python-fit 1.0.0

Features

• Common fitting curves built-in

• Default parameters for built-in functions intelligently calculated using your data.

• Fit with user defined functions, too.

• A ready-to-plot-fit always conviently returned.

• Get fit parameters and associated errors.

• Chi-squared residual.

Example Usage

Fit with built in functions:

from pylab import *
ion()
import fit
from numpy import random, exp
random.seed(0)

# Create some data to fit
x = arange(-10, 10, .2)
# A gaussian of height 10, width 2, centered at zero. With noise.
y = 10*exp(-x**2/8) + (random.rand(100) - 0.5)


# No need to provide first guess at parameters for fit.gaus
(xf, yf), params, err, chi = fit.fit(fit.gaus, x,y)

print "N:    %.2f +/- %.3f" % (params[0], err[0])
print "N:    %.2f +/- %.3f" % (params[1], err[1])
print "N:    %.2f +/- %.3f" % (params[2], err[2])

plot(x,y, 'bo', label='Data')
plot(xf, yf, 'r-', label='Fit')
legend()

Functions available:

Gaussian curve
Exponential curve
Double exponential
Polynomials for degrees 0-20
Power-Law
Crystal Ball
... and more!

Fit with user defined functions:

x = (4.2105303, 5.2631601, 6.2405997, 7.5187997, 8.7218, 9.7744402, 10.676691, 11.65414, 12.63158, 13.83459, 14.887219, 16.015039, 17.06767,
18.270679, 19.24812, 20.300751, 21.50376, 23.157888, 25.789471, 28.345871, 30.601501, 33.458643, 39.022559, 46.015039, 48.270679)
y = (0.18942001, 0.2099, 0.23891001, 0.27816002, 0.31911, 0.35836001, 0.39932001, 0.43686003, 0.46416002, 0.49829001, 0.51536004, 0.52556, 0.51876995,
0.5, 0.47271, 0.44026, 0.39249001, 0.33106002, 0.24060, 0.17746, 0.13311001, 0.11262, 0.095566, 0.095566, 0.095566)

x = array(x)
y = array(y)

# Guassian with quadratic background.
def example_function(params, x):
    N,mu,sigma,a,b,c = params
    return N*exp(-0.5 * ((x-mu)/sigma)**2 ) + a*x**2 + b*x + c

# It will still try to guess parameters, but they are dumb!
(xf,yf),p,e,chi = fit.fit(example_function, x,y)
plot(x,y, 'bo', label='Data')
plot(xf,yf, 'r-', label='Fit')
legend()

Even though example_function is defined by the user, python-fit will guess parameters (the median value of the xdata for all parameters; it works if x and y are on similar scales). If the fit fails, then provide some decent parameters as a first guess:

results = fit.fit(example_function, x, y, default_pars = [1, 12, 10, 1, 1, 1])
plot(results[0][0], results[0][1], 'r--')

Fit a sub-range:

clf()
results = fit.fit(fit.gaus, x, y, data_range=[0, 23])
plot(results[0][0], results[0][1], 'r-.')

Define your own weights to prevent outliers from wreaking havoc on your fit:

# Create some outliers.
y_outlier = y + (random.rand(len(y))**20)*3
# I'll just make a cut and say outliers are above 0.55
weights = 1. * (y_outlier < .55)
results = fit.fit(example_function, x, y_outlier, we=weights)
clf()
plot(x,y_outlier, 'bo', label='Data w/ Outliers')
plot(results[0][0], results[0][1], 'r-.', label='Fit around outliers')