LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ssbev_2stage.f
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1 *> \brief <b> SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2 *
3 * @generated from dsbev_2stage.f, fortran d -> s, Sat Nov 5 23:58:09 2016
4 *
5 * =========== DOCUMENTATION ===========
6 *
7 * Online html documentation available at
8 * http://www.netlib.org/lapack/explore-html/
9 *
10 *> \htmlonly
11 *> Download SSBEV_2STAGE + dependencies
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13 *> [TGZ]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssbev_2stage.f">
15 *> [ZIP]</a>
16 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssbev_2stage.f">
17 *> [TXT]</a>
18 *> \endhtmlonly
19 *
20 * Definition:
21 * ===========
22 *
23 * SUBROUTINE SSBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
24 * WORK, LWORK, INFO )
25 *
26 * IMPLICIT NONE
27 *
28 * .. Scalar Arguments ..
29 * CHARACTER JOBZ, UPLO
30 * INTEGER INFO, KD, LDAB, LDZ, N, LWORK
31 * ..
32 * .. Array Arguments ..
33 * REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
34 * ..
35 *
36 *
37 *> \par Purpose:
38 * =============
39 *>
40 *> \verbatim
41 *>
42 *> SSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
43 *> a real symmetric band matrix A using the 2stage technique for
44 *> the reduction to tridiagonal.
45 *> \endverbatim
46 *
47 * Arguments:
48 * ==========
49 *
50 *> \param[in] JOBZ
51 *> \verbatim
52 *> JOBZ is CHARACTER*1
53 *> = 'N': Compute eigenvalues only;
54 *> = 'V': Compute eigenvalues and eigenvectors.
55 *> Not available in this release.
56 *> \endverbatim
57 *>
58 *> \param[in] UPLO
59 *> \verbatim
60 *> UPLO is CHARACTER*1
61 *> = 'U': Upper triangle of A is stored;
62 *> = 'L': Lower triangle of A is stored.
63 *> \endverbatim
64 *>
65 *> \param[in] N
66 *> \verbatim
67 *> N is INTEGER
68 *> The order of the matrix A. N >= 0.
69 *> \endverbatim
70 *>
71 *> \param[in] KD
72 *> \verbatim
73 *> KD is INTEGER
74 *> The number of superdiagonals of the matrix A if UPLO = 'U',
75 *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
76 *> \endverbatim
77 *>
78 *> \param[in,out] AB
79 *> \verbatim
80 *> AB is REAL array, dimension (LDAB, N)
81 *> On entry, the upper or lower triangle of the symmetric band
82 *> matrix A, stored in the first KD+1 rows of the array. The
83 *> j-th column of A is stored in the j-th column of the array AB
84 *> as follows:
85 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
86 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
87 *>
88 *> On exit, AB is overwritten by values generated during the
89 *> reduction to tridiagonal form. If UPLO = 'U', the first
90 *> superdiagonal and the diagonal of the tridiagonal matrix T
91 *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
92 *> the diagonal and first subdiagonal of T are returned in the
93 *> first two rows of AB.
94 *> \endverbatim
95 *>
96 *> \param[in] LDAB
97 *> \verbatim
98 *> LDAB is INTEGER
99 *> The leading dimension of the array AB. LDAB >= KD + 1.
100 *> \endverbatim
101 *>
102 *> \param[out] W
103 *> \verbatim
104 *> W is REAL array, dimension (N)
105 *> If INFO = 0, the eigenvalues in ascending order.
106 *> \endverbatim
107 *>
108 *> \param[out] Z
109 *> \verbatim
110 *> Z is REAL array, dimension (LDZ, N)
111 *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
112 *> eigenvectors of the matrix A, with the i-th column of Z
113 *> holding the eigenvector associated with W(i).
114 *> If JOBZ = 'N', then Z is not referenced.
115 *> \endverbatim
116 *>
117 *> \param[in] LDZ
118 *> \verbatim
119 *> LDZ is INTEGER
120 *> The leading dimension of the array Z. LDZ >= 1, and if
121 *> JOBZ = 'V', LDZ >= max(1,N).
122 *> \endverbatim
123 *>
124 *> \param[out] WORK
125 *> \verbatim
126 *> WORK is REAL array, dimension LWORK
127 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
128 *> \endverbatim
129 *>
130 *> \param[in] LWORK
131 *> \verbatim
132 *> LWORK is INTEGER
133 *> The length of the array WORK. LWORK >= 1, when N <= 1;
134 *> otherwise
135 *> If JOBZ = 'N' and N > 1, LWORK must be queried.
136 *> LWORK = MAX(1, dimension) where
137 *> dimension = (2KD+1)*N + KD*NTHREADS + N
138 *> where KD is the size of the band.
139 *> NTHREADS is the number of threads used when
140 *> openMP compilation is enabled, otherwise =1.
141 *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
142 *>
143 *> If LWORK = -1, then a workspace query is assumed; the routine
144 *> only calculates the optimal size of the WORK array, returns
145 *> this value as the first entry of the WORK array, and no error
146 *> message related to LWORK is issued by XERBLA.
147 *> \endverbatim
148 *>
149 *> \param[out] INFO
150 *> \verbatim
151 *> INFO is INTEGER
152 *> = 0: successful exit
153 *> < 0: if INFO = -i, the i-th argument had an illegal value
154 *> > 0: if INFO = i, the algorithm failed to converge; i
155 *> off-diagonal elements of an intermediate tridiagonal
156 *> form did not converge to zero.
157 *> \endverbatim
158 *
159 * Authors:
160 * ========
161 *
162 *> \author Univ. of Tennessee
163 *> \author Univ. of California Berkeley
164 *> \author Univ. of Colorado Denver
165 *> \author NAG Ltd.
166 *
167 *> \ingroup realOTHEReigen
168 *
169 *> \par Further Details:
170 * =====================
171 *>
172 *> \verbatim
173 *>
174 *> All details about the 2stage techniques are available in:
175 *>
176 *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
177 *> Parallel reduction to condensed forms for symmetric eigenvalue problems
178 *> using aggregated fine-grained and memory-aware kernels. In Proceedings
179 *> of 2011 International Conference for High Performance Computing,
180 *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
181 *> Article 8 , 11 pages.
182 *> http://doi.acm.org/10.1145/2063384.2063394
183 *>
184 *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
185 *> An improved parallel singular value algorithm and its implementation
186 *> for multicore hardware, In Proceedings of 2013 International Conference
187 *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
188 *> Denver, Colorado, USA, 2013.
189 *> Article 90, 12 pages.
190 *> http://doi.acm.org/10.1145/2503210.2503292
191 *>
192 *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
193 *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
194 *> calculations based on fine-grained memory aware tasks.
195 *> International Journal of High Performance Computing Applications.
196 *> Volume 28 Issue 2, Pages 196-209, May 2014.
197 *> http://hpc.sagepub.com/content/28/2/196
198 *>
199 *> \endverbatim
200 *
201 * =====================================================================
202  SUBROUTINE ssbev_2stage( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
203  $ WORK, LWORK, INFO )
204 *
205  IMPLICIT NONE
206 *
207 * -- LAPACK driver routine --
208 * -- LAPACK is a software package provided by Univ. of Tennessee, --
209 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
210 *
211 * .. Scalar Arguments ..
212  CHARACTER JOBZ, UPLO
213  INTEGER INFO, KD, LDAB, LDZ, N, LWORK
214 * ..
215 * .. Array Arguments ..
216  REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
217 * ..
218 *
219 * =====================================================================
220 *
221 * .. Parameters ..
222  REAL ZERO, ONE
223  parameter( zero = 0.0e0, one = 1.0e0 )
224 * ..
225 * .. Local Scalars ..
226  LOGICAL LOWER, WANTZ, LQUERY
227  INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE,
228  $ llwork, lwmin, lhtrd, lwtrd, ib, indhous
229  REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
230  $ smlnum
231 * ..
232 * .. External Functions ..
233  LOGICAL LSAME
234  INTEGER ILAENV2STAGE
235  REAL SLAMCH, SLANSB
236  EXTERNAL lsame, slamch, slansb, ilaenv2stage
237 * ..
238 * .. External Subroutines ..
239  EXTERNAL slascl, sscal, ssteqr, ssterf, xerbla,
240  $ ssytrd_sb2st
241 * ..
242 * .. Intrinsic Functions ..
243  INTRINSIC sqrt
244 * ..
245 * .. Executable Statements ..
246 *
247 * Test the input parameters.
248 *
249  wantz = lsame( jobz, 'V' )
250  lower = lsame( uplo, 'L' )
251  lquery = ( lwork.EQ.-1 )
252 *
253  info = 0
254  IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
255  info = -1
256  ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
257  info = -2
258  ELSE IF( n.LT.0 ) THEN
259  info = -3
260  ELSE IF( kd.LT.0 ) THEN
261  info = -4
262  ELSE IF( ldab.LT.kd+1 ) THEN
263  info = -6
264  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
265  info = -9
266  END IF
267 *
268  IF( info.EQ.0 ) THEN
269  IF( n.LE.1 ) THEN
270  lwmin = 1
271  work( 1 ) = lwmin
272  ELSE
273  ib = ilaenv2stage( 2, 'SSYTRD_SB2ST', jobz,
274  $ n, kd, -1, -1 )
275  lhtrd = ilaenv2stage( 3, 'SSYTRD_SB2ST', jobz,
276  $ n, kd, ib, -1 )
277  lwtrd = ilaenv2stage( 4, 'SSYTRD_SB2ST', jobz,
278  $ n, kd, ib, -1 )
279  lwmin = n + lhtrd + lwtrd
280  work( 1 ) = lwmin
281  ENDIF
282 *
283  IF( lwork.LT.lwmin .AND. .NOT.lquery )
284  $ info = -11
285  END IF
286 *
287  IF( info.NE.0 ) THEN
288  CALL xerbla( 'SSBEV_2STAGE ', -info )
289  RETURN
290  ELSE IF( lquery ) THEN
291  RETURN
292  END IF
293 *
294 * Quick return if possible
295 *
296  IF( n.EQ.0 )
297  $ RETURN
298 *
299  IF( n.EQ.1 ) THEN
300  IF( lower ) THEN
301  w( 1 ) = ab( 1, 1 )
302  ELSE
303  w( 1 ) = ab( kd+1, 1 )
304  END IF
305  IF( wantz )
306  $ z( 1, 1 ) = one
307  RETURN
308  END IF
309 *
310 * Get machine constants.
311 *
312  safmin = slamch( 'Safe minimum' )
313  eps = slamch( 'Precision' )
314  smlnum = safmin / eps
315  bignum = one / smlnum
316  rmin = sqrt( smlnum )
317  rmax = sqrt( bignum )
318 *
319 * Scale matrix to allowable range, if necessary.
320 *
321  anrm = slansb( 'M', uplo, n, kd, ab, ldab, work )
322  iscale = 0
323  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
324  iscale = 1
325  sigma = rmin / anrm
326  ELSE IF( anrm.GT.rmax ) THEN
327  iscale = 1
328  sigma = rmax / anrm
329  END IF
330  IF( iscale.EQ.1 ) THEN
331  IF( lower ) THEN
332  CALL slascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
333  ELSE
334  CALL slascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
335  END IF
336  END IF
337 *
338 * Call SSYTRD_SB2ST to reduce symmetric band matrix to tridiagonal form.
339 *
340  inde = 1
341  indhous = inde + n
342  indwrk = indhous + lhtrd
343  llwork = lwork - indwrk + 1
344 *
345  CALL ssytrd_sb2st( "N", jobz, uplo, n, kd, ab, ldab, w,
346  $ work( inde ), work( indhous ), lhtrd,
347  $ work( indwrk ), llwork, iinfo )
348 *
349 * For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR.
350 *
351  IF( .NOT.wantz ) THEN
352  CALL ssterf( n, w, work( inde ), info )
353  ELSE
354  CALL ssteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
355  $ info )
356  END IF
357 *
358 * If matrix was scaled, then rescale eigenvalues appropriately.
359 *
360  IF( iscale.EQ.1 ) THEN
361  IF( info.EQ.0 ) THEN
362  imax = n
363  ELSE
364  imax = info - 1
365  END IF
366  CALL sscal( imax, one / sigma, w, 1 )
367  END IF
368 *
369 * Set WORK(1) to optimal workspace size.
370 *
371  work( 1 ) = lwmin
372 *
373  RETURN
374 *
375 * End of SSBEV_2STAGE
376 *
377  END
subroutine slascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: slascl.f:143
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
SSTEQR
Definition: ssteqr.f:131
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine ssbev_2stage(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, INFO)
SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER m...
Definition: ssbev_2stage.f:204
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine ssytrd_sb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
SSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T
Definition: ssytrd_sb2st.F:230