Pyfitting - Linear and non-linear fitting in python

Installation

To install pyfitting, simply run
pip install pyfitting

Interactive mode

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

Noninteractive mode

The module also exposes to functions. linfit for linear regression, and nonlinfit for non-linear regression.

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

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)

Additional parameters

nonlinfit has two additional parameters

• tol : describes how much each iteration should change before we assume convergence
  default value is 1e-11
• maxiter : which is the maximum times of iterations, before we stop the optimization.
  default value is 50