numpy.roots — NumPy v1.11 Manual (original) (raw)
Return the roots of a polynomial with coefficients given in p.
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] * xn + p[1] * x(n-1) + ... + p[n-1]*x + p[n]
| Parameters: | p : array_like Rank-1 array of polynomial coefficients. |
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| Returns: | out : ndarray An array containing the complex roots of the polynomial. |
| Raises: | ValueError When p cannot be converted to a rank-1 array. |
See also
Find the coefficients of a polynomial with a given sequence of roots.
Compute polynomial values.
Least squares polynomial fit.
A one-dimensional polynomial class.
Notes
The algorithm relies on computing the eigenvalues of the companion matrix [R279].
References
| [R279] | (1, 2) R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7. |
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Examples
coeff = [3.2, 2, 1] np.roots(coeff) array([-0.3125+0.46351241j, -0.3125-0.46351241j])