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python-fit

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The python-fit module is designed for people who need to fit data frequently and quickly. The module is not designed for huge amounts of control over the minimization process but rather tries to make fitting data simple and painless. If you fit two-dimensional data several times a day, every day, and you really just want to see if the fit you've made looks good against your data, check out this software. If you want one very statistically aware and neurotically controlled fit, you might consider looking elsewhere (give zunzun a look).

With python-fit, you get work done.

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, arange
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 "mu:    %.2f +/- %.3f" % (params[1], err[1])
print "sigma: %.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')

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A python module using scipy's orthogonal distance regression that makes fitting data easy.

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