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# good discussion here:  http://stackoverflow.com/questions/4308168/sigmoidal-regression-with-scipy-numpy-python-etc
# curve_fit() example from here: http://permalink.gmane.org/gmane.comp.python.scientific.user/26238
# other sigmoid functions here: http://en.wikipedia.org/wiki/Sigmoid_function

import numpy as np
import pylab
from scipy.optimize import curve_fit

def sigmoid(x, x0, k):
     y = 1 / (1 + np.exp(-k*(x-x0)))
     return y

xdata = np.array([0.0,   1.0,  3.0, 4.3, 7.0,   8.0,   8.5, 10.0, 12.0])
ydata = np.array([0.01, 0.02, 0.04, 0.11, 0.43,  0.7, 0.89, 0.95, 0.99])

popt, pcov = curve_fit(sigmoid, xdata, ydata)
print popt

x = np.linspace(-1, 15, 50)
y = sigmoid(x, *popt)

pylab.plot(xdata, ydata, 'o', label='data')
pylab.plot(x,y, label='fit')
pylab.ylim(0, 1.05)
pylab.legend(loc='best')
pylab.show()