Hi Oscar,
On Feb 17, 2014, at 7:03 PM, Oscar Benjamin <oscar.j.benja...@gmail.com> wrote:
> On 17 February 2014 22:15, "André Walker-Loud <walksl...@gmail.com>"
> <walksl...@gmail.com> wrote:
>>> This particular case is easily solved:
>>>
>>> def f_lambda(x,pars):
>>> return lambda x: poly(x,*pars)
>>>
>>> You let the closure take care of pars and return a function that takes
>>> exactly one argument x.
>>
>> Hi Oscar,
>>
>> This is the opposite of what I am trying to do. In the example, x
>> represents the data and pars represent the parameters I want to determine,
>> so it is the pars which I need passed into the "func_code.co_varnames" part
>> of f.
>
> BTW if you're trying to fit the coefficients of a polynomial then a
> general purpose optimisation function is probably not what you want to
> use. I would probably solve (in a least squares sense and after
> suitable scaling) the Vandermonde matrix.
>
> (I can explain that more if desired.)
That looks interesting (just reading the wikipedia entry on the Vandermonde
matrix).
Is there a good algorithm for picking the values the polynomial is evaluated at
to construct the matrix?
Is there a benefit to this method vs a standard linear least squares?
Given the Vandermonde matrix, how do you determine the uncertainty in the
resulting parameters?
I guess yes, I am interested to learn more.
The most common problem I am solving is fitting a sum of real exponentials to
noisy data, with the model function
C(t) = sum_n A_n e^{- E_n t}
the quantities of most interest are E_n, followed by A_n so I solve this with
non-linear regression.
To stabilize the fit, I usually do a linear-least squares for the A_n first,
solving as a function of the E_n, and then do a non-linear fit for the E_n.
Often, we construct multiple data sets which share values of E_n but have
different A_n, where A_n is promoted to a matrix, sometimes square, sometimes
not. So I want a wrapper on my chisq which can take the input parameter values
and deduce the fit function, and pass the variable names to my current
minimizer - hence my original question, and why I don’t want to write a special
case for each possible combination of n_max, and the shape of A_n.
Cheers,
Andre
_______________________________________________
Tutor maillist - Tutor@python.org
To unsubscribe or change subscription options:
https://mail.python.org/mailman/listinfo/tutor
