LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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 
)
Purpose:

CTPMLQT 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 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 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 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 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 201 of file ctpmlqt.f.

201 *
202 * -- LAPACK computational routine (version 3.7.1) --
203 * -- LAPACK is a software package provided by Univ. of Tennessee, --
204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205 * June 2017
206 *
207 * .. Scalar Arguments ..
208  CHARACTER side, trans
209  INTEGER info, k, ldv, lda, ldb, m, n, l, mb, ldt
210 * ..
211 * .. Array Arguments ..
212  COMPLEX v( ldv, * ), a( lda, * ), b( ldb, * ),
213  $ t( ldt, * ), work( * )
214 * ..
215 *
216 * =====================================================================
217 *
218 * ..
219 * .. Local Scalars ..
220  LOGICAL left, right, tran, notran
221  INTEGER i, ib, nb, lb, kf, ldaq
222 * ..
223 * .. External Functions ..
224  LOGICAL lsame
225  EXTERNAL lsame
226 * ..
227 * .. External Subroutines ..
228  EXTERNAL xerbla, ctprfb
229 * ..
230 * .. Intrinsic Functions ..
231  INTRINSIC max, min
232 * ..
233 * .. Executable Statements ..
234 *
235 * .. Test the input arguments ..
236 *
237  info = 0
238  left = lsame( side, 'L' )
239  right = lsame( side, 'R' )
240  tran = lsame( trans, 'C' )
241  notran = lsame( trans, 'N' )
242 *
243  IF ( left ) THEN
244  ldaq = max( 1, k )
245  ELSE IF ( right ) THEN
246  ldaq = max( 1, m )
247  END IF
248  IF( .NOT.left .AND. .NOT.right ) THEN
249  info = -1
250  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
251  info = -2
252  ELSE IF( m.LT.0 ) THEN
253  info = -3
254  ELSE IF( n.LT.0 ) THEN
255  info = -4
256  ELSE IF( k.LT.0 ) THEN
257  info = -5
258  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
259  info = -6
260  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
261  info = -7
262  ELSE IF( ldv.LT.k ) THEN
263  info = -9
264  ELSE IF( ldt.LT.mb ) THEN
265  info = -11
266  ELSE IF( lda.LT.ldaq ) THEN
267  info = -13
268  ELSE IF( ldb.LT.max( 1, m ) ) THEN
269  info = -15
270  END IF
271 *
272  IF( info.NE.0 ) THEN
273  CALL xerbla( 'CTPMLQT', -info )
274  RETURN
275  END IF
276 *
277 * .. Quick return if possible ..
278 *
279  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
280 *
281  IF( left .AND. notran ) THEN
282 *
283  DO i = 1, k, mb
284  ib = min( mb, k-i+1 )
285  nb = min( m-l+i+ib-1, m )
286  IF( i.GE.l ) THEN
287  lb = 0
288  ELSE
289  lb = 0
290  END IF
291  CALL ctprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
292  $ v( i, 1 ), ldv, t( 1, i ), ldt,
293  $ a( i, 1 ), lda, b, ldb, work, ib )
294  END DO
295 *
296  ELSE IF( right .AND. tran ) THEN
297 *
298  DO i = 1, k, mb
299  ib = min( mb, k-i+1 )
300  nb = min( n-l+i+ib-1, n )
301  IF( i.GE.l ) THEN
302  lb = 0
303  ELSE
304  lb = nb-n+l-i+1
305  END IF
306  CALL ctprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
307  $ v( i, 1 ), ldv, t( 1, i ), ldt,
308  $ a( 1, i ), lda, b, ldb, work, m )
309  END DO
310 *
311  ELSE IF( left .AND. tran ) THEN
312 *
313  kf = ((k-1)/mb)*mb+1
314  DO i = kf, 1, -mb
315  ib = min( mb, k-i+1 )
316  nb = min( m-l+i+ib-1, m )
317  IF( i.GE.l ) THEN
318  lb = 0
319  ELSE
320  lb = 0
321  END IF
322  CALL ctprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
323  $ v( i, 1 ), ldv, t( 1, i ), ldt,
324  $ a( i, 1 ), lda, b, ldb, work, ib )
325  END DO
326 *
327  ELSE IF( right .AND. notran ) THEN
328 *
329  kf = ((k-1)/mb)*mb+1
330  DO i = kf, 1, -mb
331  ib = min( mb, k-i+1 )
332  nb = min( n-l+i+ib-1, n )
333  IF( i.GE.l ) THEN
334  lb = 0
335  ELSE
336  lb = nb-n+l-i+1
337  END IF
338  CALL ctprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
339  $ v( i, 1 ), ldv, t( 1, i ), ldt,
340  $ a( 1, i ), lda, b, ldb, work, m )
341  END DO
342 *
343  END IF
344 *
345  RETURN
346 *
347 * End of CTPMLQT
348 *
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ctprfb.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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