numpy.roots#
- numpy.roots(p)[source]#
Return the roots of a polynomial with coefficients given in p.
Note
This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in
numpy.polynomial
is preferred. A summary of the differences can be found in the transition guide.The values in the rank-1 array p are coefficients of a polynomial. If the length of p is n+1 then the polynomial is described by:
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
- Parameters:
- parray_like
Rank-1 array of polynomial coefficients.
- Returns:
- outndarray
An array containing the roots of the polynomial.
- Raises:
- ValueError
When p cannot be converted to a rank-1 array.
See also
Notes
The algorithm relies on computing the eigenvalues of the companion matrix [1].
References
[1]R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.
Examples
>>> coeff = [3.2, 2, 1] >>> np.roots(coeff) array([-0.3125+0.46351241j, -0.3125-0.46351241j])