arrayfire / arrayfire/arrayfire-python

Bugs in af.approx1()

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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`
![download 9](https://cloud.githubusercontent.com/assets/19583419/24001222/90a839b2-0a83-11e7-8d61-dac9f4fd45a3.png)

The order of convergence comes out to be ![image](https://cloud.githubusercontent.com/assets/19583419/24001620/abd1cd74-0a84-11e7-8690-c6f68882734f.png), while the expected convergence rate is ![image](https://cloud.githubusercontent.com/assets/19583419/24001712/dffcefd4-0a84-11e7-99d5-6475b2de7c79.png). I checked with `af.INTERP.CUBIC_SPLINE` as well. Even in that case the order of convergence comes out to be ![image](https://cloud.githubusercontent.com/assets/19583419/24001738/fa04291a-0a84-11e7-8fcb-946a8b3e8602.png)

![download 8](https://cloud.githubusercontent.com/assets/19583419/24001789/174c4f2a-0a85-11e7-8af0-582a153b6123.png)

Another issue is the fact that the error doesn't drop below 1e-7. The SciPy interpolation function `interp1d` using cubic interpolation gives this:

![download 19](https://cloud.githubusercontent.com/assets/19583419/24001909/4fb536f6-0a85-11e7-8339-16767b8bd4eb.png)

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.

Guide de contribution

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Piste de recherche

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.

Rédigé par le modèle d'indexation à partir du texte de l'issue.

Évaluation

Stack technique
python
Domaine
backend
Type d'issue
Bug
Difficulté
4/5
Temps estimé
3-5 jours
Activité
À l'abandon
Clarté
À clarifier
Accessibilité débutants
30/100

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