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

 subroutine stpmlqt ( character side, character trans, integer m, integer n, integer k, integer l, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer info )

STPMLQT

Purpose:
``` STPMLQT applies a real orthogonal matrix Q obtained from a
"triangular-pentagonal" real block reflector H to a general
real matrix C, which consists of two blocks A and B.```
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 B. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix B. N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q.``` [in] L ``` L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.``` [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 STPLQT.``` [in] V ``` V is REAL array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STPLQT in B. See Further Details.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. LDV >= K.``` [in] T ``` T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by STPLQT, stored as a MB-by-K matrix.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= MB.``` [in,out] A ``` A is REAL array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).``` [in,out] B ``` B is REAL array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [out] WORK ``` WORK is REAL 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```
Further Details:
```  The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:

V = [V1] [V2].

The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
[B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

The real orthogonal matrix Q is formed from V and T.

If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.

If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.```

Definition at line 212 of file stpmlqt.f.

214*
215* -- LAPACK computational routine --
216* -- LAPACK is a software package provided by Univ. of Tennessee, --
217* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218*
219* .. Scalar Arguments ..
220 CHARACTER SIDE, TRANS
221 INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
222* ..
223* .. Array Arguments ..
224 REAL V( LDV, * ), A( LDA, * ), B( LDB, * ),
225 \$ T( LDT, * ), WORK( * )
226* ..
227*
228* =====================================================================
229*
230* ..
231* .. Local Scalars ..
232 LOGICAL LEFT, RIGHT, TRAN, NOTRAN
233 INTEGER I, IB, NB, LB, KF, LDAQ
234* ..
235* .. External Functions ..
236 LOGICAL LSAME
237 EXTERNAL lsame
238* ..
239* .. External Subroutines ..
240 EXTERNAL xerbla, stprfb
241* ..
242* .. Intrinsic Functions ..
243 INTRINSIC max, min
244* ..
245* .. Executable Statements ..
246*
247* .. Test the input arguments ..
248*
249 info = 0
250 left = lsame( side, 'L' )
251 right = lsame( side, 'R' )
252 tran = lsame( trans, 'T' )
253 notran = lsame( trans, 'N' )
254*
255 IF ( left ) THEN
256 ldaq = max( 1, k )
257 ELSE IF ( right ) THEN
258 ldaq = max( 1, m )
259 END IF
260 IF( .NOT.left .AND. .NOT.right ) THEN
261 info = -1
262 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
263 info = -2
264 ELSE IF( m.LT.0 ) THEN
265 info = -3
266 ELSE IF( n.LT.0 ) THEN
267 info = -4
268 ELSE IF( k.LT.0 ) THEN
269 info = -5
270 ELSE IF( l.LT.0 .OR. l.GT.k ) THEN
271 info = -6
272 ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0) ) THEN
273 info = -7
274 ELSE IF( ldv.LT.k ) THEN
275 info = -9
276 ELSE IF( ldt.LT.mb ) THEN
277 info = -11
278 ELSE IF( lda.LT.ldaq ) THEN
279 info = -13
280 ELSE IF( ldb.LT.max( 1, m ) ) THEN
281 info = -15
282 END IF
283*
284 IF( info.NE.0 ) THEN
285 CALL xerbla( 'STPMLQT', -info )
286 RETURN
287 END IF
288*
289* .. Quick return if possible ..
290*
291 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
292*
293 IF( left .AND. notran ) THEN
294*
295 DO i = 1, k, mb
296 ib = min( mb, k-i+1 )
297 nb = min( m-l+i+ib-1, m )
298 IF( i.GE.l ) THEN
299 lb = 0
300 ELSE
301 lb = 0
302 END IF
303 CALL stprfb( 'L', 'T', 'F', 'R', nb, n, ib, lb,
304 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
305 \$ a( i, 1 ), lda, b, ldb, work, ib )
306 END DO
307*
308 ELSE IF( right .AND. tran ) THEN
309*
310 DO i = 1, k, mb
311 ib = min( mb, k-i+1 )
312 nb = min( n-l+i+ib-1, n )
313 IF( i.GE.l ) THEN
314 lb = 0
315 ELSE
316 lb = nb-n+l-i+1
317 END IF
318 CALL stprfb( 'R', 'N', 'F', 'R', m, nb, ib, lb,
319 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
320 \$ a( 1, i ), lda, b, ldb, work, m )
321 END DO
322*
323 ELSE IF( left .AND. tran ) THEN
324*
325 kf = ((k-1)/mb)*mb+1
326 DO i = kf, 1, -mb
327 ib = min( mb, k-i+1 )
328 nb = min( m-l+i+ib-1, m )
329 IF( i.GE.l ) THEN
330 lb = 0
331 ELSE
332 lb = 0
333 END IF
334 CALL stprfb( 'L', 'N', 'F', 'R', nb, n, ib, lb,
335 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
336 \$ a( i, 1 ), lda, b, ldb, work, ib )
337 END DO
338*
339 ELSE IF( right .AND. notran ) THEN
340*
341 kf = ((k-1)/mb)*mb+1
342 DO i = kf, 1, -mb
343 ib = min( mb, k-i+1 )
344 nb = min( n-l+i+ib-1, n )
345 IF( i.GE.l ) THEN
346 lb = 0
347 ELSE
348 lb = nb-n+l-i+1
349 END IF
350 CALL stprfb( 'R', 'T', 'F', 'R', m, nb, ib, lb,
351 \$ v( i, 1 ), ldv, t( 1, i ), ldt,
352 \$ a( 1, i ), lda, b, ldb, work, m )
353 END DO
354*
355 END IF
356*
357 RETURN
358*
359* End of STPMLQT
360*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine stprfb(side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of ...
Definition stprfb.f:251
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