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

 subroutine ctpmlqt ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer MB, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, integer INFO )

CTPMLQT

Purpose:
``` CTPMLQT applies a complex unitary matrix Q obtained from a
"triangular-pentagonal" complex block reflector H to a general
complex matrix C, which consists of two blocks A and B.```
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 B. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix B. N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q.``` [in] L ``` L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.``` [in] MB ``` MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CTPLQT.``` [in] V ``` V is COMPLEX array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPLQT in B. See Further Details.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. LDV >= K.``` [in] T ``` T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPLQT, stored as a MB-by-K matrix.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= MB.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).``` [in,out] B ``` B is COMPLEX array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [out] WORK ``` WORK is COMPLEX array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Further Details:
```  The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:

V = [V1] [V2].

The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
[B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

The complex unitary matrix Q is formed from V and T.

If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.

If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.```

Definition at line 197 of file ctpmlqt.f.

199*
200* -- LAPACK computational routine --
201* -- LAPACK is a software package provided by Univ. of Tennessee, --
202* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203*
204* .. Scalar Arguments ..
205 CHARACTER SIDE, TRANS
206 INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
207* ..
208* .. Array Arguments ..
209 COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
210 \$ T( LDT, * ), WORK( * )
211* ..
212*
213* =====================================================================
214*
215* ..
216* .. Local Scalars ..
217 LOGICAL LEFT, RIGHT, TRAN, NOTRAN
218 INTEGER I, IB, NB, LB, KF, LDAQ
219* ..
220* .. External Functions ..
221 LOGICAL LSAME
222 EXTERNAL lsame
223* ..
224* .. External Subroutines ..
225 EXTERNAL xerbla, ctprfb
226* ..
227* .. Intrinsic Functions ..
228 INTRINSIC max, min
229* ..
230* .. Executable Statements ..
231*
232* .. Test the input arguments ..
233*
234 info = 0
235 left = lsame( side, 'L' )
236 right = lsame( side, 'R' )
237 tran = lsame( trans, 'C' )
238 notran = lsame( trans, 'N' )
239*
240 IF ( left ) THEN
241 ldaq = max( 1, k )
242 ELSE IF ( right ) THEN
243 ldaq = max( 1, m )
244 END IF
245 IF( .NOT.left .AND. .NOT.right ) THEN
246 info = -1
247 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
248 info = -2
249 ELSE IF( m.LT.0 ) THEN
250 info = -3
251 ELSE IF( n.LT.0 ) THEN
252 info = -4
253 ELSE IF( k.LT.0 ) THEN
254 info = -5
255 ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
256 info = -6
257 ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
258 info = -7
259 ELSE IF( ldv.LT.k ) THEN
260 info = -9
261 ELSE IF( ldt.LT.mb ) THEN
262 info = -11
263 ELSE IF( lda.LT.ldaq ) THEN
264 info = -13
265 ELSE IF( ldb.LT.max( 1, m ) ) THEN
266 info = -15
267 END IF
268*
269 IF( info.NE.0 ) THEN
270 CALL xerbla( 'CTPMLQT', -info )
271 RETURN
272 END IF
273*
274* .. Quick return if possible ..
275*
276 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
277*
278 IF( left .AND. notran ) THEN
279*
280 DO i = 1, k, mb
281 ib = min( mb, k-i+1 )
282 nb = min( m-l+i+ib-1, m )
283 IF( i.GE.l ) THEN
284 lb = 0
285 ELSE
286 lb = 0
287 END IF
288 CALL ctprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
289 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
290 \$ a( i, 1 ), lda, b, ldb, work, ib )
291 END DO
292*
293 ELSE IF( right .AND. tran ) THEN
294*
295 DO i = 1, k, mb
296 ib = min( mb, k-i+1 )
297 nb = min( n-l+i+ib-1, n )
298 IF( i.GE.l ) THEN
299 lb = 0
300 ELSE
301 lb = nb-n+l-i+1
302 END IF
303 CALL ctprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
304 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
305 \$ a( 1, i ), lda, b, ldb, work, m )
306 END DO
307*
308 ELSE IF( left .AND. tran ) THEN
309*
310 kf = ((k-1)/mb)*mb+1
311 DO i = kf, 1, -mb
312 ib = min( mb, k-i+1 )
313 nb = min( m-l+i+ib-1, m )
314 IF( i.GE.l ) THEN
315 lb = 0
316 ELSE
317 lb = 0
318 END IF
319 CALL ctprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
320 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
321 \$ a( i, 1 ), lda, b, ldb, work, ib )
322 END DO
323*
324 ELSE IF( right .AND. notran ) THEN
325*
326 kf = ((k-1)/mb)*mb+1
327 DO i = kf, 1, -mb
328 ib = min( mb, k-i+1 )
329 nb = min( n-l+i+ib-1, n )
330 IF( i.GE.l ) THEN
331 lb = 0
332 ELSE
333 lb = nb-n+l-i+1
334 END IF
335 CALL ctprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
336 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
337 \$ a( 1, i ), lda, b, ldb, work, m )
338 END DO
339*
340 END IF
341*
342 RETURN
343*
344* End of CTPMLQT
345*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a complex "triangular-pentagonal" block reflector to a complex matrix,...
Definition: ctprfb.f:251
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