You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
372 lines
11 KiB
372 lines
11 KiB
2 years ago
|
*> \brief \b SSYGVD
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
*> \htmlonly
|
||
|
|
*> Download SSYGVD + dependencies
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssygvd.f">
|
||
|
|
*> [TGZ]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssygvd.f">
|
||
|
|
*> [ZIP]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssygvd.f">
|
||
|
|
*> [TXT]</a>
|
||
|
|
*> \endhtmlonly
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
|
||
|
|
* LWORK, IWORK, LIWORK, INFO )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER JOBZ, UPLO
|
||
|
|
* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* INTEGER IWORK( * )
|
||
|
|
* REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
|
||
|
|
*> of a real generalized symmetric-definite eigenproblem, of the form
|
||
|
|
*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
|
||
|
|
*> B are assumed to be symmetric and B is also positive definite.
|
||
|
|
*> If eigenvectors are desired, it uses a divide and conquer algorithm.
|
||
|
|
*>
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] ITYPE
|
||
|
|
*> \verbatim
|
||
|
|
*> ITYPE is INTEGER
|
||
|
|
*> Specifies the problem type to be solved:
|
||
|
|
*> = 1: A*x = (lambda)*B*x
|
||
|
|
*> = 2: A*B*x = (lambda)*x
|
||
|
|
*> = 3: B*A*x = (lambda)*x
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] JOBZ
|
||
|
|
*> \verbatim
|
||
|
|
*> JOBZ is CHARACTER*1
|
||
|
|
*> = 'N': Compute eigenvalues only;
|
||
|
|
*> = 'V': Compute eigenvalues and eigenvectors.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] UPLO
|
||
|
|
*> \verbatim
|
||
|
|
*> UPLO is CHARACTER*1
|
||
|
|
*> = 'U': Upper triangles of A and B are stored;
|
||
|
|
*> = 'L': Lower triangles of A and B are stored.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The order of the matrices A and B. N >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is REAL array, dimension (LDA, N)
|
||
|
|
*> On entry, the symmetric matrix A. If UPLO = 'U', the
|
||
|
|
*> leading N-by-N upper triangular part of A contains the
|
||
|
|
*> upper triangular part of the matrix A. If UPLO = 'L',
|
||
|
|
*> the leading N-by-N lower triangular part of A contains
|
||
|
|
*> the lower triangular part of the matrix A.
|
||
|
|
*>
|
||
|
|
*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
|
||
|
|
*> matrix Z of eigenvectors. The eigenvectors are normalized
|
||
|
|
*> as follows:
|
||
|
|
*> if ITYPE = 1 or 2, Z**T*B*Z = I;
|
||
|
|
*> if ITYPE = 3, Z**T*inv(B)*Z = I.
|
||
|
|
*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
|
||
|
|
*> or the lower triangle (if UPLO='L') of A, including the
|
||
|
|
*> diagonal, is destroyed.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of the array A. LDA >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is REAL array, dimension (LDB, N)
|
||
|
|
*> On entry, the symmetric matrix B. If UPLO = 'U', the
|
||
|
|
*> leading N-by-N upper triangular part of B contains the
|
||
|
|
*> upper triangular part of the matrix B. If UPLO = 'L',
|
||
|
|
*> the leading N-by-N lower triangular part of B contains
|
||
|
|
*> the lower triangular part of the matrix B.
|
||
|
|
*>
|
||
|
|
*> On exit, if INFO <= N, the part of B containing the matrix is
|
||
|
|
*> overwritten by the triangular factor U or L from the Cholesky
|
||
|
|
*> factorization B = U**T*U or B = L*L**T.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDB
|
||
|
|
*> \verbatim
|
||
|
|
*> LDB is INTEGER
|
||
|
|
*> The leading dimension of the array B. LDB >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] W
|
||
|
|
*> \verbatim
|
||
|
|
*> W is REAL array, dimension (N)
|
||
|
|
*> If INFO = 0, the eigenvalues in ascending order.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] WORK
|
||
|
|
*> \verbatim
|
||
|
|
*> WORK is REAL array, dimension (MAX(1,LWORK))
|
||
|
|
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> LWORK is INTEGER
|
||
|
|
*> The dimension of the array WORK.
|
||
|
|
*> If N <= 1, LWORK >= 1.
|
||
|
|
*> If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
|
||
|
|
*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
|
||
|
|
*>
|
||
|
|
*> If LWORK = -1, then a workspace query is assumed; the routine
|
||
|
|
*> only calculates the optimal sizes of the WORK and IWORK
|
||
|
|
*> arrays, returns these values as the first entries of the WORK
|
||
|
|
*> and IWORK arrays, and no error message related to LWORK or
|
||
|
|
*> LIWORK is issued by XERBLA.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] IWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
|
||
|
|
*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LIWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> LIWORK is INTEGER
|
||
|
|
*> The dimension of the array IWORK.
|
||
|
|
*> If N <= 1, LIWORK >= 1.
|
||
|
|
*> If JOBZ = 'N' and N > 1, LIWORK >= 1.
|
||
|
|
*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
|
||
|
|
*>
|
||
|
|
*> If LIWORK = -1, then a workspace query is assumed; the
|
||
|
|
*> routine only calculates the optimal sizes of the WORK and
|
||
|
|
*> IWORK arrays, returns these values as the first entries of
|
||
|
|
*> the WORK and IWORK arrays, and no error message related to
|
||
|
|
*> LWORK or LIWORK is issued by XERBLA.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] INFO
|
||
|
|
*> \verbatim
|
||
|
|
*> INFO is INTEGER
|
||
|
|
*> = 0: successful exit
|
||
|
|
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
||
|
|
*> > 0: SPOTRF or SSYEVD returned an error code:
|
||
|
|
*> <= N: if INFO = i and JOBZ = 'N', then the algorithm
|
||
|
|
*> failed to converge; i off-diagonal elements of an
|
||
|
|
*> intermediate tridiagonal form did not converge to
|
||
|
|
*> zero;
|
||
|
|
*> if INFO = i and JOBZ = 'V', then the algorithm
|
||
|
|
*> failed to compute an eigenvalue while working on
|
||
|
|
*> the submatrix lying in rows and columns INFO/(N+1)
|
||
|
|
*> through mod(INFO,N+1);
|
||
|
|
*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
|
||
|
|
*> principal minor of order i of B is not positive.
|
||
|
|
*> The factorization of B could not be completed and
|
||
|
|
*> no eigenvalues or eigenvectors were computed.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup realSYeigen
|
||
|
|
*
|
||
|
|
*> \par Further Details:
|
||
|
|
* =====================
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> Modified so that no backsubstitution is performed if SSYEVD fails to
|
||
|
|
*> converge (NEIG in old code could be greater than N causing out of
|
||
|
|
*> bounds reference to A - reported by Ralf Meyer). Also corrected the
|
||
|
|
*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
*> \par Contributors:
|
||
|
|
* ==================
|
||
|
|
*>
|
||
|
|
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
|
||
|
|
*>
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
|
||
|
|
$ LWORK, IWORK, LIWORK, INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK driver routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
CHARACTER JOBZ, UPLO
|
||
|
|
INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
INTEGER IWORK( * )
|
||
|
|
REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ONE
|
||
|
|
PARAMETER ( ONE = 1.0E+0 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
LOGICAL LQUERY, UPPER, WANTZ
|
||
|
|
CHARACTER TRANS
|
||
|
|
INTEGER LIOPT, LIWMIN, LOPT, LWMIN
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
LOGICAL LSAME
|
||
|
|
EXTERNAL LSAME
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL SPOTRF, SSYEVD, SSYGST, STRMM, STRSM, XERBLA
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC MAX, REAL
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* Test the input parameters.
|
||
|
|
*
|
||
|
|
WANTZ = LSAME( JOBZ, 'V' )
|
||
|
|
UPPER = LSAME( UPLO, 'U' )
|
||
|
|
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
|
||
|
|
*
|
||
|
|
INFO = 0
|
||
|
|
IF( N.LE.1 ) THEN
|
||
|
|
LIWMIN = 1
|
||
|
|
LWMIN = 1
|
||
|
|
ELSE IF( WANTZ ) THEN
|
||
|
|
LIWMIN = 3 + 5*N
|
||
|
|
LWMIN = 1 + 6*N + 2*N**2
|
||
|
|
ELSE
|
||
|
|
LIWMIN = 1
|
||
|
|
LWMIN = 2*N + 1
|
||
|
|
END IF
|
||
|
|
LOPT = LWMIN
|
||
|
|
LIOPT = LIWMIN
|
||
|
|
IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
|
||
|
|
INFO = -2
|
||
|
|
ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
|
||
|
|
INFO = -3
|
||
|
|
ELSE IF( N.LT.0 ) THEN
|
||
|
|
INFO = -4
|
||
|
|
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
|
||
|
|
INFO = -6
|
||
|
|
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
|
||
|
|
INFO = -8
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.EQ.0 ) THEN
|
||
|
|
WORK( 1 ) = LOPT
|
||
|
|
IWORK( 1 ) = LIOPT
|
||
|
|
*
|
||
|
|
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
|
||
|
|
INFO = -11
|
||
|
|
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
|
||
|
|
INFO = -13
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'SSYGVD', -INFO )
|
||
|
|
RETURN
|
||
|
|
ELSE IF( LQUERY ) THEN
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Quick return if possible
|
||
|
|
*
|
||
|
|
IF( N.EQ.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
* Form a Cholesky factorization of B.
|
||
|
|
*
|
||
|
|
CALL SPOTRF( UPLO, N, B, LDB, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
INFO = N + INFO
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Transform problem to standard eigenvalue problem and solve.
|
||
|
|
*
|
||
|
|
CALL SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
|
||
|
|
CALL SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK,
|
||
|
|
$ INFO )
|
||
|
|
LOPT = INT( MAX( REAL( LOPT ), REAL( WORK( 1 ) ) ) )
|
||
|
|
LIOPT = INT( MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) ) )
|
||
|
|
*
|
||
|
|
IF( WANTZ .AND. INFO.EQ.0 ) THEN
|
||
|
|
*
|
||
|
|
* Backtransform eigenvectors to the original problem.
|
||
|
|
*
|
||
|
|
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
|
||
|
|
*
|
||
|
|
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
|
||
|
|
* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
TRANS = 'N'
|
||
|
|
ELSE
|
||
|
|
TRANS = 'T'
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL STRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
|
||
|
|
$ B, LDB, A, LDA )
|
||
|
|
*
|
||
|
|
ELSE IF( ITYPE.EQ.3 ) THEN
|
||
|
|
*
|
||
|
|
* For B*A*x=(lambda)*x;
|
||
|
|
* backtransform eigenvectors: x = L*y or U**T*y
|
||
|
|
*
|
||
|
|
IF( UPPER ) THEN
|
||
|
|
TRANS = 'T'
|
||
|
|
ELSE
|
||
|
|
TRANS = 'N'
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
CALL STRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
|
||
|
|
$ B, LDB, A, LDA )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
WORK( 1 ) = LOPT
|
||
|
|
IWORK( 1 ) = LIOPT
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SSYGVD
|
||
|
|
*
|
||
|
|
END
|