[feature request] fast interpolation in uniformly-spaced data

When working with uniformly-spaced data, it is possible to skip the initial search operation that an interpolation algorithm would ordinarily have to perform. This tends to speed things up significantly. It would be nice to have some specialized interpolators in SciPy that do linear interpolation and spline interpolation on uniformly-spaced data. The following sample code does linear interpolation without search:

   # Interpolate linearly, taking advantage of the fact that
   # the values in `f` are uniformly spaced.

   quo, rem= np.divmod(x, step)
   fraction= rem / step

   # Although the quotient values returned by `numpy.divmod` are integers, the
   # array dtype is 'f4'.  ==> We must force the dtype to 'i4' so that the
   # quotient values can be used for indexing:
   quo= quo.astype('i4')

   result= fraction * r[quo+1] + (1-fraction) * r[quo]

[Phillip-M-Feldman]

In all of my use cases, I define the interpolating function and then apply it exactly once, so it would be helpful if there were a way to pass a flag that says, “The caller promises that the independent variable is uniformly spaced.”

On Mon, Jun 3, 2019 at 9:38 PM Huize Wang [e-mail] wrote:

@MatthewFlamm https://github.com/MatthewFlamm Thanks! I agree that comprehensive timing is needed.

In terms of time complexity analysis, searchsorted should be O(logn) while search in uniform grid should be O(1), for 1-D case. A “uniformity check” is O(n) and I believe it should be run only once, during the interpolation class object initialization.

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[Phillip-M-Feldman]

Over the last 40 years, most of the data with which I’ve worked has been uniformly spaced in the independent variables. So, I’m inclined to think that this case is not that specialized.

On Wed, May 15, 2019 at 12:33 AM Evgeni Burovski [e-mail] wrote:

This feels best suited for specialized user code IMO.

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