 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ ztpmqrt()

 subroutine ztpmqrt ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, complex*16, dimension( ldv, * ) V, integer LDV, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer INFO )

ZTPMQRT

Purpose:
``` ZTPMQRT applies a complex orthogonal 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] NB ``` NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in CTPQRT.``` [in] V ``` V is COMPLEX*16 array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPQRT in B. See Further Details.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N).``` [in] T ``` T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= NB.``` [in,out] A ``` A is COMPLEX*16 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', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M).``` [in,out] B ``` B is COMPLEX*16 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*16 array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB 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 upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper 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 M-by-K.
[B]

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

The complex orthogonal 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 214 of file ztpmqrt.f.

216*
217* -- LAPACK computational routine --
218* -- LAPACK is a software package provided by Univ. of Tennessee, --
219* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
220*
221* .. Scalar Arguments ..
222 CHARACTER SIDE, TRANS
223 INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT
224* ..
225* .. Array Arguments ..
226 COMPLEX*16 V( LDV, * ), A( LDA, * ), B( LDB, * ), T( LDT, * ),
227 \$ WORK( * )
228* ..
229*
230* =====================================================================
231*
232* ..
233* .. Local Scalars ..
234 LOGICAL LEFT, RIGHT, TRAN, NOTRAN
235 INTEGER I, IB, MB, LB, KF, LDAQ, LDVQ
236* ..
237* .. External Functions ..
238 LOGICAL LSAME
239 EXTERNAL lsame
240* ..
241* .. External Subroutines ..
242 EXTERNAL ztprfb, xerbla
243* ..
244* .. Intrinsic Functions ..
245 INTRINSIC max, min
246* ..
247* .. Executable Statements ..
248*
249* .. Test the input arguments ..
250*
251 info = 0
252 left = lsame( side, 'L' )
253 right = lsame( side, 'R' )
254 tran = lsame( trans, 'C' )
255 notran = lsame( trans, 'N' )
256*
257 IF ( left ) THEN
258 ldvq = max( 1, m )
259 ldaq = max( 1, k )
260 ELSE IF ( right ) THEN
261 ldvq = max( 1, n )
262 ldaq = max( 1, m )
263 END IF
264 IF( .NOT.left .AND. .NOT.right ) THEN
265 info = -1
266 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
267 info = -2
268 ELSE IF( m.LT.0 ) THEN
269 info = -3
270 ELSE IF( n.LT.0 ) THEN
271 info = -4
272 ELSE IF( k.LT.0 ) THEN
273 info = -5
274 ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
275 info = -6
276 ELSE IF( nb.LT.1 .OR. (nb.GT.k .AND. k.GT.0) ) THEN
277 info = -7
278 ELSE IF( ldv.LT.ldvq ) THEN
279 info = -9
280 ELSE IF( ldt.LT.nb ) THEN
281 info = -11
282 ELSE IF( lda.LT.ldaq ) THEN
283 info = -13
284 ELSE IF( ldb.LT.max( 1, m ) ) THEN
285 info = -15
286 END IF
287*
288 IF( info.NE.0 ) THEN
289 CALL xerbla( 'ZTPMQRT', -info )
290 RETURN
291 END IF
292*
293* .. Quick return if possible ..
294*
295 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
296*
297 IF( left .AND. tran ) THEN
298*
299 DO i = 1, k, nb
300 ib = min( nb, k-i+1 )
301 mb = min( m-l+i+ib-1, m )
302 IF( i.GE.l ) THEN
303 lb = 0
304 ELSE
305 lb = mb-m+l-i+1
306 END IF
307 CALL ztprfb( 'L', 'C', 'F', 'C', mb, n, ib, lb,
308 \$ v( 1, i ), ldv, t( 1, i ), ldt,
309 \$ a( i, 1 ), lda, b, ldb, work, ib )
310 END DO
311*
312 ELSE IF( right .AND. notran ) THEN
313*
314 DO i = 1, k, nb
315 ib = min( nb, k-i+1 )
316 mb = min( n-l+i+ib-1, n )
317 IF( i.GE.l ) THEN
318 lb = 0
319 ELSE
320 lb = mb-n+l-i+1
321 END IF
322 CALL ztprfb( 'R', 'N', 'F', 'C', m, mb, ib, lb,
323 \$ v( 1, i ), ldv, t( 1, i ), ldt,
324 \$ a( 1, i ), lda, b, ldb, work, m )
325 END DO
326*
327 ELSE IF( left .AND. notran ) THEN
328*
329 kf = ((k-1)/nb)*nb+1
330 DO i = kf, 1, -nb
331 ib = min( nb, k-i+1 )
332 mb = min( m-l+i+ib-1, m )
333 IF( i.GE.l ) THEN
334 lb = 0
335 ELSE
336 lb = mb-m+l-i+1
337 END IF
338 CALL ztprfb( 'L', 'N', 'F', 'C', mb, n, ib, lb,
339 \$ v( 1, i ), ldv, t( 1, i ), ldt,
340 \$ a( i, 1 ), lda, b, ldb, work, ib )
341 END DO
342*
343 ELSE IF( right .AND. tran ) THEN
344*
345 kf = ((k-1)/nb)*nb+1
346 DO i = kf, 1, -nb
347 ib = min( nb, k-i+1 )
348 mb = min( n-l+i+ib-1, n )
349 IF( i.GE.l ) THEN
350 lb = 0
351 ELSE
352 lb = mb-n+l-i+1
353 END IF
354 CALL ztprfb( 'R', 'C', 'F', 'C', m, mb, ib, lb,
355 \$ v( 1, i ), ldv, t( 1, i ), ldt,
356 \$ a( 1, i ), lda, b, ldb, work, m )
357 END DO
358*
359 END IF
360*
361 RETURN
362*
363* End of ZTPMQRT
364*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
ZTPRFB applies a complex "triangular-pentagonal" block reflector to a complex matrix,...
Definition: ztprfb.f:251
Here is the call graph for this function:
Here is the caller graph for this function: