controltools.py 文件源码

def char_coefficients(poles):
    """
    Calculate the coefficients of a characteristic polynomial.

    Args:
        poles (list or :obj:`numpy.ndarray`): pol configuration

    Return:
        :obj:`numpy.ndarray`: coefficients
    """

    poles = np.array(poles)  # convert to numpy array
    poles = np.ravel(poles)  # transform to 1d array

    s = sp.symbols("s")
    poly = 1
    for s_i in poles:
        poly = (s - s_i) * poly
    poly = sp.expand(poly)

    # calculate the coefficient of characteristic polynomial
    n = len(poles)
    p = []
    for i in range(n):
        p.append(poly.subs([(s, 0)]))
        poly = poly - p[i]
        poly = poly / s
        poly = sp.expand(poly)

    # convert numbers and complex objects from multiplication to a complex
    # number
    p = [complex(x) for x in p]

    # if imaginary part is greater than the boundary, set imaginary part to zero
    boundary = 1e-12
    for idx, val in enumerate(p):
        if abs(val.imag) > boundary:
            msg = "Imaginary Part of the coefficient p[{}] "
            "is unequal zero ({})) for a given tolerance of {}".format(
                str(idx), str(boundary), str(val.imag))
            warnings.warn(msg)
        p[idx] = val.real

    return np.array(p, dtype=float)  # [a_0, a_1, ... , a_n-1]