 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztpmlqt()

 subroutine ztpmlqt ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer MB, 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 )

ZTPMLQT

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Purpose:
``` ZTPMLQT 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 ZTPLQT.``` [in] V ``` V is COMPLEX*16 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 ZTPLQT in B. See Further Details.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. LDV >= K.``` [in] T ``` T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZTPLQT, 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*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', LDA >= max(1,K); If SIDE = 'R', LDA >= 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*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 212 of file ztpmlqt.f.

214 *
215 * -- LAPACK computational routine --
216 * -- LAPACK is a software package provided by Univ. of Tennessee, --
217 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218 *
219 * .. Scalar Arguments ..
220  CHARACTER SIDE, TRANS
221  INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
222 * ..
223 * .. Array Arguments ..
224  COMPLEX*16 V( LDV, * ), A( LDA, * ), B( LDB, * ),
225  \$ T( LDT, * ), WORK( * )
226 * ..
227 *
228 * =====================================================================
229 *
230 * ..
231 * .. Local Scalars ..
232  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
233  INTEGER I, IB, NB, LB, KF, LDAQ
234 * ..
235 * .. External Functions ..
236  LOGICAL LSAME
237  EXTERNAL lsame
238 * ..
239 * .. External Subroutines ..
240  EXTERNAL xerbla, ztprfb
241 * ..
242 * .. Intrinsic Functions ..
243  INTRINSIC max, min
244 * ..
245 * .. Executable Statements ..
246 *
247 * .. Test the input arguments ..
248 *
249  info = 0
250  left = lsame( side, 'L' )
251  right = lsame( side, 'R' )
252  tran = lsame( trans, 'C' )
253  notran = lsame( trans, 'N' )
254 *
255  IF ( left ) THEN
256  ldaq = max( 1, k )
257  ELSE IF ( right ) THEN
258  ldaq = max( 1, m )
259  END IF
260  IF( .NOT.left .AND. .NOT.right ) THEN
261  info = -1
262  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
263  info = -2
264  ELSE IF( m.LT.0 ) THEN
265  info = -3
266  ELSE IF( n.LT.0 ) THEN
267  info = -4
268  ELSE IF( k.LT.0 ) THEN
269  info = -5
270  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
271  info = -6
272  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
273  info = -7
274  ELSE IF( ldv.LT.k ) THEN
275  info = -9
276  ELSE IF( ldt.LT.mb ) THEN
277  info = -11
278  ELSE IF( lda.LT.ldaq ) THEN
279  info = -13
280  ELSE IF( ldb.LT.max( 1, m ) ) THEN
281  info = -15
282  END IF
283 *
284  IF( info.NE.0 ) THEN
285  CALL xerbla( 'ZTPMLQT', -info )
286  RETURN
287  END IF
288 *
289 * .. Quick return if possible ..
290 *
291  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
292 *
293  IF( left .AND. notran ) THEN
294 *
295  DO i = 1, k, mb
296  ib = min( mb, k-i+1 )
297  nb = min( m-l+i+ib-1, m )
298  IF( i.GE.l ) THEN
299  lb = 0
300  ELSE
301  lb = 0
302  END IF
303  CALL ztprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
304  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
305  \$ a( i, 1 ), lda, b, ldb, work, ib )
306  END DO
307 *
308  ELSE IF( right .AND. tran ) THEN
309 *
310  DO i = 1, k, mb
311  ib = min( mb, k-i+1 )
312  nb = min( n-l+i+ib-1, n )
313  IF( i.GE.l ) THEN
314  lb = 0
315  ELSE
316  lb = nb-n+l-i+1
317  END IF
318  CALL ztprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
319  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
320  \$ a( 1, i ), lda, b, ldb, work, m )
321  END DO
322 *
323  ELSE IF( left .AND. tran ) THEN
324 *
325  kf = ((k-1)/mb)*mb+1
326  DO i = kf, 1, -mb
327  ib = min( mb, k-i+1 )
328  nb = min( m-l+i+ib-1, m )
329  IF( i.GE.l ) THEN
330  lb = 0
331  ELSE
332  lb = 0
333  END IF
334  CALL ztprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
335  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
336  \$ a( i, 1 ), lda, b, ldb, work, ib )
337  END DO
338 *
339  ELSE IF( right .AND. notran ) THEN
340 *
341  kf = ((k-1)/mb)*mb+1
342  DO i = kf, 1, -mb
343  ib = min( mb, k-i+1 )
344  nb = min( n-l+i+ib-1, n )
345  IF( i.GE.l ) THEN
346  lb = 0
347  ELSE
348  lb = nb-n+l-i+1
349  END IF
350  CALL ztprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
351  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
352  \$ a( 1, i ), lda, b, ldb, work, m )
353  END DO
354 *
355  END IF
356 *
357  RETURN
358 *
359 * End of ZTPMLQT
360 *
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 real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ztprfb.f:251
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