL 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(2) H(1)

 as returned by CGEQLF. 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':  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
          CGEQLF in the last 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 CGEQLF.
[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 cunmql.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, iinfo, iws, ldwork, lwkopt,
196  $ 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, cunm2l, 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 = max( 1, n )
226  ELSE
227  nq = n
228  nw = max( 1, 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  END IF
245 *
246  IF( info.EQ.0 ) THEN
247  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
248  lwkopt = 1
249  ELSE
250 *
251 * Determine the block size. NB may be at most NBMAX, where
252 * NBMAX is used to define the local array T.
253 *
254  nb = min( nbmax, ilaenv( 1, 'CUNMQL', side // trans, m, n,
255  $ k, -1 ) )
256  lwkopt = nw*nb
257  END IF
258  work( 1 ) = lwkopt
259 *
260  IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
261  info = -12
262  END IF
263  END IF
264 *
265  IF( info.NE.0 ) THEN
266  CALL xerbla( 'CUNMQL', -info )
267  RETURN
268  ELSE IF( lquery ) THEN
269  RETURN
270  END IF
271 *
272 * Quick return if possible
273 *
274  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
275  RETURN
276  END IF
277 *
278  nbmin = 2
279  ldwork = nw
280  IF( nb.GT.1 .AND. nb.LT.k ) THEN
281  iws = nw*nb
282  IF( lwork.LT.iws ) THEN
283  nb = lwork / ldwork
284  nbmin = max( 2, ilaenv( 2, 'CUNMQL', side // trans, m, n, k,
285  $ -1 ) )
286  END IF
287  ELSE
288  iws = nw
289  END IF
290 *
291  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
292 *
293 * Use unblocked code
294 *
295  CALL cunm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
296  $ iinfo )
297  ELSE
298 *
299 * Use blocked code
300 *
301  IF( ( left .AND. notran ) .OR.
302  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
303  i1 = 1
304  i2 = k
305  i3 = nb
306  ELSE
307  i1 = ( ( k-1 ) / nb )*nb + 1
308  i2 = 1
309  i3 = -nb
310  END IF
311 *
312  IF( left ) THEN
313  ni = n
314  ELSE
315  mi = m
316  END IF
317 *
318  DO 10 i = i1, i2, i3
319  ib = min( nb, k-i+1 )
320 *
321 * Form the triangular factor of the block reflector
322 * H = H(i+ib-1) . . . H(i+1) H(i)
323 *
324  CALL clarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
325  $ a( 1, i ), lda, tau( i ), t, ldt )
326  IF( left ) THEN
327 *
328 * H or H**H is applied to C(1:m-k+i+ib-1,1:n)
329 *
330  mi = m - k + i + ib - 1
331  ELSE
332 *
333 * H or H**H is applied to C(1:m,1:n-k+i+ib-1)
334 *
335  ni = n - k + i + ib - 1
336  END IF
337 *
338 * Apply H or H**H
339 *
340  CALL clarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
341  $ ib, a( 1, i ), lda, t, ldt, c, ldc, work,
342  $ ldwork )
343  10 CONTINUE
344  END IF
345  work( 1 ) = lwkopt
346  RETURN
347 *
348 * End of CUNMQL
349 *
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 cunm2l(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf...
Definition: cunm2l.f:161
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

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