naginterfaces.library.lapacklin.zpotrs¶
- naginterfaces.library.lapacklin.zpotrs(uplo, a, b)[source]¶
zpotrs
solves a complex Hermitian positive definite system of linear equations with multiple right-hand sides,where has been factorized by
zpotrf()
.For full information please refer to the NAG Library document for f07fs
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07fsf.html
- Parameters
- uplostr, length 1
Specifies how has been factorized.
, where is upper triangular.
, where is lower triangular.
- acomplex, array-like, shape
The Cholesky factor of , as returned by
zpotrf()
.- 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
zpotrs
is used to solve a complex Hermitian positive definite system of linear equations , this function must be preceded by a call tozpotrf()
which computes the Cholesky factorization of . The solution is computed by forward and backward substitution.If , , where is upper triangular; the solution is computed by solving and then .
If , , where is lower triangular; 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