naginterfaces.library.lapacklin.dgbsv¶
- naginterfaces.library.lapacklin.dgbsv(kl, ku, ab, b)[source]¶
dgbsv
computes the solution to a real system of linear equationswhere is an band matrix, with subdiagonals and superdiagonals, and and are matrices.
For full information please refer to the NAG Library document for f07ba
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07baf.html
- Parameters
- klint
, the number of subdiagonals within the band of the matrix .
- kuint
, the number of superdiagonals within the band of the matrix .
- abfloat, array-like, shape
The coefficient matrix .
See Further Comments for further details.
- bfloat, array-like, shape
The right-hand side matrix .
- Returns
- abfloat, ndarray, shape
If >= 0, is overwritten by details of the factorization.
- ipivint, ndarray, shape
If no constraints are violated, the pivot indices that define the permutation matrix ; at the th step row of the matrix was interchanged with row . indicates a row interchange was not required.
- bfloat, 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 )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Warns
- NagAlgorithmicWarning
- (errno )
Element of the diagonal is exactly zero. The factorization has been completed, but the factor is exactly singular, so the solution could not be computed.
- Notes
dgbsv
uses the decomposition with partial pivoting and row interchanges to factor as , where is a permutation matrix, is a product of permutation and unit lower triangular matrices with subdiagonals, and is upper triangular with superdiagonals. 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