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Merged
merged 2 commits into from
May 25, 2023
Merged

Faster indexing for BandedGeneralizedEigenvectors #364

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e2b9c09
Faster indexing for BandedGeneralizedEigenvectors
jishnub May 25, 2023
d9ac8f7
merge getindex methods
jishnub May 25, 2023
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39 changes: 20 additions & 19 deletions src/symbanded/bandedeigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -29,45 +29,46 @@ function eigvals!(A::Symmetric{T,<:BandedMatrix{T}}, B::Symmetric{T,<:BandedMatr
eigvals!(A)
end

# V = G Q
struct BandedEigenvectors{T} <: AbstractMatrix{T}
G::Vector{Givens{T}}
Q::Matrix{T}
z1::Vector{T}
end
abstract type AbstractBandedEigenvectors{T} <: AbstractMatrix{T} end

size(B::BandedEigenvectors) = size(B.Q)
getindex(B::BandedEigenvectors, i, j) = Matrix(B)[i,j]
function _getindex_vec(B::BandedEigenvectors{T}, j) where {T}
z1 = B.z1
z2 = OneElement(one(T), j, size(B,2))
getindex(B::AbstractBandedEigenvectors, i, j) = Matrix(B)[i,j]
function _getindex_vec(B, j)
z1 = _get_scratch(B)
z2 = OneElement(one(eltype(B)), j, size(B,2))
mul!(z1, B, z2)
end
function getindex(B::BandedEigenvectors, i::Int, j::Int)
function getindex(B::AbstractBandedEigenvectors, i::Union{Int, Colon, AbstractVector{Int}}, j::Int)
z = _getindex_vec(B, j)
z[i]
end
function getindex(B::BandedEigenvectors, ::Colon, j::Int)
z = _getindex_vec(B, j)
copy(z)
end
function getindex(B::BandedEigenvectors, ::Colon, jr::AbstractVector{<:Int})
function getindex(B::AbstractBandedEigenvectors, ::Colon, jr::AbstractVector{Int})
M = similar(B, size(B,1), length(jr))
for (ind, j) in enumerate(jr)
M[:, ind] = _getindex_vec(B, j)
end
return M
end

# V = G Q
struct BandedEigenvectors{T} <: AbstractBandedEigenvectors{T}
G::Vector{Givens{T}}
Q::Matrix{T}
z1::Vector{T} # scratch space, used in indexing
end

size(B::BandedEigenvectors) = size(B.Q)

_get_scratch(B::BandedEigenvectors) = B.z1

# V = S⁻¹ Q W
struct BandedGeneralizedEigenvectors{T,M<:AbstractMatrix{T}} <: AbstractMatrix{T}
struct BandedGeneralizedEigenvectors{T,M<:AbstractMatrix{T}} <: AbstractBandedEigenvectors{T}
S::SplitCholesky{T,M}
Q::Vector{Givens{T}}
W::BandedEigenvectors{T}
end

size(B::BandedGeneralizedEigenvectors) = size(B.W)
getindex(B::BandedGeneralizedEigenvectors, i, j) = Matrix(B)[i, j]
_get_scratch(B::BandedGeneralizedEigenvectors) = _get_scratch(B.W)

convert(::Type{Eigen{T, T, Matrix{T}, Vector{T}}}, F::Eigen{T, T, BandedEigenvectors{T}, Vector{T}}) where T = Eigen(F.values, Matrix(F.vectors))
convert(::Type{GeneralizedEigen{T, T, Matrix{T}, Vector{T}}}, F::GeneralizedEigen{T, T, BandedGeneralizedEigenvectors{T}, Vector{T}}) where T = GeneralizedEigen(F.values, Matrix(F.vectors))
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24 changes: 17 additions & 7 deletions test/test_symbanded.jl
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Expand Up @@ -143,15 +143,25 @@ using Test
@test V'AM*V ≈ Diagonal(Λ)
@test V'Matrix(B)*V ≈ I

# misc mul/div tests
VM = Matrix(V)
@test AM * V ≈ AM * VM
@test V * AM ≈ VM * AM
x = rand(T, size(V,2))
@test ldiv!(similar(x), V, x) ≈ ldiv!(similar(x), factorize(VM), x)

z = OneElement{T}(4, size(V,2))
@test V * z ≈ V * Vector(z)
@testset "indexing" begin
@test V[axes(V,1),1:3] ≈ VM[axes(V,1),1:3]
@test V[:,1:3] ≈ VM[:,1:3]
@test V[:,3] ≈ VM[:,3]
@test V[axes(V,1),3] ≈ VM[axes(V,1),3]
@test V[1,2] ≈ VM[1,2]
end

@testset "mul/div" begin
@test AM * V ≈ AM * VM
@test V * AM ≈ VM * AM
x = rand(T, size(V,2))
@test ldiv!(similar(x), V, x) ≈ ldiv!(similar(x), factorize(VM), x)

z = OneElement{T}(4, size(V,2))
@test V * z ≈ V * Vector(z)
end
end

@testset "eigen with mismatched parent bandwidths" begin
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