LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dtpmlqt()

subroutine dtpmlqt ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  L,
integer  MB,
double precision, dimension( ldv, * )  V,
integer  LDV,
double precision, dimension( ldt, * )  T,
integer  LDT,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
integer  INFO 
)

DTPMLQT

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

Purpose:
 DTPMQRT applies a real orthogonal matrix Q obtained from a
 "triangular-pentagonal" real block reflector H to a general
 real matrix C, which consists of two blocks A and B.
Parameters
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.
[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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  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 DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  See Further Details.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.
          LDB >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION 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
November 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='T' and SIDE='L', C is on exit replaced with Q**T * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 218 of file dtpmlqt.f.

218 *
219 * -- LAPACK computational routine (version 3.8.0) --
220 * -- LAPACK is a software package provided by Univ. of Tennessee, --
221 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
222 * November 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  DOUBLE PRECISION 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, dlarfb, dtprfb
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, 'T' )
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( 'DTPMLQT', -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 dtprfb( 'L', 'T', '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 dtprfb( '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 dtprfb( '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 dtprfb( 'R', 'T', '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 DTPMLQT
365 *
subroutine dtprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
DTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: dtprfb.f:253
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: dlarfb.f:197
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