Creating a `KernelMatrix` with custom row & column elements

[tpgillam]

In Kernel matrices documentation it's stated that elements can be of any type:

The row and columns elements may be as simple as points in $\mathbb{R}^d$ (as is the case for Nyström methods), but they can also be more complex objects such as triangles or basis functions –- the only thing required is that f(X[i],Y[j]) make sense.

However, I run into problems constructing ClusterTrees if I try to exercise this ability. Some assorted observations:

• as suggested in WavePropBase, I've implemented HMatrices.center(::MyType)::SVector{3,Float64}

• in the documentation, it's stated that ClusterTree comes from WavePropBase, but actually it seems this is no longer true.

• whilst WavePropBase's ClusterTree supports arbitrary element types, the current version in HMatrices only supports SVectors.

• Trying to use WavePropBase.ClusterTree explicitly results in a MethodError for isleaf.

Am I approaching this case incorrectly? Or is this a bug? In any case, I'm looking forward to using HMatrices, as it should be directly applicable to my problem if it can handle this case. Thanks!

[maltezfaria]

This is certainly a bug. As you correctly pointed out, this package became independent of WavePropBase at some point, and I was not sufficiently careful to test the changes thoroughly. And the documentation is certainly outdated in the places you mentioned!

Let me take a look at these issues, and I will get back to you soon with more information.

[maltezfaria]

If you have a MWE of what you are trying to achieve, that would be quite helpful in understanding/fixing the problem! Thanks.

[maltezfaria]

I made some small changes here and added a simple example to kernelmatrix.md of how you may achieve something similar to what you asked. Let me know if this is not it :-)

[tpgillam]

If you have a MWE

Here's a very minimal MWE. (In my case the type actually represents a some geometry of finite extent, and the kernel is a function of a pair of elements, in case that were to change anything)

using HMatrices
using StaticArrays

struct MyType
    a::Float64
    b::Float64
end

HMatrices.center(t::MyType) = SVector(t.a, t.b)

X = [MyType(x, 2 * x) for x in 1:10]
Y = X

f(x::MyType, y::MyType) = (x.a + x.b + y.a + y.b) / 4

K = KernelMatrix(f, X, Y)
assemble_hmatrix(K)

which gives

ERROR: LoadError: MethodError: no method matching ClusterTree(::Vector{…}, ::HyperRectangle{…}, ::UnitRange{…}, ::Vector{…}, ::Vector{…}, ::Nothing, ::Nothing)

Closest candidates are:
  ClusterTree(::Array{SVector{N, T}, 1}, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any) where {N, T}
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/clustertree.jl:25
  ClusterTree(::Any, ::Any; copy_elements, threads)
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/clustertree.jl:123
  ClusterTree(::Any; ...)
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/clustertree.jl:123

Stacktrace:
 [1] ClusterTree(elements::Vector{MyType}, splitter::CardinalitySplitter; copy_elements::Bool, threads::Bool)
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/clustertree.jl:138
 [2] ClusterTree(elements::Vector{MyType}, splitter::CardinalitySplitter)
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/clustertree.jl:123
 [3] assemble_hmatrix(K::KernelMatrix{…}; atol::Int64, rank::Int64, rtol::Float64, kwargs::@Kwargs{})
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/hmatrix.jl:324
 [4] assemble_hmatrix(K::KernelMatrix{typeof(f), Vector{MyType}, Vector{MyType}, Float64})
   @ HMatrices ~/.julia/packages/HMatrices/prQKn/src/hmatrix.jl:313
 [5] top-level scope
   @ ~/Documents/hmoo.jl:17
 [6] include(fname::String)
   @ Base.MainInclude ./client.jl:489
 [7] top-level scope
   @ REPL[3]:1

[tpgillam]

I made some small changes here and added a simple example to kernelmatrix.md of how you may achieve something similar to what you asked. Let me know if this is not it :-)

Thank you! I've tried running the example you give there (against the current release), and I get the same ClusterTree error as I quoted above.

[tpgillam]

Ahh sorry, I just saw the map(center, ...) that you added when moving the function. Won't test it right now but I suspect that should do the trick.

[maltezfaria]

Thanks for the MWE. I just tested it, and it runs on the dev branch. I will probably get this merged today, together with some other small changes I want to add, and tag a minor version. Let me know if that does not fix your issues.

For reference, it was indeed the commit simplifying the ClusterTree structure that broke the functionality you wanted!

[maltezfaria]

Fixed in #52