To install pyfitting, simply run
pip install pyfitting
The gui can be used in the following way
from pyfitting import cftool
#Create some test data
f = lambda x, p: return p[0]*(x**2) + p[1]*x+p[2]*sin(x)
x = np.arange(0,100,1/1000)
y = f(x,[0.1,0.5,100]) + np.random.normal(0,1,len(x))
yerr = np.ones((len(x),1))*100
cftool(x,y,yerr=yerr)If the error on y is not know, it can be left out
The module also exposes to functions. linfit for linear regression, and nonlinfit for non-linear regression.
linfit can be used simply like the following
from pyfitting import linfit
#Generate some test data
f = lambda x: return 5*x+27
x = np.arange(0,100,1/1000)
y = f(x) + np.random.normal(0,1,len(x))
yerr = np.ones((len(x),1))*100
fit = linfit(x, y, yerr=yerr)linfit returns a dict with three values. The parameters p, the reduced chi square chi2_red, and a function f which can be used to evaluate the fit
Non-linear regression works almost the same as linear. The only difference is, that nonlinfit two additional parameters. The function f, and starting values for the parameters p.
The function can either be passed as a string, where the parameters are named p[0],p[1] etx.
from pyfitting import nonlinfit
#Generate some test data
f = lambda x: return 5*x+27
x = np.arange(0,100,1/1000)
y = f(x) + np.random.normal(0,1,len(x))
yerr = np.ones((len(x),1))*100
#starting value for the parameters
p_start = [1,1]
fit = nonlinfit('p[0]*x + p[1]', x, y, p_start, yerr=yerr)It is also possible to pass a declared function.
Please note, that automatic differentiation is used, so any non-linear functions should be imported from autodiff
from pyfitting import nonlinfit
from autodiff import sin
#Generate some test data
f = lambda x, p : return p[0]*x + p[1]*sin(x)
x = np.arange(0,100,1/1000)
y = f(x,[5,27]) + np.random.normal(0,1,len(x))
yerr = np.ones((len(x),1))*100
#starting values for the parameter
p_start = [1, 1]
fit = nonlinfit(f, x, y, yerr=yerr)nonlinfit has two additional parameters
tol: describes how much each iteration should change before we assume convergence
default value is 1e-11maxiter: which is the maximum times of iterations, before we stop the optimization.
default value is 50