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License: MIT License
Any place with copy, hcat, vcat, zip, list comprehension is a place where memory is allocated. Tracking these down and replacing them with reused buffers will improve performance.
Geoff had some good ideas about our method.
This is a big problem in Algebraic Multigrid if C is a matrix mapping vertices to communities. Then we need to update C but read from a matrix C'AC. So our write optimized DS is a vector for C. and our Read optimized DS is a CSC for C'AC, but we will calculate a sparse update to C'AC by using the formula:
(C+D)'A(C+D) = C'AC + D'AC + C'AD + D'AD
where for undirected graphs we can exploit symmetry.
We can batch updates up to the point where Time to compute (C+D)'A(C+D)
< Time to compute C'AC + D'AC + C'AD + D'AD
We should compare with the streaming of A' = A+D
where (C+d)'(A+D)(C+d)
We need to make the PGSQL implementation faster.
compare performance with serial baseline
This is already done, ๐ญ ๐ผ
Since dense matrices will always be faster for accessing individual entries than a sparse matrix, the real question about cross over is size. How big of a dense matrix can you store?
Pencil and paper analysis of algorithm operations
We need a way to count the edge reads, degree reads/updates, and writes to various data structures.
Here is an example type for how to embed a sparse 3 tensor into a dense matrix.
type Messages{T<:Real, G} <: AbstractArray{T, 3}
nrows::Int
ncols::Int
edges::Dict{Tuple{Int, Int}, Int}
states::UnitRange
storage::Array{T, 2}
end
Base.size(m::Messages) = (m.nrows, m.ncols, length(m.states))
function Base.getindex(m::Messages, I::Vararg{Int})
pair = I[1:2]
if pair in keys(m.edges)
return m.storage[m.edges[pair], I[3]]
else
throw(KeyError(pair))
end
end
function Base.setindex!(m::Messages, v, I::Vararg{Int})
pair = I[1:2]
if pair in keys(m.edges)
return m.storage[m.edges[pair], I[3]] = v
else
throw(KeyError(pair))
end
end
Multithreaded calls to rand serialize. Each thread should have their own RNG.
Here is the roadmap for the semester
Some major restrictions imposed by stinger make this algorithm non straightforward to implement using STINGER
Vector{Int64}
stored along with the STINGER data structure and only insert and remove edges that aren't self loops. This does increase complexity in writing code using the structure though.Can the current test suite be used to check for type stability?
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