Structural non-allocating array-like interpolation

[SouthEndMusic]

I have the following 🍇 about the current implementation:

• Array-valued interpolations are allocating;
• Different methods for scalar and array interpolation per interpolation type yields code duplication;
• Support for array-valued interpolation is inconsistent.

As far as I'm aware, for every interpolation type the array-valued interpolation can be defined by a per-index scalar interpolation.

I propose:

• Array Interpolation objects get a pre-allocated value, derivative and integral on which computations are done in-place;
• We define a function get_u(A.u, i) which gets the appropriate view of a slice of u.

Related issues:

• Interpolation convenience methods for higher dimensional data #118
• Reduce allocations in vector-valued interpolations #361

[sathvikbhagavan]

As far as I'm aware, for every interpolation type the array-valued interpolation can be defined by a per-index scalar interpolation.

Wouldn't that allocate more as compared to having an implementation for arrays?

[SouthEndMusic]

How so?

I didn't say that to inform the implementation btw, more to have a consistent way of defining what array-valued interpolation means.

[sathvikbhagavan]

I didn't say that to inform the implementation btw, more to have a consistent way of defining what array-valued interpolation means.

Oh, ok. I was thinking having an interpolation object for every time series for higher order arrays might be expensive in both memory and time. Hence, it might be better to have separate dispatches for array valued where everything is vectorized.

[SouthEndMusic]

That's something that I wondered about: is it better to use different code for scalar and array cases, and why is that?

[ChrisRackauckas]

You cannot write in-place code for scalars since they are immutable. Scalar code can be non-allocating while having caches for arrays cannot be. So if you want both to be non-allocating, you need different code for both.

Array-valued interpolations are allocating;

The in-place form is not supposed to be?

[SouthEndMusic]

The in-place form is not supposed to be?

To be fair I didn't test this, but I assumed because there is no pre-allocated cache available in e.g. the _interpolate methods to compute the array-valued output in-place. Looking at the _interpolate methods for typeof(u) <: AbstractMatrix, these all allocate the output.

I'm sure it's not always possible, but if the evaluation methods return @. <expression> and that output is immediately assigned to pre-allocated memory, maybe that is not allocating?