LAPACK  3.8.0 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 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': 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 DTPLQT.``` [in] V ``` V is COMPLEX*16 array, dimension (LDA,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DTPLQT 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 DTPLQT, 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', 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*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```
Date
June 2017
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 real 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 218 of file ztpmlqt.f.

218 *
219 * -- LAPACK computational routine (version 3.7.1) --
220 * -- LAPACK is a software package provided by Univ. of Tennessee, --
221 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
222 * June 2017
223 *
224 * .. Scalar Arguments ..
225  CHARACTER side, trans
226  INTEGER info, k, ldv, lda, ldb, m, n, l, mb, ldt
227 * ..
228 * .. Array Arguments ..
229  COMPLEX*16 v( ldv, * ), a( lda, * ), b( ldb, * ),
230  \$ t( ldt, * ), work( * )
231 * ..
232 *
233 * =====================================================================
234 *
235 * ..
236 * .. Local Scalars ..
237  LOGICAL left, right, tran, notran
238  INTEGER i, ib, nb, lb, kf, ldaq
239 * ..
240 * .. External Functions ..
241  LOGICAL lsame
242  EXTERNAL lsame
243 * ..
244 * .. External Subroutines ..
245  EXTERNAL xerbla, ztprfb
246 * ..
247 * .. Intrinsic Functions ..
248  INTRINSIC max, min
249 * ..
250 * .. Executable Statements ..
251 *
252 * .. Test the input arguments ..
253 *
254  info = 0
255  left = lsame( side, 'L' )
256  right = lsame( side, 'R' )
257  tran = lsame( trans, 'C' )
258  notran = lsame( trans, 'N' )
259 *
260  IF ( left ) THEN
261  ldaq = max( 1, k )
262  ELSE IF ( right ) THEN
263  ldaq = max( 1, m )
264  END IF
265  IF( .NOT.left .AND. .NOT.right ) THEN
266  info = -1
267  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
268  info = -2
269  ELSE IF( m.LT.0 ) THEN
270  info = -3
271  ELSE IF( n.LT.0 ) THEN
272  info = -4
273  ELSE IF( k.LT.0 ) THEN
274  info = -5
275  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
276  info = -6
277  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
278  info = -7
279  ELSE IF( ldv.LT.k ) THEN
280  info = -9
281  ELSE IF( ldt.LT.mb ) THEN
282  info = -11
283  ELSE IF( lda.LT.ldaq ) THEN
284  info = -13
285  ELSE IF( ldb.LT.max( 1, m ) ) THEN
286  info = -15
287  END IF
288 *
289  IF( info.NE.0 ) THEN
290  CALL xerbla( 'ZTPMLQT', -info )
291  RETURN
292  END IF
293 *
294 * .. Quick return if possible ..
295 *
296  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
297 *
298  IF( left .AND. notran ) THEN
299 *
300  DO i = 1, k, mb
301  ib = min( mb, k-i+1 )
302  nb = min( m-l+i+ib-1, m )
303  IF( i.GE.l ) THEN
304  lb = 0
305  ELSE
306  lb = 0
307  END IF
308  CALL ztprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
309  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
310  \$ a( i, 1 ), lda, b, ldb, work, ib )
311  END DO
312 *
313  ELSE IF( right .AND. tran ) THEN
314 *
315  DO i = 1, k, mb
316  ib = min( mb, k-i+1 )
317  nb = min( n-l+i+ib-1, n )
318  IF( i.GE.l ) THEN
319  lb = 0
320  ELSE
321  lb = nb-n+l-i+1
322  END IF
323  CALL ztprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
324  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
325  \$ a( 1, i ), lda, b, ldb, work, m )
326  END DO
327 *
328  ELSE IF( left .AND. tran ) THEN
329 *
330  kf = ((k-1)/mb)*mb+1
331  DO i = kf, 1, -mb
332  ib = min( mb, k-i+1 )
333  nb = min( m-l+i+ib-1, m )
334  IF( i.GE.l ) THEN
335  lb = 0
336  ELSE
337  lb = 0
338  END IF
339  CALL ztprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
340  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
341  \$ a( i, 1 ), lda, b, ldb, work, ib )
342  END DO
343 *
344  ELSE IF( right .AND. notran ) THEN
345 *
346  kf = ((k-1)/mb)*mb+1
347  DO i = kf, 1, -mb
348  ib = min( mb, k-i+1 )
349  nb = min( n-l+i+ib-1, n )
350  IF( i.GE.l ) THEN
351  lb = 0
352  ELSE
353  lb = nb-n+l-i+1
354  END IF
355  CALL ztprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
356  \$ v( i, 1 ), ldv, t( 1, i ), ldt,
357  \$ a( 1, i ), lda, b, ldb, work, m )
358  END DO
359 *
360  END IF
361 *
362  RETURN
363 *
364 * End of ZTPMLQT
365 *
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:253
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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