naginterfaces.library.lapackeig.dsygst¶
- naginterfaces.library.lapackeig.dsygst(itype, uplo, a, b)[source]¶
dsygst
reduces a real symmetric-definite generalized eigenproblem , or to the standard form , where is a real symmetric matrix and has been factorized bylapacklin.dpotrf
.For full information please refer to the NAG Library document for f08se
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08sef.html
- Parameters
- itypeint
Indicates how the standard form is computed.
if , ;
if , .
or
if , ;
if , .
- uplostr, length 1
Indicates whether the upper or lower triangular part of is stored and how has been factorized.
The upper triangular part of is stored and .
The lower triangular part of is stored and .
- afloat, array-like, shape
The symmetric matrix .
- bfloat, array-like, shape
The Cholesky factor of as specified by and returned by
lapacklin.dpotrf
.
- Returns
- afloat, ndarray, shape
The upper or lower triangle of is overwritten by the corresponding upper or lower triangle of as specified by and .
- 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: .
- Notes
To reduce the real symmetric-definite generalized eigenproblem , or to the standard form ,
dsygst
must be preceded by a call tolapacklin.dpotrf
which computes the Cholesky factorization of ; must be positive definite.The different problem types are specified by the argument , as indicated in the table below. The table shows how is computed by the function, and also how the eigenvectors of the original problem can be recovered from the eigenvectors of the standard form.
Problem
‘U’ ‘L’
‘U’ ‘L’
‘U’ ‘L’
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore