LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dormlq()

 subroutine dormlq ( 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 )

DORMLQ

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Purpose:
DORMLQ 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 DGELQF. 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,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 DGELQF in the first k rows of its array argument A. [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 DGELQF. [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

Definition at line 165 of file dormlq.f.

167 *
168 * -- LAPACK computational routine --
169 * -- LAPACK is a software package provided by Univ. of Tennessee, --
170 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171 *
172 * .. Scalar Arguments ..
173  CHARACTER SIDE, TRANS
174  INTEGER INFO, K, LDA, LDC, LWORK, M, N
175 * ..
176 * .. Array Arguments ..
177  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  INTEGER NBMAX, LDT, TSIZE
184  parameter( nbmax = 64, ldt = nbmax+1,
185  \$ tsize = ldt*nbmax )
186 * ..
187 * .. Local Scalars ..
188  LOGICAL LEFT, LQUERY, NOTRAN
189  CHARACTER TRANST
190  INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
191  \$ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
192 * ..
193 * .. External Functions ..
194  LOGICAL LSAME
195  INTEGER ILAENV
196  EXTERNAL lsame, ilaenv
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL dlarfb, dlarft, dorml2, xerbla
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max, min
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input arguments
207 *
208  info = 0
209  left = lsame( side, 'L' )
210  notran = lsame( trans, 'N' )
211  lquery = ( lwork.EQ.-1 )
212 *
213 * NQ is the order of Q and NW is the minimum dimension of WORK
214 *
215  IF( left ) THEN
216  nq = m
217  nw = max( 1, n )
218  ELSE
219  nq = n
220  nw = max( 1, m )
221  END IF
222  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223  info = -1
224  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225  info = -2
226  ELSE IF( m.LT.0 ) THEN
227  info = -3
228  ELSE IF( n.LT.0 ) THEN
229  info = -4
230  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231  info = -5
232  ELSE IF( lda.LT.max( 1, k ) ) THEN
233  info = -7
234  ELSE IF( ldc.LT.max( 1, m ) ) THEN
235  info = -10
236  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
237  info = -12
238  END IF
239 *
240  IF( info.EQ.0 ) THEN
241 *
242 * Compute the workspace requirements
243 *
244  nb = min( nbmax, ilaenv( 1, 'DORMLQ', side // trans, m, n, k,
245  \$ -1 ) )
246  lwkopt = nw*nb + tsize
247  work( 1 ) = lwkopt
248  END IF
249 *
250  IF( info.NE.0 ) THEN
251  CALL xerbla( 'DORMLQ', -info )
252  RETURN
253  ELSE IF( lquery ) THEN
254  RETURN
255  END IF
256 *
257 * Quick return if possible
258 *
259  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
260  work( 1 ) = 1
261  RETURN
262  END IF
263 *
264  nbmin = 2
265  ldwork = nw
266  IF( nb.GT.1 .AND. nb.LT.k ) THEN
267  IF( lwork.LT.lwkopt ) THEN
268  nb = (lwork-tsize) / ldwork
269  nbmin = max( 2, ilaenv( 2, 'DORMLQ', side // trans, m, n, k,
270  \$ -1 ) )
271  END IF
272  END IF
273 *
274  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
275 *
276 * Use unblocked code
277 *
278  CALL dorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
279  \$ iinfo )
280  ELSE
281 *
282 * Use blocked code
283 *
284  iwt = 1 + nw*nb
285  IF( ( left .AND. notran ) .OR.
286  \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
287  i1 = 1
288  i2 = k
289  i3 = nb
290  ELSE
291  i1 = ( ( k-1 ) / nb )*nb + 1
292  i2 = 1
293  i3 = -nb
294  END IF
295 *
296  IF( left ) THEN
297  ni = n
298  jc = 1
299  ELSE
300  mi = m
301  ic = 1
302  END IF
303 *
304  IF( notran ) THEN
305  transt = 'T'
306  ELSE
307  transt = 'N'
308  END IF
309 *
310  DO 10 i = i1, i2, i3
311  ib = min( nb, k-i+1 )
312 *
313 * Form the triangular factor of the block reflector
314 * H = H(i) H(i+1) . . . H(i+ib-1)
315 *
316  CALL dlarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
317  \$ lda, tau( i ), work( iwt ), ldt )
318  IF( left ) THEN
319 *
320 * H or H**T is applied to C(i:m,1:n)
321 *
322  mi = m - i + 1
323  ic = i
324  ELSE
325 *
326 * H or H**T is applied to C(1:m,i:n)
327 *
328  ni = n - i + 1
329  jc = i
330  END IF
331 *
332 * Apply H or H**T
333 *
334  CALL dlarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
335  \$ a( i, i ), lda, work( iwt ), ldt,
336  \$ c( ic, jc ), ldc, work, ldwork )
337  10 CONTINUE
338  END IF
339  work( 1 ) = lwkopt
340  RETURN
341 *
342 * End of DORMLQ
343 *
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 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:163
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 dorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
Definition: dorml2.f:159
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