# Copyright (c) 2013 Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
# Copyright (c) 2013 Centre national de la recherche scientifique (CNRS)
# Copyright (c) 2020 Simons Foundation
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You may obtain a copy of the License at
# https:#www.gnu.org/licenses/gpl-3.0.txt
#
# Authors: Olivier Parcollet, Nils Wentzell
from scipy.optimize import leastsq
import numpy as np, inspect as ins
[docs]
class Fit:
"""
A simple general functional fit of a X,Y plot
Given a function f(x, p0,p1,p2 ...) with parameters p0, ..., p2, and an init guess
it adjust the parameters with least square method.
The fitting is done at construction
`self.param` is the tuple of adjusted parameters.
The object is callable : `self(x) = f(x, *self.param)`, so it can be plotted e.g.
"""
[docs]
def __init__ (self, x_array, y_array, fitter, p0 = None ) :
"""
:param x_array,y_array: curve to fit, as two 1d numpy arrays
:param fitter: a tuple (F, name, init_value_default) where :
* F is a function : `(x, *param_tuple)` -> y, which act on numpy arrays x and y
* name is string for which name%param_tuple gives the TeX representation of the function
* init_value_default is the default init point of the minimization
:param p0: init guess of the fit. If None, uses the init_value_default of the function.
"""
self.function, self.fname, p00 = fitter
assert len(ins.getargspec(self.function)[0])== len(p00) + 1, "error in number of parameters"
assert len(y_array) == len(x_array)
assert len(y_array) > len (p00)
errfunc = lambda x : np.abs ( self.function(x_array,*x) - y_array[:])
self.param, success = leastsq(errfunc, p0 if p0 else p00 )
def __str__ (self) : return (self.fname%tuple(self.param) or 'Fit').replace("+ -","-")
def __repr__ (self) : return str(self)
def __repr_tex__ (self) : return str(self)
def __call__ (self,x) : return self.function(x,*self.param)
# a collection of useful fit ...
linear = lambda X, a,b : a * X + b, r"$%f x + %f$" , (1,1)
quadratic = lambda X, a,b,c : (a * X + b)*X + c, r"$%f x^2 + %f x + %f$" , (0,1,1)