我正在尝试使用有理函数将曲线拟合到X和Y数据点。在Matlab中,可以使用cftool完成此操作(http://de.mathworks.com/help/curvefit/rational.html)。但是,我想在Python中做同样的事情。我尝试使用scipy.optimize.curve_fit(),但它最初需要一个函数,而我没有。
您有一个函数,它是有理函数。因此,您需要设置该函数并执行拟合操作。由于curve_fit要求您以非列表的形式提供参数,因此我提供了一个额外的函数,用于在分子和分母中均为三次多项式的特定情况下进行拟合。
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')