1: *> \brief \b DSYGV_2STAGE
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 DSYGV_2STAGE + dependencies
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygv_2stage.f">
13: *> [TGZ]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygv_2stage.f">
15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygv_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE DSYGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
24: * WORK, LWORK, INFO )
25: *
26: * IMPLICIT NONE
27: *
28: * .. Scalar Arguments ..
29: * CHARACTER JOBZ, UPLO
30: * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
31: * ..
32: * .. Array Arguments ..
33: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> DSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
43: *> of a real generalized symmetric-definite eigenproblem, of the form
44: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
45: *> Here A and B are assumed to be symmetric and B is also
46: *> positive definite.
47: *> This routine use the 2stage technique for the reduction to tridiagonal
48: *> which showed higher performance on recent architecture and for large
49: *> sizes N>2000.
50: *> \endverbatim
51: *
52: * Arguments:
53: * ==========
54: *
55: *> \param[in] ITYPE
56: *> \verbatim
57: *> ITYPE is INTEGER
58: *> Specifies the problem type to be solved:
59: *> = 1: A*x = (lambda)*B*x
60: *> = 2: A*B*x = (lambda)*x
61: *> = 3: B*A*x = (lambda)*x
62: *> \endverbatim
63: *>
64: *> \param[in] JOBZ
65: *> \verbatim
66: *> JOBZ is CHARACTER*1
67: *> = 'N': Compute eigenvalues only;
68: *> = 'V': Compute eigenvalues and eigenvectors.
69: *> Not available in this release.
70: *> \endverbatim
71: *>
72: *> \param[in] UPLO
73: *> \verbatim
74: *> UPLO is CHARACTER*1
75: *> = 'U': Upper triangles of A and B are stored;
76: *> = 'L': Lower triangles of A and B are stored.
77: *> \endverbatim
78: *>
79: *> \param[in] N
80: *> \verbatim
81: *> N is INTEGER
82: *> The order of the matrices A and B. N >= 0.
83: *> \endverbatim
84: *>
85: *> \param[in,out] A
86: *> \verbatim
87: *> A is DOUBLE PRECISION array, dimension (LDA, N)
88: *> On entry, the symmetric matrix A. If UPLO = 'U', the
89: *> leading N-by-N upper triangular part of A contains the
90: *> upper triangular part of the matrix A. If UPLO = 'L',
91: *> the leading N-by-N lower triangular part of A contains
92: *> the lower triangular part of the matrix A.
93: *>
94: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
95: *> matrix Z of eigenvectors. The eigenvectors are normalized
96: *> as follows:
97: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
98: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
99: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
100: *> or the lower triangle (if UPLO='L') of A, including the
101: *> diagonal, is destroyed.
102: *> \endverbatim
103: *>
104: *> \param[in] LDA
105: *> \verbatim
106: *> LDA is INTEGER
107: *> The leading dimension of the array A. LDA >= max(1,N).
108: *> \endverbatim
109: *>
110: *> \param[in,out] B
111: *> \verbatim
112: *> B is DOUBLE PRECISION array, dimension (LDB, N)
113: *> On entry, the symmetric positive definite matrix B.
114: *> If UPLO = 'U', the leading N-by-N upper triangular part of B
115: *> contains the upper triangular part of the matrix B.
116: *> If UPLO = 'L', the leading N-by-N lower triangular part of B
117: *> contains the lower triangular part of the matrix B.
118: *>
119: *> On exit, if INFO <= N, the part of B containing the matrix is
120: *> overwritten by the triangular factor U or L from the Cholesky
121: *> factorization B = U**T*U or B = L*L**T.
122: *> \endverbatim
123: *>
124: *> \param[in] LDB
125: *> \verbatim
126: *> LDB is INTEGER
127: *> The leading dimension of the array B. LDB >= max(1,N).
128: *> \endverbatim
129: *>
130: *> \param[out] W
131: *> \verbatim
132: *> W is DOUBLE PRECISION array, dimension (N)
133: *> If INFO = 0, the eigenvalues in ascending order.
134: *> \endverbatim
135: *>
136: *> \param[out] WORK
137: *> \verbatim
138: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
139: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
140: *> \endverbatim
141: *>
142: *> \param[in] LWORK
143: *> \verbatim
144: *> LWORK is INTEGER
145: *> The length of the array WORK. LWORK >= 1, when N <= 1;
146: *> otherwise
147: *> If JOBZ = 'N' and N > 1, LWORK must be queried.
148: *> LWORK = MAX(1, dimension) where
149: *> dimension = max(stage1,stage2) + (KD+1)*N + 2*N
150: *> = N*KD + N*max(KD+1,FACTOPTNB)
151: *> + max(2*KD*KD, KD*NTHREADS)
152: *> + (KD+1)*N + 2*N
153: *> where KD is the blocking size of the reduction,
154: *> FACTOPTNB is the blocking used by the QR or LQ
155: *> algorithm, usually FACTOPTNB=128 is a good choice
156: *> NTHREADS is the number of threads used when
157: *> openMP compilation is enabled, otherwise =1.
158: *> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
159: *>
160: *> If LWORK = -1, then a workspace query is assumed; the routine
161: *> only calculates the optimal size of the WORK array, returns
162: *> this value as the first entry of the WORK array, and no error
163: *> message related to LWORK is issued by XERBLA.
164: *> \endverbatim
165: *>
166: *> \param[out] INFO
167: *> \verbatim
168: *> INFO is INTEGER
169: *> = 0: successful exit
170: *> < 0: if INFO = -i, the i-th argument had an illegal value
171: *> > 0: DPOTRF or DSYEV returned an error code:
172: *> <= N: if INFO = i, DSYEV failed to converge;
173: *> i off-diagonal elements of an intermediate
174: *> tridiagonal form did not converge to zero;
175: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
176: *> minor of order i of B is not positive definite.
177: *> The factorization of B could not be completed and
178: *> no eigenvalues or eigenvectors were computed.
179: *> \endverbatim
180: *
181: * Authors:
182: * ========
183: *
184: *> \author Univ. of Tennessee
185: *> \author Univ. of California Berkeley
186: *> \author Univ. of Colorado Denver
187: *> \author NAG Ltd.
188: *
189: *> \ingroup doubleSYeigen
190: *
191: *> \par Further Details:
192: * =====================
193: *>
194: *> \verbatim
195: *>
196: *> All details about the 2stage techniques are available in:
197: *>
198: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
199: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
200: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
201: *> of 2011 International Conference for High Performance Computing,
202: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
203: *> Article 8 , 11 pages.
204: *> http://doi.acm.org/10.1145/2063384.2063394
205: *>
206: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
207: *> An improved parallel singular value algorithm and its implementation
208: *> for multicore hardware, In Proceedings of 2013 International Conference
209: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
210: *> Denver, Colorado, USA, 2013.
211: *> Article 90, 12 pages.
212: *> http://doi.acm.org/10.1145/2503210.2503292
213: *>
214: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
215: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
216: *> calculations based on fine-grained memory aware tasks.
217: *> International Journal of High Performance Computing Applications.
218: *> Volume 28 Issue 2, Pages 196-209, May 2014.
219: *> http://hpc.sagepub.com/content/28/2/196
220: *>
221: *> \endverbatim
222: *
223: * =====================================================================
224: SUBROUTINE DSYGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
225: $ WORK, LWORK, INFO )
226: *
227: IMPLICIT NONE
228: *
229: * -- LAPACK driver routine --
230: * -- LAPACK is a software package provided by Univ. of Tennessee, --
231: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232: *
233: * .. Scalar Arguments ..
234: CHARACTER JOBZ, UPLO
235: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
236: * ..
237: * .. Array Arguments ..
238: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
239: * ..
240: *
241: * =====================================================================
242: *
243: * .. Parameters ..
244: DOUBLE PRECISION ONE
245: PARAMETER ( ONE = 1.0D+0 )
246: * ..
247: * .. Local Scalars ..
248: LOGICAL LQUERY, UPPER, WANTZ
249: CHARACTER TRANS
250: INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
251: * ..
252: * .. External Functions ..
253: LOGICAL LSAME
254: INTEGER ILAENV2STAGE
255: EXTERNAL LSAME, ILAENV2STAGE
256: * ..
257: * .. External Subroutines ..
258: EXTERNAL DPOTRF, DSYGST, DTRMM, DTRSM, XERBLA,
259: $ DSYEV_2STAGE
260: * ..
261: * .. Intrinsic Functions ..
262: INTRINSIC MAX
263: * ..
264: * .. Executable Statements ..
265: *
266: * Test the input parameters.
267: *
268: WANTZ = LSAME( JOBZ, 'V' )
269: UPPER = LSAME( UPLO, 'U' )
270: LQUERY = ( LWORK.EQ.-1 )
271: *
272: INFO = 0
273: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
274: INFO = -1
275: ELSE IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
276: INFO = -2
277: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
278: INFO = -3
279: ELSE IF( N.LT.0 ) THEN
280: INFO = -4
281: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
282: INFO = -6
283: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
284: INFO = -8
285: END IF
286: *
287: IF( INFO.EQ.0 ) THEN
288: KD = ILAENV2STAGE( 1, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1 )
289: IB = ILAENV2STAGE( 2, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
290: LHTRD = ILAENV2STAGE( 3, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
291: LWTRD = ILAENV2STAGE( 4, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
292: LWMIN = 2*N + LHTRD + LWTRD
293: WORK( 1 ) = LWMIN
294: *
295: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
296: INFO = -11
297: END IF
298: END IF
299: *
300: IF( INFO.NE.0 ) THEN
301: CALL XERBLA( 'DSYGV_2STAGE ', -INFO )
302: RETURN
303: ELSE IF( LQUERY ) THEN
304: RETURN
305: END IF
306: *
307: * Quick return if possible
308: *
309: IF( N.EQ.0 )
310: $ RETURN
311: *
312: * Form a Cholesky factorization of B.
313: *
314: CALL DPOTRF( UPLO, N, B, LDB, INFO )
315: IF( INFO.NE.0 ) THEN
316: INFO = N + INFO
317: RETURN
318: END IF
319: *
320: * Transform problem to standard eigenvalue problem and solve.
321: *
322: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
323: CALL DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
324: *
325: IF( WANTZ ) THEN
326: *
327: * Backtransform eigenvectors to the original problem.
328: *
329: NEIG = N
330: IF( INFO.GT.0 )
331: $ NEIG = INFO - 1
332: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
333: *
334: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
335: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
336: *
337: IF( UPPER ) THEN
338: TRANS = 'N'
339: ELSE
340: TRANS = 'T'
341: END IF
342: *
343: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
344: $ B, LDB, A, LDA )
345: *
346: ELSE IF( ITYPE.EQ.3 ) THEN
347: *
348: * For B*A*x=(lambda)*x;
349: * backtransform eigenvectors: x = L*y or U**T*y
350: *
351: IF( UPPER ) THEN
352: TRANS = 'T'
353: ELSE
354: TRANS = 'N'
355: END IF
356: *
357: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
358: $ B, LDB, A, LDA )
359: END IF
360: END IF
361: *
362: WORK( 1 ) = LWMIN
363: RETURN
364: *
365: * End of DSYGV_2STAGE
366: *
367: END
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