LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
dormrz.f File Reference

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Functions/Subroutines

subroutine dormrz (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
 DORMRZ More...
 

Function/Subroutine Documentation

subroutine dormrz ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  L,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DORMRZ

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Purpose:
 DORMRZ overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'T':      Q**T * C       C * Q**T

 where Q is a real orthogonal matrix defined as the product of k
 elementary reflectors

       Q = H(1) H(2) . . . H(k)

 as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N
 if SIDE = 'R'.
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 C. M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix C. N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.
[in]L
          L is INTEGER
          The number of columns of the matrix A containing
          the meaningful part of the Householder reflectors.
          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          DTZRZF in the last k rows of its array argument A.
          A is modified by the routine but restored on exit.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DTZRZF.
[in,out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
          blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[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 2011
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
 

Definition at line 191 of file dormrz.f.

191 *
192 * -- LAPACK computational routine (version 3.4.0) --
193 * -- LAPACK is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * November 2011
196 *
197 * .. Scalar Arguments ..
198  CHARACTER side, trans
199  INTEGER info, k, l, lda, ldc, lwork, m, n
200 * ..
201 * .. Array Arguments ..
202  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. Parameters ..
208  INTEGER nbmax, ldt
209  parameter( nbmax = 64, ldt = nbmax+1 )
210 * ..
211 * .. Local Scalars ..
212  LOGICAL left, lquery, notran
213  CHARACTER transt
214  INTEGER i, i1, i2, i3, ib, ic, iinfo, iws, ja, jc,
215  $ ldwork, lwkopt, mi, nb, nbmin, ni, nq, nw
216 * ..
217 * .. Local Arrays ..
218  DOUBLE PRECISION t( ldt, nbmax )
219 * ..
220 * .. External Functions ..
221  LOGICAL lsame
222  INTEGER ilaenv
223  EXTERNAL lsame, ilaenv
224 * ..
225 * .. External Subroutines ..
226  EXTERNAL dlarzb, dlarzt, dormr3, xerbla
227 * ..
228 * .. Intrinsic Functions ..
229  INTRINSIC max, min
230 * ..
231 * .. Executable Statements ..
232 *
233 * Test the input arguments
234 *
235  info = 0
236  left = lsame( side, 'L' )
237  notran = lsame( trans, 'N' )
238  lquery = ( lwork.EQ.-1 )
239 *
240 * NQ is the order of Q and NW is the minimum dimension of WORK
241 *
242  IF( left ) THEN
243  nq = m
244  nw = max( 1, n )
245  ELSE
246  nq = n
247  nw = max( 1, m )
248  END IF
249  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
250  info = -1
251  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
252  info = -2
253  ELSE IF( m.LT.0 ) THEN
254  info = -3
255  ELSE IF( n.LT.0 ) THEN
256  info = -4
257  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
258  info = -5
259  ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
260  $ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
261  info = -6
262  ELSE IF( lda.LT.max( 1, k ) ) THEN
263  info = -8
264  ELSE IF( ldc.LT.max( 1, m ) ) THEN
265  info = -11
266  END IF
267 *
268  IF( info.EQ.0 ) THEN
269  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
270  lwkopt = 1
271  ELSE
272 *
273 * Determine the block size. NB may be at most NBMAX, where
274 * NBMAX is used to define the local array T.
275 *
276  nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
277  $ k, -1 ) )
278  lwkopt = nw*nb
279  END IF
280  work( 1 ) = lwkopt
281 *
282  IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
283  info = -13
284  END IF
285  END IF
286 *
287  IF( info.NE.0 ) THEN
288  CALL xerbla( 'DORMRZ', -info )
289  RETURN
290  ELSE IF( lquery ) THEN
291  RETURN
292  END IF
293 *
294 * Quick return if possible
295 *
296  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
297  work( 1 ) = 1
298  RETURN
299  END IF
300 *
301  nbmin = 2
302  ldwork = nw
303  IF( nb.GT.1 .AND. nb.LT.k ) THEN
304  iws = nw*nb
305  IF( lwork.LT.iws ) THEN
306  nb = lwork / ldwork
307  nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
308  $ -1 ) )
309  END IF
310  ELSE
311  iws = nw
312  END IF
313 *
314  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
315 *
316 * Use unblocked code
317 *
318  CALL dormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc,
319  $ work, iinfo )
320  ELSE
321 *
322 * Use blocked code
323 *
324  IF( ( left .AND. .NOT.notran ) .OR.
325  $ ( .NOT.left .AND. notran ) ) THEN
326  i1 = 1
327  i2 = k
328  i3 = nb
329  ELSE
330  i1 = ( ( k-1 ) / nb )*nb + 1
331  i2 = 1
332  i3 = -nb
333  END IF
334 *
335  IF( left ) THEN
336  ni = n
337  jc = 1
338  ja = m - l + 1
339  ELSE
340  mi = m
341  ic = 1
342  ja = n - l + 1
343  END IF
344 *
345  IF( notran ) THEN
346  transt = 'T'
347  ELSE
348  transt = 'N'
349  END IF
350 *
351  DO 10 i = i1, i2, i3
352  ib = min( nb, k-i+1 )
353 *
354 * Form the triangular factor of the block reflector
355 * H = H(i+ib-1) . . . H(i+1) H(i)
356 *
357  CALL dlarzt( 'Backward', 'Rowwise', l, ib, a( i, ja ), lda,
358  $ tau( i ), t, ldt )
359 *
360  IF( left ) THEN
361 *
362 * H or H**T is applied to C(i:m,1:n)
363 *
364  mi = m - i + 1
365  ic = i
366  ELSE
367 *
368 * H or H**T is applied to C(1:m,i:n)
369 *
370  ni = n - i + 1
371  jc = i
372  END IF
373 *
374 * Apply H or H**T
375 *
376  CALL dlarzb( side, transt, 'Backward', 'Rowwise', mi, ni,
377  $ ib, l, a( i, ja ), lda, t, ldt, c( ic, jc ),
378  $ ldc, work, ldwork )
379  10 CONTINUE
380 *
381  END IF
382 *
383  work( 1 ) = lwkopt
384 *
385  RETURN
386 *
387 * End of DORMRZ
388 *
subroutine dlarzt(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARZT forms the triangular factor T of a block reflector H = I - vtvH.
Definition: dlarzt.f:187
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dormr3(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stz...
Definition: dormr3.f:180
subroutine dlarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARZB applies a block reflector or its transpose to a general matrix.
Definition: dlarzb.f:185
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83

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