LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dgemqr()

 subroutine dgemqr ( character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info )

DGEMQR

Purpose:
``` DGEMQR 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 blocked elementary reflectors computed by tall skinny
QR factorization (DGEQR)```
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 A. 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 DOUBLE PRECISION array, dimension (LDA,K) Part of the data structure to represent Q as returned by DGEQR.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).``` [in] T ``` T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by DGEQR.``` [in] TSIZE ``` TSIZE is INTEGER The dimension of the array T. TSIZE >= 5.``` [in,out] C ``` C is DOUBLE PRECISION 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 ` (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK is issued by XERBLA.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Further Details
``` These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
DLATSQR or DGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, DGEQR will use either
DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
the QR factorization.
This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
multiply matrix Q by another matrix.
Further Details in DLATMSQR or DGEMQRT.```

Definition at line 172 of file dgemqr.f.

174*
175* -- LAPACK computational routine --
176* -- LAPACK is a software package provided by Univ. of Tennessee, --
177* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178*
179* .. Scalar Arguments ..
180 CHARACTER SIDE, TRANS
181 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
182* ..
183* .. Array Arguments ..
184 DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
185* ..
186*
187* =====================================================================
188*
189* ..
190* .. Local Scalars ..
191 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
192 INTEGER MB, NB, LW, NBLCKS, MN
193* ..
194* .. External Functions ..
195 LOGICAL LSAME
196 EXTERNAL lsame
197* ..
198* .. External Subroutines ..
199 EXTERNAL dgemqrt, dlamtsqr, xerbla
200* ..
201* .. Intrinsic Functions ..
202 INTRINSIC int, max, min, mod
203* ..
204* .. Executable Statements ..
205*
206* Test the input arguments
207*
208 lquery = lwork.EQ.-1
209 notran = lsame( trans, 'N' )
210 tran = lsame( trans, 'T' )
211 left = lsame( side, 'L' )
212 right = lsame( side, 'R' )
213*
214 mb = int( t( 2 ) )
215 nb = int( t( 3 ) )
216 IF( left ) THEN
217 lw = n * nb
218 mn = m
219 ELSE
220 lw = mb * nb
221 mn = n
222 END IF
223*
224 IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
225 IF( mod( mn - k, mb - k ).EQ.0 ) THEN
226 nblcks = ( mn - k ) / ( mb - k )
227 ELSE
228 nblcks = ( mn - k ) / ( mb - k ) + 1
229 END IF
230 ELSE
231 nblcks = 1
232 END IF
233*
234 info = 0
235 IF( .NOT.left .AND. .NOT.right ) THEN
236 info = -1
237 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
238 info = -2
239 ELSE IF( m.LT.0 ) THEN
240 info = -3
241 ELSE IF( n.LT.0 ) THEN
242 info = -4
243 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
244 info = -5
245 ELSE IF( lda.LT.max( 1, mn ) ) THEN
246 info = -7
247 ELSE IF( tsize.LT.5 ) THEN
248 info = -9
249 ELSE IF( ldc.LT.max( 1, m ) ) THEN
250 info = -11
251 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
252 info = -13
253 END IF
254*
255 IF( info.EQ.0 ) THEN
256 work( 1 ) = lw
257 END IF
258*
259 IF( info.NE.0 ) THEN
260 CALL xerbla( 'DGEMQR', -info )
261 RETURN
262 ELSE IF( lquery ) THEN
263 RETURN
264 END IF
265*
266* Quick return if possible
267*
268 IF( min( m, n, k ).EQ.0 ) THEN
269 RETURN
270 END IF
271*
272 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
273 \$ .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
274 CALL dgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
275 \$ nb, c, ldc, work, info )
276 ELSE
277 CALL dlamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
278 \$ nb, c, ldc, work, lwork, info )
279 END IF
280*
281 work( 1 ) = lw
282*
283 RETURN
284*
285* End of DGEMQR
286*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
DGEMQRT
Definition dgemqrt.f:168
subroutine dlamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMTSQR
Definition dlamtsqr.f:199
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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