# naginterfaces.library.lapacklin.zpbsv¶

naginterfaces.library.lapacklin.zpbsv(uplo, kd, ab, b)[source]

zpbsv computes the solution to a complex system of linear equations

where is an Hermitian positive definite band matrix of bandwidth and and are matrices.

For full information please refer to the NAG Library document for f07hn

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07hnf.html

Parameters
uplostr, length 1

If , the upper triangle of is stored.

If , the lower triangle of is stored.

kdint

, the number of superdiagonals of the matrix if , or the number of subdiagonals if .

abcomplex, array-like, shape

The upper or lower triangle of the Hermitian band matrix .

bcomplex, array-like, shape

The right-hand side matrix .

Returns
abcomplex, ndarray, shape

If no exception or warning is raised, the triangular factor or from the Cholesky factorization or of the band matrix , in the same storage format as .

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 )

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

zpbsv uses the Cholesky decomposition to factor as if or if , where is an upper triangular band matrix, and is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as . 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