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

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Functions/Subroutines

subroutine dormql (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
 DORMQL More...
 

Function/Subroutine Documentation

subroutine dormql ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
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 
)

DORMQL

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Purpose:
 DORMQL 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(k) . . . H(2) H(1)

 as returned by DGEQLF. 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]A
          A is DOUBLE PRECISION array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          DGEQLF in the last k columns of its array argument A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).
[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 DGEQLF.
[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**T*C or C*Q**T 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

Definition at line 171 of file dormql.f.

171 *
172 * -- LAPACK computational routine (version 3.4.0) --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 * November 2011
176 *
177 * .. Scalar Arguments ..
178  CHARACTER side, trans
179  INTEGER info, k, lda, ldc, lwork, m, n
180 * ..
181 * .. Array Arguments ..
182  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  INTEGER nbmax, ldt
189  parameter( nbmax = 64, ldt = nbmax+1 )
190 * ..
191 * .. Local Scalars ..
192  LOGICAL left, lquery, notran
193  INTEGER i, i1, i2, i3, ib, iinfo, iws, ldwork, lwkopt,
194  $ mi, nb, nbmin, ni, nq, nw
195 * ..
196 * .. Local Arrays ..
197  DOUBLE PRECISION t( ldt, nbmax )
198 * ..
199 * .. External Functions ..
200  LOGICAL lsame
201  INTEGER ilaenv
202  EXTERNAL lsame, ilaenv
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL dlarfb, dlarft, dorm2l, xerbla
206 * ..
207 * .. Intrinsic Functions ..
208  INTRINSIC max, min
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input arguments
213 *
214  info = 0
215  left = lsame( side, 'L' )
216  notran = lsame( trans, 'N' )
217  lquery = ( lwork.EQ.-1 )
218 *
219 * NQ is the order of Q and NW is the minimum dimension of WORK
220 *
221  IF( left ) THEN
222  nq = m
223  nw = max( 1, n )
224  ELSE
225  nq = n
226  nw = max( 1, m )
227  END IF
228  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
229  info = -1
230  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
231  info = -2
232  ELSE IF( m.LT.0 ) THEN
233  info = -3
234  ELSE IF( n.LT.0 ) THEN
235  info = -4
236  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
237  info = -5
238  ELSE IF( lda.LT.max( 1, nq ) ) THEN
239  info = -7
240  ELSE IF( ldc.LT.max( 1, m ) ) THEN
241  info = -10
242  END IF
243 *
244  IF( info.EQ.0 ) THEN
245  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
246  lwkopt = 1
247  ELSE
248 *
249 * Determine the block size. NB may be at most NBMAX, where
250 * NBMAX is used to define the local array T.
251 *
252  nb = min( nbmax, ilaenv( 1, 'DORMQL', side // trans, m, n,
253  $ k, -1 ) )
254  lwkopt = nw*nb
255  END IF
256  work( 1 ) = lwkopt
257 *
258  IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
259  info = -12
260  END IF
261  END IF
262 *
263  IF( info.NE.0 ) THEN
264  CALL xerbla( 'DORMQL', -info )
265  RETURN
266  ELSE IF( lquery ) THEN
267  RETURN
268  END IF
269 *
270 * Quick return if possible
271 *
272  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
273  RETURN
274  END IF
275 *
276  nbmin = 2
277  ldwork = nw
278  IF( nb.GT.1 .AND. nb.LT.k ) THEN
279  iws = nw*nb
280  IF( lwork.LT.iws ) THEN
281  nb = lwork / ldwork
282  nbmin = max( 2, ilaenv( 2, 'DORMQL', side // trans, m, n, k,
283  $ -1 ) )
284  END IF
285  ELSE
286  iws = nw
287  END IF
288 *
289  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
290 *
291 * Use unblocked code
292 *
293  CALL dorm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
294  $ iinfo )
295  ELSE
296 *
297 * Use blocked code
298 *
299  IF( ( left .AND. notran ) .OR.
300  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
301  i1 = 1
302  i2 = k
303  i3 = nb
304  ELSE
305  i1 = ( ( k-1 ) / nb )*nb + 1
306  i2 = 1
307  i3 = -nb
308  END IF
309 *
310  IF( left ) THEN
311  ni = n
312  ELSE
313  mi = m
314  END IF
315 *
316  DO 10 i = i1, i2, i3
317  ib = min( nb, k-i+1 )
318 *
319 * Form the triangular factor of the block reflector
320 * H = H(i+ib-1) . . . H(i+1) H(i)
321 *
322  CALL dlarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
323  $ a( 1, i ), lda, tau( i ), t, ldt )
324  IF( left ) THEN
325 *
326 * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
327 *
328  mi = m - k + i + ib - 1
329  ELSE
330 *
331 * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
332 *
333  ni = n - k + i + ib - 1
334  END IF
335 *
336 * Apply H or H**T
337 *
338  CALL dlarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
339  $ ib, a( 1, i ), lda, t, ldt, c, ldc, work,
340  $ ldwork )
341  10 CONTINUE
342  END IF
343  work( 1 ) = lwkopt
344  RETURN
345 *
346 * End of DORMQL
347 *
subroutine dlarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: dlarft.f:165
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dorm2l(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sge...
Definition: dorm2l.f:161
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83

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