naginterfaces.library.lapacklin.zherfs¶
- naginterfaces.library.lapacklin.zherfs(uplo, n, a, af, ipiv, b, x)[source]¶
zherfs
returns error bounds for the solution of a complex Hermitian indefinite system of linear equations with multiple right-hand sides, . It improves the solution by iterative refinement, in order to reduce the backward error as much as possible.For full information please refer to the NAG Library document for f07mv
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07mvf.html
- Parameters
- uplostr, length 1
Specifies whether the upper or lower triangular part of is stored and how is to be factorized.
The upper triangular part of is stored and is factorized as , where is upper triangular.
The lower triangular part of is stored and is factorized as , where is lower triangular.
- nint
, the order of the matrix .
- acomplex, array-like, shape
The original Hermitian matrix as supplied to
zhetrf()
.- afcomplex, array-like, shape
Details of the factorization of , as returned by
zhetrf()
.- ipivint, array-like, shape
Details of the interchanges and the block structure of , as returned by
zhetrf()
.- bcomplex, array-like, shape
The right-hand side matrix .
- xcomplex, array-like, shape
The solution matrix , as returned by
zhetrs()
.
- Returns
- xcomplex, ndarray, shape
The improved solution matrix .
- ferrfloat, ndarray, shape
contains an estimated error bound for the th solution vector, that is, the th column of , for .
- berrfloat, ndarray, shape
contains the component-wise backward error bound for the th solution vector, that is, the th column of , for .
- 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
zherfs
returns the backward errors and estimated bounds on the forward errors for the solution of a complex Hermitian indefinite system of linear equations with multiple right-hand sides . The function handles each right-hand side vector (stored as a column of the matrix ) independently, so we describe the function ofzherfs
in terms of a single right-hand side and solution .Given a computed solution , the function computes the component-wise backward error . This is the size of the smallest relative perturbation in each element of and such that is the exact solution of a perturbed system
Then the function estimates a bound for the component-wise forward error in the computed solution, defined by:
where is the true solution.
For details of the method, see the F07 Introduction.
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore