Move LowRankMatrix to LowRankApprox (or new package LowRankMatrices.jl)

[dlfivefifty]

LowRankMatrix is not actually a HierarchicalMatrix, so maybe it lives better in LowRankApprox. This would also make it easier to use the LowRankApprox algorithms.

[MikaelSlevinsky]

BarycentricMatrix2D isn't a hierarchical matrix either, but it would have been unreasonable to ship hierarchical matrices without them.

Probably could use an AbstractLowRankMatrix somewhere to collect all possible structures.

[dlfivefifty]

Why do you need to store the diagonal in LowRankMatrix?

[dlfivefifty]

Wait. your LowRankMatrix is always an SVD.

Why not use Base.LinAlg.SVD?

[MikaelSlevinsky]

The diagonal doesn't matter for performance (because of https://github.com/JuliaMatrices/HierarchicalMatrices.jl/blob/master/src/blas06.jl#L40). Is it always an SVD? I don't think so, but the fields strongly hint that it should be.

[dlfivefifty]

Your override of norm means U and V have to be orthogonal, i.e. it's an SVD

[MikaelSlevinsky]

You're right.

[dlfivefifty]

It overlaps with PartialSVD https://github.com/JuliaMatrices/LowRankApprox.jl/blob/master/src/psvd.jl

[MikaelSlevinsky]

Do we have support for the CUR factorization anywhere? http://www.math.vt.edu/people/embree/cur_talk.pdf

[dlfivefifty]

https://github.com/JuliaMatrices/LowRankApprox.jl/blob/master/src/cur.jl

[MikaelSlevinsky]

I wonder if that leads to a 'two-sided' butterfly algorithm

[MikaelSlevinsky]

Having its own version of LowRankMatrix allows me to introduce thread-safe temporary storage 95d7c81.