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Structured broadcasting for UpperHessenberg #1325

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228ea11
Structured broadcasting for UpperHessenberg
jishnub Apr 30, 2025
8890486
Test for rectangular `UpperHessenberg`
jishnub May 4, 2025
428d9d8
Unwrap `UpperHessenberg` in broadcast
jishnub Jun 3, 2025
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3 changes: 3 additions & 0 deletions src/hessenberg.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -59,6 +59,9 @@ size(H::UpperHessenberg) = size(H.data)
axes(H::UpperHessenberg) = axes(H.data)
parent(H::UpperHessenberg) = H.data

upperhessenbergdata(H::UpperHessenberg) = H.data
upperhessenbergdata(A) = A

# similar behaves like UpperTriangular
similar(H::UpperHessenberg, ::Type{T}) where {T} = UpperHessenberg(similar(H.data, T))
similar(H::UpperHessenberg, ::Type{T}, dims::Dims{N}) where {T,N} = similar(H.data, T, dims)
Expand Down
46 changes: 41 additions & 5 deletions src/structuredbroadcast.jl
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Expand Up @@ -8,8 +8,12 @@
StructuredMatrixStyle{T}(::Val{2}) where {T} = StructuredMatrixStyle{T}()
StructuredMatrixStyle{T}(::Val{N}) where {T,N} = Broadcast.DefaultArrayStyle{N}()

const StructuredMatrix{T} = Union{Diagonal{T},Bidiagonal{T},SymTridiagonal{T},Tridiagonal{T},LowerTriangular{T},UnitLowerTriangular{T},UpperTriangular{T},UnitUpperTriangular{T}}
for ST in (Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal,LowerTriangular,UnitLowerTriangular,UpperTriangular,UnitUpperTriangular)
const StructuredMatrix{T} = Union{Diagonal{T},Bidiagonal{T},SymTridiagonal{T},Tridiagonal{T},
LowerTriangular{T},UnitLowerTriangular{T},UpperTriangular{T},UnitUpperTriangular{T},
UpperHessenberg{T}}
for ST in (Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal,
LowerTriangular,UnitLowerTriangular,UpperTriangular,UnitUpperTriangular,
UpperHessenberg)
@eval Broadcast.BroadcastStyle(::Type{<:$ST}) = $(StructuredMatrixStyle{ST}())
end

Expand All @@ -27,28 +31,46 @@
StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}) =
StructuredMatrixStyle{UpperTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{UpperHessenberg}) =
StructuredMatrixStyle{UpperHessenberg}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{Bidiagonal}, ::StructuredMatrixStyle{Diagonal}) =
StructuredMatrixStyle{Bidiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Bidiagonal}, ::StructuredMatrixStyle{<:Union{Bidiagonal,SymTridiagonal,Tridiagonal}}) =
StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Bidiagonal}, ::StructuredMatrixStyle{UpperHessenberg}) =
StructuredMatrixStyle{UpperHessenberg}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{SymTridiagonal}, ::StructuredMatrixStyle{<:Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal}}) =
StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{SymTridiagonal}, ::StructuredMatrixStyle{UpperHessenberg}) =
StructuredMatrixStyle{UpperHessenberg}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Tridiagonal}, ::StructuredMatrixStyle{<:Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal}}) =
StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Tridiagonal}, ::StructuredMatrixStyle{UpperHessenberg}) =
StructuredMatrixStyle{UpperHessenberg}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{LowerTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,LowerTriangular,UnitLowerTriangular}}) =
StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UpperTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,UpperTriangular,UnitUpperTriangular}}) =
StructuredMatrixStyle{UpperTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UpperTriangular}, ::StructuredMatrixStyle{UpperHessenberg}) =
StructuredMatrixStyle{UpperHessenberg}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UnitLowerTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,LowerTriangular,UnitLowerTriangular}}) =
StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UnitUpperTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,UpperTriangular,UnitUpperTriangular}}) =
StructuredMatrixStyle{UpperTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UnitUpperTriangular}, ::StructuredMatrixStyle{UpperHessenberg}) =

Check warning on line 63 in src/structuredbroadcast.jl

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StructuredMatrixStyle{UpperHessenberg}()

function Broadcast.BroadcastStyle(::StructuredMatrixStyle{UpperHessenberg},
::StructuredMatrixStyle{<:Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal,UnitUpperTriangular,UpperTriangular}})
StructuredMatrixStyle{UpperHessenberg}()
end

Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}, ::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}) =
Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}, ::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular,UpperHessenberg}}) =
StructuredMatrixStyle{Matrix}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}, ::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}) =
Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular,UpperHessenberg}}, ::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}) =
StructuredMatrixStyle{Matrix}()

# Make sure that `StructuredMatrixStyle{Matrix}` doesn't ever end up falling
Expand Down Expand Up @@ -97,7 +119,7 @@
Tridiagonal(Array{ElType}(undef, n1),Array{ElType}(undef, n),Array{ElType}(undef, n1))
end
function structured_broadcast_alloc(bc, ::Type{T}, ::Type{ElType},
sz::NTuple{2,Integer}) where {ElType,T<:UpperOrLowerTriangular}
sz::NTuple{2,Integer}) where {ElType,T<:Union{UpperOrLowerTriangular, UpperHessenberg}}
T(Array{ElType}(undef, sz))
end
structured_broadcast_alloc(bc, ::Type{Matrix}, ::Type{ElType}, sz::NTuple{2,Integer}) where {ElType} =
Expand Down Expand Up @@ -278,6 +300,7 @@
end
_preprocess_broadcasted(::Type{LowerTriangular}, A) = lowertridata(A)
_preprocess_broadcasted(::Type{UpperTriangular}, A) = uppertridata(A)
_preprocess_broadcasted(::Type{UpperHessenberg}, A) = upperhessenbergdata(A)

function copyto!(dest::LowerTriangular, bc::Broadcasted{<:StructuredMatrixStyle})
isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
Expand Down Expand Up @@ -305,6 +328,19 @@
return dest
end

function copyto!(dest::UpperHessenberg, bc::Broadcasted{<:StructuredMatrixStyle})
isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
axs = axes(dest)
axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
bc_unwrapped = preprocess_broadcasted(UpperHessenberg, bc)
for j in axs[2]
for i in 1:min(size(dest.data,1), j+1)
@inbounds dest.data[i,j] = bc_unwrapped[CartesianIndex(i, j)]
end
end
return dest
end

# We can also implement `map` and its promotion in terms of broadcast with a stricter dimension check
function map(f, A::StructuredMatrix, Bs::StructuredMatrix...)
sz = size(A)
Expand Down
16 changes: 14 additions & 2 deletions test/structuredbroadcast.jl
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Expand Up @@ -22,8 +22,9 @@ using .Main.SizedArrays
S = SymTridiagonal(rand(N), rand(max(0,N-1)))
U = UpperTriangular(rand(N,N))
L = LowerTriangular(rand(N,N))
UH = UpperHessenberg(rand(N,N))
M = Matrix(rand(N,N))
structuredarrays = (D, B, T, U, L, M, S)
structuredarrays = (D, B, T, U, L, M, S, UH)
fstructuredarrays = map(Array, structuredarrays)
@testset "$(nameof(typeof(X)))" for (X, fX) in zip(structuredarrays, fstructuredarrays)
@test (Q = broadcast(sin, X); typeof(Q) == typeof(X) && Q == broadcast(sin, fX))
Expand Down Expand Up @@ -135,6 +136,7 @@ end
T = Tridiagonal(rand(max(0,N-1)), rand(N), rand(max(0,N-1)))
◣ = LowerTriangular(rand(N,N))
◥ = UpperTriangular(rand(N,N))
UH = UpperHessenberg(rand(N,N))
M = Matrix(rand(N,N))

@test broadcast!(sin, copy(D), D)::Diagonal == sin.(D)::Diagonal
Expand All @@ -143,13 +145,15 @@ end
@test broadcast!(sin, copy(T), T)::Tridiagonal == sin.(T)::Tridiagonal
@test broadcast!(sin, copy(◣), ◣)::LowerTriangular == sin.(◣)::LowerTriangular
@test broadcast!(sin, copy(◥), ◥)::UpperTriangular == sin.(◥)::UpperTriangular
@test broadcast!(sin, copy(UH), UH)::UpperHessenberg == sin.(UH)::UpperHessenberg
@test broadcast!(sin, copy(M), M)::Matrix == sin.(M)::Matrix
@test broadcast!(*, copy(D), D, A) == Diagonal(broadcast(*, D, A))
@test broadcast!(*, copy(Bu), Bu, A) == Bidiagonal(broadcast(*, Bu, A), :U)
@test broadcast!(*, copy(Bl), Bl, A) == Bidiagonal(broadcast(*, Bl, A), :L)
@test broadcast!(*, copy(T), T, A) == Tridiagonal(broadcast(*, T, A))
@test broadcast!(*, copy(◣), ◣, A) == LowerTriangular(broadcast(*, ◣, A))
@test broadcast!(*, copy(◥), ◥, A) == UpperTriangular(broadcast(*, ◥, A))
@test broadcast!(*, copy(UH), UH, A) == UpperHessenberg(broadcast(*, UH, A))
@test broadcast!(*, copy(M), M, A) == Matrix(broadcast(*, M, A))

if N > 2
Expand Down Expand Up @@ -181,8 +185,9 @@ end
S = SymTridiagonal(rand(N), rand(N - 1))
U = UpperTriangular(rand(N,N))
L = LowerTriangular(rand(N,N))
UH = UpperHessenberg(rand(N,N))
M = Matrix(rand(N,N))
structuredarrays = (M, D, B, T, S, U, L)
structuredarrays = (M, D, B, T, S, U, L, UH)
fstructuredarrays = map(Array, structuredarrays)
for (X, fX) in zip(structuredarrays, fstructuredarrays)
@test (Q = map(sin, X); typeof(Q) == typeof(X) && Q == map(sin, fX))
Expand Down Expand Up @@ -396,4 +401,11 @@ end
end
end

@testset "Rectangular UpperHessenberg" begin
UH = UpperHessenberg(ones(4,3))
UH2 = UH .+ UH .- UH
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Would that even work with

Suggested change
UH2 = UH .+ UH .- UH
UH2 = UH + UH - UH

?

@test UH2 == UH
@test UH2 isa UpperHessenberg
end

end