python 中的有理函数曲线拟合

Question

我正在尝试使用有理函数将曲线拟合到 X 和 Y 数据点。它可以在 Matlab 中使用 cftool 完成（http://de.mathworks.com/help/curvefit/rational.html). However, I am looking to do the same in Python. I have tried to use scipy.optimize.curve_fit()，但它最初需要一个函数，我没有。

Answer 1

你有函数，是有理函数。所以你需要设置功能并执行拟合。由于 curve_fit 要求您提供参数而不是列表，因此我提供了一个附加函数，该函数在分子和分母中对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')

python 中的有理函数曲线拟合

Rational function curve fitting in python

python

matlab

curve-fitting

scipy