sgntools.py

def sgns(*args):
    for i in args:
        if i < 0:
            break
    else:
        return 1

    for i in args:
        if i > 0:
            break
    else:
        return -1

    return 0


def sq_func_sgn(a, b, c):
    r"""
    let f(x) = a+bx+cx^2, x \in [0, 1]
    :return: f(x)>=0? 1; f(x)<=0? -1; 0
    """
    f0 = a
    f1 = a + b + c
    fm = 0
    if c != 0:
        x_m = -b / (2 * c)
        if 0 <= x_m <= 1:
            fm = a + b * x_m + c * x_m**2

    return sgns(f0, f1, fm)


def lin_func_sgn(a, b):
    return sgns(a, a + b)