LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cunmql()

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

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

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':  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
          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 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 166 of file cunmql.f.

168*
169* -- LAPACK computational routine --
170* -- LAPACK is a software package provided by Univ. of Tennessee, --
171* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172*
173* .. Scalar Arguments ..
174 CHARACTER SIDE, TRANS
175 INTEGER INFO, K, LDA, LDC, LWORK, M, N
176* ..
177* .. Array Arguments ..
178 COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
179 $ WORK( * )
180* ..
181*
182* =====================================================================
183*
184* .. Parameters ..
185 INTEGER NBMAX, LDT, TSIZE
186 parameter( nbmax = 64, ldt = nbmax+1,
187 $ tsize = ldt*nbmax )
188* ..
189* .. Local Scalars ..
190 LOGICAL LEFT, LQUERY, NOTRAN
191 INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
192 $ MI, NB, NBMIN, NI, NQ, NW
193* ..
194* .. External Functions ..
195 LOGICAL LSAME
196 INTEGER ILAENV
197 EXTERNAL lsame, ilaenv
198* ..
199* .. External Subroutines ..
200 EXTERNAL clarfb, clarft, cunm2l, xerbla
201* ..
202* .. Intrinsic Functions ..
203 INTRINSIC max, min
204* ..
205* .. Executable Statements ..
206*
207* Test the input arguments
208*
209 info = 0
210 left = lsame( side, 'L' )
211 notran = lsame( trans, 'N' )
212 lquery = ( lwork.EQ.-1 )
213*
214* NQ is the order of Q and NW is the minimum dimension of WORK
215*
216 IF( left ) THEN
217 nq = m
218 nw = max( 1, n )
219 ELSE
220 nq = n
221 nw = max( 1, m )
222 END IF
223 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
224 info = -1
225 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
226 info = -2
227 ELSE IF( m.LT.0 ) THEN
228 info = -3
229 ELSE IF( n.LT.0 ) THEN
230 info = -4
231 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
232 info = -5
233 ELSE IF( lda.LT.max( 1, nq ) ) THEN
234 info = -7
235 ELSE IF( ldc.LT.max( 1, m ) ) THEN
236 info = -10
237 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
238 info = -12
239 END IF
240*
241 IF( info.EQ.0 ) THEN
242*
243* Compute the workspace requirements
244*
245 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
246 lwkopt = 1
247 ELSE
248 nb = min( nbmax, ilaenv( 1, 'CUNMQL', side // trans, m, n,
249 $ k, -1 ) )
250 lwkopt = nw*nb + tsize
251 END IF
252 work( 1 ) = lwkopt
253 END IF
254*
255 IF( info.NE.0 ) THEN
256 CALL xerbla( 'CUNMQL', -info )
257 RETURN
258 ELSE IF( lquery ) THEN
259 RETURN
260 END IF
261*
262* Quick return if possible
263*
264 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
265 RETURN
266 END IF
267*
268* Determine the block size
269*
270 nbmin = 2
271 ldwork = nw
272 IF( nb.GT.1 .AND. nb.LT.k ) THEN
273 IF( lwork.LT.lwkopt ) THEN
274 nb = (lwork-tsize) / ldwork
275 nbmin = max( 2, ilaenv( 2, 'CUNMQL', side // trans, m, n, k,
276 $ -1 ) )
277 END IF
278 END IF
279*
280 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
281*
282* Use unblocked code
283*
284 CALL cunm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
285 $ iinfo )
286 ELSE
287*
288* Use blocked code
289*
290 iwt = 1 + nw*nb
291 IF( ( left .AND. notran ) .OR.
292 $ ( .NOT.left .AND. .NOT.notran ) ) THEN
293 i1 = 1
294 i2 = k
295 i3 = nb
296 ELSE
297 i1 = ( ( k-1 ) / nb )*nb + 1
298 i2 = 1
299 i3 = -nb
300 END IF
301*
302 IF( left ) THEN
303 ni = n
304 ELSE
305 mi = m
306 END IF
307*
308 DO 10 i = i1, i2, i3
309 ib = min( nb, k-i+1 )
310*
311* Form the triangular factor of the block reflector
312* H = H(i+ib-1) . . . H(i+1) H(i)
313*
314 CALL clarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
315 $ a( 1, i ), lda, tau( i ), work( iwt ), ldt )
316 IF( left ) THEN
317*
318* H or H**H is applied to C(1:m-k+i+ib-1,1:n)
319*
320 mi = m - k + i + ib - 1
321 ELSE
322*
323* H or H**H is applied to C(1:m,1:n-k+i+ib-1)
324*
325 ni = n - k + i + ib - 1
326 END IF
327*
328* Apply H or H**H
329*
330 CALL clarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
331 $ ib, a( 1, i ), lda, work( iwt ), ldt, c, ldc,
332 $ work, ldwork )
333 10 CONTINUE
334 END IF
335 work( 1 ) = lwkopt
336 RETURN
337*
338* End of CUNMQL
339*
ilaenv
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
clarfb
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
clarft
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:163
cunm2l
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:159
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