Add spline interpolation

[wbenoit26]

Adding the spline interpolation into ml4gw and integrating it into the Q-transform. Still a lot to do, but I wanted to get something pushed so people could take a look at it. The main changes compared to the original are:

• Unification of 1D and 2D splines into a single class. I noticed that the 1D interpolation was for some reason a lot slower than the 2D, so I tried to generalize the 2D to handle both cases. There are some percent-level discrepancies between the two that I still need to track down though.
• Pre-calculating the basis matrices. Based on the parameters of the Q-transform, we know the input and output shapes of the interpolation, so we can save a little time by calculating these up front. I've included the option to specify different input and output coordinates after object initialization if desired, but for our use case, I think we generally won't need to do that.
• Allowing a channel dimension in addition to a batch dimension so that we can interpolate data from multiple detectors at the same time.
• Some formatting changes to bring things more in line with how things are set up in ml4gw

To-do:

• [x] Establish consistency with original code. For 2D, the results agree exactly, but I want to track down the difference for the 1D case.
• The difference between the 1D and 2D comes down to numerical precision. Even after casting everything to double, minor deviations accumulate from various factors: different data input shape, einsum vs. matmul, order of multiplication, etc. These deviations get exacerbated by the final torch.linalg.solve in calculating the spline coefficients. I don't think there's anything I can do about this, but the approach is valid and the typical error between the two methods is small, so I'm going to mark this as done.
• [x] Make a nicer/more intuitive API for SplineInterpolate. The current setup makes it a little awkward to do 1D interpolation,and I want to put back the functionality from the original code that allowed specifying just the input/output size.
• [x] Add data validation checks to SplineInterpolate
• [ ] Set up rigorous testing against scipy. I know that this interpolation has edge effects that aren't present in scipy, but it would be good to ensure that everything mostly agrees.
• [x] Improve integration with SingleQTransform. It would be nice to be able to specify whether the full spline interpolation is desired, or whether some preset torch option is sufficient. This is particularly important because the matrix inversion that occurs during the spline interpolation takes up a lot of memory for large matrices, and so may not be desirable for some use cases.
• [x] Documentation
• [x] Add Q-transform tests with spline interpolation
• [x] There's possibly some more optimization to be done by using the fact that many of the Q-tiles have the same shape, so they can be stacked and interpolated as a group.
• [ ] Figure out what the memory constraints are

[wbenoit26]

@EthanMarx This is at the point that it would be good to have you take a look at it. There remain a couple of issues with matching exactly with SciPy's implementation, but I think the code is usable with the caveats that I describe in the documentation.

[EthanMarx]

So the spline interpolation is a general interpolator that could be (potentially) used for different use cases, and then you are just implementing it for the Qtransform?

[wbenoit26]

Exactly, yeah