Fitting a big (and variable) number of datasets with shared and individual parameters in Python

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I have N (approx. 1000) datasets that I want to fit with the same polynomial model, where the second and higher order should be shared parameters and the first order will be individual to each set. The number of datasets will not always be same, but might vary.

To do so, I have a matrix with shape N x length and an x vector with shape length, which is valid for all datasets.

By searching for a solution, I came across symfit, but apparently it seems like, it is impossible to give all datasets in a matrix to symfit. Instead symfit asks to give every vector seperately, which seems difficult to me.

Have you ever done something similar? Or an idea how to solve it?

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