Math.py 文件源码

def fit_cubic(y0, y1, g0, g1):
    """Fit cubic polynomial to function values and derivatives at x = 0, 1.

    Returns position and function value of minimum if fit succeeds. Fit does
    not succeeds if

    1. polynomial doesn't have extrema or
    2. maximum is from (0,1) or
    3. maximum is closer to 0.5 than minimum
    """
    a = 2*(y0-y1)+g0+g1
    b = -3*(y0-y1)-2*g0-g1
    p = np.array([a, b, g0, y0])
    r = np.roots(np.polyder(p))
    if not np.isreal(r).all():
        return None, None
    r = sorted(x.real for x in r)
    if p[0] > 0:
        maxim, minim = r
    else:
        minim, maxim = r
    if 0 < maxim < 1 and abs(minim-0.5) > abs(maxim-0.5):
        return None, None
    return minim, np.polyval(p, minim)