LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
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 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
November 2015

Definition at line 169 of file dormql.f.

169 *
170 * -- LAPACK computational routine (version 3.6.0) --
171 * -- LAPACK is a software package provided by Univ. of Tennessee, --
172 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173 * November 2015
174 *
175 * .. Scalar Arguments ..
176  CHARACTER side, trans
177  INTEGER info, k, lda, ldc, lwork, m, n
178 * ..
179 * .. Array Arguments ..
180  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
181 * ..
182 *
183 * =====================================================================
184 *
185 * .. Parameters ..
186  INTEGER nbmax, ldt, tsize
187  parameter ( nbmax = 64, ldt = nbmax+1,
188  $ tsize = ldt*nbmax )
189 * ..
190 * .. Local Scalars ..
191  LOGICAL left, lquery, notran
192  INTEGER i, i1, i2, i3, ib, iinfo, iwt, ldwork, lwkopt,
193  $ mi, nb, nbmin, ni, nq, nw
194 * ..
195 * .. External Functions ..
196  LOGICAL lsame
197  INTEGER ilaenv
198  EXTERNAL lsame, ilaenv
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL dlarfb, dlarft, dorm2l, xerbla
202 * ..
203 * .. Intrinsic Functions ..
204  INTRINSIC max, min
205 * ..
206 * .. Executable Statements ..
207 *
208 * Test the input arguments
209 *
210  info = 0
211  left = lsame( side, 'L' )
212  notran = lsame( trans, 'N' )
213  lquery = ( lwork.EQ.-1 )
214 *
215 * NQ is the order of Q and NW is the minimum dimension of WORK
216 *
217  IF( left ) THEN
218  nq = m
219  nw = max( 1, n )
220  ELSE
221  nq = n
222  nw = max( 1, m )
223  END IF
224  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
225  info = -1
226  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
227  info = -2
228  ELSE IF( m.LT.0 ) THEN
229  info = -3
230  ELSE IF( n.LT.0 ) THEN
231  info = -4
232  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
233  info = -5
234  ELSE IF( lda.LT.max( 1, nq ) ) THEN
235  info = -7
236  ELSE IF( ldc.LT.max( 1, m ) ) THEN
237  info = -10
238  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
239  info = -12
240  END IF
241 *
242  IF( info.EQ.0 ) THEN
243 *
244 * Compute the workspace requirements
245 *
246  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
247  lwkopt = 1
248  ELSE
249  nb = min( nbmax, ilaenv( 1, 'DORMQL', side // trans, m, n,
250  $ k, -1 ) )
251  lwkopt = nw*nb + tsize
252  END IF
253  work( 1 ) = lwkopt
254  END IF
255 *
256  IF( info.NE.0 ) THEN
257  CALL xerbla( 'DORMQL', -info )
258  RETURN
259  ELSE IF( lquery ) THEN
260  RETURN
261  END IF
262 *
263 * Quick return if possible
264 *
265  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
266  RETURN
267  END IF
268 *
269  nbmin = 2
270  ldwork = nw
271  IF( nb.GT.1 .AND. nb.LT.k ) THEN
272  IF( lwork.LT.nw*nb+tsize ) THEN
273  nb = (lwork-tsize) / ldwork
274  nbmin = max( 2, ilaenv( 2, 'DORMQL', side // trans, m, n, k,
275  $ -1 ) )
276  END IF
277  END IF
278 *
279  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
280 *
281 * Use unblocked code
282 *
283  CALL dorm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
284  $ iinfo )
285  ELSE
286 *
287 * Use blocked code
288 *
289  iwt = 1 + nw*nb
290  IF( ( left .AND. notran ) .OR.
291  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
292  i1 = 1
293  i2 = k
294  i3 = nb
295  ELSE
296  i1 = ( ( k-1 ) / nb )*nb + 1
297  i2 = 1
298  i3 = -nb
299  END IF
300 *
301  IF( left ) THEN
302  ni = n
303  ELSE
304  mi = m
305  END IF
306 *
307  DO 10 i = i1, i2, i3
308  ib = min( nb, k-i+1 )
309 *
310 * Form the triangular factor of the block reflector
311 * H = H(i+ib-1) . . . H(i+1) H(i)
312 *
313  CALL dlarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
314  $ a( 1, i ), lda, tau( i ), work( iwt ), ldt )
315  IF( left ) THEN
316 *
317 * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
318 *
319  mi = m - k + i + ib - 1
320  ELSE
321 *
322 * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
323 *
324  ni = n - k + i + ib - 1
325  END IF
326 *
327 * Apply H or H**T
328 *
329  CALL dlarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
330  $ ib, a( 1, i ), lda, work( iwt ), ldt, c, ldc,
331  $ work, ldwork )
332  10 CONTINUE
333  END IF
334  work( 1 ) = lwkopt
335  RETURN
336 *
337 * End of DORMQL
338 *
dlarfb
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
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
dlarft
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
ilaenv
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
dorm2l
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
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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