On Aug 29, 4:50 am, Oscar Gerardo Lazo Arjona
<algebraicame...@gmail.com> wrote:
> Hello!
>
> I have tried to fit some data about an harmonic oscillator to a sine
> function, but without success.
>
> Well, the find_fit command does return the values of constants, but they
> don't fit the data at all!
>
> I've attatched a worksheet showing this. The first cells are for
> retrieving the data from a file, just look at the two plots and how the
> fitted function (in red) doesn't match the data at all...
>
> Any ideas?
>
> Thanks
>
> Oscar
Basically, the find_fit function has problems to find a good initial
guess (especially for the period)
You could try to help it.
I can see two ways to do it, using the fact that you expect a sin
function.
First, guess the parameters yourself:
you could look for sign changes to guess the period, this would give
you:
sage: initial_omega = pi.n()/mean(differences([0.5*(data1[i][0]+data1[i
+1][0]) for i in range(len(data1)-1) if data1[i][1]*data1[i+1][1] <
0]))
it seems to be enough:
sage:
fit=find_fit(data1,model,parameters=[x0,omega,phi],initial_guess=[1,
omega_i, 1],solution_dict=True); fit
{x0: 0.051021428637755981, phi: -0.021166741696878096, omega:
9.521221611651983}
(nb: you could also find youself better initial guesses for the other
parameters:
x0_i = max([y for x,y in data1])
phi_i = sorted(data1, key=lambda t:abs(t[1]))[0][1]
)
Second possibility, "clean the data", it would be a lot easier if we
have only one period:
sage: min(i for i,(x,y) in enumerate(data1) if y*data1[0][1]<0) #
first sign change
17
sage: min(i for i,(x,y) in enumerate(data1) if y*data1[0][1]<0) #
second sign change
34
sage: data2 = data1[17:34]
sage: fit2=find_fit(data2,model,solution_dict=True); fit2
{x0: 0.05240254787043807, phi: 6.2763562528486139, omega:
9.5651019068351939}
You can even go back to data1:
sage:
fit=find_fit(data1,model,parameters=[x0,omega,phi],initial_guess=[fit2[x0],
fit2[omega], fit2[phi]],solution_dict=True); fit
{x0: 0.051021428642885822, phi: 6.2620185789145335, omega:
9.5212216134899759}
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