LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cunmbr()

 subroutine cunmbr ( character VECT, 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 )

CUNMBR

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Purpose:
``` If VECT = 'Q', CUNMBR 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

If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'C':      P**H * C       C * P**H

Here Q and P**H are the unitary matrices determined by CGEBRD when
reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the unitary matrix Q or P**H that is applied.

If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).```
Parameters
 [in] VECT ``` VECT is CHARACTER*1 = 'Q': apply Q or Q**H; = 'P': apply P or P**H.``` [in] SIDE ``` SIDE is CHARACTER*1 = 'L': apply Q, Q**H, P or P**H from the Left; = 'R': apply Q, Q**H, P or P**H from the Right.``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': No transpose, apply Q or P; = 'C': Conjugate transpose, apply Q**H or P**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 If VECT = 'Q', the number of columns in the original matrix reduced by CGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by CGEBRD. K >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by CGEBRD.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).``` [in] TAU ``` TAU is COMPLEX array, dimension (min(nq,K)) TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by CGEBRD in the array argument TAUQ or TAUP.``` [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 or P*C or P**H*C or C*P or C*P**H.``` [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); if N = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.) 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```

Definition at line 195 of file cunmbr.f.

197 *
198 * -- LAPACK computational routine --
199 * -- LAPACK is a software package provided by Univ. of Tennessee, --
200 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201 *
202 * .. Scalar Arguments ..
203  CHARACTER SIDE, TRANS, VECT
204  INTEGER INFO, K, LDA, LDC, LWORK, M, N
205 * ..
206 * .. Array Arguments ..
207  COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
208  \$ WORK( * )
209 * ..
210 *
211 * =====================================================================
212 *
213 * .. Local Scalars ..
214  LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
215  CHARACTER TRANST
216  INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
217 * ..
218 * .. External Functions ..
219  LOGICAL LSAME
220  INTEGER ILAENV
221  EXTERNAL ilaenv, lsame
222 * ..
223 * .. External Subroutines ..
224  EXTERNAL cunmlq, cunmqr, xerbla
225 * ..
226 * .. Intrinsic Functions ..
227  INTRINSIC max, min
228 * ..
229 * .. Executable Statements ..
230 *
231 * Test the input arguments
232 *
233  info = 0
234  applyq = lsame( vect, 'Q' )
235  left = lsame( side, 'L' )
236  notran = lsame( trans, 'N' )
237  lquery = ( lwork.EQ.-1 )
238 *
239 * NQ is the order of Q or P and NW is the minimum dimension of WORK
240 *
241  IF( left ) THEN
242  nq = m
243  nw = max( 1, n )
244  ELSE
245  nq = n
246  nw = max( 1, m )
247  END IF
248  IF( .NOT.applyq .AND. .NOT.lsame( vect, 'P' ) ) THEN
249  info = -1
250  ELSE IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
251  info = -2
252  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
253  info = -3
254  ELSE IF( m.LT.0 ) THEN
255  info = -4
256  ELSE IF( n.LT.0 ) THEN
257  info = -5
258  ELSE IF( k.LT.0 ) THEN
259  info = -6
260  ELSE IF( ( applyq .AND. lda.LT.max( 1, nq ) ) .OR.
261  \$ ( .NOT.applyq .AND. lda.LT.max( 1, min( nq, k ) ) ) )
262  \$ THEN
263  info = -8
264  ELSE IF( ldc.LT.max( 1, m ) ) THEN
265  info = -11
266  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
267  info = -13
268  END IF
269 *
270  IF( info.EQ.0 ) THEN
271  IF( m.GT.0 .AND. n.GT.0 ) THEN
272  IF( applyq ) THEN
273  IF( left ) THEN
274  nb = ilaenv( 1, 'CUNMQR', side // trans, m-1, n, m-1,
275  \$ -1 )
276  ELSE
277  nb = ilaenv( 1, 'CUNMQR', side // trans, m, n-1, n-1,
278  \$ -1 )
279  END IF
280  ELSE
281  IF( left ) THEN
282  nb = ilaenv( 1, 'CUNMLQ', side // trans, m-1, n, m-1,
283  \$ -1 )
284  ELSE
285  nb = ilaenv( 1, 'CUNMLQ', side // trans, m, n-1, n-1,
286  \$ -1 )
287  END IF
288  END IF
289  lwkopt = nw*nb
290  ELSE
291  lwkopt = 1
292  END IF
293  work( 1 ) = lwkopt
294  END IF
295 *
296  IF( info.NE.0 ) THEN
297  CALL xerbla( 'CUNMBR', -info )
298  RETURN
299  ELSE IF( lquery ) THEN
300  RETURN
301  END IF
302 *
303 * Quick return if possible
304 *
305  IF( m.EQ.0 .OR. n.EQ.0 )
306  \$ RETURN
307 *
308  IF( applyq ) THEN
309 *
310 * Apply Q
311 *
312  IF( nq.GE.k ) THEN
313 *
314 * Q was determined by a call to CGEBRD with nq >= k
315 *
316  CALL cunmqr( side, trans, m, n, k, a, lda, tau, c, ldc,
317  \$ work, lwork, iinfo )
318  ELSE IF( nq.GT.1 ) THEN
319 *
320 * Q was determined by a call to CGEBRD with nq < k
321 *
322  IF( left ) THEN
323  mi = m - 1
324  ni = n
325  i1 = 2
326  i2 = 1
327  ELSE
328  mi = m
329  ni = n - 1
330  i1 = 1
331  i2 = 2
332  END IF
333  CALL cunmqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
334  \$ c( i1, i2 ), ldc, work, lwork, iinfo )
335  END IF
336  ELSE
337 *
338 * Apply P
339 *
340  IF( notran ) THEN
341  transt = 'C'
342  ELSE
343  transt = 'N'
344  END IF
345  IF( nq.GT.k ) THEN
346 *
347 * P was determined by a call to CGEBRD with nq > k
348 *
349  CALL cunmlq( side, transt, m, n, k, a, lda, tau, c, ldc,
350  \$ work, lwork, iinfo )
351  ELSE IF( nq.GT.1 ) THEN
352 *
353 * P was determined by a call to CGEBRD with nq <= k
354 *
355  IF( left ) THEN
356  mi = m - 1
357  ni = n
358  i1 = 2
359  i2 = 1
360  ELSE
361  mi = m
362  ni = n - 1
363  i1 = 1
364  i2 = 2
365  END IF
366  CALL cunmlq( side, transt, mi, ni, nq-1, a( 1, 2 ), lda,
367  \$ tau, c( i1, i2 ), ldc, work, lwork, iinfo )
368  END IF
369  END IF
370  work( 1 ) = lwkopt
371  RETURN
372 *
373 * End of CUNMBR
374 *
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 cunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMLQ
Definition: cunmlq.f:168
subroutine cunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMQR
Definition: cunmqr.f:168
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