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

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sormrq ( 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 
)

SORMRQ

Download SORMRQ + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SORMRQ 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 SGERQF. 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
          SGERQF in the last 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 SGERQF.
[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 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 172 of file sormrq.f.

172 *
173 * -- LAPACK computational routine (version 3.4.0) --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 * November 2011
177 *
178 * .. Scalar Arguments ..
179  CHARACTER side, trans
180  INTEGER info, k, lda, ldc, lwork, m, n
181 * ..
182 * .. Array Arguments ..
183  REAL a( lda, * ), c( ldc, * ), tau( * ),
184  $ work( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * .. Parameters ..
190  INTEGER nbmax, ldt
191  parameter( nbmax = 64, ldt = nbmax+1 )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL left, lquery, notran
195  CHARACTER transt
196  INTEGER i, i1, i2, i3, ib, iinfo, iws, ldwork, lwkopt,
197  $ mi, nb, nbmin, ni, nq, nw
198 * ..
199 * .. Local Arrays ..
200  REAL t( ldt, nbmax )
201 * ..
202 * .. External Functions ..
203  LOGICAL lsame
204  INTEGER ilaenv
205  EXTERNAL lsame, ilaenv
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL slarfb, slarft, sormr2, xerbla
209 * ..
210 * .. Intrinsic Functions ..
211  INTRINSIC max, min
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input arguments
216 *
217  info = 0
218  left = lsame( side, 'L' )
219  notran = lsame( trans, 'N' )
220  lquery = ( lwork.EQ.-1 )
221 *
222 * NQ is the order of Q and NW is the minimum dimension of WORK
223 *
224  IF( left ) THEN
225  nq = m
226  nw = max( 1, n )
227  ELSE
228  nq = n
229  nw = max( 1, m )
230  END IF
231  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
232  info = -1
233  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
234  info = -2
235  ELSE IF( m.LT.0 ) THEN
236  info = -3
237  ELSE IF( n.LT.0 ) THEN
238  info = -4
239  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
240  info = -5
241  ELSE IF( lda.LT.max( 1, k ) ) THEN
242  info = -7
243  ELSE IF( ldc.LT.max( 1, m ) ) THEN
244  info = -10
245  END IF
246 *
247  IF( info.EQ.0 ) THEN
248  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
249  lwkopt = 1
250  ELSE
251 *
252 * Determine the block size. NB may be at most NBMAX, where
253 * NBMAX is used to define the local array T.
254 *
255  nb = min( nbmax, ilaenv( 1, 'SORMRQ', side // trans, m, n,
256  $ k, -1 ) )
257  lwkopt = nw*nb
258  END IF
259  work( 1 ) = lwkopt
260 *
261  IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
262  info = -12
263  END IF
264  END IF
265 *
266  IF( info.NE.0 ) THEN
267  CALL xerbla( 'SORMRQ', -info )
268  RETURN
269  ELSE IF( lquery ) THEN
270  RETURN
271  END IF
272 *
273 * Quick return if possible
274 *
275  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
276  RETURN
277  END IF
278 *
279  nbmin = 2
280  ldwork = nw
281  IF( nb.GT.1 .AND. nb.LT.k ) THEN
282  iws = nw*nb
283  IF( lwork.LT.iws ) THEN
284  nb = lwork / ldwork
285  nbmin = max( 2, ilaenv( 2, 'SORMRQ', side // trans, m, n, k,
286  $ -1 ) )
287  END IF
288  ELSE
289  iws = nw
290  END IF
291 *
292  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
293 *
294 * Use unblocked code
295 *
296  CALL sormr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
297  $ iinfo )
298  ELSE
299 *
300 * Use blocked code
301 *
302  IF( ( left .AND. .NOT.notran ) .OR.
303  $ ( .NOT.left .AND. notran ) ) THEN
304  i1 = 1
305  i2 = k
306  i3 = nb
307  ELSE
308  i1 = ( ( k-1 ) / nb )*nb + 1
309  i2 = 1
310  i3 = -nb
311  END IF
312 *
313  IF( left ) THEN
314  ni = n
315  ELSE
316  mi = m
317  END IF
318 *
319  IF( notran ) THEN
320  transt = 'T'
321  ELSE
322  transt = 'N'
323  END IF
324 *
325  DO 10 i = i1, i2, i3
326  ib = min( nb, k-i+1 )
327 *
328 * Form the triangular factor of the block reflector
329 * H = H(i+ib-1) . . . H(i+1) H(i)
330 *
331  CALL slarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
332  $ a( i, 1 ), lda, tau( i ), t, ldt )
333  IF( left ) THEN
334 *
335 * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
336 *
337  mi = m - k + i + ib - 1
338  ELSE
339 *
340 * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
341 *
342  ni = n - k + i + ib - 1
343  END IF
344 *
345 * Apply H or H**T
346 *
347  CALL slarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
348  $ ib, a( i, 1 ), lda, t, ldt, c, ldc, work,
349  $ ldwork )
350  10 CONTINUE
351  END IF
352  work( 1 ) = lwkopt
353  RETURN
354 *
355 * End of SORMRQ
356 *
subroutine sormr2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sge...
Definition: sormr2.f:161
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
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:165

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