naginterfaces.library.lapacklin.dpttrf

naginterfaces.library.lapacklin.dpttrf(d, e)

dpttrf computes the modified Cholesky factorization of a real $n\times n$ symmetric positive definite tridiagonal matrix $A$.

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

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f07/f07jdf.html

Parameters

dfloat, array-like, shape $\left(n\right)$

Must contain the $n$ diagonal elements of the matrix $A$.

efloat, array-like, shape $(n-1)$

Must contain the $(n-1)$ subdiagonal elements of the matrix $A$.

Returns

dfloat, ndarray, shape $\left(n\right)$

Is overwritten by the $n$ diagonal elements of the diagonal matrix $D$ from the $LD{L}^T$ factorization of $A$.

efloat, ndarray, shape $(n-1)$

Is overwritten by the $(n-1)$ subdiagonal elements of the lower bidiagonal matrix $L$. ($e$ can also be regarded as containing the $(n-1)$ superdiagonal elements of the upper bidiagonal matrix $U$.)

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $(i>0)\text{and}(i<n)$)

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

(errno $(i>0)\text{and}\left(n\right)$)

The leading minor of order $n$ is not positive definite, the factorization was completed, but $d[n-1]\le 0$.

Notes

dpttrf factorizes the matrix $A$ as

$$A=LD{L}^T\text{,}$$

where $L$ is a unit lower bidiagonal matrix and $D$ is a diagonal matrix with positive diagonal elements. The factorization may also be regarded as having the form $U^{T}DU$, where $U$ is a unit upper bidiagonal matrix.