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

 subroutine sormrq ( character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info )

SORMRQ

Purpose:
``` SORMRQ 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)

as returned by SGERQF. 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] A ``` A is REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,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 SGERQF in the last k rows of its array argument A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K).``` [in] TAU ``` TAU is REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.``` [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 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 ``` WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.``` [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 sormrq.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, LDA, LDC, LWORK, M, N
176* ..
177* .. Array Arguments ..
178 REAL A( LDA, * ), C( LDC, * ), TAU( * ),
179 \$ WORK( * )
180* ..
181*
182* =====================================================================
183*
184* .. Parameters ..
185 INTEGER NBMAX, LDT, TSIZE
186 parameter( nbmax = 64, ldt = nbmax+1,
187 \$ tsize = ldt*nbmax )
188* ..
189* .. Local Scalars ..
190 LOGICAL LEFT, LQUERY, NOTRAN
191 CHARACTER TRANST
192 INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
193 \$ MI, NB, NBMIN, NI, NQ, NW
194* ..
195* .. External Functions ..
196 LOGICAL LSAME
197 INTEGER ILAENV
198 REAL SROUNDUP_LWORK
199 EXTERNAL lsame, ilaenv, sroundup_lwork
200* ..
201* .. External Subroutines ..
202 EXTERNAL slarfb, slarft, sormr2, xerbla
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC max, min
206* ..
207* .. Executable Statements ..
208*
209* Test the input arguments
210*
211 info = 0
212 left = lsame( side, 'L' )
213 notran = lsame( trans, 'N' )
214 lquery = ( lwork.EQ.-1 )
215*
216* NQ is the order of Q and NW is the minimum dimension of WORK
217*
218 IF( left ) THEN
219 nq = m
220 nw = max( 1, n )
221 ELSE
222 nq = n
223 nw = max( 1, m )
224 END IF
225 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
226 info = -1
227 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
228 info = -2
229 ELSE IF( m.LT.0 ) THEN
230 info = -3
231 ELSE IF( n.LT.0 ) THEN
232 info = -4
233 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
234 info = -5
235 ELSE IF( lda.LT.max( 1, k ) ) THEN
236 info = -7
237 ELSE IF( ldc.LT.max( 1, m ) ) THEN
238 info = -10
239 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
240 info = -12
241 END IF
242*
243 IF( info.EQ.0 ) THEN
244*
245* Compute the workspace requirements
246*
247 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
248 lwkopt = 1
249 ELSE
250 nb = min( nbmax, ilaenv( 1, 'SORMRQ', side // trans, m, n,
251 \$ k, -1 ) )
252 lwkopt = nw*nb + tsize
253 END IF
254 work( 1 ) = sroundup_lwork(lwkopt)
255 END IF
256*
257 IF( info.NE.0 ) THEN
258 CALL xerbla( 'SORMRQ', -info )
259 RETURN
260 ELSE IF( lquery ) THEN
261 RETURN
262 END IF
263*
264* Quick return if possible
265*
266 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
267 RETURN
268 END IF
269*
270 nbmin = 2
271 ldwork = nw
272 IF( nb.GT.1 .AND. nb.LT.k ) THEN
273 IF( lwork.LT.lwkopt ) THEN
274 nb = (lwork-tsize) / ldwork
275 nbmin = max( 2, ilaenv( 2, 'SORMRQ', side // trans, m, n, k,
276 \$ -1 ) )
277 END IF
278 END IF
279*
280 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
281*
282* Use unblocked code
283*
284 CALL sormr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
285 \$ iinfo )
286 ELSE
287*
288* Use blocked code
289*
290 iwt = 1 + nw*nb
291 IF( ( left .AND. .NOT.notran ) .OR.
292 \$ ( .NOT.left .AND. notran ) ) THEN
293 i1 = 1
294 i2 = k
295 i3 = nb
296 ELSE
297 i1 = ( ( k-1 ) / nb )*nb + 1
298 i2 = 1
299 i3 = -nb
300 END IF
301*
302 IF( left ) THEN
303 ni = n
304 ELSE
305 mi = m
306 END IF
307*
308 IF( notran ) THEN
309 transt = 'T'
310 ELSE
311 transt = 'N'
312 END IF
313*
314 DO 10 i = i1, i2, i3
315 ib = min( nb, k-i+1 )
316*
317* Form the triangular factor of the block reflector
318* H = H(i+ib-1) . . . H(i+1) H(i)
319*
320 CALL slarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
321 \$ a( i, 1 ), lda, tau( i ), work( iwt ), ldt )
322 IF( left ) THEN
323*
324* H or H**T is applied to C(1:m-k+i+ib-1,1:n)
325*
326 mi = m - k + i + ib - 1
327 ELSE
328*
329* H or H**T is applied to C(1:m,1:n-k+i+ib-1)
330*
331 ni = n - k + i + ib - 1
332 END IF
333*
334* Apply H or H**T
335*
336 CALL slarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
337 \$ ib, a( i, 1 ), lda, work( iwt ), ldt, c, ldc,
338 \$ work, ldwork )
339 10 CONTINUE
340 END IF
341 work( 1 ) = sroundup_lwork(lwkopt)
342 RETURN
343*
344* End of SORMRQ
345*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
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
subroutine slarft(direct, storev, n, k, v, ldv, tau, t, ldt)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition slarft.f:163
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine sormr2(side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sge...
Definition sormr2.f:159
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