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Jul 10, 2025
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Introduce eachblockaxes, more general blocklengths #476

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53b9365
Introduce eachblockaxes, more general blocklengths
mtfishman Jul 8, 2025
e81491a
Fix docstest, more tests
mtfishman Jul 8, 2025
405a8f4
Merge branch 'master' into mf/blocklengths
mtfishman Jul 9, 2025
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1 change: 1 addition & 0 deletions docs/src/lib/public.md
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Original file line number Diff line number Diff line change
Expand Up @@ -37,6 +37,7 @@ blockfirsts
blocklasts
blocklengths
blocksizes
eachblockaxes
blocks
eachblock
blockcheckbounds
Expand Down
2 changes: 1 addition & 1 deletion src/BlockArrays.jl
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Expand Up @@ -5,7 +5,7 @@ using LinearAlgebra, ArrayLayouts, FillArrays
export AbstractBlockArray, AbstractBlockMatrix, AbstractBlockVector, AbstractBlockVecOrMat
export Block, getblock, getblock!, setblock!, eachblock, blocks
export blockaxes, blocksize, blocklength, blockcheckbounds, BlockBoundsError, BlockIndex, BlockIndexRange
export blocksizes, blocklengths, blocklasts, blockfirsts, blockisequal
export blocksizes, blocklengths, eachblockaxes, blocklasts, blockfirsts, blockisequal
export BlockRange, blockedrange, BlockedUnitRange, BlockedOneTo

export BlockArray, BlockMatrix, BlockVector, BlockVecOrMat, mortar
Expand Down
97 changes: 88 additions & 9 deletions src/blocks.jl
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Expand Up @@ -93,6 +93,21 @@
a
end

# AbstractArray version of `Iterators.product`.
# https://en.wikipedia.org/wiki/Cartesian_product
# https://github.com/lazyLibraries/ProductArrays.jl
# https://github.com/JuliaData/SplitApplyCombine.jl#productviewf-a-b
# https://github.com/JuliaArrays/MappedArrays.jl/pull/42
struct ProductArray{T,N,V<:Tuple{Vararg{AbstractVector,N}}} <: AbstractArray{T,N}
vectors::V
end
ProductArray(vectors::Vararg{AbstractVector,N}) where {N} =
ProductArray{Tuple{map(eltype, vectors)...},N,typeof(vectors)}(vectors)
Base.size(p::ProductArray) = map(length, p.vectors)
Base.axes(p::ProductArray) = map(Base.axes1, p.vectors)
@propagate_inbounds getindex(p::ProductArray{T,N}, I::Vararg{Int,N}) where {T,N} =
map((v, i) -> v[i], p.vectors, I)

"""
blocksizes(A::AbstractArray)
blocksizes(A::AbstractArray, d::Integer)
Expand All @@ -110,7 +125,7 @@
1.0 │ 1.0 │ 1.0

julia> blocksizes(A)
2×3 BlockArrays.BlockSizes{Tuple{Int64, Int64}, 2, BlockMatrix{Float64, Matrix{Matrix{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}, BlockedOneTo{Int64, Vector{Int64}}}}}:
2×3 BlockArrays.ProductArray{Tuple{Int64, Int64}, 2, Tuple{Vector{Int64}, Vector{Int64}}}:
(2, 1) (2, 1) (2, 1)
(1, 1) (1, 1) (1, 1)

Expand All @@ -124,16 +139,80 @@
1
```
"""
blocksizes(A::AbstractArray) = BlockSizes(A)
blocksizes(A::AbstractArray) = ProductArray(map(blocklengths, axes(A))...)
@inline blocksizes(A::AbstractArray, d::Integer) = blocklengths(axes(A, d))

struct BlockSizes{T,N,A<:AbstractArray{<:Any,N}} <: AbstractArray{T,N}
"""
blocklengths(A::AbstractArray)

Return an iterator over the lengths of each block.
See also blocksizes.

# Examples
```jldoctest
julia> A = BlockArray(ones(3,3),[2,1],[1,1,1])
2×3-blocked 3×3 BlockMatrix{Float64}:
1.0 │ 1.0 │ 1.0
1.0 │ 1.0 │ 1.0
─────┼───────┼─────
1.0 │ 1.0 │ 1.0

julia> blocklengths(A)
2×3 BlockArrays.BlockLengths{Int64, 2, BlockMatrix{Float64, Matrix{Matrix{Float64}}, Tuple{BlockedOneTo{Int64, Vector{Int64}}, BlockedOneTo{Int64, Vector{Int64}}}}}:
2 2 2
1 1 1

julia> blocklengths(A)[1,2]
2
```
"""
blocklengths(A::AbstractArray) = BlockLengths(A)
blocklengths(A::AbstractVector) = map(length, blocks(A))

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struct BlockLengths{T,N,A<:AbstractArray{<:Any,N}} <: AbstractArray{T,N}
array::A
end
BlockSizes(a::AbstractArray{<:Any,N}) where {N} =
BlockSizes{Tuple{eltype.(axes(a))...},N,typeof(a)}(a)
BlockLengths(a::AbstractArray{<:Any,N}) where {N} =
BlockLengths{typeof(length(a)),N,typeof(a)}(a)

size(bs::BlockSizes) = blocksize(bs.array)
axes(bs::BlockSizes) = map(br -> Int.(br), blockaxes(bs.array))
@propagate_inbounds getindex(a::BlockSizes{T,N}, i::Vararg{Int,N}) where {T,N} =
size(view(a.array, Block.(i)...))
size(bs::BlockLengths) = blocksize(bs.array)
axes(bs::BlockLengths) = map(br -> Int.(br), blockaxes(bs.array))
@propagate_inbounds getindex(a::BlockLengths{T,N}, i::Vararg{Int,N}) where {T,N} =
length(view(a.array, Block.(i)...))

"""
eachblockaxes(A::AbstractArray)
eachblockaxes(A::AbstractArray, d::Integer)

Return an iterator over the axes of each block.
See also blocksizes and blocklengths.

# Examples
```jldoctest
julia> A = BlockArray(ones(3,3),[2,1],[1,1,1])
2×3-blocked 3×3 BlockMatrix{Float64}:
1.0 │ 1.0 │ 1.0
1.0 │ 1.0 │ 1.0
─────┼───────┼─────
1.0 │ 1.0 │ 1.0

julia> eachblockaxes(A)
2×3 BlockArrays.ProductArray{Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}, 2, Tuple{Vector{Base.OneTo{Int64}}, Vector{Base.OneTo{Int64}}}}:
(Base.OneTo(2), Base.OneTo(1)) … (Base.OneTo(2), Base.OneTo(1))
(Base.OneTo(1), Base.OneTo(1)) (Base.OneTo(1), Base.OneTo(1))

julia> eachblockaxes(A)[1,2]
(Base.OneTo(2), Base.OneTo(1))

julia> eachblockaxes(A,2)
3-element Vector{Base.OneTo{Int64}}:
Base.OneTo(1)
Base.OneTo(1)
Base.OneTo(1)
```
"""
eachblockaxes(A::AbstractArray) =
ProductArray(map(ax -> map(Base.axes1, blocks(ax)), axes(A))...)
eachblockaxes(A::AbstractVector) = map(axes, blocks(Base.axes1(A)))
eachblockaxes(A::AbstractArray, d::Integer) = map(Base.axes1, blocks(axes(A, d)))
eachblockaxes1(A::AbstractArray) = map(Base.axes1, blocks(Base.axes1(A)))
88 changes: 77 additions & 11 deletions test/test_blocks.jl
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@@ -1,6 +1,7 @@
module TestBlocks

using Test, BlockArrays
import BlockArrays: eachblockaxes1

@testset "blocks" begin
@testset "blocks(::BlockVector)" begin
Expand Down Expand Up @@ -143,18 +144,18 @@ end
@test @inferred(size(bs)) == (2, 2)
@test @inferred(length(bs)) == 4
@test @inferred(axes(bs)) == (1:2, 1:2)
@test @inferred(eltype(bs)) === Tuple{Int,Int}
@test @inferred(eltype(bs)) ≡ Tuple{Int,Int}
@test bs == [(2, 3) (2, 1); (3, 3) (3, 1)]
@test @inferred(bs[1, 1]) == (2, 3)
@test @inferred(bs[2, 1]) == (3, 3)
@test @inferred(bs[1, 2]) == (2, 1)
@test @inferred(bs[2, 2]) == (3, 1)
@test @inferred(bs[1]) == (2, 3)
@test @inferred(bs[2]) == (3, 3)
@test @inferred(bs[3]) == (2, 1)
@test @inferred(bs[4]) == (3, 1)
@test blocksizes(A, 1) == [2, 3]
@test blocksizes(A, 2) == [3, 1]
@test @inferred(bs[1, 1]) ≡ (2, 3)
@test @inferred(bs[2, 1]) ≡ (3, 3)
@test @inferred(bs[1, 2]) ≡ (2, 1)
@test @inferred(bs[2, 2]) ≡ (3, 1)
@test @inferred(bs[1]) ≡ (2, 3)
@test @inferred(bs[2]) ≡ (3, 3)
@test @inferred(bs[3]) ≡ (2, 1)
@test @inferred(bs[4]) ≡ (3, 1)
@test @inferred((x -> blocksizes(x, 1))(A)) == [2, 3]
@test @inferred((x -> blocksizes(x, 2))(A)) == [3, 1]
end

@testset "Inference: issue #425" begin
Expand All @@ -166,4 +167,69 @@ end
end
end

@testset "blocklengths" begin
v = Array(reshape(1:20, (5, 4)))
A = BlockArray(v, [2, 3], [3, 1])
bls = @inferred(blocklengths(A))
@test bls == [6 2; 9 3]
@test @inferred(length(bls)) ≡ 4
@test @inferred(size(bls)) ≡ (2, 2)
@test @inferred(eltype(bls)) ≡ Int
@test @inferred(bls[1, 1]) ≡ 6
@test @inferred(bls[2, 1]) ≡ 9
@test @inferred(bls[1, 2]) ≡ 2
@test @inferred(bls[2, 2]) ≡ 3
@test @inferred(bls[1]) ≡ 6
@test @inferred(bls[2]) ≡ 9
@test @inferred(bls[3]) ≡ 2
@test @inferred(bls[4]) ≡ 3
end

@testset "eachblockaxes" begin
v = Array(reshape(1:20, (5, 4)))
A = BlockArray(v, [2, 3], [3, 1])
bas = @inferred(eachblockaxes(A))
@test bas == [(Base.OneTo(2), Base.OneTo(3)) (Base.OneTo(2), Base.OneTo(1)); (Base.OneTo(3), Base.OneTo(3)) (Base.OneTo(3), Base.OneTo(1))]
@test @inferred(length(bas)) ≡ 4
@test @inferred(size(bas)) ≡ (2, 2)
@test @inferred(eltype(bas)) ≡ Tuple{Base.OneTo{Int},Base.OneTo{Int}}
@test @inferred(bas[1, 1]) ≡ (Base.OneTo(2), Base.OneTo(3))
@test @inferred(bas[2, 1]) ≡ (Base.OneTo(3), Base.OneTo(3))
@test @inferred(bas[1, 2]) ≡ (Base.OneTo(2), Base.OneTo(1))
@test @inferred(bas[2, 2]) ≡ (Base.OneTo(3), Base.OneTo(1))
@test @inferred(bas[1]) ≡ (Base.OneTo(2), Base.OneTo(3))
@test @inferred(bas[2]) ≡ (Base.OneTo(3), Base.OneTo(3))
@test @inferred(bas[3]) ≡ (Base.OneTo(2), Base.OneTo(1))
@test @inferred(bas[4]) ≡ (Base.OneTo(3), Base.OneTo(1))

bas2 = @inferred (x -> eachblockaxes(x, 2))(A)
@test bas2 == [Base.OneTo(3), Base.OneTo(1)]
@test length(bas2) ≡ 2
@test size(bas2) ≡ (2,)
@test @inferred(eltype(bas2)) ≡ Base.OneTo{Int}
@test @inferred(bas2[1]) ≡ Base.OneTo(3)
@test @inferred(bas2[2]) ≡ Base.OneTo(1)
@test @inferred((x -> eachblockaxes(x, 3))(A)) == [Base.OneTo(1)]

V = mortar([[2, 3], [4, 5, 6]])
@test @inferred(eachblockaxes(V)) == [(Base.OneTo(2),), (Base.OneTo(3),)]
@test @inferred((x -> eachblockaxes(x, 1))(V)) == [Base.OneTo(2), Base.OneTo(3)]
@test @inferred((x -> eachblockaxes(x, 2))(V)) == [Base.OneTo(1)]
end

@testset "eachblockaxes1" begin
v = Array(reshape(1:20, (5, 4)))
A = BlockArray(v, [2, 3], [3, 1])
bas = @inferred(eachblockaxes1(A))
@test bas == [Base.OneTo(2), Base.OneTo(3)]
@test @inferred(length(bas)) ≡ 2
@test @inferred(size(bas)) ≡ (2,)
@test @inferred(eltype(bas)) ≡ Base.OneTo{Int}
@test @inferred(bas[1]) ≡ Base.OneTo(2)
@test @inferred(bas[2]) ≡ Base.OneTo(3)

@test @inferred(eachblockaxes1(mortar([[2, 3], [4, 5, 6]]))) == [Base.OneTo(2), Base.OneTo(3)]
@test @inferred(eachblockaxes1(fill(2))) == [Base.OneTo(1)]
end

end # module
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