Annotation of rpl/lapack/lapack/dsyev_2stage.f, revision 1.2
1.1 bertrand 1: *> \brief <b> DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
2: *
3: * @precisions fortran d -> s
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download DSYEV_2STAGE + dependencies
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevd_2stage.f">
13: *> [TGZ]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevd_2stage.f">
15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevd_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
24: * INFO )
25: *
26: * IMPLICIT NONE
27: *
28: * .. Scalar Arguments ..
29: * CHARACTER JOBZ, UPLO
30: * INTEGER INFO, LDA, LWORK, N
31: * ..
32: * .. Array Arguments ..
33: * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> DSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
43: *> real symmetric 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,out] A
72: *> \verbatim
73: *> A is DOUBLE PRECISION array, dimension (LDA, N)
74: *> On entry, the symmetric matrix A. If UPLO = 'U', the
75: *> leading N-by-N upper triangular part of A contains the
76: *> upper triangular part of the matrix A. If UPLO = 'L',
77: *> the leading N-by-N lower triangular part of A contains
78: *> the lower triangular part of the matrix A.
79: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
80: *> orthonormal eigenvectors of the matrix A.
81: *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
82: *> or the upper triangle (if UPLO='U') of A, including the
83: *> diagonal, is destroyed.
84: *> \endverbatim
85: *>
86: *> \param[in] LDA
87: *> \verbatim
88: *> LDA is INTEGER
89: *> The leading dimension of the array A. LDA >= max(1,N).
90: *> \endverbatim
91: *>
92: *> \param[out] W
93: *> \verbatim
94: *> W is DOUBLE PRECISION array, dimension (N)
95: *> If INFO = 0, the eigenvalues in ascending order.
96: *> \endverbatim
97: *>
98: *> \param[out] WORK
99: *> \verbatim
100: *> WORK is DOUBLE PRECISION array, dimension LWORK
101: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
102: *> \endverbatim
103: *>
104: *> \param[in] LWORK
105: *> \verbatim
106: *> LWORK is INTEGER
107: *> The length of the array WORK. LWORK >= 1, when N <= 1;
108: *> otherwise
109: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
110: *> LWORK = MAX(1, dimension) where
111: *> dimension = max(stage1,stage2) + (KD+1)*N + 2*N
112: *> = N*KD + N*max(KD+1,FACTOPTNB)
113: *> + max(2*KD*KD, KD*NTHREADS)
114: *> + (KD+1)*N + 2*N
115: *> where KD is the blocking size of the reduction,
116: *> FACTOPTNB is the blocking used by the QR or LQ
117: *> algorithm, usually FACTOPTNB=128 is a good choice
118: *> NTHREADS is the number of threads used when
119: *> openMP compilation is enabled, otherwise =1.
120: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
121: *>
122: *> If LWORK = -1, then a workspace query is assumed; the routine
123: *> only calculates the optimal size of the WORK array, returns
124: *> this value as the first entry of the WORK array, and no error
125: *> message related to LWORK is issued by XERBLA.
126: *> \endverbatim
127: *>
128: *> \param[out] INFO
129: *> \verbatim
130: *> INFO is INTEGER
131: *> = 0: successful exit
132: *> < 0: if INFO = -i, the i-th argument had an illegal value
133: *> > 0: if INFO = i, the algorithm failed to converge; i
134: *> off-diagonal elements of an intermediate tridiagonal
135: *> form did not converge to zero.
136: *> \endverbatim
137: *
138: * Authors:
139: * ========
140: *
141: *> \author Univ. of Tennessee
142: *> \author Univ. of California Berkeley
143: *> \author Univ. of Colorado Denver
144: *> \author NAG Ltd.
145: *
146: *> \date December 2016
147: *
148: *> \ingroup doubleSYeigen
149: *
150: *> \par Further Details:
151: * =====================
152: *>
153: *> \verbatim
154: *>
155: *> All details about the 2stage techniques are available in:
156: *>
157: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
158: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
159: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
160: *> of 2011 International Conference for High Performance Computing,
161: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
162: *> Article 8 , 11 pages.
163: *> http://doi.acm.org/10.1145/2063384.2063394
164: *>
165: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
166: *> An improved parallel singular value algorithm and its implementation
167: *> for multicore hardware, In Proceedings of 2013 International Conference
168: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
169: *> Denver, Colorado, USA, 2013.
170: *> Article 90, 12 pages.
171: *> http://doi.acm.org/10.1145/2503210.2503292
172: *>
173: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
174: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
175: *> calculations based on fine-grained memory aware tasks.
176: *> International Journal of High Performance Computing Applications.
177: *> Volume 28 Issue 2, Pages 196-209, May 2014.
178: *> http://hpc.sagepub.com/content/28/2/196
179: *>
180: *> \endverbatim
181: *
182: * =====================================================================
183: SUBROUTINE DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
184: $ INFO )
185: *
186: IMPLICIT NONE
187: *
188: * -- LAPACK driver routine (version 3.7.0) --
189: * -- LAPACK is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191: * December 2016
192: *
193: * .. Scalar Arguments ..
194: CHARACTER JOBZ, UPLO
195: INTEGER INFO, LDA, LWORK, N
196: * ..
197: * .. Array Arguments ..
198: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
199: * ..
200: *
201: * =====================================================================
202: *
203: * .. Parameters ..
204: DOUBLE PRECISION ZERO, ONE
205: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
206: * ..
207: * .. Local Scalars ..
208: LOGICAL LOWER, LQUERY, WANTZ
209: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
210: $ LLWORK, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
211: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
212: $ SMLNUM
213: * ..
214: * .. External Functions ..
215: LOGICAL LSAME
216: INTEGER ILAENV
217: DOUBLE PRECISION DLAMCH, DLANSY
218: EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY
219: * ..
220: * .. External Subroutines ..
221: EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF,
222: $ XERBLA, DSYTRD_2STAGE
223: * ..
224: * .. Intrinsic Functions ..
225: INTRINSIC MAX, SQRT
226: * ..
227: * .. Executable Statements ..
228: *
229: * Test the input parameters.
230: *
231: WANTZ = LSAME( JOBZ, 'V' )
232: LOWER = LSAME( UPLO, 'L' )
233: LQUERY = ( LWORK.EQ.-1 )
234: *
235: INFO = 0
236: IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
237: INFO = -1
238: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
239: INFO = -2
240: ELSE IF( N.LT.0 ) THEN
241: INFO = -3
242: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
243: INFO = -5
244: END IF
245: *
246: IF( INFO.EQ.0 ) THEN
247: KD = ILAENV( 17, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 )
248: IB = ILAENV( 18, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
249: LHTRD = ILAENV( 19, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
250: LWTRD = ILAENV( 20, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
251: LWMIN = 2*N + LHTRD + LWTRD
252: WORK( 1 ) = LWMIN
253: *
254: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
255: $ INFO = -8
256: END IF
257: *
258: IF( INFO.NE.0 ) THEN
259: CALL XERBLA( 'DSYEV_2STAGE ', -INFO )
260: RETURN
261: ELSE IF( LQUERY ) THEN
262: RETURN
263: END IF
264: *
265: * Quick return if possible
266: *
267: IF( N.EQ.0 ) THEN
268: RETURN
269: END IF
270: *
271: IF( N.EQ.1 ) THEN
272: W( 1 ) = A( 1, 1 )
273: WORK( 1 ) = 2
274: IF( WANTZ )
275: $ A( 1, 1 ) = ONE
276: RETURN
277: END IF
278: *
279: * Get machine constants.
280: *
281: SAFMIN = DLAMCH( 'Safe minimum' )
282: EPS = DLAMCH( 'Precision' )
283: SMLNUM = SAFMIN / EPS
284: BIGNUM = ONE / SMLNUM
285: RMIN = SQRT( SMLNUM )
286: RMAX = SQRT( BIGNUM )
287: *
288: * Scale matrix to allowable range, if necessary.
289: *
290: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
291: ISCALE = 0
292: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
293: ISCALE = 1
294: SIGMA = RMIN / ANRM
295: ELSE IF( ANRM.GT.RMAX ) THEN
296: ISCALE = 1
297: SIGMA = RMAX / ANRM
298: END IF
299: IF( ISCALE.EQ.1 )
300: $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
301: *
302: * Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
303: *
304: INDE = 1
305: INDTAU = INDE + N
306: INDHOUS = INDTAU + N
307: INDWRK = INDHOUS + LHTRD
308: LLWORK = LWORK - INDWRK + 1
309: *
310: CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK( INDE ),
311: $ WORK( INDTAU ), WORK( INDHOUS ), LHTRD,
312: $ WORK( INDWRK ), LLWORK, IINFO )
313: *
314: * For eigenvalues only, call DSTERF. For eigenvectors, first call
315: * DORGTR to generate the orthogonal matrix, then call DSTEQR.
316: *
317: IF( .NOT.WANTZ ) THEN
318: CALL DSTERF( N, W, WORK( INDE ), INFO )
319: ELSE
320: * Not available in this release, and agrument checking should not
321: * let it getting here
322: RETURN
323: CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
324: $ LLWORK, IINFO )
325: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ),
326: $ INFO )
327: END IF
328: *
329: * If matrix was scaled, then rescale eigenvalues appropriately.
330: *
331: IF( ISCALE.EQ.1 ) THEN
332: IF( INFO.EQ.0 ) THEN
333: IMAX = N
334: ELSE
335: IMAX = INFO - 1
336: END IF
337: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
338: END IF
339: *
340: * Set WORK(1) to optimal workspace size.
341: *
342: WORK( 1 ) = LWMIN
343: *
344: RETURN
345: *
346: * End of DSYEV_2STAGE
347: *
348: END
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