naginterfaces.library.lapacklin.zposv

naginterfaces.library.lapacklin.zposv(uplo, a, b)[source]

zposv computes the solution to a complex system of linear equations

where is an Hermitian positive definite matrix and and are matrices.

For full information please refer to the NAG Library document for f07fn

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07fnf.html

Parameters
uplostr, length 1

If , the upper triangle of is stored.

If , the lower triangle of is stored.

acomplex, array-like, shape

The Hermitian matrix .

bcomplex, array-like, shape

The right-hand side matrix .

Returns
acomplex, ndarray, shape

If no exception or warning is raised, the factor or from the Cholesky factorization or .

bcomplex, ndarray, shape

If no exception or warning is raised, 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: .

(errno )

The leading minor of order of is not positive definite, so the factorization could not be completed, and the solution has not been computed.

Notes

zposv uses the Cholesky decomposition to factor as if or if , where is an upper triangular matrix and is a lower triangular matrix. The factored form of is then used to solve the system of equations .

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore