naginterfaces.library.lapacklin.zpttrs

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

zpttrs computes the solution to a complex system of linear equations , where is an Hermitian positive definite tridiagonal matrix and and are matrices, using the factorization returned by zpttrf().

For full information please refer to the NAG Library document for f07js

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07jsf.html

Parameters
uplostr, length 1

Specifies the form of the factorization as follows:

.

.

dfloat, array-like, shape

Must contain the diagonal elements of the diagonal matrix from the or factorization of .

ecomplex, array-like, shape

If , must contain the superdiagonal elements of the unit upper bidiagonal matrix from the factorization of .

If , must contain the subdiagonal elements of the unit lower bidiagonal matrix from the factorization of .

bcomplex, array-like, shape

The matrix of right-hand sides .

Returns
bcomplex, ndarray, shape

The solution matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zpttrs should be preceded by a call to zpttrf(), which computes a modified Cholesky factorization of the matrix as

where is a unit lower bidiagonal matrix and is a diagonal matrix, with positive diagonal elements. zpttrs then utilizes the factorization to solve the required equations. Note that the factorization may also be regarded as having the form , where 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