LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sormlq()

 subroutine sormlq ( character SIDE, character TRANS, integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO )

SORMLQ

Purpose:
``` SORMLQ 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 SGELQF. 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 REAL 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 SGELQF 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 REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF.``` [in,out] C ``` C is REAL 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 REAL 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 166 of file sormlq.f.

168 *
169 * -- LAPACK computational routine --
170 * -- LAPACK is a software package provided by Univ. of Tennessee, --
171 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172 *
173 * .. Scalar Arguments ..
174  CHARACTER SIDE, TRANS
175  INTEGER INFO, K, LDA, LDC, LWORK, M, N
176 * ..
177 * .. Array Arguments ..
178  REAL A( LDA, * ), C( LDC, * ), TAU( * ),
179  \$ WORK( * )
180 * ..
181 *
182 * =====================================================================
183 *
184 * .. Parameters ..
185  INTEGER NBMAX, LDT, TSIZE
186  parameter( nbmax = 64, ldt = nbmax+1,
187  \$ tsize = ldt*nbmax )
188 * ..
189 * .. Local Scalars ..
190  LOGICAL LEFT, LQUERY, NOTRAN
191  CHARACTER TRANST
192  INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
193  \$ LWKOPT, 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 slarfb, slarft, sorml2, 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, k ) ) 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  nb = min( nbmax, ilaenv( 1, 'SORMLQ', side // trans, m, n, k,
247  \$ -1 ) )
248  lwkopt = nw*nb + tsize
249  work( 1 ) = lwkopt
250  END IF
251 *
252  IF( info.NE.0 ) THEN
253  CALL xerbla( 'SORMLQ', -info )
254  RETURN
255  ELSE IF( lquery ) THEN
256  RETURN
257  END IF
258 *
259 * Quick return if possible
260 *
261  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
262  work( 1 ) = 1
263  RETURN
264  END IF
265 *
266  nbmin = 2
267  ldwork = nw
268  IF( nb.GT.1 .AND. nb.LT.k ) THEN
269  IF( lwork.LT.lwkopt ) THEN
270  nb = (lwork-tsize) / ldwork
271  nbmin = max( 2, ilaenv( 2, 'SORMLQ', side // trans, m, n, k,
272  \$ -1 ) )
273  END IF
274  END IF
275 *
276  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
277 *
278 * Use unblocked code
279 *
280  CALL sorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
281  \$ iinfo )
282  ELSE
283 *
284 * Use blocked code
285 *
286  iwt = 1 + nw*nb
287  IF( ( left .AND. notran ) .OR.
288  \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
289  i1 = 1
290  i2 = k
291  i3 = nb
292  ELSE
293  i1 = ( ( k-1 ) / nb )*nb + 1
294  i2 = 1
295  i3 = -nb
296  END IF
297 *
298  IF( left ) THEN
299  ni = n
300  jc = 1
301  ELSE
302  mi = m
303  ic = 1
304  END IF
305 *
306  IF( notran ) THEN
307  transt = 'T'
308  ELSE
309  transt = 'N'
310  END IF
311 *
312  DO 10 i = i1, i2, i3
313  ib = min( nb, k-i+1 )
314 *
315 * Form the triangular factor of the block reflector
316 * H = H(i) H(i+1) . . . H(i+ib-1)
317 *
318  CALL slarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
319  \$ lda, tau( i ), work( iwt ), ldt )
320  IF( left ) THEN
321 *
322 * H or H**T is applied to C(i:m,1:n)
323 *
324  mi = m - i + 1
325  ic = i
326  ELSE
327 *
328 * H or H**T is applied to C(1:m,i:n)
329 *
330  ni = n - i + 1
331  jc = i
332  END IF
333 *
334 * Apply H or H**T
335 *
336  CALL slarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
337  \$ a( i, i ), lda, work( iwt ), ldt,
338  \$ c( ic, jc ), ldc, work, ldwork )
339  10 CONTINUE
340  END IF
341  work( 1 ) = lwkopt
342  RETURN
343 *
344 * End of SORMLQ
345 *
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 slarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: slarfb.f:197
subroutine slarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: slarft.f:163
subroutine sorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
Definition: sorml2.f:159
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