LAPACK  3.10.1
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.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
 

Definition at line 185 of file dormrz.f.

187 *
188 * -- LAPACK computational routine --
189 * -- LAPACK is a software package provided by Univ. of Tennessee, --
190 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191 *
192 * .. Scalar Arguments ..
193  CHARACTER SIDE, TRANS
194  INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
195 * ..
196 * .. Array Arguments ..
197  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
198 * ..
199 *
200 * =====================================================================
201 *
202 * .. Parameters ..
203  INTEGER NBMAX, LDT, TSIZE
204  parameter( nbmax = 64, ldt = nbmax+1,
205  $ tsize = ldt*nbmax )
206 * ..
207 * .. Local Scalars ..
208  LOGICAL LEFT, LQUERY, NOTRAN
209  CHARACTER TRANST
210  INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JA, JC,
211  $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
212 * ..
213 * .. External Functions ..
214  LOGICAL LSAME
215  INTEGER ILAENV
216  EXTERNAL lsame, ilaenv
217 * ..
218 * .. External Subroutines ..
219  EXTERNAL dlarzb, dlarzt, dormr3, xerbla
220 * ..
221 * .. Intrinsic Functions ..
222  INTRINSIC max, min
223 * ..
224 * .. Executable Statements ..
225 *
226 * Test the input arguments
227 *
228  info = 0
229  left = lsame( side, 'L' )
230  notran = lsame( trans, 'N' )
231  lquery = ( lwork.EQ.-1 )
232 *
233 * NQ is the order of Q and NW is the minimum dimension of WORK
234 *
235  IF( left ) THEN
236  nq = m
237  nw = max( 1, n )
238  ELSE
239  nq = n
240  nw = max( 1, m )
241  END IF
242  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
243  info = -1
244  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
245  info = -2
246  ELSE IF( m.LT.0 ) THEN
247  info = -3
248  ELSE IF( n.LT.0 ) THEN
249  info = -4
250  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
251  info = -5
252  ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
253  $ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
254  info = -6
255  ELSE IF( lda.LT.max( 1, k ) ) THEN
256  info = -8
257  ELSE IF( ldc.LT.max( 1, m ) ) THEN
258  info = -11
259  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
260  info = -13
261  END IF
262 *
263  IF( info.EQ.0 ) THEN
264 *
265 * Compute the workspace requirements
266 *
267  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
268  lwkopt = 1
269  ELSE
270  nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
271  $ k, -1 ) )
272  lwkopt = nw*nb + tsize
273  END IF
274  work( 1 ) = lwkopt
275  END IF
276 *
277  IF( info.NE.0 ) THEN
278  CALL xerbla( 'DORMRZ', -info )
279  RETURN
280  ELSE IF( lquery ) THEN
281  RETURN
282  END IF
283 *
284 * Quick return if possible
285 *
286  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
287  work( 1 ) = 1
288  RETURN
289  END IF
290 *
291  nbmin = 2
292  ldwork = nw
293  IF( nb.GT.1 .AND. nb.LT.k ) THEN
294  IF( lwork.LT.lwkopt ) THEN
295  nb = (lwork-tsize) / ldwork
296  nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
297  $ -1 ) )
298  END IF
299  END IF
300 *
301  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
302 *
303 * Use unblocked code
304 *
305  CALL dormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc,
306  $ work, iinfo )
307  ELSE
308 *
309 * Use blocked code
310 *
311  iwt = 1 + nw*nb
312  IF( ( left .AND. .NOT.notran ) .OR.
313  $ ( .NOT.left .AND. notran ) ) THEN
314  i1 = 1
315  i2 = k
316  i3 = nb
317  ELSE
318  i1 = ( ( k-1 ) / nb )*nb + 1
319  i2 = 1
320  i3 = -nb
321  END IF
322 *
323  IF( left ) THEN
324  ni = n
325  jc = 1
326  ja = m - l + 1
327  ELSE
328  mi = m
329  ic = 1
330  ja = n - l + 1
331  END IF
332 *
333  IF( notran ) THEN
334  transt = 'T'
335  ELSE
336  transt = 'N'
337  END IF
338 *
339  DO 10 i = i1, i2, i3
340  ib = min( nb, k-i+1 )
341 *
342 * Form the triangular factor of the block reflector
343 * H = H(i+ib-1) . . . H(i+1) H(i)
344 *
345  CALL dlarzt( 'Backward', 'Rowwise', l, ib, a( i, ja ), lda,
346  $ tau( i ), work( iwt ), ldt )
347 *
348  IF( left ) THEN
349 *
350 * H or H**T is applied to C(i:m,1:n)
351 *
352  mi = m - i + 1
353  ic = i
354  ELSE
355 *
356 * H or H**T is applied to C(1:m,i:n)
357 *
358  ni = n - i + 1
359  jc = i
360  END IF
361 *
362 * Apply H or H**T
363 *
364  CALL dlarzb( side, transt, 'Backward', 'Rowwise', mi, ni,
365  $ ib, l, a( i, ja ), lda, work( iwt ), ldt,
366  $ c( ic, jc ), ldc, work, ldwork )
367  10 CONTINUE
368 *
369  END IF
370 *
371  work( 1 ) = lwkopt
372 *
373  RETURN
374 *
375 * End of DORMRZ
376 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:185
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:178
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:183
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