LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dormrz()

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

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

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 good performance, LWORK should generally be larger.

          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
December 2016
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
 

Definition at line 189 of file dormrz.f.

189 *
190 * -- LAPACK computational routine (version 3.7.0) --
191 * -- LAPACK is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 * December 2016
194 *
195 * .. Scalar Arguments ..
196  CHARACTER side, trans
197  INTEGER info, k, l, lda, ldc, lwork, m, n
198 * ..
199 * .. Array Arguments ..
200  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
201 * ..
202 *
203 * =====================================================================
204 *
205 * .. Parameters ..
206  INTEGER nbmax, ldt, tsize
207  parameter( nbmax = 64, ldt = nbmax+1,
208  $ tsize = ldt*nbmax )
209 * ..
210 * .. Local Scalars ..
211  LOGICAL left, lquery, notran
212  CHARACTER transt
213  INTEGER i, i1, i2, i3, ib, ic, iinfo, iwt, ja, jc,
214  $ ldwork, lwkopt, mi, nb, nbmin, ni, nq, nw
215 * ..
216 * .. External Functions ..
217  LOGICAL lsame
218  INTEGER ilaenv
219  EXTERNAL lsame, ilaenv
220 * ..
221 * .. External Subroutines ..
222  EXTERNAL dlarzb, dlarzt, dormr3, xerbla
223 * ..
224 * .. Intrinsic Functions ..
225  INTRINSIC max, min
226 * ..
227 * .. Executable Statements ..
228 *
229 * Test the input arguments
230 *
231  info = 0
232  left = lsame( side, 'L' )
233  notran = lsame( trans, 'N' )
234  lquery = ( lwork.EQ.-1 )
235 *
236 * NQ is the order of Q and NW is the minimum dimension of WORK
237 *
238  IF( left ) THEN
239  nq = m
240  nw = max( 1, n )
241  ELSE
242  nq = n
243  nw = max( 1, m )
244  END IF
245  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
246  info = -1
247  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
248  info = -2
249  ELSE IF( m.LT.0 ) THEN
250  info = -3
251  ELSE IF( n.LT.0 ) THEN
252  info = -4
253  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
254  info = -5
255  ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
256  $ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
257  info = -6
258  ELSE IF( lda.LT.max( 1, k ) ) THEN
259  info = -8
260  ELSE IF( ldc.LT.max( 1, m ) ) THEN
261  info = -11
262  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
263  info = -13
264  END IF
265 *
266  IF( info.EQ.0 ) THEN
267 *
268 * Compute the workspace requirements
269 *
270  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
271  lwkopt = 1
272  ELSE
273  nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
274  $ k, -1 ) )
275  lwkopt = nw*nb + tsize
276  END IF
277  work( 1 ) = lwkopt
278  END IF
279 *
280  IF( info.NE.0 ) THEN
281  CALL xerbla( 'DORMRZ', -info )
282  RETURN
283  ELSE IF( lquery ) THEN
284  RETURN
285  END IF
286 *
287 * Quick return if possible
288 *
289  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
290  work( 1 ) = 1
291  RETURN
292  END IF
293 *
294  nbmin = 2
295  ldwork = nw
296  IF( nb.GT.1 .AND. nb.LT.k ) THEN
297  IF( lwork.LT.nw*nb+tsize ) THEN
298  nb = (lwork-tsize) / ldwork
299  nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
300  $ -1 ) )
301  END IF
302  END IF
303 *
304  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
305 *
306 * Use unblocked code
307 *
308  CALL dormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc,
309  $ work, iinfo )
310  ELSE
311 *
312 * Use blocked code
313 *
314  iwt = 1 + nw*nb
315  IF( ( left .AND. .NOT.notran ) .OR.
316  $ ( .NOT.left .AND. notran ) ) THEN
317  i1 = 1
318  i2 = k
319  i3 = nb
320  ELSE
321  i1 = ( ( k-1 ) / nb )*nb + 1
322  i2 = 1
323  i3 = -nb
324  END IF
325 *
326  IF( left ) THEN
327  ni = n
328  jc = 1
329  ja = m - l + 1
330  ELSE
331  mi = m
332  ic = 1
333  ja = n - l + 1
334  END IF
335 *
336  IF( notran ) THEN
337  transt = 'T'
338  ELSE
339  transt = 'N'
340  END IF
341 *
342  DO 10 i = i1, i2, i3
343  ib = min( nb, k-i+1 )
344 *
345 * Form the triangular factor of the block reflector
346 * H = H(i+ib-1) . . . H(i+1) H(i)
347 *
348  CALL dlarzt( 'Backward', 'Rowwise', l, ib, a( i, ja ), lda,
349  $ tau( i ), work( iwt ), ldt )
350 *
351  IF( left ) THEN
352 *
353 * H or H**T is applied to C(i:m,1:n)
354 *
355  mi = m - i + 1
356  ic = i
357  ELSE
358 *
359 * H or H**T is applied to C(1:m,i:n)
360 *
361  ni = n - i + 1
362  jc = i
363  END IF
364 *
365 * Apply H or H**T
366 *
367  CALL dlarzb( side, transt, 'Backward', 'Rowwise', mi, ni,
368  $ ib, l, a( i, ja ), lda, work( iwt ), ldt,
369  $ c( ic, jc ), ldc, work, ldwork )
370  10 CONTINUE
371 *
372  END IF
373 *
374  work( 1 ) = lwkopt
375 *
376  RETURN
377 *
378 * End of DORMRZ
379 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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 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
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