 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cgemlqt()

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

CGEMLQT

Purpose:
``` CGEMLQT overwrites the general complex 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 unitary 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 CGELQT.

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': Conjugate 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 CGELQT.``` [in] V ``` V is COMPLEX 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 CGELQT 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 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CGELQT, 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 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 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```

Definition at line 151 of file cgemlqt.f.

153 *
154 * -- LAPACK computational routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  CHARACTER SIDE, TRANS
160  INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
161 * ..
162 * .. Array Arguments ..
163  COMPLEX V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * ..
169 * .. Local Scalars ..
170  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
171  INTEGER I, IB, LDWORK, KF, Q
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL xerbla, clarfb
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max, min
182 * ..
183 * .. Executable Statements ..
184 *
185 * .. Test the input arguments ..
186 *
187  info = 0
188  left = lsame( side, 'L' )
189  right = lsame( side, 'R' )
190  tran = lsame( trans, 'C' )
191  notran = lsame( trans, 'N' )
192 *
193  IF( left ) THEN
194  ldwork = max( 1, n )
195  q = m
196  ELSE IF ( right ) THEN
197  ldwork = max( 1, m )
198  q = n
199  END IF
200  IF( .NOT.left .AND. .NOT.right ) THEN
201  info = -1
202  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
203  info = -2
204  ELSE IF( m.LT.0 ) THEN
205  info = -3
206  ELSE IF( n.LT.0 ) THEN
207  info = -4
208  ELSE IF( k.LT.0 .OR. k.GT.q ) THEN
209  info = -5
210  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
211  info = -6
212  ELSE IF( ldv.LT.max( 1, k ) ) THEN
213  info = -8
214  ELSE IF( ldt.LT.mb ) THEN
215  info = -10
216  ELSE IF( ldc.LT.max( 1, m ) ) THEN
217  info = -12
218  END IF
219 *
220  IF( info.NE.0 ) THEN
221  CALL xerbla( 'CGEMLQT', -info )
222  RETURN
223  END IF
224 *
225 * .. Quick return if possible ..
226 *
227  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
228 *
229  IF( left .AND. notran ) THEN
230 *
231  DO i = 1, k, mb
232  ib = min( mb, k-i+1 )
233  CALL clarfb( 'L', 'C', 'F', 'R', m-i+1, n, ib,
234  \$ v( i, i ), ldv, t( 1, i ), ldt,
235  \$ c( i, 1 ), ldc, work, ldwork )
236  END DO
237 *
238  ELSE IF( right .AND. tran ) THEN
239 *
240  DO i = 1, k, mb
241  ib = min( mb, k-i+1 )
242  CALL clarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
243  \$ v( i, i ), ldv, t( 1, i ), ldt,
244  \$ c( 1, i ), ldc, work, ldwork )
245  END DO
246 *
247  ELSE IF( left .AND. tran ) THEN
248 *
249  kf = ((k-1)/mb)*mb+1
250  DO i = kf, 1, -mb
251  ib = min( mb, k-i+1 )
252  CALL clarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
253  \$ v( i, i ), ldv, t( 1, i ), ldt,
254  \$ c( i, 1 ), ldc, work, ldwork )
255  END DO
256 *
257  ELSE IF( right .AND. notran ) THEN
258 *
259  kf = ((k-1)/mb)*mb+1
260  DO i = kf, 1, -mb
261  ib = min( mb, k-i+1 )
262  CALL clarfb( 'R', 'C', 'F', 'R', m, n-i+1, ib,
263  \$ v( i, i ), ldv, t( 1, i ), ldt,
264  \$ c( 1, i ), ldc, work, ldwork )
265  END DO
266 *
267  END IF
268 *
269  RETURN
270 *
271 * End of CGEMLQT
272 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: clarfb.f:197
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