[SciPy-User] Sigmoid Curve Fitting
Warren Weckesser
warren.weckesser@enthought....
Mon Sep 20 22:54:44 CDT 2010
On 9/20/10 8:38 PM, Chris Spencer wrote:
> Hi,
>
> Does Scipy contain the ability to fit a sigmoid curve to a set of data points?
>
> I found some Numpy code
> (http://pingswept.org/2009/01/24/least-squares-polynomial-fitting-in-python/)
> for fitting curves using the least squares method, but it only seems
> to fit parabolas to my sigmoid data.
>
You can use curve_fit (scipy.optimize.curve_fit).
Which family of sigmoid functions do you want to use?
See http://en.wikipedia.org/wiki/Sigmoid_function for a few possibilities.
If, for example, you want to fit the following family to your data:
f(x) = 1/(1 + exp(-k*(x-x0)))
(which has two parameters, k and x0), you can do something like this:
-----
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()
-----
This script generates the attached plot.
Warren
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