LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ctpmqrt()

subroutine ctpmqrt ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  L,
integer  NB,
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 
)

CTPMQRT

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

Purpose:
 CTPMQRT 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':  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]NB
          NB is INTEGER
          The block size used for the storage of T.  K >= NB >= 1.
          This must be the same value of NB used to generate T
          in CTPQRT.
[in]V
          V is COMPLEX array, dimension (LDV,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CTPQRT 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 CTPQRT, stored as a NB-by-K matrix.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
[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*NB if SIDE = 'L', or  M*NB 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 upper trapezoidal, consisting of the first L
  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper 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 M-by-K.
                      [B]

  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

  The complex 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 214 of file ctpmqrt.f.

216 *
217 * -- LAPACK computational routine --
218 * -- LAPACK is a software package provided by Univ. of Tennessee, --
219 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
220 *
221 * .. Scalar Arguments ..
222  CHARACTER SIDE, TRANS
223  INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT
224 * ..
225 * .. Array Arguments ..
226  COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ), T( LDT, * ),
227  $ WORK( * )
228 * ..
229 *
230 * =====================================================================
231 *
232 * ..
233 * .. Local Scalars ..
234  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
235  INTEGER I, IB, MB, LB, KF, LDAQ, LDVQ
236 * ..
237 * .. External Functions ..
238  LOGICAL LSAME
239  EXTERNAL lsame
240 * ..
241 * .. External Subroutines ..
242  EXTERNAL ctprfb, xerbla
243 * ..
244 * .. Intrinsic Functions ..
245  INTRINSIC max, min
246 * ..
247 * .. Executable Statements ..
248 *
249 * .. Test the input arguments ..
250 *
251  info = 0
252  left = lsame( side, 'L' )
253  right = lsame( side, 'R' )
254  tran = lsame( trans, 'C' )
255  notran = lsame( trans, 'N' )
256 *
257  IF ( left ) THEN
258  ldvq = max( 1, m )
259  ldaq = max( 1, k )
260  ELSE IF ( right ) THEN
261  ldvq = max( 1, n )
262  ldaq = max( 1, m )
263  END IF
264  IF( .NOT.left .AND. .NOT.right ) THEN
265  info = -1
266  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
267  info = -2
268  ELSE IF( m.LT.0 ) THEN
269  info = -3
270  ELSE IF( n.LT.0 ) THEN
271  info = -4
272  ELSE IF( k.LT.0 ) THEN
273  info = -5
274  ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
275  info = -6
276  ELSE IF( nb.LT.1 .OR. (nb.GT.k .AND. k.GT.0) ) THEN
277  info = -7
278  ELSE IF( ldv.LT.ldvq ) THEN
279  info = -9
280  ELSE IF( ldt.LT.nb ) THEN
281  info = -11
282  ELSE IF( lda.LT.ldaq ) THEN
283  info = -13
284  ELSE IF( ldb.LT.max( 1, m ) ) THEN
285  info = -15
286  END IF
287 *
288  IF( info.NE.0 ) THEN
289  CALL xerbla( 'CTPMQRT', -info )
290  RETURN
291  END IF
292 *
293 * .. Quick return if possible ..
294 *
295  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
296 *
297  IF( left .AND. tran ) THEN
298 *
299  DO i = 1, k, nb
300  ib = min( nb, k-i+1 )
301  mb = min( m-l+i+ib-1, m )
302  IF( i.GE.l ) THEN
303  lb = 0
304  ELSE
305  lb = mb-m+l-i+1
306  END IF
307  CALL ctprfb( 'L', 'C', 'F', 'C', mb, n, ib, lb,
308  $ v( 1, i ), ldv, t( 1, i ), ldt,
309  $ a( i, 1 ), lda, b, ldb, work, ib )
310  END DO
311 *
312  ELSE IF( right .AND. notran ) THEN
313 *
314  DO i = 1, k, nb
315  ib = min( nb, k-i+1 )
316  mb = min( n-l+i+ib-1, n )
317  IF( i.GE.l ) THEN
318  lb = 0
319  ELSE
320  lb = mb-n+l-i+1
321  END IF
322  CALL ctprfb( 'R', 'N', 'F', 'C', m, mb, ib, lb,
323  $ v( 1, i ), ldv, t( 1, i ), ldt,
324  $ a( 1, i ), lda, b, ldb, work, m )
325  END DO
326 *
327  ELSE IF( left .AND. notran ) THEN
328 *
329  kf = ((k-1)/nb)*nb+1
330  DO i = kf, 1, -nb
331  ib = min( nb, k-i+1 )
332  mb = min( m-l+i+ib-1, m )
333  IF( i.GE.l ) THEN
334  lb = 0
335  ELSE
336  lb = mb-m+l-i+1
337  END IF
338  CALL ctprfb( 'L', 'N', 'F', 'C', mb, n, ib, lb,
339  $ v( 1, i ), ldv, t( 1, i ), ldt,
340  $ a( i, 1 ), lda, b, ldb, work, ib )
341  END DO
342 *
343  ELSE IF( right .AND. tran ) THEN
344 *
345  kf = ((k-1)/nb)*nb+1
346  DO i = kf, 1, -nb
347  ib = min( nb, k-i+1 )
348  mb = min( n-l+i+ib-1, n )
349  IF( i.GE.l ) THEN
350  lb = 0
351  ELSE
352  lb = mb-n+l-i+1
353  END IF
354  CALL ctprfb( 'R', 'C', 'F', 'C', m, mb, ib, lb,
355  $ v( 1, i ), ldv, t( 1, i ), ldt,
356  $ a( 1, i ), lda, b, ldb, work, m )
357  END DO
358 *
359  END IF
360 *
361  RETURN
362 *
363 * End of CTPMQRT
364 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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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