LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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

Download ZTPMLQT + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
ztprfb
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
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