CODEWITHSUNDEEP
python
GBA13
GBA13

Reputation: 215

Curve fit equation not properly fitting curve

I am using this code to curve fit some data:

def extract_parameters(Ts, ts):
    def model(t, Ti, Ta, c):
        return (Ti - Ta)*math.e**(-t / c) + Ta
    popt, pcov = cf(model, Ts, ts, p0 = (10, 6, 7))
    Ti, Ta, c = popt
    maxx = max(Ts)
    xfine = np.linspace(0, maxx, 101)
    print "xfine: ", xfine
    yfitted = model(xfine, *popt)
    print "yfittted", yfitted
    pl.plot(Ts, ts, 'o', label = 'data point')
    pl.plot(xfine, yfitted, label = 'fit')
    pylab.legend()
    pylab.show()
    return Ti, Ta, c

When I enter:

 extract_parameters([1,2,3,4,5,6],[100,60,50,40,45,34])

I get a perfect fit

but when I enter:

extract_parameters([1,2,3,4,5,6,7],[100,80,70,65,60,58,56])

I get this instead enter image description here

Can anyone see why? The curve fit changes drastically?

Upvotes: 0

Views: 337

Answers (1)

unutbu
unutbu

Reputation: 881027

Optimizers like curve_fit try to find the optimal fit, but don't always succeed. Notice that extract_parameters([1,2,3,4,5,6],[100,60,50,40,45,34]) returns

(196.85292746741234, 38.185643828689777, 1.0537367332516778)

That means it started with an initial parameter guess of p0 = (10, 6, 7) and found its way to quite a different location.

You can help the optimizer out by picking an initial guess which is closer to the optimal value. Simply by changing it to

p0 = (100, 6, 7)

allows

extract_parameters([1,2,3,4,5,6,7],[100,80,70,65,60,58,56])

to find a better fit: (131.71232607048836, 54.894539483338022, 1.8503931318517444).

enter image description here

Upvotes: 2

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