LAPACK  3.9.1
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 
)

CTPMLQT

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 (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
          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.
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 199 of file ctpmlqt.f.

201 *
202 * -- LAPACK computational routine --
203 * -- LAPACK is a software package provided by Univ. of Tennessee, --
204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205 *
206 * .. Scalar Arguments ..
207  CHARACTER SIDE, TRANS
208  INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
209 * ..
210 * .. Array Arguments ..
211  COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
212  $ T( LDT, * ), WORK( * )
213 * ..
214 *
215 * =====================================================================
216 *
217 * ..
218 * .. Local Scalars ..
219  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
220  INTEGER I, IB, NB, LB, KF, LDAQ
221 * ..
222 * .. External Functions ..
223  LOGICAL LSAME
224  EXTERNAL lsame
225 * ..
226 * .. External Subroutines ..
227  EXTERNAL xerbla, ctprfb
228 * ..
229 * .. Intrinsic Functions ..
230  INTRINSIC max, min
231 * ..
232 * .. Executable Statements ..
233 *
234 * .. Test the input arguments ..
235 *
236  info = 0
237  left = lsame( side, 'L' )
238  right = lsame( side, 'R' )
239  tran = lsame( trans, 'C' )
240  notran = lsame( trans, 'N' )
241 *
242  IF ( left ) THEN
243  ldaq = max( 1, k )
244  ELSE IF ( right ) THEN
245  ldaq = max( 1, m )
246  END IF
247  IF( .NOT.left .AND. .NOT.right ) THEN
248  info = -1
249  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
250  info = -2
251  ELSE IF( m.LT.0 ) THEN
252  info = -3
253  ELSE IF( n.LT.0 ) THEN
254  info = -4
255  ELSE IF( k.LT.0 ) THEN
256  info = -5
257  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
258  info = -6
259  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
260  info = -7
261  ELSE IF( ldv.LT.k ) THEN
262  info = -9
263  ELSE IF( ldt.LT.mb ) THEN
264  info = -11
265  ELSE IF( lda.LT.ldaq ) THEN
266  info = -13
267  ELSE IF( ldb.LT.max( 1, m ) ) THEN
268  info = -15
269  END IF
270 *
271  IF( info.NE.0 ) THEN
272  CALL xerbla( 'CTPMLQT', -info )
273  RETURN
274  END IF
275 *
276 * .. Quick return if possible ..
277 *
278  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
279 *
280  IF( left .AND. notran ) THEN
281 *
282  DO i = 1, k, mb
283  ib = min( mb, k-i+1 )
284  nb = min( m-l+i+ib-1, m )
285  IF( i.GE.l ) THEN
286  lb = 0
287  ELSE
288  lb = 0
289  END IF
290  CALL ctprfb( 'L', 'C', 'F', 'R', nb, n, ib, lb,
291  $ v( i, 1 ), ldv, t( 1, i ), ldt,
292  $ a( i, 1 ), lda, b, ldb, work, ib )
293  END DO
294 *
295  ELSE IF( right .AND. tran ) THEN
296 *
297  DO i = 1, k, mb
298  ib = min( mb, k-i+1 )
299  nb = min( n-l+i+ib-1, n )
300  IF( i.GE.l ) THEN
301  lb = 0
302  ELSE
303  lb = nb-n+l-i+1
304  END IF
305  CALL ctprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
306  $ v( i, 1 ), ldv, t( 1, i ), ldt,
307  $ a( 1, i ), lda, b, ldb, work, m )
308  END DO
309 *
310  ELSE IF( left .AND. tran ) THEN
311 *
312  kf = ((k-1)/mb)*mb+1
313  DO i = kf, 1, -mb
314  ib = min( mb, k-i+1 )
315  nb = min( m-l+i+ib-1, m )
316  IF( i.GE.l ) THEN
317  lb = 0
318  ELSE
319  lb = 0
320  END IF
321  CALL ctprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
322  $ v( i, 1 ), ldv, t( 1, i ), ldt,
323  $ a( i, 1 ), lda, b, ldb, work, ib )
324  END DO
325 *
326  ELSE IF( right .AND. notran ) THEN
327 *
328  kf = ((k-1)/mb)*mb+1
329  DO i = kf, 1, -mb
330  ib = min( mb, k-i+1 )
331  nb = min( n-l+i+ib-1, n )
332  IF( i.GE.l ) THEN
333  lb = 0
334  ELSE
335  lb = nb-n+l-i+1
336  END IF
337  CALL ctprfb( 'R', 'C', 'F', 'R', m, nb, ib, lb,
338  $ v( i, 1 ), ldv, t( 1, i ), ldt,
339  $ a( 1, i ), lda, b, ldb, work, m )
340  END DO
341 *
342  END IF
343 *
344  RETURN
345 *
346 * End of CTPMLQT
347 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
ctprfb
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:251
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