naginterfaces.library.lapacklin.dpttrs

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

dpttrs computes the solution to a real system of linear equations , where is an symmetric positive definite tridiagonal matrix and and are matrices, using the factorization returned by dpttrf().

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

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07jef.html

Parameters
dfloat, array-like, shape

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

efloat, array-like, shape

Must contain the subdiagonal elements of the unit lower bidiagonal matrix . ( can also be regarded as the superdiagonal of the unit upper bidiagonal matrix from the factorization of .)

bfloat, array-like, shape

The matrix of right-hand sides .

Returns
bfloat, ndarray, shape

The solution matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dpttrs should be preceded by a call to dpttrf(), 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. dpttrs 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