LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sgemqrt()

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

SGEMQRT

Purpose:
``` SGEMQRT 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) = I - V T V**T

generated using the compact WY representation as returned by SGEQRT.

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] NB ``` NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in SGEQRT.``` [in] V ``` V is REAL array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRT in the first K columns of its array argument A.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).``` [in] T ``` T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by SGEQRT, stored as a NB-by-N matrix.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= NB.``` [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, Q**T C, 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. The dimension of WORK is N*NB if SIDE = 'L', or M*NB 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 166 of file sgemqrt.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, LDV, LDC, M, N, NB, LDT
176 * ..
177 * .. Array Arguments ..
178  REAL V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
179 * ..
180 *
181 * =====================================================================
182 *
183 * ..
184 * .. Local Scalars ..
185  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
186  INTEGER I, IB, LDWORK, KF, Q
187 * ..
188 * .. External Functions ..
189  LOGICAL LSAME
190  EXTERNAL lsame
191 * ..
192 * .. External Subroutines ..
193  EXTERNAL xerbla, slarfb
194 * ..
195 * .. Intrinsic Functions ..
196  INTRINSIC max, min
197 * ..
198 * .. Executable Statements ..
199 *
200 * .. Test the input arguments ..
201 *
202  info = 0
203  left = lsame( side, 'L' )
204  right = lsame( side, 'R' )
205  tran = lsame( trans, 'T' )
206  notran = lsame( trans, 'N' )
207 *
208  IF( left ) THEN
209  ldwork = max( 1, n )
210  q = m
211  ELSE IF ( right ) THEN
212  ldwork = max( 1, m )
213  q = n
214  END IF
215  IF( .NOT.left .AND. .NOT.right ) THEN
216  info = -1
217  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
218  info = -2
219  ELSE IF( m.LT.0 ) THEN
220  info = -3
221  ELSE IF( n.LT.0 ) THEN
222  info = -4
223  ELSE IF( k.LT.0 .OR. k.GT.q ) THEN
224  info = -5
225  ELSE IF( nb.LT.1 .OR. (nb.GT.k .AND. k.GT.0)) THEN
226  info = -6
227  ELSE IF( ldv.LT.max( 1, q ) ) THEN
228  info = -8
229  ELSE IF( ldt.LT.nb ) THEN
230  info = -10
231  ELSE IF( ldc.LT.max( 1, m ) ) THEN
232  info = -12
233  END IF
234 *
235  IF( info.NE.0 ) THEN
236  CALL xerbla( 'SGEMQRT', -info )
237  RETURN
238  END IF
239 *
240 * .. Quick return if possible ..
241 *
242  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
243 *
244  IF( left .AND. tran ) THEN
245 *
246  DO i = 1, k, nb
247  ib = min( nb, k-i+1 )
248  CALL slarfb( 'L', 'T', 'F', 'C', m-i+1, n, ib,
249  \$ v( i, i ), ldv, t( 1, i ), ldt,
250  \$ c( i, 1 ), ldc, work, ldwork )
251  END DO
252 *
253  ELSE IF( right .AND. notran ) THEN
254 *
255  DO i = 1, k, nb
256  ib = min( nb, k-i+1 )
257  CALL slarfb( 'R', 'N', 'F', 'C', m, n-i+1, ib,
258  \$ v( i, i ), ldv, t( 1, i ), ldt,
259  \$ c( 1, i ), ldc, work, ldwork )
260  END DO
261 *
262  ELSE IF( left .AND. notran ) THEN
263 *
264  kf = ((k-1)/nb)*nb+1
265  DO i = kf, 1, -nb
266  ib = min( nb, k-i+1 )
267  CALL slarfb( 'L', 'N', 'F', 'C', m-i+1, n, ib,
268  \$ v( i, i ), ldv, t( 1, i ), ldt,
269  \$ c( i, 1 ), ldc, work, ldwork )
270  END DO
271 *
272  ELSE IF( right .AND. tran ) THEN
273 *
274  kf = ((k-1)/nb)*nb+1
275  DO i = kf, 1, -nb
276  ib = min( nb, k-i+1 )
277  CALL slarfb( 'R', 'T', 'F', 'C', m, n-i+1, ib,
278  \$ v( i, i ), ldv, t( 1, i ), ldt,
279  \$ c( 1, i ), ldc, work, ldwork )
280  END DO
281 *
282  END IF
283 *
284  RETURN
285 *
286 * End of SGEMQRT
287 *
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
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