LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
chbev_2stage.f
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1 *> \brief <b> CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2 *
3 * @generated from zhbev_2stage.f, fortran z -> c, Sat Nov 5 23:18:20 2016
4 *
5 * =========== DOCUMENTATION ===========
6 *
7 * Online html documentation available at
8 * http://www.netlib.org/lapack/explore-html/
9 *
10 *> \htmlonly
11 *> Download CHBEV_2STAGE + dependencies
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13 *> [TGZ]</a>
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15 *> [ZIP]</a>
16 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chbev_2stage.f">
17 *> [TXT]</a>
18 *> \endhtmlonly
19 *
20 * Definition:
21 * ===========
22 *
23 * SUBROUTINE CHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
24 * WORK, LWORK, RWORK, 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 RWORK( * ), W( * )
34 * COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
35 * ..
36 *
37 *
38 *> \par Purpose:
39 * =============
40 *>
41 *> \verbatim
42 *>
43 *> CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
44 *> a complex Hermitian band matrix A using the 2stage technique for
45 *> the reduction to tridiagonal.
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] JOBZ
52 *> \verbatim
53 *> JOBZ is CHARACTER*1
54 *> = 'N': Compute eigenvalues only;
55 *> = 'V': Compute eigenvalues and eigenvectors.
56 *> Not available in this release.
57 *> \endverbatim
58 *>
59 *> \param[in] UPLO
60 *> \verbatim
61 *> UPLO is CHARACTER*1
62 *> = 'U': Upper triangle of A is stored;
63 *> = 'L': Lower triangle of A is stored.
64 *> \endverbatim
65 *>
66 *> \param[in] N
67 *> \verbatim
68 *> N is INTEGER
69 *> The order of the matrix A. N >= 0.
70 *> \endverbatim
71 *>
72 *> \param[in] KD
73 *> \verbatim
74 *> KD is INTEGER
75 *> The number of superdiagonals of the matrix A if UPLO = 'U',
76 *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
77 *> \endverbatim
78 *>
79 *> \param[in,out] AB
80 *> \verbatim
81 *> AB is COMPLEX array, dimension (LDAB, N)
82 *> On entry, the upper or lower triangle of the Hermitian band
83 *> matrix A, stored in the first KD+1 rows of the array. The
84 *> j-th column of A is stored in the j-th column of the array AB
85 *> as follows:
86 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
87 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
88 *>
89 *> On exit, AB is overwritten by values generated during the
90 *> reduction to tridiagonal form. If UPLO = 'U', the first
91 *> superdiagonal and the diagonal of the tridiagonal matrix T
92 *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
93 *> the diagonal and first subdiagonal of T are returned in the
94 *> first two rows of AB.
95 *> \endverbatim
96 *>
97 *> \param[in] LDAB
98 *> \verbatim
99 *> LDAB is INTEGER
100 *> The leading dimension of the array AB. LDAB >= KD + 1.
101 *> \endverbatim
102 *>
103 *> \param[out] W
104 *> \verbatim
105 *> W is REAL array, dimension (N)
106 *> If INFO = 0, the eigenvalues in ascending order.
107 *> \endverbatim
108 *>
109 *> \param[out] Z
110 *> \verbatim
111 *> Z is COMPLEX array, dimension (LDZ, N)
112 *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
113 *> eigenvectors of the matrix A, with the i-th column of Z
114 *> holding the eigenvector associated with W(i).
115 *> If JOBZ = 'N', then Z is not referenced.
116 *> \endverbatim
117 *>
118 *> \param[in] LDZ
119 *> \verbatim
120 *> LDZ is INTEGER
121 *> The leading dimension of the array Z. LDZ >= 1, and if
122 *> JOBZ = 'V', LDZ >= max(1,N).
123 *> \endverbatim
124 *>
125 *> \param[out] WORK
126 *> \verbatim
127 *> WORK is COMPLEX array, dimension LWORK
128 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
129 *> \endverbatim
130 *>
131 *> \param[in] LWORK
132 *> \verbatim
133 *> LWORK is INTEGER
134 *> The length of the array WORK. LWORK >= 1, when N <= 1;
135 *> otherwise
136 *> If JOBZ = 'N' and N > 1, LWORK must be queried.
137 *> LWORK = MAX(1, dimension) where
138 *> dimension = (2KD+1)*N + KD*NTHREADS
139 *> where KD is the size of the band.
140 *> NTHREADS is the number of threads used when
141 *> openMP compilation is enabled, otherwise =1.
142 *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
143 *>
144 *> If LWORK = -1, then a workspace query is assumed; the routine
145 *> only calculates the optimal sizes of the WORK, RWORK and
146 *> IWORK arrays, returns these values as the first entries of
147 *> the WORK, RWORK and IWORK arrays, and no error message
148 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
149 *> \endverbatim
150 *>
151 *> \param[out] RWORK
152 *> \verbatim
153 *> RWORK is REAL array, dimension (max(1,3*N-2))
154 *> \endverbatim
155 *>
156 *> \param[out] INFO
157 *> \verbatim
158 *> INFO is INTEGER
159 *> = 0: successful exit.
160 *> < 0: if INFO = -i, the i-th argument had an illegal value.
161 *> > 0: if INFO = i, the algorithm failed to converge; i
162 *> off-diagonal elements of an intermediate tridiagonal
163 *> form did not converge to zero.
164 *> \endverbatim
165 *
166 * Authors:
167 * ========
168 *
169 *> \author Univ. of Tennessee
170 *> \author Univ. of California Berkeley
171 *> \author Univ. of Colorado Denver
172 *> \author NAG Ltd.
173 *
174 *> \ingroup complexOTHEReigen
175 *
176 *> \par Further Details:
177 * =====================
178 *>
179 *> \verbatim
180 *>
181 *> All details about the 2stage techniques are available in:
182 *>
183 *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
184 *> Parallel reduction to condensed forms for symmetric eigenvalue problems
185 *> using aggregated fine-grained and memory-aware kernels. In Proceedings
186 *> of 2011 International Conference for High Performance Computing,
187 *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
188 *> Article 8 , 11 pages.
189 *> http://doi.acm.org/10.1145/2063384.2063394
190 *>
191 *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
192 *> An improved parallel singular value algorithm and its implementation
193 *> for multicore hardware, In Proceedings of 2013 International Conference
194 *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
195 *> Denver, Colorado, USA, 2013.
196 *> Article 90, 12 pages.
197 *> http://doi.acm.org/10.1145/2503210.2503292
198 *>
199 *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
200 *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
201 *> calculations based on fine-grained memory aware tasks.
202 *> International Journal of High Performance Computing Applications.
203 *> Volume 28 Issue 2, Pages 196-209, May 2014.
204 *> http://hpc.sagepub.com/content/28/2/196
205 *>
206 *> \endverbatim
207 *
208 * =====================================================================
209  SUBROUTINE chbev_2stage( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
210  $ WORK, LWORK, RWORK, INFO )
211 *
212  IMPLICIT NONE
213 *
214 * -- LAPACK driver routine --
215 * -- LAPACK is a software package provided by Univ. of Tennessee, --
216 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
217 *
218 * .. Scalar Arguments ..
219  CHARACTER JOBZ, UPLO
220  INTEGER INFO, KD, LDAB, LDZ, N, LWORK
221 * ..
222 * .. Array Arguments ..
223  REAL RWORK( * ), W( * )
224  COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
225 * ..
226 *
227 * =====================================================================
228 *
229 * .. Parameters ..
230  REAL ZERO, ONE
231  parameter( zero = 0.0e0, one = 1.0e0 )
232 * ..
233 * .. Local Scalars ..
234  LOGICAL LOWER, WANTZ, LQUERY
235  INTEGER IINFO, IMAX, INDE, INDWRK, INDRWK, ISCALE,
236  $ llwork, lwmin, lhtrd, lwtrd, ib, indhous
237  REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
238  $ smlnum
239 * ..
240 * .. External Functions ..
241  LOGICAL LSAME
242  INTEGER ILAENV2STAGE
243  REAL SLAMCH, CLANHB
244  EXTERNAL lsame, slamch, clanhb, ilaenv2stage
245 * ..
246 * .. External Subroutines ..
247  EXTERNAL sscal, ssterf, xerbla, clascl, csteqr,
249 * ..
250 * .. Intrinsic Functions ..
251  INTRINSIC real, sqrt
252 * ..
253 * .. Executable Statements ..
254 *
255 * Test the input parameters.
256 *
257  wantz = lsame( jobz, 'V' )
258  lower = lsame( uplo, 'L' )
259  lquery = ( lwork.EQ.-1 )
260 *
261  info = 0
262  IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
263  info = -1
264  ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
265  info = -2
266  ELSE IF( n.LT.0 ) THEN
267  info = -3
268  ELSE IF( kd.LT.0 ) THEN
269  info = -4
270  ELSE IF( ldab.LT.kd+1 ) THEN
271  info = -6
272  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
273  info = -9
274  END IF
275 *
276  IF( info.EQ.0 ) THEN
277  IF( n.LE.1 ) THEN
278  lwmin = 1
279  work( 1 ) = lwmin
280  ELSE
281  ib = ilaenv2stage( 2, 'CHETRD_HB2ST', jobz,
282  $ n, kd, -1, -1 )
283  lhtrd = ilaenv2stage( 3, 'CHETRD_HB2ST', jobz,
284  $ n, kd, ib, -1 )
285  lwtrd = ilaenv2stage( 4, 'CHETRD_HB2ST', jobz,
286  $ n, kd, ib, -1 )
287  lwmin = lhtrd + lwtrd
288  work( 1 ) = lwmin
289  ENDIF
290 *
291  IF( lwork.LT.lwmin .AND. .NOT.lquery )
292  $ info = -11
293  END IF
294 *
295  IF( info.NE.0 ) THEN
296  CALL xerbla( 'CHBEV_2STAGE ', -info )
297  RETURN
298  ELSE IF( lquery ) THEN
299  RETURN
300  END IF
301 *
302 * Quick return if possible
303 *
304  IF( n.EQ.0 )
305  $ RETURN
306 *
307  IF( n.EQ.1 ) THEN
308  IF( lower ) THEN
309  w( 1 ) = real( ab( 1, 1 ) )
310  ELSE
311  w( 1 ) = real( ab( kd+1, 1 ) )
312  END IF
313  IF( wantz )
314  $ z( 1, 1 ) = one
315  RETURN
316  END IF
317 *
318 * Get machine constants.
319 *
320  safmin = slamch( 'Safe minimum' )
321  eps = slamch( 'Precision' )
322  smlnum = safmin / eps
323  bignum = one / smlnum
324  rmin = sqrt( smlnum )
325  rmax = sqrt( bignum )
326 *
327 * Scale matrix to allowable range, if necessary.
328 *
329  anrm = clanhb( 'M', uplo, n, kd, ab, ldab, rwork )
330  iscale = 0
331  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
332  iscale = 1
333  sigma = rmin / anrm
334  ELSE IF( anrm.GT.rmax ) THEN
335  iscale = 1
336  sigma = rmax / anrm
337  END IF
338  IF( iscale.EQ.1 ) THEN
339  IF( lower ) THEN
340  CALL clascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
341  ELSE
342  CALL clascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
343  END IF
344  END IF
345 *
346 * Call CHBTRD_HB2ST to reduce Hermitian band matrix to tridiagonal form.
347 *
348  inde = 1
349  indhous = 1
350  indwrk = indhous + lhtrd
351  llwork = lwork - indwrk + 1
352 *
353  CALL chetrd_hb2st( "N", jobz, uplo, n, kd, ab, ldab, w,
354  $ rwork( inde ), work( indhous ), lhtrd,
355  $ work( indwrk ), llwork, iinfo )
356 *
357 * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR.
358 *
359  IF( .NOT.wantz ) THEN
360  CALL ssterf( n, w, rwork( inde ), info )
361  ELSE
362  indrwk = inde + n
363  CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
364  $ rwork( indrwk ), info )
365  END IF
366 *
367 * If matrix was scaled, then rescale eigenvalues appropriately.
368 *
369  IF( iscale.EQ.1 ) THEN
370  IF( info.EQ.0 ) THEN
371  imax = n
372  ELSE
373  imax = info - 1
374  END IF
375  CALL sscal( imax, one / sigma, w, 1 )
376  END IF
377 *
378 * Set WORK(1) to optimal workspace size.
379 *
380  work( 1 ) = lwmin
381 *
382  RETURN
383 *
384 * End of CHBEV_2STAGE
385 *
386  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine chetrd_2stage(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO)
CHETRD_2STAGE
subroutine clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:143
subroutine chetrd_hb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T
Definition: chetrd_hb2st.F:230
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
subroutine chbev_2stage(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, INFO)
CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER m...
Definition: chbev_2stage.f:211
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79