ShapedArray type and/or protocol

[stephentyrone]

Add a ShapedArray type and/or protocol suitable for use as the common currency type for vectors / linear algebra / image processing / tensors, like ndarray is for numpy.

This should hew pretty closely to what S4TF already does with their ShapedArray type; it doesn't need to be identical, but we need to have a good reason for any changes.

[dabrahams]

@stephentyrone Are you familiar with MTL4?

[dastrobu]

A ndarray like type for swift would be great!
Some features of NymPy's array would be great to see:

• contiguous and non contiguous array handling
• array slices with strides
• copy free array reshaping

I implemented a basic NdArray type for Swift a while a go, implementing theses features. It is currently more like a draft implementation than meant for production use.

Regarding linear algebra operations, I would recommend not to implement them in Swift and just call BLAS and LAPACK routines available on Linux platforms and from the Apple Accelerate framework on mac platforms. BLAS and LAPACK have been optimised for decades and there are many implementations available optimised for specific platforms or tuned for specific machines (ATLAS). As far as I know the Fortran implementations are still fastest and one should simply link theses implementations like NumPy and many other linear algebra packages do.

Not being too familiar with the ShapedArray type, I think it lacks support for non-contiguous arrays and array slices with strides.

[stephentyrone]

Not being too familiar with the ShapedArray type, I think it lacks support for non-contiguous arrays and array slices with strides.

ShapedArray in S4TF does not support strides arrays or slices, and only supports one dimension ordering. My intention for SN is to both of these things (ndarray is a good mental model).

Regarding linear algebra operations, I would recommend not to implement them in Swift and just call BLAS and LAPACK routines available on Linux platforms and from the Apple Accelerate framework on mac platforms.

My intention is to make BLAS and LAPACK available using the shaped array type, but it should also be possible to implement linear algebra--this is a great check to ensure that we have a sufficiently powerful API to describe new operations in the future. So I'll also be implementing some of the BLAS and LAPACK operations in a module as an easy way to flush out API limitations and optimization shortcomings.

[awav]

Hello, @stephentyrone! I thought you might be interested in this PR, tensorflow/swift-apis#680. In it, I propose to define math protocols for shaped arrays in swift-apis. This is quite close to what you are doing with swift-numerics. Plus, I'm more than happy to help out with linear algebra implementation in swift-numerics.

[phewdry]

Hi Artem am wondering on current status for this issue?

Hello, @stephentyrone! I thought you might be interested in this PR, tensorflow/swift-apis#680. In it, I propose to define math protocols for shaped arrays in swift-apis. This is quite close to what you are doing with swift-numerics. Plus, I'm more than happy to help out with linear algebra implementation in swift-numerics.

[SharanSMenon]

Is this coming?

[Datamance]

Following this - it would be really nice to have a great NDArray-like API (and all the other numpy goodies) sitting on top of BLAS and LAPACK, but in the Swift Runtime. I think the closest thing out there is Surge but that uses Accelerate and OpenCV under the hood.

[dastrobu]

@Datamance note that Accelerate is using BLAS and LAPACK under the hood, so I think there is nothing wrong with that approach.

Surge does have quite good linear algebra support! Compared to numpy, Surge seams to be missing array slicing with strides. Having multiple views on the same data (different shape, different strides) is one of the great features of numpy I guess.

There is also Matft, which supports slicing and strides, but is not supporting generic elements. Then there is NdArray (written by me as mentioned earlier in #6 (comment)) with focus on slices and strides while keeping generic elements. But currently, linear algebra support is very limited.

I guess there are many more Numpy'ish packages out there, all having some strengths and shortcomings. So having an official swift-numerics type would be great.

[superlopuh]

One thing that I would suggest is to have the interface be flexible enough to be compatible with TACO and the MLIR implementation. It really seems like a great abstraction over dense and sparse arrays, and when the MLIR project gets wider adoption it would be great to leverage all the optimisations that make more sense in the compiler than in framework code.