Curve fitting with global optimization routines

## Project description

Most curve fitting algorithms rely on local optimization routines. These demand good estimates of the fit parameters.

Instead, this module allows to use global optimization routines of scipy.optimize to minimize the squared deviation function.

## Installation

This module can be installed from PyPI

```pip3 install curve_fit.annealing
```

## Example

Let us fit a beat signal with two sinus functions, with a total of 6 free parameters.

By default, the curve_fit function of this module will use the scipy.optimize.dual_annealing method to find the global optimum of the curve fitting problem. The dual annealing algorithm requires bounds for the fitting parameters. Other global optimization methods like scipy.optimize.basinhopping require an initial guess of the parameters instead.

```import numpy as np
from matplotlib import pyplot as plt
from curve_fit import annealing

def f(x,p):
# Sum of two sinus functions
return p[0]*np.sin(p[1]*x + p[2]) + p[3]*np.sin(p[4]*x+p[5])

xdata = np.linspace(-100,100,1000)
ydata = f(xdata, [1, 1, 0, 1, 0.9, 0])

plt.plot(xdata, ydata, label='data')
bounds=[[0,2],[0,2],[0,2*np.pi],[0,2],[0,2],[0,2*np.pi]]

result = annealing.curve_fit(f, xdata, ydata, bounds=bounds)

p_opt = result.x # optimal fit parameters
ydata_res = f(xdata, p_opt)
plt.plot(xdata, ydata_res, label='fit')
plt.legend()
plt.grid()

plt.show()
```
```result = annealing.curve_fit(f, xdata, ydata, method='basinhopping', x0=np.zeros(6))
```

## API

curve_fit(f, xdata, ydata, [method='dual_annealing', args, kwargs])

Fit function f to data with selectable optimization method from scipy.optimize.

Parameters:
f: callable
The model function, f(xdata, p). The second argument holds the fitting parameters.
xdata : array_like or object
The independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object.
ydata : array_like
The dependent data, a length M array - nominally f(xdata, ...).
method : str
scipy.optimize method to use for non-linear least squares minimization. Default is ‘dual_annealing’.
args, kwargs : tuple and dict, optional
Additional arguments passed to the optimization method.
Returns:
Return OptimizeResult object. The x attribute holds the fitting parameters.