naginterfaces.library.lapacklin.zsptrs¶
- naginterfaces.library.lapacklin.zsptrs(uplo, n, ap, ipiv, b)[source]¶
zsptrs
solves a complex symmetric system of linear equations with multiple right-hand sides,where has been factorized by
zsptrf()
, using packed storage.For full information please refer to the NAG Library document for f07qs
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07qsf.html
- Parameters
- uplostr, length 1
Specifies how has been factorized.
, where is upper triangular.
, where is lower triangular.
- nint
, the order of the matrix .
- apcomplex, array-like, shape
The factorization of stored in packed form, as returned by
zsptrf()
.- ipivint, array-like, shape
Details of the interchanges and the block structure of , as returned by
zsptrf()
.- bcomplex, array-like, shape
The right-hand side matrix .
- Returns
- bcomplex, ndarray, shape
The solution matrix .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zsptrs
is used to solve a complex symmetric system of linear equations , the function must be preceded by a call tozsptrf()
which computes the Bunch–Kaufman factorization of , using packed storage.If , , where is a permutation matrix, is an upper triangular matrix and is a symmetric block diagonal matrix with and blocks; the solution is computed by solving and then .
If , , where is a lower triangular matrix; the solution is computed by solving and then .
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore