 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zunmbr()

 subroutine zunmbr ( character VECT, character SIDE, character TRANS, integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZUNMBR

Purpose:
``` If VECT = 'Q', ZUNMBR 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', ZUNMBR 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 ZGEBRD 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 ZGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by ZGEBRD. K >= 0.``` [in] A ``` A is COMPLEX*16 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 ZGEBRD.``` [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*16 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 ZGEBRD in the array argument TAUQ or TAUP.``` [in,out] C ``` C is COMPLEX*16 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*16 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 194 of file zunmbr.f.

196*
197* -- LAPACK computational routine --
198* -- LAPACK is a software package provided by Univ. of Tennessee, --
199* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
200*
201* .. Scalar Arguments ..
202 CHARACTER SIDE, TRANS, VECT
203 INTEGER INFO, K, LDA, LDC, LWORK, M, N
204* ..
205* .. Array Arguments ..
206 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
207* ..
208*
209* =====================================================================
210*
211* .. Local Scalars ..
212 LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
213 CHARACTER TRANST
214 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
215* ..
216* .. External Functions ..
217 LOGICAL LSAME
218 INTEGER ILAENV
219 EXTERNAL lsame, ilaenv
220* ..
221* .. External Subroutines ..
222 EXTERNAL xerbla, zunmlq, zunmqr
223* ..
224* .. Intrinsic Functions ..
225 INTRINSIC max, min
226* ..
227* .. Executable Statements ..
228*
229* Test the input arguments
230*
231 info = 0
232 applyq = lsame( vect, 'Q' )
233 left = lsame( side, 'L' )
234 notran = lsame( trans, 'N' )
235 lquery = ( lwork.EQ.-1 )
236*
237* NQ is the order of Q or P and NW is the minimum dimension of WORK
238*
239 IF( left ) THEN
240 nq = m
241 nw = max( 1, n )
242 ELSE
243 nq = n
244 nw = max( 1, m )
245 END IF
246 IF( .NOT.applyq .AND. .NOT.lsame( vect, 'P' ) ) THEN
247 info = -1
248 ELSE IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
249 info = -2
250 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
251 info = -3
252 ELSE IF( m.LT.0 ) THEN
253 info = -4
254 ELSE IF( n.LT.0 ) THEN
255 info = -5
256 ELSE IF( k.LT.0 ) THEN
257 info = -6
258 ELSE IF( ( applyq .AND. lda.LT.max( 1, nq ) ) .OR.
259 \$ ( .NOT.applyq .AND. lda.LT.max( 1, min( nq, k ) ) ) )
260 \$ THEN
261 info = -8
262 ELSE IF( ldc.LT.max( 1, m ) ) THEN
263 info = -11
264 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
265 info = -13
266 END IF
267*
268 IF( info.EQ.0 ) THEN
269 IF( m.GT.0 .AND. n.GT.0 ) THEN
270 IF( applyq ) THEN
271 IF( left ) THEN
272 nb = ilaenv( 1, 'ZUNMQR', side // trans, m-1, n, m-1,
273 \$ -1 )
274 ELSE
275 nb = ilaenv( 1, 'ZUNMQR', side // trans, m, n-1, n-1,
276 \$ -1 )
277 END IF
278 ELSE
279 IF( left ) THEN
280 nb = ilaenv( 1, 'ZUNMLQ', side // trans, m-1, n, m-1,
281 \$ -1 )
282 ELSE
283 nb = ilaenv( 1, 'ZUNMLQ', side // trans, m, n-1, n-1,
284 \$ -1 )
285 END IF
286 END IF
287 lwkopt = nw*nb
288 ELSE
289 lwkopt = 1
290 END IF
291 work( 1 ) = lwkopt
292 END IF
293*
294 IF( info.NE.0 ) THEN
295 CALL xerbla( 'ZUNMBR', -info )
296 RETURN
297 ELSE IF( lquery ) THEN
298 RETURN
299 END IF
300*
301* Quick return if possible
302*
303 IF( m.EQ.0 .OR. n.EQ.0 )
304 \$ RETURN
305*
306 IF( applyq ) THEN
307*
308* Apply Q
309*
310 IF( nq.GE.k ) THEN
311*
312* Q was determined by a call to ZGEBRD with nq >= k
313*
314 CALL zunmqr( side, trans, m, n, k, a, lda, tau, c, ldc,
315 \$ work, lwork, iinfo )
316 ELSE IF( nq.GT.1 ) THEN
317*
318* Q was determined by a call to ZGEBRD with nq < k
319*
320 IF( left ) THEN
321 mi = m - 1
322 ni = n
323 i1 = 2
324 i2 = 1
325 ELSE
326 mi = m
327 ni = n - 1
328 i1 = 1
329 i2 = 2
330 END IF
331 CALL zunmqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
332 \$ c( i1, i2 ), ldc, work, lwork, iinfo )
333 END IF
334 ELSE
335*
336* Apply P
337*
338 IF( notran ) THEN
339 transt = 'C'
340 ELSE
341 transt = 'N'
342 END IF
343 IF( nq.GT.k ) THEN
344*
345* P was determined by a call to ZGEBRD with nq > k
346*
347 CALL zunmlq( side, transt, m, n, k, a, lda, tau, c, ldc,
348 \$ work, lwork, iinfo )
349 ELSE IF( nq.GT.1 ) THEN
350*
351* P was determined by a call to ZGEBRD with nq <= k
352*
353 IF( left ) THEN
354 mi = m - 1
355 ni = n
356 i1 = 2
357 i2 = 1
358 ELSE
359 mi = m
360 ni = n - 1
361 i1 = 1
362 i2 = 2
363 END IF
364 CALL zunmlq( side, transt, mi, ni, nq-1, a( 1, 2 ), lda,
365 \$ tau, c( i1, i2 ), ldc, work, lwork, iinfo )
366 END IF
367 END IF
368 work( 1 ) = lwkopt
369 RETURN
370*
371* End of ZUNMBR
372*
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 zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:167
subroutine zunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQR
Definition: zunmqr.f:167
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