curve_fit.annealing
===============================
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()
Or use scipy.optimize.basinhopping_ ::
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.
.. _scipy.optimize: https://docs.scipy.org/doc/scipy/reference/optimize.html
.. _scipy.optimize.dual_annealing: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.dual_annealing.html#scipy.optimize.dual_annealing
.. _scipy.optimize.basinhopping: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.basinhopping.html#scipy.optimize.basinhopping
