naginterfaces.library.lapacklin.dpttrf

naginterfaces.library.lapacklin.dpttrf(d, e)[source]

dpttrf computes the modified Cholesky factorization of a real symmetric positive definite tridiagonal matrix .

For full information please refer to the NAG Library document for f07jd

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07jdf.html

Parameters
dfloat, array-like, shape

Must contain the diagonal elements of the matrix .

efloat, array-like, shape

Must contain the subdiagonal elements of the matrix .

Returns
dfloat, ndarray, shape

Is overwritten by the diagonal elements of the diagonal matrix from the factorization of .

efloat, ndarray, shape

Is overwritten by the subdiagonal elements of the lower bidiagonal matrix . ( can also be regarded as containing the superdiagonal elements of the upper bidiagonal matrix .)

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

The leading minor of order is not positive definite, the factorization could not be completed.

(errno )

The leading minor of order is not positive definite, the factorization was completed, but .

Notes

dpttrf factorizes the matrix as

where is a unit lower bidiagonal matrix and is a diagonal matrix with positive diagonal elements. The factorization may also be regarded as having the form , where is a unit upper bidiagonal matrix.