naginterfaces.library.lapacklin.zhptrs

naginterfaces.library.lapacklin.zhptrs(uplo, n, ap, ipiv, b)[source]

zhptrs solves a complex Hermitian indefinite system of linear equations with multiple right-hand sides,

where has been factorized by zhptrf(), using packed storage.

For full information please refer to the NAG Library document for f07ps

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07psf.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 zhptrf().

ipivint, array-like, shape

Details of the interchanges and the block structure of , as returned by zhptrf().

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

zhptrs is used to solve a complex Hermitian indefinite system of linear equations , the function must be preceded by a call to zhptrf() which computes the Bunch–Kaufman factorization of , using packed storage.

If , , where is a permutation matrix, is an upper triangular matrix and is an Hermitian 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