1: *> \brief \b DSYGV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYGV + 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/dsygv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
22: * LWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DSYGV computes all the eigenvalues, and optionally, the eigenvectors
39: *> of a real generalized symmetric-definite eigenproblem, of the form
40: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
41: *> Here A and B are assumed to be symmetric and B is also
42: *> positive definite.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] ITYPE
49: *> \verbatim
50: *> ITYPE is INTEGER
51: *> Specifies the problem type to be solved:
52: *> = 1: A*x = (lambda)*B*x
53: *> = 2: A*B*x = (lambda)*x
54: *> = 3: B*A*x = (lambda)*x
55: *> \endverbatim
56: *>
57: *> \param[in] JOBZ
58: *> \verbatim
59: *> JOBZ is CHARACTER*1
60: *> = 'N': Compute eigenvalues only;
61: *> = 'V': Compute eigenvalues and eigenvectors.
62: *> \endverbatim
63: *>
64: *> \param[in] UPLO
65: *> \verbatim
66: *> UPLO is CHARACTER*1
67: *> = 'U': Upper triangles of A and B are stored;
68: *> = 'L': Lower triangles of A and B are stored.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> The order of the matrices A and B. N >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in,out] A
78: *> \verbatim
79: *> A is DOUBLE PRECISION array, dimension (LDA, N)
80: *> On entry, the symmetric matrix A. If UPLO = 'U', the
81: *> leading N-by-N upper triangular part of A contains the
82: *> upper triangular part of the matrix A. If UPLO = 'L',
83: *> the leading N-by-N lower triangular part of A contains
84: *> the lower triangular part of the matrix A.
85: *>
86: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
87: *> matrix Z of eigenvectors. The eigenvectors are normalized
88: *> as follows:
89: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
90: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
91: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
92: *> or the lower triangle (if UPLO='L') of A, including the
93: *> diagonal, is destroyed.
94: *> \endverbatim
95: *>
96: *> \param[in] LDA
97: *> \verbatim
98: *> LDA is INTEGER
99: *> The leading dimension of the array A. LDA >= max(1,N).
100: *> \endverbatim
101: *>
102: *> \param[in,out] B
103: *> \verbatim
104: *> B is DOUBLE PRECISION array, dimension (LDB, N)
105: *> On entry, the symmetric positive definite matrix B.
106: *> If UPLO = 'U', the leading N-by-N upper triangular part of B
107: *> contains the upper triangular part of the matrix B.
108: *> If UPLO = 'L', the leading N-by-N lower triangular part of B
109: *> contains the lower triangular part of the matrix B.
110: *>
111: *> On exit, if INFO <= N, the part of B containing the matrix is
112: *> overwritten by the triangular factor U or L from the Cholesky
113: *> factorization B = U**T*U or B = L*L**T.
114: *> \endverbatim
115: *>
116: *> \param[in] LDB
117: *> \verbatim
118: *> LDB is INTEGER
119: *> The leading dimension of the array B. LDB >= max(1,N).
120: *> \endverbatim
121: *>
122: *> \param[out] W
123: *> \verbatim
124: *> W is DOUBLE PRECISION array, dimension (N)
125: *> If INFO = 0, the eigenvalues in ascending order.
126: *> \endverbatim
127: *>
128: *> \param[out] WORK
129: *> \verbatim
130: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
131: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132: *> \endverbatim
133: *>
134: *> \param[in] LWORK
135: *> \verbatim
136: *> LWORK is INTEGER
137: *> The length of the array WORK. LWORK >= max(1,3*N-1).
138: *> For optimal efficiency, LWORK >= (NB+2)*N,
139: *> where NB is the blocksize for DSYTRD returned by ILAENV.
140: *>
141: *> If LWORK = -1, then a workspace query is assumed; the routine
142: *> only calculates the optimal size of the WORK array, returns
143: *> this value as the first entry of the WORK array, and no error
144: *> message related to LWORK is issued by XERBLA.
145: *> \endverbatim
146: *>
147: *> \param[out] INFO
148: *> \verbatim
149: *> INFO is INTEGER
150: *> = 0: successful exit
151: *> < 0: if INFO = -i, the i-th argument had an illegal value
152: *> > 0: DPOTRF or DSYEV returned an error code:
153: *> <= N: if INFO = i, DSYEV failed to converge;
154: *> i off-diagonal elements of an intermediate
155: *> tridiagonal form did not converge to zero;
156: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
157: *> minor of order i of B is not positive definite.
158: *> The factorization of B could not be completed and
159: *> no eigenvalues or eigenvectors were computed.
160: *> \endverbatim
161: *
162: * Authors:
163: * ========
164: *
165: *> \author Univ. of Tennessee
166: *> \author Univ. of California Berkeley
167: *> \author Univ. of Colorado Denver
168: *> \author NAG Ltd.
169: *
170: *> \ingroup doubleSYeigen
171: *
172: * =====================================================================
173: SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
174: $ LWORK, INFO )
175: *
176: * -- LAPACK driver routine --
177: * -- LAPACK is a software package provided by Univ. of Tennessee, --
178: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
179: *
180: * .. Scalar Arguments ..
181: CHARACTER JOBZ, UPLO
182: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
183: * ..
184: * .. Array Arguments ..
185: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
186: * ..
187: *
188: * =====================================================================
189: *
190: * .. Parameters ..
191: DOUBLE PRECISION ONE
192: PARAMETER ( ONE = 1.0D+0 )
193: * ..
194: * .. Local Scalars ..
195: LOGICAL LQUERY, UPPER, WANTZ
196: CHARACTER TRANS
197: INTEGER LWKMIN, LWKOPT, NB, NEIG
198: * ..
199: * .. External Functions ..
200: LOGICAL LSAME
201: INTEGER ILAENV
202: EXTERNAL LSAME, ILAENV
203: * ..
204: * .. External Subroutines ..
205: EXTERNAL DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA
206: * ..
207: * .. Intrinsic Functions ..
208: INTRINSIC MAX
209: * ..
210: * .. Executable Statements ..
211: *
212: * Test the input parameters.
213: *
214: WANTZ = LSAME( JOBZ, 'V' )
215: UPPER = LSAME( UPLO, 'U' )
216: LQUERY = ( LWORK.EQ.-1 )
217: *
218: INFO = 0
219: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
220: INFO = -1
221: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
222: INFO = -2
223: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
224: INFO = -3
225: ELSE IF( N.LT.0 ) THEN
226: INFO = -4
227: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
228: INFO = -6
229: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
230: INFO = -8
231: END IF
232: *
233: IF( INFO.EQ.0 ) THEN
234: LWKMIN = MAX( 1, 3*N - 1 )
235: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
236: LWKOPT = MAX( LWKMIN, ( NB + 2 )*N )
237: WORK( 1 ) = LWKOPT
238: *
239: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
240: INFO = -11
241: END IF
242: END IF
243: *
244: IF( INFO.NE.0 ) THEN
245: CALL XERBLA( 'DSYGV ', -INFO )
246: RETURN
247: ELSE IF( LQUERY ) THEN
248: RETURN
249: END IF
250: *
251: * Quick return if possible
252: *
253: IF( N.EQ.0 )
254: $ RETURN
255: *
256: * Form a Cholesky factorization of B.
257: *
258: CALL DPOTRF( UPLO, N, B, LDB, INFO )
259: IF( INFO.NE.0 ) THEN
260: INFO = N + INFO
261: RETURN
262: END IF
263: *
264: * Transform problem to standard eigenvalue problem and solve.
265: *
266: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
267: CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
268: *
269: IF( WANTZ ) THEN
270: *
271: * Backtransform eigenvectors to the original problem.
272: *
273: NEIG = N
274: IF( INFO.GT.0 )
275: $ NEIG = INFO - 1
276: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
277: *
278: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
279: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
280: *
281: IF( UPPER ) THEN
282: TRANS = 'N'
283: ELSE
284: TRANS = 'T'
285: END IF
286: *
287: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
288: $ B, LDB, A, LDA )
289: *
290: ELSE IF( ITYPE.EQ.3 ) THEN
291: *
292: * For B*A*x=(lambda)*x;
293: * backtransform eigenvectors: x = L*y or U**T*y
294: *
295: IF( UPPER ) THEN
296: TRANS = 'T'
297: ELSE
298: TRANS = 'N'
299: END IF
300: *
301: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
302: $ B, LDB, A, LDA )
303: END IF
304: END IF
305: *
306: WORK( 1 ) = LWKOPT
307: RETURN
308: *
309: * End of DSYGV
310: *
311: END
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