Curve fitting in Python using scipy

Question

I want to fit a curve to some data using curve_fit in scipy. After I searched for the syntax I found this,

import numpy as np
from scipy.optimize import curve_fit

def func(x, a, b, c):
     return a * np.exp(-b * x) + c

xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5)
ydata = y + 0.2 * np.random.normal(size=len(xdata))

popt, pcov = curve_fit(func, xdata, ydata)

But the documentation is not really clear, specially regarding the parameters of the function func, I know x is the numpy array of independent variable values, but what are a, b, and c? Also, what does this line mean,

a * np.exp(-b * x) + c

to calculate y we call func with the independent variables and other parameters, but what is ydata? And why do we calculate it this way,

ydata = y + 0.2 * np.random.normal(size=len(xdata))

One last thing, if I get the fitted model (the equation) by scipy inside some function, how can I use it in another one?

Any help is appreciated. Thanks.

xnx · Accepted Answer · 2015-06-27 21:49:40Z

2

curve_fit fits a set of data, ydata, with each point given at a value of the independent variable, x, to some model function. In the example, the model function is a * exp(-b * x) + c, where a, b and c are some constants to be determined to best represent the data with this model.

The y calculated by func is the value of the model function at each data point, x.

In the example, ydata is simulated by the fit function with some random Gaussian (normally-distributed) noise added to it:

ydata = y + 0.2 * np.random.normal(size=len(xdata))

You can see this by plotting y (green line) and ydata (blue dots) against xdata:

enter image description here

To use the fitted parameters, popt, pass them to func:

yfit = func(xdata, *popt)

A plot will show you a comparison of the "exact" (green line) and fit (blue line):

enter image description here

edited Jun 27, 2015 at 21:49

answered Jun 27, 2015 at 21:42

xnx

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5 Comments

Dania Over a year ago

Thanks @xnx, in ydata, why the quantity is multiplied by .2? And what is good initial choice of a,b, and c? Because I've tried this curve_fit function with different a,b, and c and it doesn't fit at all, my data is scattered, is there a better solution than curve fit?

xnx Over a year ago

The 0.2 just rescales the noise so there isn't too much of it for the example; if you can't fit your particular data well to this func, perhaps there simply aren't any a, b, c that do the job well with this model. The solution is to use a different model function, func!

Dania Over a year ago

Thank you, Is there any well known nonlinear function to use? Also, from your answer I understand that y is the model, and ydata is just some randomly generated data made to show the effect of the fitted curve y, is this correct?

xnx Over a year ago

That's right. I'm afraid without knowing what your data represent, it's impossible to recommend a nonlinear function. Usually you would have a model function in mind before you attempt to fit.

Dania Over a year ago

Good, I will select the most appropriate function to the data shape. Thanks.

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