python numpy/scipy curve fitting

Question

I have some points and I am trying to fit curve for this points. I know that there exist scipy.optimize.curve_fit function, but I do not understand documentation, i.e how to use this function.

My points: np.array([(1, 1), (2, 4), (3, 1), (9, 3)])

Can anybody explain how to do that?

Answer 1

I suggest you to start with simple polynomial fit, scipy.optimize.curve_fit tries to fit a function f that you must know to a set of points.

This is a simple 3 degree polynomial fit using numpy.polyfit and poly1d, the first performs a least squares polynomial fit and the second calculates the new points:

import numpy as np import matplotlib.pyplot as plt  points = np.array([(1, 1), (2, 4), (3, 1), (9, 3)]) # get x and y vectors x = points[:,0] y = points[:,1]  # calculate polynomial z = np.polyfit(x, y, 3) f = np.poly1d(z)  # calculate new x's and y's x_new = np.linspace(x[0], x[-1], 50) y_new = f(x_new)  plt.plot(x,y,'o', x_new, y_new) plt.xlim([x[0]-1, x[-1] + 1 ]) plt.show() 

Answer 2

You'll first need to separate your numpy array into two separate arrays containing x and y values.

x = [1, 2, 3, 9] y = [1, 4, 1, 3] 

curve_fit also requires a function that provides the type of fit you would like. For instance, a linear fit would use a function like

def func(x, a, b):     return a*x + b 

scipy.optimize.curve_fit(func, x, y) will return a numpy array containing two arrays: the first will contain values for a and b that best fit your data, and the second will be the covariance of the optimal fit parameters.

Here's an example for a linear fit with the data you provided.

import numpy as np from scipy.optimize import curve_fit  x = np.array([1, 2, 3, 9]) y = np.array([1, 4, 1, 3])  def fit_func(x, a, b):     return a*x + b  params = curve_fit(fit_func, x, y)  [a, b] = params[0] 

This code will return a = 0.135483870968 and b = 1.74193548387

Here's a plot with your points and the linear fit... which is clearly a bad one, but you can change the fitting function to obtain whatever type of fit you would like.