naginterfaces.library.lapacklin.zptsv

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

zptsv computes the solution to a complex system of linear equations

where is an Hermitian positive definite tridiagonal matrix, and and are matrices.

For full information please refer to the NAG Library document for f07jn

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07jnf.html

Parameters
dfloat, array-like, shape

The diagonal elements of the tridiagonal matrix .

ecomplex, array-like, shape

The subdiagonal elements of the tridiagonal matrix .

bcomplex, array-like, shape

The right-hand side matrix .

Returns
dfloat, ndarray, shape

The diagonal elements of the diagonal matrix from the factorization .

ecomplex, ndarray, shape

The subdiagonal elements of the unit bidiagonal factor from the factorization of . ( can also be regarded as the superdiagonal of the unit bidiagonal factor from the factorization of .)

bcomplex, ndarray, shape

If no exception or warning is raised, the solution matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

The leading minor of order is not positive definite, and the solution has not been computed. The factorization has not been completed unless .

Notes

zptsv factors as . The factored form of 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