polynomial.py 文件源码

def polyroots(c):
    """
    Compute the roots of a polynomial.

    Return the roots (a.k.a. "zeros") of the polynomial

    .. math:: p(x) = \\sum_i c[i] * x^i.

    Parameters
    ----------
    c : 1-D array_like
        1-D array of polynomial coefficients.

    Returns
    -------
    out : ndarray
        Array of the roots of the polynomial. If all the roots are real,
        then `out` is also real, otherwise it is complex.

    See Also
    --------
    chebroots

    Notes
    -----
    The root estimates are obtained as the eigenvalues of the companion
    matrix, Roots far from the origin of the complex plane may have large
    errors due to the numerical instability of the power series for such
    values. Roots with multiplicity greater than 1 will also show larger
    errors as the value of the series near such points is relatively
    insensitive to errors in the roots. Isolated roots near the origin can
    be improved by a few iterations of Newton's method.

    Examples
    --------
    >>> import numpy.polynomial.polynomial as poly
    >>> poly.polyroots(poly.polyfromroots((-1,0,1)))
    array([-1.,  0.,  1.])
    >>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype
    dtype('float64')
    >>> j = complex(0,1)
    >>> poly.polyroots(poly.polyfromroots((-j,0,j)))
    array([  0.00000000e+00+0.j,   0.00000000e+00+1.j,   2.77555756e-17-1.j])

    """
    # c is a trimmed copy
    [c] = pu.as_series([c])
    if len(c) < 2:
        return np.array([], dtype=c.dtype)
    if len(c) == 2:
        return np.array([-c[0]/c[1]])

    m = polycompanion(c)
    r = la.eigvals(m)
    r.sort()
    return r


#
# polynomial class
#