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Improve symmetrization for sparse factors #62

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29 changes: 27 additions & 2 deletions src/factorization.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -235,7 +235,25 @@ julia> LowRankOpt.symmetrize_factorization([1, 0], [0, 1])
0.5 0.0
```
"""
function symmetrize_factorization(L, R; use_krylov = true)
function symmetrize_factorization(L, R; kws...)
I = findall(axes(L, 1)) do i
any(!iszero, L[i, :]) || any(!iszero, R[i, :])
end
if I == axes(L, 1)
_sub_symmetrize_factorization(L, R; kws...)
else
sub = _sub_symmetrize_factorization(L[I, :], R[I, :]; kws...)
factor = if sub.factor isa SparseArrays.AbstractSparseArray
SparseArrays.spzeros(size(L, 1), max_rank(sub))
else
zeros(size(L, 1), max_rank(sub))
end
factor[I, :] = sub.factor
return Factorization(factor, sub.scaling)
end
end

function _sub_symmetrize_factorization(L, R; use_krylov = true)
sym = LinearAlgebra.Symmetric((L * R' + R * L') / 2)
r = 2size(L, 2)
if use_krylov
Expand All @@ -246,7 +264,14 @@ function symmetrize_factorization(L, R; use_krylov = true)
end
σ = sortperm(abs.(eigvals), rev = true)
keep = σ[1:r]
return Factorization(factor[:, keep], eigvals[keep])
new_factor = factor[:, keep]
if L isa SparseArrays.AbstractSparseArray && R isa SparseArrays.AbstractSparseArray
# TODO We should also do the computation on a subset of indices that is the union
# of the indices of L and R
new_factor = SparseArrays.sparse(new_factor)
SparseArrays.droptol!(new_factor, Base.rtoldefault(eltype(new_factor)))
end
return Factorization(new_factor, eigvals[keep])
end

struct TriangleVectorization{T,M<:AbstractMatrix{T}} <: AbstractVector{T}
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