LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zgemlqt()

 subroutine zgemlqt ( character SIDE, character TRANS, integer M, integer N, integer K, integer MB, complex*16, dimension( ldv, * ) V, integer LDV, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer INFO )

ZGEMLQT

Purpose:
ZGEMLQT overwrites the general real M-by-N matrix C with

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'C':   Q**H C            C Q**H

where Q is a complex orthogonal matrix defined as the product of K
elementary reflectors:

Q = H(1) H(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by ZGELQT.

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**H from the Left; = 'R': apply Q or Q**H from the Right. [in] TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**H. [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] MB MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DGELQT. [in] V V is COMPLEX*16 array, dimension (LDV,M) if SIDE = 'L', (LDV,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 DGELQT in the first K rows of its array argument A. [in] LDV LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K). [in] T T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DGELQT, stored as a MB-by-K matrix. [in] LDT LDT is INTEGER The leading dimension of the array T. LDT >= MB. [in,out] C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. [in] LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). [out] WORK WORK is COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Date
November 2017

Definition at line 170 of file zgemlqt.f.

170 *
171 * -- LAPACK computational routine (version 3.8.0) --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 * November 2017
175 *
176 * .. Scalar Arguments ..
177  CHARACTER side, trans
178  INTEGER info, k, ldv, ldc, m, n, mb, ldt
179 * ..
180 * .. Array Arguments ..
181  COMPLEX*16 v( ldv, * ), c( ldc, * ), t( ldt, * ), work( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * ..
187 * .. Local Scalars ..
188  LOGICAL left, right, tran, notran
189  INTEGER i, ib, ldwork, kf
190 * ..
191 * .. External Functions ..
192  LOGICAL lsame
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL xerbla, zlarfb
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max, min
200 * ..
201 * .. Executable Statements ..
202 *
203 * .. Test the input arguments ..
204 *
205  info = 0
206  left = lsame( side, 'L' )
207  right = lsame( side, 'R' )
208  tran = lsame( trans, 'C' )
209  notran = lsame( trans, 'N' )
210 *
211  IF( left ) THEN
212  ldwork = max( 1, n )
213  ELSE IF ( right ) THEN
214  ldwork = max( 1, m )
215  END IF
216  IF( .NOT.left .AND. .NOT.right ) THEN
217  info = -1
218  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
219  info = -2
220  ELSE IF( m.LT.0 ) THEN
221  info = -3
222  ELSE IF( n.LT.0 ) THEN
223  info = -4
224  ELSE IF( k.LT.0) THEN
225  info = -5
226  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
227  info = -6
228  ELSE IF( ldv.LT.max( 1, k ) ) THEN
229  info = -8
230  ELSE IF( ldt.LT.mb ) THEN
231  info = -10
232  ELSE IF( ldc.LT.max( 1, m ) ) THEN
233  info = -12
234  END IF
235 *
236  IF( info.NE.0 ) THEN
237  CALL xerbla( 'ZGEMLQT', -info )
238  RETURN
239  END IF
240 *
241 * .. Quick return if possible ..
242 *
243  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
244 *
245  IF( left .AND. notran ) THEN
246 *
247  DO i = 1, k, mb
248  ib = min( mb, k-i+1 )
249  CALL zlarfb( 'L', 'C', 'F', 'R', m-i+1, n, ib,
250  \$ v( i, i ), ldv, t( 1, i ), ldt,
251  \$ c( i, 1 ), ldc, work, ldwork )
252  END DO
253 *
254  ELSE IF( right .AND. tran ) THEN
255 *
256  DO i = 1, k, mb
257  ib = min( mb, k-i+1 )
258  CALL zlarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
259  \$ v( i, i ), ldv, t( 1, i ), ldt,
260  \$ c( 1, i ), ldc, work, ldwork )
261  END DO
262 *
263  ELSE IF( left .AND. tran ) THEN
264 *
265  kf = ((k-1)/mb)*mb+1
266  DO i = kf, 1, -mb
267  ib = min( mb, k-i+1 )
268  CALL zlarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
269  \$ v( i, i ), ldv, t( 1, i ), ldt,
270  \$ c( i, 1 ), ldc, work, ldwork )
271  END DO
272 *
273  ELSE IF( right .AND. notran ) THEN
274 *
275  kf = ((k-1)/mb)*mb+1
276  DO i = kf, 1, -mb
277  ib = min( mb, k-i+1 )
278  CALL zlarfb( 'R', 'C', 'F', 'R', m, n-i+1, ib,
279  \$ v( i, i ), ldv, t( 1, i ), ldt,
280  \$ c( 1, i ), ldc, work, ldwork )
281  END DO
282 *
283  END IF
284 *
285  RETURN
286 *
287 * End of ZGEMLQT
288 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: zlarfb.f:197
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