naginterfaces.library.zeros.quartic_real¶
- naginterfaces.library.zeros.quartic_real(e, a, b, c, d)[source]¶
quartic_real
determines the roots of a quartic equation with real coefficients.For full information please refer to the NAG Library document for c02al
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/c02/c02alf.html
- Parameters
- efloat
, the coefficient of .
- afloat
, the coefficient of .
- bfloat
, the coefficient of .
- cfloat
, the coefficient of .
- dfloat
, the constant coefficient.
- Returns
- zerocomplex, ndarray, shape
contains the th root.
- errestfloat, ndarray, shape
contains an approximate error estimate for the th root.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
The companion matrix cannot be formed without overflow.
- (errno )
Failure to converge in
lapackeig.dhseqr
.
- Notes
In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.
quartic_real
attempts to find the roots of the quartic equationwhere , , , and are real coefficients with . The roots are located by finding the eigenvalues of the associated (upper Hessenberg) companion matrix given by
The eigenvalues are obtained by a call to
lapackeig.dhseqr
. Further details can be found in Further Comments.To obtain the roots of a cubic equation,
cubic_real()
can be used.
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore