naginterfaces.library.lapacklin.zgetrf

naginterfaces.library.lapacklin.zgetrf(a)[source]

zgetrf computes the factorization of a complex matrix.

For full information please refer to the NAG Library document for f07ar

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07arf.html

Parameters
acomplex, array-like, shape

The matrix .

Returns
acomplex, ndarray, shape

The factors and from the factorization ; the unit diagonal elements of are not stored.

ipivint, ndarray, shape

The pivot indices that define the permutation matrix. At the th step, if then row of the matrix was interchanged with row , for . indicates that, at the th step, a row interchange was not required.

Raises
NagValueError
(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, and division by zero will occur if it is used to solve a system of equations.

Notes

zgetrf forms the factorization of a complex matrix as , where is a permutation matrix, is lower triangular with unit diagonal elements (lower trapezoidal if ) and is upper triangular (upper trapezoidal if ). Usually is square , and both and are triangular. The function uses partial pivoting, with row interchanges.

References

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