# naginterfaces.library.lapackeig.zpbstf¶

naginterfaces.library.lapackeig.zpbstf(uplo, kb, bb)[source]

zpbstf computes a split Cholesky factorization of a complex Hermitian positive definite band matrix.

For full information please refer to the NAG Library document for f08ut

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08utf.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of is stored.

The upper triangular part of is stored.

The lower triangular part of is stored.

kbint

If , the number of superdiagonals, , of the matrix .

If , the number of subdiagonals, , of the matrix .

bbcomplex, array-like, shape

The Hermitian positive definite band matrix .

Returns
bbcomplex, ndarray, shape

is overwritten by the elements of its split Cholesky factor .

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 factorization could not be completed, because the updated element would be the square root of a negative number. Hence is not positive definite. This may indicate an error in forming the matrix .

Notes

zpbstf computes a split Cholesky factorization of a complex Hermitian positive definite band matrix . It is designed to be used in conjunction with zhbgst().

The factorization has the form , where is a band matrix of the same bandwidth as and the following structure: is upper triangular in the first rows, and transposed — hence, lower triangular — in the remaining rows. For example, if and , then