florisvb/PyNumDiff

AI Summary: This issue proposes extending the package's methods, currently designed for univariate data streams, to support multidimensional arrays with an `axis` parameter, similar to NumPy. The goal is to generalize functionality across multiple dimensions while ensuring high performance by pushing computational loops down to compiled C, rather than relying on slower Python-level iteration.

AI Summary: This issue aims to enhance `PolyDiff` to handle variable step sizes and missing data, as `np.polyfit` currently fails with NaNs and `slide_function` doesn't support non-uniform spacing. This requires refactoring, NaN-checking, and careful consideration of how optimal polynomial degree and window size might fluctuate with non-uniform data. The changes will impact `polydiff` and other functions dependent on `slide_function` or kernel functions, potentially complicating general parameterization and optimization.

AI Summary: The `utility.slide_function` is currently inefficient, storing weights and results in a large array, leading to $\Omega(N^2)$ time complexity. This approach was chosen for its perceived simplicity in handling a complex combination step using NumPy. The issue proposes finding a more space-efficient method to improve performance, which would benefit `polydiff`, `lineardiff`, and `jerk_sliding`.

AI Summary: The issue proposes a fundamental change to the library's API to support non-equispaced data points, moving from a `(x, dt)` interface to `(x, t)`. This would require evaluating each method's compatibility, potentially re-implementing some or raising errors for methods that inherently rely on equispaced data (e.g., Fourier spectral, Savitsky-Golay).