6th degree curve fitting with numpy/scipy

Question

I have a very specific requirement for interpolating nonlinear data using a 6th degree polynomial. I've seen numpy/scipy routines (scipy.interpolate.InterpolatedUnivariateSpline) that allow interpolation only up to degree 5.

Even if there's no direct function to do this, is there a way to replicate Excel's LINEST linear regression algorithm in Python? LINEST allows 6th degree curve-fitting but I do NOT want to use Excel for anything as this calculation is part of a much larger Python script.

Any help would be appreciated!

Answer 1

You can use scipy.optimize.curve_fit to fit whatever function you want (within reason) to your data. The signature of this function is

curve_fit(f, xdata, ydata, p0=None, sigma=None, **kw)

and it uses non-linear least squares fitting to fit a function f to the data ydata(xdata). In your case I would try something like:

import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def _polynomial(x, *p):
    """Polynomial fitting function of arbitrary degree."""
    poly = 0.
    for i, n in enumerate(p):
        poly += n * x**i
    return poly

# Define some test data:
x = numpy.linspace(0., numpy.pi)
y = numpy.cos(x) + 0.05 * numpy.random.normal(size=len(x))

# p0 is the initial guess for the fitting coefficients, set the length
# of this to be the order of the polynomial you want to fit. Here I
# have set all the initial guesses to 1., you may have a better idea of
# what values to expect based on your data.
p0 = numpy.ones(6,)

coeff, var_matrix = curve_fit(_polynomial, x, y, p0=p0)

yfit = [_polynomial(xx, *tuple(coeff)) for xx in x] # I'm sure there is a better
                                                    # way of doing this

plt.plot(x, y, label='Test data')
plt.plot(x, yfit, label='fitted data')

plt.show()

which should give you something like: