naginterfaces.library.lapacklin.dpttrs

naginterfaces.library.lapacklin.dpttrs(d, e, b)

dpttrs computes the solution to a real system of linear equations $AX=B$, where $A$ is an $n\times n$ symmetric positive definite tridiagonal matrix and $X$ and $B$ are $n\times r$ matrices, using the $LD{L}^T$ factorization returned by dpttrf().

For full information please refer to the NAG Library document for f07je

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f07/f07jef.html

Parameters

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

Must contain the $n$ diagonal elements of the diagonal matrix $D$ from the $LD{L}^T$ factorization of $A$.

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

Must contain the $(n-1)$ subdiagonal elements of the unit lower bidiagonal matrix $L$. ($e$ can also be regarded as the superdiagonal of the unit upper bidiagonal matrix $U$ from the $U^{T}DU$ factorization of $A$.)

bfloat, array-like, shape $(n,\text{nrhs})$

The $n\times r$ matrix of right-hand sides $B$.

Returns

bfloat, ndarray, shape $(n,\text{nrhs})$

The $n\times r$ solution matrix $X$.

Raises

NagValueError

(errno $-1$)

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

Constraint: $n\ge 0$.

(errno $-2$)

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

Constraint: $\text{nrhs}\ge 0$.

Notes

dpttrs should be preceded by a call to dpttrf(), which computes a modified Cholesky factorization of 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. dpttrs then utilizes the factorization to solve the required equations. Note that the factorization may also be regarded as having the form $U^{T}DU$, where $U$ is a unit upper bidiagonal matrix.

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