naginterfaces.library.lapacklin.dptsv

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

dptsv computes the solution to a real system of linear equations

$$AX=B\text{,}$$

where $A$ is an $n\times n$ symmetric positive definite tridiagonal matrix, and $X$ and $B$ are $n\times r$ matrices.

For full information please refer to the NAG Library document for f07ja

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07jaf.html

Parameters

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

The $n$ diagonal elements of the tridiagonal matrix $A$.

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

The $(n-1)$ subdiagonal elements of the tridiagonal matrix $A$.

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

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

Returns

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

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

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

The $(n-1)$ subdiagonal elements of the unit bidiagonal factor $L$ from the $LD{L}^T$ factorization of $A$. ($e$ can also be regarded as the superdiagonal of the unit bidiagonal factor $U$ from the $U^{T}DU$ factorization of $A$.)

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

If no exception or warning is raised, 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: $\text{nrhs}\ge 0$.

(errno $i>0$)

The leading minor of order $⟨value⟩$ is not positive definite, and the solution has not been computed. The factorization has not been completed unless $n=⟨value⟩$.

Notes

dptsv factors $A$ as $A=LD{L}^T$. The factored form of $A$ is then used to solve the system of equations.

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

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