# naginterfaces.library.lapacklin.zgbsv¶

naginterfaces.library.lapacklin.zgbsv(kl, ku, ab, b)[source]

zgbsv computes the solution to a complex system of linear equations

where is an band matrix, with subdiagonals and superdiagonals, and and are matrices.

For full information please refer to the NAG Library document for f07bn

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07bnf.html

Parameters
klint

, the number of subdiagonals within the band of the matrix .

kuint

, the number of superdiagonals within the band of the matrix .

abcomplex, array-like, shape

The coefficient matrix .

See Further Comments for further details.

bcomplex, array-like, shape

The right-hand side matrix .

Returns
abcomplex, ndarray, shape

If >= 0, is overwritten by details of the factorization.

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: .

(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

zgbsv uses the decomposition with partial pivoting and row interchanges to factor as , where is a permutation matrix, is a product of permutation and unit lower triangular matrices with subdiagonals, and is upper triangular with superdiagonals. 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