[WIP] SparseVector

[lindahua]

This is based on the discussion in #11324. This PR remains WIP, and it is doing the following:

• Add the SparseVector type.
• Add methods of the SparseVector type.
• Add methods that interact with both SparseMatrix and SparseVector.
• Add relevant linear algebraic methods.
• Add a complete test suite.
• Add documentation.

[ViralBShah]

We will also need methods for AbstractMatrix and SparseVector. It would be nice to have some ways to iterate over both sparse matrices and vectors with the same API.

[mlubin]

As @StefanKarpinski suggested, let's make sure we have complete code coverage for this.

[lindahua]

Depending on the decision in #11408

[lindahua]

The last commit of this PR passed tests (as shown by Travis-ci). The appveyor issue is unrelated. Of course, more tests are to be added.

[tkelman]

The AppVeyor failure is not unrelated. I can reproduce it by running make testall1 locally on this branch, even on 64-bit Linux. It's most likely some dumb variable name conflict.

[lindahua]

Note: I am now working towards the NIPS 2015 submission deadline on June 6. Will resume the efforts here afterwards.

[tkelman]

Thanks for the update Dahua. Good luck with your submission.

[tkelman]

#11583 would be good to address here, once you get back to this.

[ViralBShah]

@lindahua Do you think we can do this in the next couple of weeks - which would make it possible to include in 0.4?

[lindahua]

I don't think I can have much time coding Julia in the coming month, as I have to kick start some new research projects. However, this is not a very difficult tasks, and I wish people interested in this PR can continue the efforts ...

[lindahua]

I am now resuming the efforts on this.

[tkelman]

I have a cleaned-up branch of this at https://github.com/JuliaLang/julia/tree/tk/sparsevec that you should start from, that at least passes tests. It doesn't address the unchecked items in the list up top though.

[lindahua]

Thanks, I will look into that.

[lindahua]

This PR is going to change the semantics of several functions (e.g. sparsevec will return an instance of SparseVector instead of SparseMatrixCSC) and may possibly break some client codes. Given that we are now very late in the 0.4 cycle, I think it is better to make this happen post-0.4.

Also, many more functions are being actively implemented, tested, and tuned in the SparseVectors package.

I am closing this, and will make another PR, when:

• Julia 0.4 is released; and
• The package SparseVectors already implements all the functions needed to be transferred to the Base.

[tkelman]

How do you plan on making the SparseVectors package correctly implement things that are currently buggy in base? Non-exported replacements like SparseVectors.sparsevec ?

[lindahua]

I am now adding sparsevector to the package, which plays a similar role as sparsevec but returns a SparseVector instance. This function will be renamed to sparsevec when transferred to the Base.

[tkelman]

Sounds reasonable. Will the package try to change base's indexing rules, returning a SparseVector from column slicing of a SparseMatrixCSC? I think that's the biggest most important change here that would be worth the possible breakage no matter when we decide to do it, but may as well do this right instead of rushing it.

[lindahua]

Sure, will explore the slicing stuff as next major step in the package development.

Currently, we have view(A, :, i) that returns a SparseVectorView instance when A is a sparse matrix and i is an integer. But will of course do more later.

[mbauman]

Hearty bump!

Any chance this could be revisited in the near future? Missing a real vector makes indexing into sparse matrices wonky. And it only gets stranger if we drop scalar dimensions — because then S[1,:] becomes… a 1-column matrix?

[lindahua]

I figure maybe I have to say that I probably won't be able to find enough time to push forward this PR before mid November.

The SparseVectors package has been quite stable. Anyone who are willing to push forward this please feel free to make a PR based on the whole / part / or none of that package.