This is a simple module which contains vectorised interpolators for linear and cubic-spline interpolation. It is compatible with torch's autograd. It extends torchinterp1d with Cubic Spline function with a few extrapolation options.

History:

• v0.1 11/7/2024 - Initial version, single function interpolation, both linear and cubic spline.
• v0.2 18/9/2024 - Implemented parallel handling of independent interpolations
  20/9/2024 - Fixed a forgotten contiguous conversion for already batched parameters

Usage:

Initialise the interpolation function with:

f_int = interpolatorch.InterpolateLinear(x_vals, y_vals, extrapolate = False, ext=0, ext_value=None)

where x_vals and y_vals have shape (N_b, N_t), with N_b counting the number of independent interpolations and N_t corresponds to the number of indices in each data set. x_vals needs to be sorted in dim=1.

Then call with f_int(x) with any torch tensor x. If dim=0 of x has size N_b, then each element of these will be used to evaluate different interpolation functions. Otherwise, x will be assumed to apply to all interpolation functions.

Same rules apply to interpolatorch.CubicSplines.

If extrapolating:

• ext = 0 : continuous extrapolation using the relationship at the closest boundary
• ext = 1 : second order discontinuous extrapolation using the constant value at the closest boundary
• ext = 2 : (potentially) first order discontinuous extrapolation using the values provided in ext_value.

To do:

Currently, a single pair of extrapolation values are supported in ext = 2 option. Separate pairs for each interpolation functions will be supported... if I need it.