Annotation of rpl/lapack/lapack/dsygvx.f, revision 1.11
1.10 bertrand 1: *> \brief \b DSYGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYGVX + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygvx.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygvx.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
22: * VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
23: * LWORK, IWORK, IFAIL, INFO )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER JOBZ, RANGE, UPLO
27: * INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
28: * DOUBLE PRECISION ABSTOL, VL, VU
29: * ..
30: * .. Array Arguments ..
31: * INTEGER IFAIL( * ), IWORK( * )
32: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ),
33: * $ Z( LDZ, * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> DSYGVX computes selected eigenvalues, and optionally, 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. Here A
45: *> and B are assumed to be symmetric and B is also positive definite.
46: *> Eigenvalues and eigenvectors can be selected by specifying either a
47: *> range of values or a range of indices for the desired eigenvalues.
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] ITYPE
54: *> \verbatim
55: *> ITYPE is INTEGER
56: *> Specifies the problem type to be solved:
57: *> = 1: A*x = (lambda)*B*x
58: *> = 2: A*B*x = (lambda)*x
59: *> = 3: B*A*x = (lambda)*x
60: *> \endverbatim
61: *>
62: *> \param[in] JOBZ
63: *> \verbatim
64: *> JOBZ is CHARACTER*1
65: *> = 'N': Compute eigenvalues only;
66: *> = 'V': Compute eigenvalues and eigenvectors.
67: *> \endverbatim
68: *>
69: *> \param[in] RANGE
70: *> \verbatim
71: *> RANGE is CHARACTER*1
72: *> = 'A': all eigenvalues will be found.
73: *> = 'V': all eigenvalues in the half-open interval (VL,VU]
74: *> will be found.
75: *> = 'I': the IL-th through IU-th eigenvalues will be found.
76: *> \endverbatim
77: *>
78: *> \param[in] UPLO
79: *> \verbatim
80: *> UPLO is CHARACTER*1
81: *> = 'U': Upper triangle of A and B are stored;
82: *> = 'L': Lower triangle of A and B are stored.
83: *> \endverbatim
84: *>
85: *> \param[in] N
86: *> \verbatim
87: *> N is INTEGER
88: *> The order of the matrix pencil (A,B). N >= 0.
89: *> \endverbatim
90: *>
91: *> \param[in,out] A
92: *> \verbatim
93: *> A is DOUBLE PRECISION array, dimension (LDA, N)
94: *> On entry, the symmetric matrix A. If UPLO = 'U', the
95: *> leading N-by-N upper triangular part of A contains the
96: *> upper triangular part of the matrix A. If UPLO = 'L',
97: *> the leading N-by-N lower triangular part of A contains
98: *> the lower triangular part of the matrix A.
99: *>
100: *> On exit, the lower triangle (if UPLO='L') or the upper
101: *> triangle (if UPLO='U') of A, including the diagonal, is
102: *> destroyed.
103: *> \endverbatim
104: *>
105: *> \param[in] LDA
106: *> \verbatim
107: *> LDA is INTEGER
108: *> The leading dimension of the array A. LDA >= max(1,N).
109: *> \endverbatim
110: *>
111: *> \param[in,out] B
112: *> \verbatim
113: *> B is DOUBLE PRECISION array, dimension (LDB, N)
114: *> On entry, the symmetric matrix B. If UPLO = 'U', the
115: *> leading N-by-N upper triangular part of B contains the
116: *> upper triangular part of the matrix B. If UPLO = 'L',
117: *> the leading N-by-N lower triangular part of B contains
118: *> the lower triangular part of the matrix B.
119: *>
120: *> On exit, if INFO <= N, the part of B containing the matrix is
121: *> overwritten by the triangular factor U or L from the Cholesky
122: *> factorization B = U**T*U or B = L*L**T.
123: *> \endverbatim
124: *>
125: *> \param[in] LDB
126: *> \verbatim
127: *> LDB is INTEGER
128: *> The leading dimension of the array B. LDB >= max(1,N).
129: *> \endverbatim
130: *>
131: *> \param[in] VL
132: *> \verbatim
133: *> VL is DOUBLE PRECISION
134: *> \endverbatim
135: *>
136: *> \param[in] VU
137: *> \verbatim
138: *> VU is DOUBLE PRECISION
139: *> If RANGE='V', the lower and upper bounds of the interval to
140: *> be searched for eigenvalues. VL < VU.
141: *> Not referenced if RANGE = 'A' or 'I'.
142: *> \endverbatim
143: *>
144: *> \param[in] IL
145: *> \verbatim
146: *> IL is INTEGER
147: *> \endverbatim
148: *>
149: *> \param[in] IU
150: *> \verbatim
151: *> IU is INTEGER
152: *> If RANGE='I', the indices (in ascending order) of the
153: *> smallest and largest eigenvalues to be returned.
154: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
155: *> Not referenced if RANGE = 'A' or 'V'.
156: *> \endverbatim
157: *>
158: *> \param[in] ABSTOL
159: *> \verbatim
160: *> ABSTOL is DOUBLE PRECISION
161: *> The absolute error tolerance for the eigenvalues.
162: *> An approximate eigenvalue is accepted as converged
163: *> when it is determined to lie in an interval [a,b]
164: *> of width less than or equal to
165: *>
166: *> ABSTOL + EPS * max( |a|,|b| ) ,
167: *>
168: *> where EPS is the machine precision. If ABSTOL is less than
169: *> or equal to zero, then EPS*|T| will be used in its place,
170: *> where |T| is the 1-norm of the tridiagonal matrix obtained
171: *> by reducing C to tridiagonal form, where C is the symmetric
172: *> matrix of the standard symmetric problem to which the
173: *> generalized problem is transformed.
174: *>
175: *> Eigenvalues will be computed most accurately when ABSTOL is
176: *> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
177: *> If this routine returns with INFO>0, indicating that some
178: *> eigenvectors did not converge, try setting ABSTOL to
179: *> 2*DLAMCH('S').
180: *> \endverbatim
181: *>
182: *> \param[out] M
183: *> \verbatim
184: *> M is INTEGER
185: *> The total number of eigenvalues found. 0 <= M <= N.
186: *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
187: *> \endverbatim
188: *>
189: *> \param[out] W
190: *> \verbatim
191: *> W is DOUBLE PRECISION array, dimension (N)
192: *> On normal exit, the first M elements contain the selected
193: *> eigenvalues in ascending order.
194: *> \endverbatim
195: *>
196: *> \param[out] Z
197: *> \verbatim
198: *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
199: *> If JOBZ = 'N', then Z is not referenced.
200: *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
201: *> contain the orthonormal eigenvectors of the matrix A
202: *> corresponding to the selected eigenvalues, with the i-th
203: *> column of Z holding the eigenvector associated with W(i).
204: *> The eigenvectors are normalized as follows:
205: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
206: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
207: *>
208: *> If an eigenvector fails to converge, then that column of Z
209: *> contains the latest approximation to the eigenvector, and the
210: *> index of the eigenvector is returned in IFAIL.
211: *> Note: the user must ensure that at least max(1,M) columns are
212: *> supplied in the array Z; if RANGE = 'V', the exact value of M
213: *> is not known in advance and an upper bound must be used.
214: *> \endverbatim
215: *>
216: *> \param[in] LDZ
217: *> \verbatim
218: *> LDZ is INTEGER
219: *> The leading dimension of the array Z. LDZ >= 1, and if
220: *> JOBZ = 'V', LDZ >= max(1,N).
221: *> \endverbatim
222: *>
223: *> \param[out] WORK
224: *> \verbatim
225: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
226: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
227: *> \endverbatim
228: *>
229: *> \param[in] LWORK
230: *> \verbatim
231: *> LWORK is INTEGER
232: *> The length of the array WORK. LWORK >= max(1,8*N).
233: *> For optimal efficiency, LWORK >= (NB+3)*N,
234: *> where NB is the blocksize for DSYTRD returned by ILAENV.
235: *>
236: *> If LWORK = -1, then a workspace query is assumed; the routine
237: *> only calculates the optimal size of the WORK array, returns
238: *> this value as the first entry of the WORK array, and no error
239: *> message related to LWORK is issued by XERBLA.
240: *> \endverbatim
241: *>
242: *> \param[out] IWORK
243: *> \verbatim
244: *> IWORK is INTEGER array, dimension (5*N)
245: *> \endverbatim
246: *>
247: *> \param[out] IFAIL
248: *> \verbatim
249: *> IFAIL is INTEGER array, dimension (N)
250: *> If JOBZ = 'V', then if INFO = 0, the first M elements of
251: *> IFAIL are zero. If INFO > 0, then IFAIL contains the
252: *> indices of the eigenvectors that failed to converge.
253: *> If JOBZ = 'N', then IFAIL is not referenced.
254: *> \endverbatim
255: *>
256: *> \param[out] INFO
257: *> \verbatim
258: *> INFO is INTEGER
259: *> = 0: successful exit
260: *> < 0: if INFO = -i, the i-th argument had an illegal value
261: *> > 0: DPOTRF or DSYEVX returned an error code:
262: *> <= N: if INFO = i, DSYEVX failed to converge;
263: *> i eigenvectors failed to converge. Their indices
264: *> are stored in array IFAIL.
265: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
266: *> minor of order i of B is not positive definite.
267: *> The factorization of B could not be completed and
268: *> no eigenvalues or eigenvectors were computed.
269: *> \endverbatim
270: *
271: * Authors:
272: * ========
273: *
274: *> \author Univ. of Tennessee
275: *> \author Univ. of California Berkeley
276: *> \author Univ. of Colorado Denver
277: *> \author NAG Ltd.
278: *
279: *> \date November 2011
280: *
281: *> \ingroup doubleSYeigen
282: *
283: *> \par Contributors:
284: * ==================
285: *>
286: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
287: *
288: * =====================================================================
1.1 bertrand 289: SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
290: $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
291: $ LWORK, IWORK, IFAIL, INFO )
292: *
1.10 bertrand 293: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 294: * -- LAPACK is a software package provided by Univ. of Tennessee, --
295: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 bertrand 296: * November 2011
1.1 bertrand 297: *
298: * .. Scalar Arguments ..
299: CHARACTER JOBZ, RANGE, UPLO
300: INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
301: DOUBLE PRECISION ABSTOL, VL, VU
302: * ..
303: * .. Array Arguments ..
304: INTEGER IFAIL( * ), IWORK( * )
305: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ),
306: $ Z( LDZ, * )
307: * ..
308: *
309: * =====================================================================
310: *
311: * .. Parameters ..
312: DOUBLE PRECISION ONE
313: PARAMETER ( ONE = 1.0D+0 )
314: * ..
315: * .. Local Scalars ..
316: LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
317: CHARACTER TRANS
318: INTEGER LWKMIN, LWKOPT, NB
319: * ..
320: * .. External Functions ..
321: LOGICAL LSAME
322: INTEGER ILAENV
323: EXTERNAL LSAME, ILAENV
324: * ..
325: * .. External Subroutines ..
326: EXTERNAL DPOTRF, DSYEVX, DSYGST, DTRMM, DTRSM, XERBLA
327: * ..
328: * .. Intrinsic Functions ..
329: INTRINSIC MAX, MIN
330: * ..
331: * .. Executable Statements ..
332: *
333: * Test the input parameters.
334: *
335: UPPER = LSAME( UPLO, 'U' )
336: WANTZ = LSAME( JOBZ, 'V' )
337: ALLEIG = LSAME( RANGE, 'A' )
338: VALEIG = LSAME( RANGE, 'V' )
339: INDEIG = LSAME( RANGE, 'I' )
340: LQUERY = ( LWORK.EQ.-1 )
341: *
342: INFO = 0
343: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
344: INFO = -1
345: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
346: INFO = -2
347: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
348: INFO = -3
349: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
350: INFO = -4
351: ELSE IF( N.LT.0 ) THEN
352: INFO = -5
353: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
354: INFO = -7
355: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
356: INFO = -9
357: ELSE
358: IF( VALEIG ) THEN
359: IF( N.GT.0 .AND. VU.LE.VL )
360: $ INFO = -11
361: ELSE IF( INDEIG ) THEN
362: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
363: INFO = -12
364: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
365: INFO = -13
366: END IF
367: END IF
368: END IF
369: IF (INFO.EQ.0) THEN
370: IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
371: INFO = -18
372: END IF
373: END IF
374: *
375: IF( INFO.EQ.0 ) THEN
376: LWKMIN = MAX( 1, 8*N )
377: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
378: LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
379: WORK( 1 ) = LWKOPT
380: *
381: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
382: INFO = -20
383: END IF
384: END IF
385: *
386: IF( INFO.NE.0 ) THEN
387: CALL XERBLA( 'DSYGVX', -INFO )
388: RETURN
389: ELSE IF( LQUERY ) THEN
390: RETURN
391: END IF
392: *
393: * Quick return if possible
394: *
395: M = 0
396: IF( N.EQ.0 ) THEN
397: RETURN
398: END IF
399: *
400: * Form a Cholesky factorization of B.
401: *
402: CALL DPOTRF( UPLO, N, B, LDB, INFO )
403: IF( INFO.NE.0 ) THEN
404: INFO = N + INFO
405: RETURN
406: END IF
407: *
408: * Transform problem to standard eigenvalue problem and solve.
409: *
410: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
411: CALL DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
412: $ M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
413: *
414: IF( WANTZ ) THEN
415: *
416: * Backtransform eigenvectors to the original problem.
417: *
418: IF( INFO.GT.0 )
419: $ M = INFO - 1
420: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
421: *
422: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.9 bertrand 423: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
1.1 bertrand 424: *
425: IF( UPPER ) THEN
426: TRANS = 'N'
427: ELSE
428: TRANS = 'T'
429: END IF
430: *
431: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
432: $ LDB, Z, LDZ )
433: *
434: ELSE IF( ITYPE.EQ.3 ) THEN
435: *
436: * For B*A*x=(lambda)*x;
1.9 bertrand 437: * backtransform eigenvectors: x = L*y or U**T*y
1.1 bertrand 438: *
439: IF( UPPER ) THEN
440: TRANS = 'T'
441: ELSE
442: TRANS = 'N'
443: END IF
444: *
445: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
446: $ LDB, Z, LDZ )
447: END IF
448: END IF
449: *
450: * Set WORK(1) to optimal workspace size.
451: *
452: WORK( 1 ) = LWKOPT
453: *
454: RETURN
455: *
456: * End of DSYGVX
457: *
458: END
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