Rational function curve fitting in python

Question

I am trying to fit a curve to X and Y data points using a rational function. It can be done in Matlab using the cftool (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(), but it initially requires a function, which I don't have.

Answer 1

You have the function, it is the rational function. So you need to set up the function and perform the fitting. As curve_fit requires that you supply your arguments not as lists, I supplied an additional function which does the fitting on the specific case of third degree polynomial in both the numerator as well as the denominator.

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')