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

Go to the source code of this file.

Functions/Subroutines

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

Function/Subroutine Documentation

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

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

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 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 sormlq.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, ic, iinfo, iws, jc, ldwork,
197  $ lwkopt, 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, sorml2, 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 = n
227  ELSE
228  nq = n
229  nw = 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  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
246  info = -12
247  END IF
248 *
249  IF( info.EQ.0 ) THEN
250 *
251 * Determine the block size. NB may be at most NBMAX, where NBMAX
252 * is used to define the local array T.
253 *
254  nb = min( nbmax, ilaenv( 1, 'SORMLQ', side // trans, m, n, k,
255  $ -1 ) )
256  lwkopt = max( 1, nw )*nb
257  work( 1 ) = lwkopt
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'SORMLQ', -info )
262  RETURN
263  ELSE IF( lquery ) THEN
264  RETURN
265  END IF
266 *
267 * Quick return if possible
268 *
269  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
270  work( 1 ) = 1
271  RETURN
272  END IF
273 *
274  nbmin = 2
275  ldwork = nw
276  IF( nb.GT.1 .AND. nb.LT.k ) THEN
277  iws = nw*nb
278  IF( lwork.LT.iws ) THEN
279  nb = lwork / ldwork
280  nbmin = max( 2, ilaenv( 2, 'SORMLQ', side // trans, m, n, k,
281  $ -1 ) )
282  END IF
283  ELSE
284  iws = nw
285  END IF
286 *
287  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
288 *
289 * Use unblocked code
290 *
291  CALL sorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
292  $ iinfo )
293  ELSE
294 *
295 * Use blocked code
296 *
297  IF( ( left .AND. notran ) .OR.
298  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
299  i1 = 1
300  i2 = k
301  i3 = nb
302  ELSE
303  i1 = ( ( k-1 ) / nb )*nb + 1
304  i2 = 1
305  i3 = -nb
306  END IF
307 *
308  IF( left ) THEN
309  ni = n
310  jc = 1
311  ELSE
312  mi = m
313  ic = 1
314  END IF
315 *
316  IF( notran ) THEN
317  transt = 'T'
318  ELSE
319  transt = 'N'
320  END IF
321 *
322  DO 10 i = i1, i2, i3
323  ib = min( nb, k-i+1 )
324 *
325 * Form the triangular factor of the block reflector
326 * H = H(i) H(i+1) . . . H(i+ib-1)
327 *
328  CALL slarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
329  $ lda, tau( i ), t, ldt )
330  IF( left ) THEN
331 *
332 * H or H**T is applied to C(i:m,1:n)
333 *
334  mi = m - i + 1
335  ic = i
336  ELSE
337 *
338 * H or H**T is applied to C(1:m,i:n)
339 *
340  ni = n - i + 1
341  jc = i
342  END IF
343 *
344 * Apply H or H**T
345 *
346  CALL slarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
347  $ a( i, i ), lda, t, ldt, c( ic, jc ), ldc, work,
348  $ ldwork )
349  10 CONTINUE
350  END IF
351  work( 1 ) = lwkopt
352  RETURN
353 *
354 * End of SORMLQ
355 *
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: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

Here is the call graph for this function:

Here is the caller graph for this function: