LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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ssb2st_kernels.f
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1*> \brief \b SSB2ST_KERNELS
2*
3* @generated from zhb2st_kernels.f, fortran z -> s, Wed Dec 7 08:22:40 2016
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download SSB2ST_KERNELS + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssb2st_kernels.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssb2st_kernels.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssb2st_kernels.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE SSB2ST_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* REAL A( LDA, * ), V( * ),
36* TAU( * ), WORK( * )
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> SSB2ST_KERNELS is an internal routine used by the SSYTRD_SB2ST
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 REAL 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 REAL 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 REAL 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 REAL array. Workspace of size nb.
130*> \endverbatim
131*>
132*>
133*> \par Further Details:
134* =====================
135*>
136*> \verbatim
137*>
138*> Implemented by Azzam Haidar.
139*>
140*> All details are available on technical report, SC11, SC13 papers.
141*>
142*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
143*> Parallel reduction to condensed forms for symmetric eigenvalue problems
144*> using aggregated fine-grained and memory-aware kernels. In Proceedings
145*> of 2011 International Conference for High Performance Computing,
146*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
147*> Article 8 , 11 pages.
148*> http://doi.acm.org/10.1145/2063384.2063394
149*>
150*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
151*> An improved parallel singular value algorithm and its implementation
152*> for multicore hardware, In Proceedings of 2013 International Conference
153*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
154*> Denver, Colorado, USA, 2013.
155*> Article 90, 12 pages.
156*> http://doi.acm.org/10.1145/2503210.2503292
157*>
158*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
159*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
160*> calculations based on fine-grained memory aware tasks.
161*> International Journal of High Performance Computing Applications.
162*> Volume 28 Issue 2, Pages 196-209, May 2014.
163*> http://hpc.sagepub.com/content/28/2/196
164*>
165*> \endverbatim
166*>
167* =====================================================================
168 SUBROUTINE ssb2st_kernels( UPLO, WANTZ, TTYPE,
169 $ ST, ED, SWEEP, N, NB, IB,
170 $ A, LDA, V, TAU, LDVT, WORK)
171*
172 IMPLICIT NONE
173*
174* -- LAPACK computational routine --
175* -- LAPACK is a software package provided by Univ. of Tennessee, --
176* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177*
178* .. Scalar Arguments ..
179 CHARACTER UPLO
180 LOGICAL WANTZ
181 INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
182* ..
183* .. Array Arguments ..
184 REAL A( LDA, * ), V( * ),
185 $ TAU( * ), WORK( * )
186* ..
187*
188* =====================================================================
189*
190* .. Parameters ..
191 REAL ZERO, ONE
192 PARAMETER ( ZERO = 0.0e+0,
193 $ one = 1.0e+0 )
194* ..
195* .. Local Scalars ..
196 LOGICAL UPPER
197 INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS,
198 $ dpos, ofdpos, ajeter
199 REAL CTMP
200* ..
201* .. External Subroutines ..
202 EXTERNAL slarfg, slarfx, slarfy
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC mod
206* .. External Functions ..
207 LOGICAL LSAME
208 EXTERNAL LSAME
209* ..
210* ..
211* .. Executable Statements ..
212*
213 ajeter = ib + ldvt
214 upper = lsame( uplo, 'U' )
215
216 IF( upper ) THEN
217 dpos = 2 * nb + 1
218 ofdpos = 2 * nb
219 ELSE
220 dpos = 1
221 ofdpos = 2
222 ENDIF
223
224*
225* Upper case
226*
227 IF( upper ) THEN
228*
229 IF( wantz ) THEN
230 vpos = mod( sweep-1, 2 ) * n + st
231 taupos = mod( sweep-1, 2 ) * n + st
232 ELSE
233 vpos = mod( sweep-1, 2 ) * n + st
234 taupos = mod( sweep-1, 2 ) * n + st
235 ENDIF
236*
237 IF( ttype.EQ.1 ) THEN
238 lm = ed - st + 1
239*
240 v( vpos ) = one
241 DO 10 i = 1, lm-1
242 v( vpos+i ) = ( a( ofdpos-i, st+i ) )
243 a( ofdpos-i, st+i ) = zero
244 10 CONTINUE
245 ctmp = ( a( ofdpos, st ) )
246 CALL slarfg( lm, ctmp, v( vpos+1 ), 1,
247 $ tau( taupos ) )
248 a( ofdpos, st ) = ctmp
249*
250 lm = ed - st + 1
251 CALL slarfy( uplo, lm, v( vpos ), 1,
252 $ ( tau( taupos ) ),
253 $ a( dpos, st ), lda-1, work)
254 ENDIF
255*
256 IF( ttype.EQ.3 ) THEN
257*
258 lm = ed - st + 1
259 CALL slarfy( uplo, lm, v( vpos ), 1,
260 $ ( tau( taupos ) ),
261 $ a( dpos, st ), lda-1, work)
262 ENDIF
263*
264 IF( ttype.EQ.2 ) THEN
265 j1 = ed+1
266 j2 = min( ed+nb, n )
267 ln = ed-st+1
268 lm = j2-j1+1
269 IF( lm.GT.0) THEN
270 CALL slarfx( 'Left', ln, lm, v( vpos ),
271 $ ( tau( taupos ) ),
272 $ a( dpos-nb, j1 ), lda-1, work)
273*
274 IF( wantz ) THEN
275 vpos = mod( sweep-1, 2 ) * n + j1
276 taupos = mod( sweep-1, 2 ) * n + j1
277 ELSE
278 vpos = mod( sweep-1, 2 ) * n + j1
279 taupos = mod( sweep-1, 2 ) * n + j1
280 ENDIF
281*
282 v( vpos ) = one
283 DO 30 i = 1, lm-1
284 v( vpos+i ) =
285 $ ( a( dpos-nb-i, j1+i ) )
286 a( dpos-nb-i, j1+i ) = zero
287 30 CONTINUE
288 ctmp = ( a( dpos-nb, j1 ) )
289 CALL slarfg( lm, ctmp, v( vpos+1 ), 1, tau( taupos ) )
290 a( dpos-nb, j1 ) = ctmp
291*
292 CALL slarfx( '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 slarfg( lm, a( ofdpos, st-1 ), v( vpos+1 ), 1,
319 $ tau( taupos ) )
320*
321 lm = ed - st + 1
322*
323 CALL slarfy( 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 slarfy( 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 slarfx( '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 slarfg( lm, a( dpos+nb, st ), v( vpos+1 ), 1,
363 $ tau( taupos ) )
364*
365 CALL slarfx( '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 SSB2ST_KERNELS
376*
377 END
slarfx
subroutine slarfx(SIDE, M, N, V, TAU, C, LDC, WORK)
SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the ...
Definition: slarfx.f:120
slarfg
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
slarfy
subroutine slarfy(UPLO, N, V, INCV, TAU, C, LDC, WORK)
SLARFY
Definition: slarfy.f:108
ssb2st_kernels
subroutine ssb2st_kernels(UPLO, WANTZ, TTYPE, ST, ED, SWEEP, N, NB, IB, A, LDA, V, TAU, LDVT, WORK)
SSB2ST_KERNELS
Definition: ssb2st_kernels.f:171