Today I pair-coded with Matt Daunt (NYU) a general kernel-based interpolator in jax. Actually, I am not certain that what we wrote can be handled by jax gracefully, because I don't understand the functional programming model. But I learned that interpolation is harder than I thought: If your interpolator is higher-order than linear, the interpolation involves solving an inverse problem. The fast interpolators (like spline) have such solutions coded with clever iteration schemes that require only one pass through the data, like the fast GPs we love. But if you want to write something general, you might have to suck up some (sparse) linear algebra. Daunt and I discussed strategies for our spectroscopic model, given these realities.
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