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zhb2st_kernels.f
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1*> \brief \b ZHB2ST_KERNELS
2*
3* @precisions fortran z -> s d c
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download ZHB2ST_KERNELS + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhb2st_kernels.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhb2st_kernels.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhb2st_kernels.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE ZHB2ST_KERNELS( UPLO, WANTZ, TTYPE,
24* ST, ED, SWEEP, N, NB, IB,
25* A, LDA, V, TAU, LDVT, WORK)
26*
27* IMPLICIT NONE
28*
29* .. Scalar Arguments ..
30* CHARACTER UPLO
31* LOGICAL WANTZ
32* INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
33* ..
34* .. Array Arguments ..
35* COMPLEX*16 A( LDA, * ), V( * ),
36* TAU( * ), WORK( * )
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> ZHB2ST_KERNELS is an internal routine used by the ZHETRD_HB2ST
44*> subroutine.
45*> \endverbatim
46*
47* Arguments:
48* ==========
49*
50*> \param[in] UPLO
51*> \verbatim
52*> UPLO is CHARACTER*1
53*> \endverbatim
54*>
55*> \param[in] WANTZ
56*> \verbatim
57*> WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
58*> Eigenvalue/Eigenvectors.
59*> \endverbatim
60*>
61*> \param[in] TTYPE
62*> \verbatim
63*> TTYPE is INTEGER
64*> \endverbatim
65*>
66*> \param[in] ST
67*> \verbatim
68*> ST is INTEGER
69*> internal parameter for indices.
70*> \endverbatim
71*>
72*> \param[in] ED
73*> \verbatim
74*> ED is INTEGER
75*> internal parameter for indices.
76*> \endverbatim
77*>
78*> \param[in] SWEEP
79*> \verbatim
80*> SWEEP is INTEGER
81*> internal parameter for indices.
82*> \endverbatim
83*>
84*> \param[in] N
85*> \verbatim
86*> N is INTEGER. The order of the matrix A.
87*> \endverbatim
88*>
89*> \param[in] NB
90*> \verbatim
91*> NB is INTEGER. The size of the band.
92*> \endverbatim
93*>
94*> \param[in] IB
95*> \verbatim
96*> IB is INTEGER.
97*> \endverbatim
98*>
99*> \param[in, out] A
100*> \verbatim
101*> A is COMPLEX*16 array. A pointer to the matrix A.
102*> \endverbatim
103*>
104*> \param[in] LDA
105*> \verbatim
106*> LDA is INTEGER. The leading dimension of the matrix A.
107*> \endverbatim
108*>
109*> \param[out] V
110*> \verbatim
111*> V is COMPLEX*16 array, dimension 2*n if eigenvalues only are
112*> requested or to be queried for vectors.
113*> \endverbatim
114*>
115*> \param[out] TAU
116*> \verbatim
117*> TAU is COMPLEX*16 array, dimension (2*n).
118*> The scalar factors of the Householder reflectors are stored
119*> in this array.
120*> \endverbatim
121*>
122*> \param[in] LDVT
123*> \verbatim
124*> LDVT is INTEGER.
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*> WORK is COMPLEX*16 array. Workspace of size nb.
130*> \endverbatim
131*>
132*> \par Further Details:
133* =====================
134*>
135*> \verbatim
136*>
137*> Implemented by Azzam Haidar.
138*>
139*> All details are available on technical report, SC11, SC13 papers.
140*>
141*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
142*> Parallel reduction to condensed forms for symmetric eigenvalue problems
143*> using aggregated fine-grained and memory-aware kernels. In Proceedings
144*> of 2011 International Conference for High Performance Computing,
145*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
146*> Article 8 , 11 pages.
147*> http://doi.acm.org/10.1145/2063384.2063394
148*>
149*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
150*> An improved parallel singular value algorithm and its implementation
151*> for multicore hardware, In Proceedings of 2013 International Conference
152*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
153*> Denver, Colorado, USA, 2013.
154*> Article 90, 12 pages.
155*> http://doi.acm.org/10.1145/2503210.2503292
156*>
157*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
158*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
159*> calculations based on fine-grained memory aware tasks.
160*> International Journal of High Performance Computing Applications.
161*> Volume 28 Issue 2, Pages 196-209, May 2014.
162*> http://hpc.sagepub.com/content/28/2/196
163*>
164*> \endverbatim
165*>
166* =====================================================================
167 SUBROUTINE zhb2st_kernels( UPLO, WANTZ, TTYPE,
168 $ ST, ED, SWEEP, N, NB, IB,
169 $ A, LDA, V, TAU, LDVT, WORK)
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 COMPLEX*16 A( LDA, * ), V( * ),
184 $ TAU( * ), WORK( * )
185* ..
186*
187* =====================================================================
188*
189* .. Parameters ..
190 COMPLEX*16 ZERO, ONE
191 PARAMETER ( ZERO = ( 0.0d+0, 0.0d+0 ),
192 $ one = ( 1.0d+0, 0.0d+0 ) )
193* ..
194* .. Local Scalars ..
195 LOGICAL UPPER
196 INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS,
197 $ dpos, ofdpos, ajeter
198 COMPLEX*16 CTMP
199* ..
200* .. External Subroutines ..
201 EXTERNAL zlarfg, zlarfx, zlarfy
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC dconjg, 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 ) = dconjg( a( ofdpos-i, st+i ) )
242 a( ofdpos-i, st+i ) = zero
243 10 CONTINUE
244 ctmp = dconjg( a( ofdpos, st ) )
245 CALL zlarfg( lm, ctmp, v( vpos+1 ), 1,
246 $ tau( taupos ) )
247 a( ofdpos, st ) = ctmp
248*
249 lm = ed - st + 1
250 CALL zlarfy( uplo, lm, v( vpos ), 1,
251 $ dconjg( 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 zlarfy( uplo, lm, v( vpos ), 1,
259 $ dconjg( 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 zlarfx( 'Left', ln, lm, v( vpos ),
270 $ dconjg( 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 $ dconjg( a( dpos-nb-i, j1+i ) )
285 a( dpos-nb-i, j1+i ) = zero
286 30 CONTINUE
287 ctmp = dconjg( a( dpos-nb, j1 ) )
288 CALL zlarfg( lm, ctmp, v( vpos+1 ), 1, tau( taupos ) )
289 a( dpos-nb, j1 ) = ctmp
290*
291 CALL zlarfx( 'Right', ln-1, lm, v( vpos ),
292 $ tau( taupos ),
293 $ a( dpos-nb+1, j1 ), lda-1, work)
294 ENDIF
295 ENDIF
296*
297* Lower case
298*
299 ELSE
300*
301 IF( wantz ) THEN
302 vpos = mod( sweep-1, 2 ) * n + st
303 taupos = mod( sweep-1, 2 ) * n + st
304 ELSE
305 vpos = mod( sweep-1, 2 ) * n + st
306 taupos = mod( sweep-1, 2 ) * n + st
307 ENDIF
308*
309 IF( ttype.EQ.1 ) THEN
310 lm = ed - st + 1
311*
312 v( vpos ) = one
313 DO 20 i = 1, lm-1
314 v( vpos+i ) = a( ofdpos+i, st-1 )
315 a( ofdpos+i, st-1 ) = zero
316 20 CONTINUE
317 CALL zlarfg( lm, a( ofdpos, st-1 ), v( vpos+1 ), 1,
318 $ tau( taupos ) )
319*
320 lm = ed - st + 1
321*
322 CALL zlarfy( uplo, lm, v( vpos ), 1,
323 $ dconjg( tau( taupos ) ),
324 $ a( dpos, st ), lda-1, work)
325
326 ENDIF
327*
328 IF( ttype.EQ.3 ) THEN
329 lm = ed - st + 1
330*
331 CALL zlarfy( uplo, lm, v( vpos ), 1,
332 $ dconjg( tau( taupos ) ),
333 $ a( dpos, st ), lda-1, work)
334
335 ENDIF
336*
337 IF( ttype.EQ.2 ) THEN
338 j1 = ed+1
339 j2 = min( ed+nb, n )
340 ln = ed-st+1
341 lm = j2-j1+1
342*
343 IF( lm.GT.0) THEN
344 CALL zlarfx( 'Right', lm, ln, v( vpos ),
345 $ tau( taupos ), a( dpos+nb, st ),
346 $ lda-1, work)
347*
348 IF( wantz ) THEN
349 vpos = mod( sweep-1, 2 ) * n + j1
350 taupos = mod( sweep-1, 2 ) * n + j1
351 ELSE
352 vpos = mod( sweep-1, 2 ) * n + j1
353 taupos = mod( sweep-1, 2 ) * n + j1
354 ENDIF
355*
356 v( vpos ) = one
357 DO 40 i = 1, lm-1
358 v( vpos+i ) = a( dpos+nb+i, st )
359 a( dpos+nb+i, st ) = zero
360 40 CONTINUE
361 CALL zlarfg( lm, a( dpos+nb, st ), v( vpos+1 ), 1,
362 $ tau( taupos ) )
363*
364 CALL zlarfx( 'Left', lm, ln-1, v( vpos ),
365 $ dconjg( tau( taupos ) ),
366 $ a( dpos+nb-1, st+1 ), lda-1, work)
367
368 ENDIF
369 ENDIF
370 ENDIF
371*
372 RETURN
373*
374* End of ZHB2ST_KERNELS
375*
376 END
zlarfy
subroutine zlarfy(uplo, n, v, incv, tau, c, ldc, work)
ZLARFY
Definition zlarfy.f:108
zlarfg
subroutine zlarfg(n, alpha, x, incx, tau)
ZLARFG generates an elementary reflector (Householder matrix).
Definition zlarfg.f:106
zlarfx
subroutine zlarfx(side, m, n, v, tau, c, ldc, work)
ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the ...
Definition zlarfx.f:119
min
#define min(a, b)
Definition macros.h:20
zhb2st_kernels
subroutine zhb2st_kernels(uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)
ZHB2ST_KERNELS
Definition zhb2st_kernels.f:170