LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgemqr()

 subroutine cgemqr ( character SIDE, character TRANS, integer M, integer N, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) T, integer TSIZE, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( * ) WORK, integer LWORK, integer INFO )

CGEMQR

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

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**H * C       C * Q**H

where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by tall skinny
QR factorization (CGEQR)```
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 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 COMPLEX array, dimension (LDA,K) Part of the data structure to represent Q as returned by CGEQR.``` [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 COMPLEX array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by CGEQR.``` [in] TSIZE ``` TSIZE is INTEGER The dimension of the array T. TSIZE >= 5.``` [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 or Q**H*C or C*Q**H or C*Q.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ` (workspace) COMPLEX 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
CLATSQR or CGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, CGEQR will use either
CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
the QR factorization.
This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
multiply matrix Q by another matrix.
Further Details in CLAMTSQR or CGEMQRT.```

Definition at line 170 of file cgemqr.f.

172*
173* -- LAPACK computational routine --
174* -- LAPACK is a software package provided by Univ. of Tennessee, --
175* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176*
177* .. Scalar Arguments ..
178 CHARACTER SIDE, TRANS
179 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
180* ..
181* .. Array Arguments ..
182 COMPLEX A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
183* ..
184*
185* =====================================================================
186*
187* ..
188* .. Local Scalars ..
189 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
190 INTEGER MB, NB, LW, NBLCKS, MN
191* ..
192* .. External Functions ..
193 LOGICAL LSAME
194 EXTERNAL lsame
195* ..
196* .. External Subroutines ..
197 EXTERNAL cgemqrt, clamtsqr, xerbla
198* ..
199* .. Intrinsic Functions ..
200 INTRINSIC int, max, min, mod
201* ..
202* .. Executable Statements ..
203*
204* Test the input arguments
205*
206 lquery = lwork.EQ.-1
207 notran = lsame( trans, 'N' )
208 tran = lsame( trans, 'C' )
209 left = lsame( side, 'L' )
210 right = lsame( side, 'R' )
211*
212 mb = int( t( 2 ) )
213 nb = int( t( 3 ) )
214 IF( left ) THEN
215 lw = n * nb
216 mn = m
217 ELSE
218 lw = mb * nb
219 mn = n
220 END IF
221*
222 IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
223 IF( mod( mn - k, mb - k ).EQ.0 ) THEN
224 nblcks = ( mn - k ) / ( mb - k )
225 ELSE
226 nblcks = ( mn - k ) / ( mb - k ) + 1
227 END IF
228 ELSE
229 nblcks = 1
230 END IF
231*
232 info = 0
233 IF( .NOT.left .AND. .NOT.right ) THEN
234 info = -1
235 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
236 info = -2
237 ELSE IF( m.LT.0 ) THEN
238 info = -3
239 ELSE IF( n.LT.0 ) THEN
240 info = -4
241 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
242 info = -5
243 ELSE IF( lda.LT.max( 1, mn ) ) THEN
244 info = -7
245 ELSE IF( tsize.LT.5 ) THEN
246 info = -9
247 ELSE IF( ldc.LT.max( 1, m ) ) THEN
248 info = -11
249 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
250 info = -13
251 END IF
252*
253 IF( info.EQ.0 ) THEN
254 work( 1 ) = lw
255 END IF
256*
257 IF( info.NE.0 ) THEN
258 CALL xerbla( 'CGEMQR', -info )
259 RETURN
260 ELSE IF( lquery ) THEN
261 RETURN
262 END IF
263*
264* Quick return if possible
265*
266 IF( min( m, n, k ).EQ.0 ) THEN
267 RETURN
268 END IF
269*
270 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
271 \$ .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
272 CALL cgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
273 \$ nb, c, ldc, work, info )
274 ELSE
275 CALL clamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
276 \$ nb, c, ldc, work, lwork, info )
277 END IF
278*
279 work( 1 ) = lw
280*
281 RETURN
282*
283* End of CGEMQR
284*
subroutine clamtsqr(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
CLAMTSQR
Definition: clamtsqr.f:197
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMQRT
Definition: cgemqrt.f:168
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