Fitting 2D Y-data in python

Question

I have a general class of non-linear problem where I have 2 or more vectors of y-data that are coupled in a dependent, but known, way to 2 or more vectors of x-data, and I want to find the parameters. I'm looking for a way to adapt the basic non-linear fit model in python to take both sets of data into account.

In a general case, I might have the pair:

[y1(x1, x2; A, B), y2(x1, x2; A, B)]

As a concrete example, I might have:

y1 = A sin(B x1) + e^(-A x1)

y2 = A x1^2 + B x2 + log[A x2]

(Assume these are not analytically solvable, or might present inefficiencies if solved). I know all the values y1, y2 and x1, x2, and I want to find an estimate for A and B that takes into account the data from both ys. I could just fit one or the other equation and get an estimate for A and B.

For example, imagine if y2 did not depend on B (or did so very weakly). It still gives strong information about the value of A that I want y1 to take into account.

As a secondary question, how would I use this method to put different weights on the two sets of the y-data?

Edit:

One potential approach I can think of would be to stack all the y-data into a single column, and then use the function to process the expected y1,y2, and then end the function with something like return vstack((y1,y2)) so I could compare the two sets? Then I could just have a weighting function that matches the length of this joined function?

You used lot of text in your question. It would have been much easier to understand you if you would have included a simple example of what you want, in terms of sample input an output — Sheldore, Jun 05 '19 at 19:14
Can your nonlinear fit method handle vector-valued functions as in your proposed approach? — Davis Herring, Jun 05 '19 at 20:10
Depending on the level of generalization you need, you could just use `scipy.optimize.leastsq` and write your own residual function including weights. Most of the time that's not a big deal, but can become tricky if you want have e.g. variable amount of equations or data sets. Did you have a look at `lmfit`? I'm not using that, but it might be capable of doing what you want. — mikuszefski, Jun 06 '19 at 07:52
You may have a look [here](https://stackoverflow.com/a/20341726/803359) — mikuszefski, Jun 06 '19 at 07:57

score 0 · Answer 1 · answered Jun 06 '19 at 08:35

I think you can follow this symfit example here, and adapt it to your problem. So that would be something like:

from symfit import variables, parameters, Fit, sin, exp, log

x_1, x_2, y_1, y_2 = variables('x_1, x_2, y_1, y_2')
A, B = parameters('A, B')

model_dict = {
    y_1: A * sin(B * x_1) + exp(-A * x_1),
    y_2: A * x_1**2 + B * x_2 + log(A * x_2)
}

fit = Fit(model_dict, x_1=x1data, y_1=y1data, x_2=x2data, 
          y_2=y2data, sigma_y_1=y1stdev, sigma_y_2=y2stdev)
fit_result = fit.execute()

This example already includes different weights on the different y_1 and y_2 by providing the standard deviations as extra information.

Disclaimer: I'm the author of symfit.

Fitting 2D Y-data in python

1 Answers1