naginterfaces.library.lapackeig.dsbgst¶
- naginterfaces.library.lapackeig.dsbgst(vect, uplo, ka, kb, ab, bb)[source]¶
dsbgst
reduces a real symmetric-definite generalized eigenproblem to the standard form , where and are band matrices, is a real symmetric matrix, and has been factorized bydpbstf()
.For full information please refer to the NAG Library document for f08ue
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08uef.html
- Parameters
- vectstr, length 1
Indicates whether is to be returned.
is not returned.
is returned.
- uplostr, length 1
Indicates whether the upper or lower triangular part of is stored.
The upper triangular part of is stored.
The lower triangular part of is stored.
- kaint
If , the number of superdiagonals, , of the matrix .
If , the number of subdiagonals, , of the matrix .
- kbint
If , the number of superdiagonals, , of the matrix .
If , the number of subdiagonals, , of the matrix .
- abfloat, array-like, shape
The upper or lower triangle of the symmetric band matrix .
- bbfloat, array-like, shape
The banded split Cholesky factor of as specified by , and and returned by
dpbstf()
.
- Returns
- abfloat, ndarray, shape
The upper or lower triangle of is overwritten by the corresponding upper or lower triangle of as specified by .
- xfloat, ndarray, shape
The matrix , if .
If , is not referenced.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
To reduce the real symmetric-definite generalized eigenproblem to the standard form , where , and are banded,
dsbgst
must be preceded by a call todpbstf()
which computes the split Cholesky factorization of the positive definite matrix : . The split Cholesky factorization, compared with the ordinary Cholesky factorization, allows the work to be approximately halved.This function overwrites with , where and is a orthogonal matrix chosen (implicitly) to preserve the bandwidth of . The function also has an option to allow the accumulation of , and then, if is an eigenvector of , is an eigenvector of the original system.
- References
Crawford, C R, 1973, Reduction of a band-symmetric generalized eigenvalue problem, Comm. ACM (16), 41–44
Kaufman, L, 1984, Banded eigenvalue solvers on vector machines, ACM Trans. Math. Software (10), 73–86