LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dsb2st_kernels()

subroutine dsb2st_kernels ( character uplo,
logical wantz,
integer ttype,
integer st,
integer ed,
integer sweep,
integer n,
integer nb,
integer ib,
double precision, dimension( lda, * ) a,
integer lda,
double precision, dimension( * ) v,
double precision, dimension( * ) tau,
integer ldvt,
double precision, dimension( * ) work )

DSB2ST_KERNELS

Download DSB2ST_KERNELS + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DSB2ST_KERNELS is an internal routine used by the DSYTRD_SB2ST
!> subroutine.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>
[in]WANTZ
!>          WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
!>          Eigenvalue/Eigenvectors.
!>
[in]TTYPE
!>          TTYPE is INTEGER
!>
[in]ST
!>          ST is INTEGER
!>          internal parameter for indices.
!>
[in]ED
!>          ED is INTEGER
!>          internal parameter for indices.
!>
[in]SWEEP
!>          SWEEP is INTEGER
!>          internal parameter for indices.
!>
[in]N
!>          N is INTEGER. The order of the matrix A.
!>
[in]NB
!>          NB is INTEGER. The size of the band.
!>
[in]IB
!>          IB is INTEGER.
!>
[in,out]A
!>          A is DOUBLE PRECISION array. A pointer to the matrix A.
!>
[in]LDA
!>          LDA is INTEGER. The leading dimension of the matrix A.
!>
[out]V
!>          V is DOUBLE PRECISION array, dimension 2*n if eigenvalues only are
!>          requested or to be queried for vectors.
!>
[out]TAU
!>          TAU is DOUBLE PRECISION array, dimension (2*n).
!>          The scalar factors of the Householder reflectors are stored
!>          in this array.
!>
[in]LDVT
!>          LDVT is INTEGER.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array. Workspace of size nb.
!>
Further Details:
!>
!>  Implemented by Azzam Haidar.
!>
!>  All details are available on technical report, SC11, SC13 papers.
!>
!>  Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
!>  Parallel reduction to condensed forms for symmetric eigenvalue problems
!>  using aggregated fine-grained and memory-aware kernels. In Proceedings
!>  of 2011 International Conference for High Performance Computing,
!>  Networking, Storage and Analysis (SC '11), New York, NY, USA,
!>  Article 8 , 11 pages.
!>  http://doi.acm.org/10.1145/2063384.2063394
!>
!>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
!>  An improved parallel singular value algorithm and its implementation
!>  for multicore hardware, In Proceedings of 2013 International Conference
!>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
!>  Denver, Colorado, USA, 2013.
!>  Article 90, 12 pages.
!>  http://doi.acm.org/10.1145/2503210.2503292
!>
!>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
!>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
!>  calculations based on fine-grained memory aware tasks.
!>  International Journal of High Performance Computing Applications.
!>  Volume 28 Issue 2, Pages 196-209, May 2014.
!>  http://hpc.sagepub.com/content/28/2/196
!>
!>

Definition at line 167 of file dsb2st_kernels.f.

170*
171 IMPLICIT NONE
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 UPLO
179 LOGICAL WANTZ
180 INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
181* ..
182* .. Array Arguments ..
183 DOUBLE PRECISION A( LDA, * ), V( * ),
184 $ TAU( * ), WORK( * )
185* ..
186*
187* =====================================================================
188*
189* .. Parameters ..
190 DOUBLE PRECISION ZERO, ONE
191 parameter( zero = 0.0d+0,
192 $ one = 1.0d+0 )
193* ..
194* .. Local Scalars ..
195 LOGICAL UPPER
196 INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS,
197 $ DPOS, OFDPOS, AJETER
198 DOUBLE PRECISION CTMP
199* ..
200* .. External Subroutines ..
201 EXTERNAL dlarfg, dlarfx, dlarfy
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC mod
205* .. External Functions ..
206 LOGICAL LSAME
207 EXTERNAL lsame
208* ..
209* ..
210* .. Executable Statements ..
211*
212 ajeter = ib + ldvt
213 upper = lsame( uplo, 'U' )
214
215 IF( upper ) THEN
216 dpos = 2 * nb + 1
217 ofdpos = 2 * nb
218 ELSE
219 dpos = 1
220 ofdpos = 2
221 ENDIF
222
223*
224* Upper case
225*
226 IF( upper ) THEN
227*
228 IF( wantz ) THEN
229 vpos = mod( sweep-1, 2 ) * n + st
230 taupos = mod( sweep-1, 2 ) * n + st
231 ELSE
232 vpos = mod( sweep-1, 2 ) * n + st
233 taupos = mod( sweep-1, 2 ) * n + st
234 ENDIF
235*
236 IF( ttype.EQ.1 ) THEN
237 lm = ed - st + 1
238*
239 v( vpos ) = one
240 DO 10 i = 1, lm-1
241 v( vpos+i ) = ( a( ofdpos-i, st+i ) )
242 a( ofdpos-i, st+i ) = zero
243 10 CONTINUE
244 ctmp = ( a( ofdpos, st ) )
245 CALL dlarfg( lm, ctmp, v( vpos+1 ), 1,
246 $ tau( taupos ) )
247 a( ofdpos, st ) = ctmp
248*
249 lm = ed - st + 1
250 CALL dlarfy( uplo, lm, v( vpos ), 1,
251 $ ( tau( taupos ) ),
252 $ a( dpos, st ), lda-1, work)
253 ENDIF
254*
255 IF( ttype.EQ.3 ) THEN
256*
257 lm = ed - st + 1
258 CALL dlarfy( uplo, lm, v( vpos ), 1,
259 $ ( tau( taupos ) ),
260 $ a( dpos, st ), lda-1, work)
261 ENDIF
262*
263 IF( ttype.EQ.2 ) THEN
264 j1 = ed+1
265 j2 = min( ed+nb, n )
266 ln = ed-st+1
267 lm = j2-j1+1
268 IF( lm.GT.0) THEN
269 CALL dlarfx( 'Left', ln, lm, v( vpos ),
270 $ ( tau( taupos ) ),
271 $ a( dpos-nb, j1 ), lda-1, work)
272*
273 IF( wantz ) THEN
274 vpos = mod( sweep-1, 2 ) * n + j1
275 taupos = mod( sweep-1, 2 ) * n + j1
276 ELSE
277 vpos = mod( sweep-1, 2 ) * n + j1
278 taupos = mod( sweep-1, 2 ) * n + j1
279 ENDIF
280*
281 v( vpos ) = one
282 DO 30 i = 1, lm-1
283 v( vpos+i ) =
284 $ ( a( dpos-nb-i, j1+i ) )
285 a( dpos-nb-i, j1+i ) = zero
286 30 CONTINUE
287 ctmp = ( a( dpos-nb, j1 ) )
288 CALL dlarfg( lm, ctmp, v( vpos+1 ), 1,
289 $ tau( taupos ) )
290 a( dpos-nb, j1 ) = ctmp
291*
292 CALL dlarfx( 'Right', ln-1, lm, v( vpos ),
293 $ tau( taupos ),
294 $ a( dpos-nb+1, j1 ), lda-1, work)
295 ENDIF
296 ENDIF
297*
298* Lower case
299*
300 ELSE
301*
302 IF( wantz ) THEN
303 vpos = mod( sweep-1, 2 ) * n + st
304 taupos = mod( sweep-1, 2 ) * n + st
305 ELSE
306 vpos = mod( sweep-1, 2 ) * n + st
307 taupos = mod( sweep-1, 2 ) * n + st
308 ENDIF
309*
310 IF( ttype.EQ.1 ) THEN
311 lm = ed - st + 1
312*
313 v( vpos ) = one
314 DO 20 i = 1, lm-1
315 v( vpos+i ) = a( ofdpos+i, st-1 )
316 a( ofdpos+i, st-1 ) = zero
317 20 CONTINUE
318 CALL dlarfg( lm, a( ofdpos, st-1 ), v( vpos+1 ), 1,
319 $ tau( taupos ) )
320*
321 lm = ed - st + 1
322*
323 CALL dlarfy( uplo, lm, v( vpos ), 1,
324 $ ( tau( taupos ) ),
325 $ a( dpos, st ), lda-1, work)
326
327 ENDIF
328*
329 IF( ttype.EQ.3 ) THEN
330 lm = ed - st + 1
331*
332 CALL dlarfy( uplo, lm, v( vpos ), 1,
333 $ ( tau( taupos ) ),
334 $ a( dpos, st ), lda-1, work)
335
336 ENDIF
337*
338 IF( ttype.EQ.2 ) THEN
339 j1 = ed+1
340 j2 = min( ed+nb, n )
341 ln = ed-st+1
342 lm = j2-j1+1
343*
344 IF( lm.GT.0) THEN
345 CALL dlarfx( 'Right', lm, ln, v( vpos ),
346 $ tau( taupos ), a( dpos+nb, st ),
347 $ lda-1, work)
348*
349 IF( wantz ) THEN
350 vpos = mod( sweep-1, 2 ) * n + j1
351 taupos = mod( sweep-1, 2 ) * n + j1
352 ELSE
353 vpos = mod( sweep-1, 2 ) * n + j1
354 taupos = mod( sweep-1, 2 ) * n + j1
355 ENDIF
356*
357 v( vpos ) = one
358 DO 40 i = 1, lm-1
359 v( vpos+i ) = a( dpos+nb+i, st )
360 a( dpos+nb+i, st ) = zero
361 40 CONTINUE
362 CALL dlarfg( lm, a( dpos+nb, st ), v( vpos+1 ), 1,
363 $ tau( taupos ) )
364*
365 CALL dlarfx( 'Left', lm, ln-1, v( vpos ),
366 $ ( tau( taupos ) ),
367 $ a( dpos+nb-1, st+1 ), lda-1, work)
368
369 ENDIF
370 ENDIF
371 ENDIF
372*
373 RETURN
374*
375* End of DSB2ST_KERNELS
376*
dlarfg
subroutine dlarfg(n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).
Definition dlarfg.f:104
dlarfx
subroutine dlarfx(side, m, n, v, tau, c, ldc, work)
DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the ...
Definition dlarfx.f:118
dlarfy
subroutine dlarfy(uplo, n, v, incv, tau, c, ldc, work)
DLARFY
Definition dlarfy.f:108
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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