curve_fit in scipy

[Gary Herron]

This is a Python forum, but what you are asking is not a Python 
question.  You might find a better source of answers on a scipy specific 
forum.

But here's my attempt at answers:



On 06/19/2018 08:26 AM, sharan.basappa at gmail.com wrote:
> Hi All,
>
> I am working out an exercise on curve_fit function available scipy package.
>
> While I understand in general about curve_fit, I am unable to understand the following:
>
> params, params_covariance = optimize.curve_fit(test_func, x_data, y_data,
>                                                 p0=[2, 2])
>
> Firstly, I don't understand why test_func is passed as an argument to cur_fit

You are trying to fit a curve to some data, right.  The curve_fit 
procedure needs to know what curve you are trying to fit.  Is it a 
linear curve, exponential, polynomial or ...?  In this example it's a 
sine function with parameters for regulating amplitude and frequency.  
But it could be any function with any parameters.  To be more precise, 
test_function is not a single function y=f(x), but a whole family of 
functions y=f(x; a,b) where a and b define a particular function.

> Secondly, I don't understand how curve_fit knows the number of arguments that test_func takes.

Part of the dynamic nature of Python is that a function carries with it 
the number of parameters (as just one among many such properties).  We 
call it "introspection" when we examine such properties of objects.  The 
curve_fit function usees such an introspection to find that 
test_function has two parameters (a and b) defining the family of curves.

>
> Full code is available below for reference:
>
> import numpy as np
>
> # Seed the random number generator for reproducibility
> np.random.seed(0)
>
> x_data = np.linspace(-5, 5, num=50)
> y_data = 2.9 * np.sin(1.5 * x_data) + np.random.normal(size=50)
>
> # And plot it
> import matplotlib.pyplot as plt
> plt.figure(figsize=(6, 4))
> plt.scatter(x_data, y_data)
>
> from scipy import optimize
>
> def test_func(x, a, b):
>      return a * np.sin(b * x)
>
> params, params_covariance = optimize.curve_fit(test_func, x_data, y_data,
>                                                 p0=[2, 2])
>
> print(params)
>
> plt.figure(figsize=(6, 4))
> plt.scatter(x_data, y_data, label='Data')
> plt.plot(x_data, test_func(x_data, params[0], params[1]),
>           label='Fitted function')
>
> plt.legend(loc='best')
>
> plt.show()

-- 
Dr. Gary Herron
Professor of Computer Science
DigiPen Institute of Technology
(425) 895-4418