arrayfire / arrayfire/arrayfire-python
Bugs in af.approx1()
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- Python
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Description
Convergence checks performed on the ArrayFire routines for interpolation seem to indicate a few mistakes:
The following plot is generated using `af.INTERP.CUBIC`
The order of convergence comes out to be , while the expected convergence rate is . I checked with `af.INTERP.CUBIC_SPLINE` as well. Even in that case the order of convergence comes out to be 
Another issue is the fact that the error doesn't drop below 1e-7. The SciPy interpolation function `interp1d` using cubic interpolation gives this:
For your reference - this is the [code](https://gist.github.com/ShyamSS-95/ad0065e984b76d1ccaecc5e21b425734) I'd used to generate the plots.
Also regarding issue #130 - I've realised that the mistake was on my part. I should have added the off-set in the indexing to the normalized interpolant points.
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Research direction
Start by running the linked reproduction code and examining af.approx1 with af.INTERP.CUBIC and af.INTERP.CUBIC_SPLINE. Compare the observed convergence rates and error floor with SciPy's interp1d; done means identifying and correcting the interpolation behavior so the expected convergence and accuracy are restored.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- python
- Domain
- backend
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 30/100