我正在尝试使用有理函数将曲线拟合到X和Y数据点.可以使用cftool(http://de.mathworks.com/help/curvefit/rational.html)在Matlab中完成.但是,我希望在Python中做同样的事情.我尝试使用scipy.optimize.curve_fit,但最初需要一个功能,而我没有.

解决方法:

您具有功能,它是理性功能.因此,您需要设置功能并执行拟合.由于curve_fit要求您提供的参数不是列表形式,因此我提供了一个附加函数,用于对分子和分母中三次多项式的特定情况进行拟合.

def rational(x, p, q):
    """
    The general rational function description.
    p is a list with the polynomial coefficients in the numerator
    q is a list with the polynomial coefficients (except the first one)
    in the denominator
    The zeroth order coefficient of the denominator polynomial is fixed at 1.
    Numpy stores coefficients in [x**2 + x + 1] order, so the fixed
    zeroth order denominator coefficent must comes last. (Edited.)
    """
    return np.polyval(p, x) / np.polyval(q + [1.0], x)

def rational3_3(x, p0, p1, p2, q1, q2):
    return rational(x, [p0, p1, p2], [q1, q2])

x = np.linspace(0, 10, 100)  
y = rational(x, [-0.2, 0.3, 0.5], [-1.0, 2.0])
ynoise = y * (1.0 + np.random.normal(scale=0.1, size=x.shape))
popt, pcov = curve_fit(rational3_3, x, ynoise, p0=(0.2, 0.3, 0.5, -1.0, 2.0))
print popt

plt.plot(x, y, label='original')
plt.plot(x, ynoise, '.', label='data')
plt.plot(x, rational3_3(x, *popt), label='fit')