# naginterfaces.library.lapacklin.dgbtrf¶

naginterfaces.library.lapacklin.dgbtrf(m, kl, ku, ab)[source]

dgbtrf computes the factorization of a real band matrix.

For full information please refer to the NAG Library document for f07bd

https://www.nag.com/numeric/nl/nagdoc_29.2/flhtml/f07/f07bdf.html

Parameters
mint

, the number of rows of the matrix .

klint

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

kuint

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

abfloat, array-like, shape

The matrix .

See Further Comments for further details.

Returns
abfloat, ndarray, shape

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

ipivint, ndarray, shape

The pivot indices that define the permutation matrix. At the th step, if then row of the matrix was interchanged with row , for . indicates that, at the th step, a row interchange was not required.

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, and division by zero will occur if it is used to solve a system of equations.

Notes

dgbtrf forms the factorization of a real band matrix using partial pivoting, with row interchanges. Usually , and then, if has nonzero subdiagonals and nonzero superdiagonals, the factorization has the form , where is a permutation matrix, is a lower triangular matrix with unit diagonal elements and at most nonzero elements in each column, and is an upper triangular band matrix with superdiagonals.

Note that is not a band matrix, but the nonzero elements of can be stored in the same space as the subdiagonal elements of . is a band matrix but with additional superdiagonals compared with . These additional superdiagonals are created by the row interchanges.

References

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