naginterfaces.library.lapacklin.zgesv

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

zgesv computes the solution to a complex system of linear equations

where is an matrix and and are matrices.

For full information please refer to the NAG Library document for f07an

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07anf.html

Parameters
acomplex, array-like, shape

The coefficient matrix .

bcomplex, array-like, shape

The right-hand side matrix .

Returns
acomplex, ndarray, shape

The factors and from the factorization ; the unit diagonal elements of are not stored.

ipivint, ndarray, shape

If no constraints are violated, the pivot indices that define the permutation matrix ; at the th step row of the matrix was interchanged with row . indicates a row interchange was not required.

bcomplex, ndarray, shape

If no exception or warning is raised, the solution matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

Element of the diagonal is exactly zero. The factorization has been completed, but the factor is exactly singular, so the solution could not be computed.

Notes

zgesv uses the decomposition with partial pivoting and row interchanges to factor as

where is a permutation matrix, is unit lower triangular, and is upper triangular. 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