How To Fit Parametric Equations To Data Points In Python

I am looking for a way to fit parametric equations to a set of data points, using Python. As a simple example, given is the following set of data points: import numpy as np x_data

Solution 1:

You can use polyfit, but please take care that the length of t must match the length of data points

import numpy as np

tt = np.linspace(0, 5, len(x_data))

x_params = np.polyfit(tt, x_data, 1)
y_params = np.polyfit(tt, y_data, 2)

Change the third parameter to the degree that you think fits your data.

To get the function you can use

y = np.poly1d(y_params)

t = np.arange(0, 5, 0.1)

plot(t, y(t))
plot(tt, y_data, 'o')

Solution 2:

Since the relation between x and y is a quadratic one, you can use np.polyfit to get the coefficients. According to your equations, your x and y relation is:

y = a2*((x-b1)/a1)**2 + b2*((x-b1)/a1) + c2

Using polyfit, we get

y_data = np.array([2, 0, 3, 7, 13])
x_data = np.array([1, 2, 3, 4, 5])
np.polyfit(x_data,y_data,2)
[p2,p1,p0] = list(array([ 1.21428571, -4.38571429,  4.8       ]))

The values of a1, b1, a2, b2, c2 can be obtained by solving the following eqns

p2 = a2/a1**2

p1 = -2b1*a2/a1**2 + b2/a1

p0 = a2*b1**2/a1**2 -b2*b1/a1 + c2