Annotation of rpl/lapack/lapack/dsygv.f, revision 1.9
1.9 ! 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 DSYGV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygv.f">
! 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: *> \date November 2011
! 171: *
! 172: *> \ingroup doubleSYeigen
! 173: *
! 174: * =====================================================================
1.1 bertrand 175: SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
176: $ LWORK, INFO )
177: *
1.9 ! bertrand 178: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 179: * -- LAPACK is a software package provided by Univ. of Tennessee, --
180: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 181: * November 2011
1.1 bertrand 182: *
183: * .. Scalar Arguments ..
184: CHARACTER JOBZ, UPLO
185: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
186: * ..
187: * .. Array Arguments ..
188: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
189: * ..
190: *
191: * =====================================================================
192: *
193: * .. Parameters ..
194: DOUBLE PRECISION ONE
195: PARAMETER ( ONE = 1.0D+0 )
196: * ..
197: * .. Local Scalars ..
198: LOGICAL LQUERY, UPPER, WANTZ
199: CHARACTER TRANS
200: INTEGER LWKMIN, LWKOPT, NB, NEIG
201: * ..
202: * .. External Functions ..
203: LOGICAL LSAME
204: INTEGER ILAENV
205: EXTERNAL LSAME, ILAENV
206: * ..
207: * .. External Subroutines ..
208: EXTERNAL DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA
209: * ..
210: * .. Intrinsic Functions ..
211: INTRINSIC MAX
212: * ..
213: * .. Executable Statements ..
214: *
215: * Test the input parameters.
216: *
217: WANTZ = LSAME( JOBZ, 'V' )
218: UPPER = LSAME( UPLO, 'U' )
219: LQUERY = ( LWORK.EQ.-1 )
220: *
221: INFO = 0
222: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
223: INFO = -1
224: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
225: INFO = -2
226: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
227: INFO = -3
228: ELSE IF( N.LT.0 ) THEN
229: INFO = -4
230: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
231: INFO = -6
232: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
233: INFO = -8
234: END IF
235: *
236: IF( INFO.EQ.0 ) THEN
237: LWKMIN = MAX( 1, 3*N - 1 )
238: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
239: LWKOPT = MAX( LWKMIN, ( NB + 2 )*N )
240: WORK( 1 ) = LWKOPT
241: *
242: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
243: INFO = -11
244: END IF
245: END IF
246: *
247: IF( INFO.NE.0 ) THEN
248: CALL XERBLA( 'DSYGV ', -INFO )
249: RETURN
250: ELSE IF( LQUERY ) THEN
251: RETURN
252: END IF
253: *
254: * Quick return if possible
255: *
256: IF( N.EQ.0 )
257: $ RETURN
258: *
259: * Form a Cholesky factorization of B.
260: *
261: CALL DPOTRF( UPLO, N, B, LDB, INFO )
262: IF( INFO.NE.0 ) THEN
263: INFO = N + INFO
264: RETURN
265: END IF
266: *
267: * Transform problem to standard eigenvalue problem and solve.
268: *
269: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
270: CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
271: *
272: IF( WANTZ ) THEN
273: *
274: * Backtransform eigenvectors to the original problem.
275: *
276: NEIG = N
277: IF( INFO.GT.0 )
278: $ NEIG = INFO - 1
279: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
280: *
281: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 282: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
1.1 bertrand 283: *
284: IF( UPPER ) THEN
285: TRANS = 'N'
286: ELSE
287: TRANS = 'T'
288: END IF
289: *
290: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
291: $ B, LDB, A, LDA )
292: *
293: ELSE IF( ITYPE.EQ.3 ) THEN
294: *
295: * For B*A*x=(lambda)*x;
1.8 bertrand 296: * backtransform eigenvectors: x = L*y or U**T*y
1.1 bertrand 297: *
298: IF( UPPER ) THEN
299: TRANS = 'T'
300: ELSE
301: TRANS = 'N'
302: END IF
303: *
304: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
305: $ B, LDB, A, LDA )
306: END IF
307: END IF
308: *
309: WORK( 1 ) = LWKOPT
310: RETURN
311: *
312: * End of DSYGV
313: *
314: END
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