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Support higher order diff (#117)
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* Support higher order diff

* add tests

* Update test_calculus.jl

* Update calculus.jl

* Generalise some routines
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@dlfivefifty
dlfivefifty authored Jan 28, 2025
1 parent f241cf7 commit 538c66f
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2 changes: 1 addition & 1 deletion Project.toml
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@@ -1,7 +1,7 @@
name = "QuasiArrays"
uuid = "c4ea9172-b204-11e9-377d-29865faadc5c"
authors = ["Sheehan Olver <solver@mac.com>"]
version = "0.11.9"
version = "0.12"

[deps]
ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
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2 changes: 1 addition & 1 deletion src/QuasiArrays.jl
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Expand Up @@ -3,7 +3,7 @@ using Base, LinearAlgebra, LazyArrays, ArrayLayouts, DomainSets, FillArrays, Sta
import Base: getindex, size, axes, axes1, length, ==, isequal, iterate, CartesianIndices, LinearIndices,
Indices, IndexStyle, getindex, setindex!, parent, vec, convert, similar, copy, copyto!, zero,
map, eachindex, eltype, first, last, firstindex, lastindex, in, reshape, permutedims, all,
isreal, iszero, isempty, empty, isapprox, fill!, getproperty, showarg
isreal, iszero, isone, isempty, empty, isapprox, fill!, getproperty, showarg
import Base: @_inline_meta, DimOrInd, OneTo, @_propagate_inbounds_meta, @_noinline_meta,
DimsInteger, error_if_canonical_getindex, @propagate_inbounds, _return_type,
safe_tail, front, tail, _getindex, _maybe_reshape, index_ndims, _unsafe_getindex,
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39 changes: 18 additions & 21 deletions src/calculus.jl
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Expand Up @@ -51,40 +51,37 @@ cumsum_size(::NTuple{N,Integer}, A, dims) where N = error("Not implemented")
# diff
####

@inline diff(a::AbstractQuasiArray; dims::Integer=1) = diff_layout(MemoryLayout(a), a, dims)
function diff_layout(LAY::ApplyLayout{typeof(*)}, V::AbstractQuasiVector, dims...)
@inline diff(a::AbstractQuasiArray, order...; dims::Integer=1) = diff_layout(MemoryLayout(a), a, order...; dims)
function diff_layout(LAY::ApplyLayout{typeof(*)}, V::AbstractQuasiVecOrMat, order...; dims=1)
a = arguments(LAY, V)
*(diff(a[1]), tail(a)...)
dims == 1 || throw(ArgumentError("cannot differentiate a vector along dimension $dims"))
*(diff(a[1], order...), tail(a)...)
end

function diff_layout(LAY::ApplyLayout{typeof(*)}, V::AbstractQuasiMatrix, dims=1)
a = arguments(LAY, V)
@assert dims == 1 #for type stability, for now
# if dims == 1
*(diff(a[1]), tail(a)...)
# else
# *(front(a)..., diff(a[end]; dims=dims))
# end
diff_layout(::MemoryLayout, A, order...; dims...) = diff_size(size(A), A, order...; dims...)
diff_size(sz, a; dims...) = error("diff not implemented for $(typeof(a))")
function diff_size(sz, a, order; dims...)
order < 0 && throw(ArgumentError("order must be non-negative"))
order == 0 && return a
isone(order) ? diff(a) : diff(diff(a), order-1)
end

diff_layout(::MemoryLayout, A, dims...) = diff_size(size(A), A, dims...)
diff_size(sz, a, dims...) = error("diff not implemented for $(typeof(a))")

diff(x::Inclusion; dims::Integer=1) = ones(eltype(x), diffaxes(x))
diff(c::AbstractQuasiFill{<:Any,1}; dims::Integer=1) = zeros(eltype(c), diffaxes(axes(c,1)))
function diff(c::AbstractQuasiFill{<:Any,2}; dims::Integer=1)
diff(x::Inclusion, order::Int; dims::Integer=1) = fill(ifelse(isone(order), one(eltype(x)), zero(eltype(x))), diffaxes(x,order))
diff(c::AbstractQuasiFill{<:Any,1}, order...; dims::Integer=1) = zeros(eltype(c), diffaxes(axes(c,1),order...))
function diff(c::AbstractQuasiFill{<:Any,2}, order...; dims::Integer=1)
a,b = axes(c)
if dims == 1
zeros(eltype(c), diffaxes(a), b)
zeros(eltype(c), diffaxes(a, order...), b)
else
zeros(eltype(c), a, diffaxes(b))
zeros(eltype(c), a, diffaxes(b, order...))
end
end


diffaxes(a::Inclusion{<:Any,<:AbstractVector}) = Inclusion(a.domain[1:end-1])
diffaxes(a::OneTo) = oneto(length(a)-1)
diffaxes(a) = a # default is differentiation does not change axes
diffaxes(a::Inclusion{<:Any,<:AbstractVector}, order=1) = Inclusion(a.domain[1:end-order])
diffaxes(a::OneTo, order=1) = oneto(length(a)-order)
diffaxes(a, order...) = a # default is differentiation does not change axes

diff(b::QuasiVector; dims::Integer=1) = QuasiVector(diff(b.parent) ./ diff(b.axes[1]), (diffaxes(axes(b,1)),))
function diff(A::QuasiMatrix; dims::Integer=1)
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12 changes: 6 additions & 6 deletions src/quasibroadcast.jl
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Expand Up @@ -186,13 +186,13 @@ LazyArrays._broadcast_mul_mul((A,b)::Tuple{AbstractQuasiMatrix,AbstractQuasiVect
# support (A .* B) * y
_broadcasted_mul(a::Tuple{Number,Vararg{Any}}, b::AbstractQuasiVector) = (first(a)*sum(b), _broadcasted_mul(tail(a), b)...)
_broadcasted_mul(a::Tuple{Number,Vararg{Any}}, B::AbstractQuasiMatrix) = (first(a)*sum(B; dims=1), _broadcasted_mul(tail(a), B)...)
_broadcasted_mul(a::Tuple{AbstractQuasiVector,Vararg{Any}}, b::AbstractQuasiVector) = (first(a)*sum(b), _broadcasted_mul(tail(a), b)...)
_broadcasted_mul(a::Tuple{AbstractQuasiVector,Vararg{Any}}, B::AbstractQuasiMatrix) = (first(a)*sum(B; dims=1), _broadcasted_mul(tail(a), B)...)
_broadcasted_mul(A::Tuple{AbstractQuasiMatrix,Vararg{Any}}, b::AbstractQuasiVector) = (axes(first(A),2) == Base.OneTo(1) ? first(A)*sum(b) : (first(A)*b), _broadcasted_mul(tail(A), b)...)
_broadcasted_mul(A::Tuple{AbstractQuasiMatrix,Vararg{Any}}, B::AbstractQuasiMatrix) = (axes(first(A),2) == Base.OneTo(1) ? first(A)*sum(B; dims=1) : (first(A)*B), _broadcasted_mul(tail(A), B)...)
_broadcasted_mul(a::Tuple{AbstractQuasiVector,Vararg{Any}}, b::AbstractQuasiOrVector) = (first(a)*sum(b), _broadcasted_mul(tail(a), b)...)
_broadcasted_mul(a::Tuple{AbstractQuasiVector,Vararg{Any}}, B::AbstractQuasiOrMatrix) = (first(a)*sum(B; dims=1), _broadcasted_mul(tail(a), B)...)
_broadcasted_mul(A::Tuple{AbstractQuasiMatrix,Vararg{Any}}, b::AbstractQuasiOrVector) = (axes(first(A),2) == Base.OneTo(1) ? first(A)*sum(b) : (first(A)*b), _broadcasted_mul(tail(A), b)...)
_broadcasted_mul(A::Tuple{AbstractQuasiMatrix,Vararg{Any}}, B::AbstractQuasiOrMatrix) = (axes(first(A),2) == Base.OneTo(1) ? first(A)*sum(B; dims=1) : (first(A)*B), _broadcasted_mul(tail(A), B)...)
_broadcasted_mul(A::AbstractQuasiMatrix, b::Tuple{Number,Vararg{Any}}) = (sum(A; dims=2)*first(b)[1], _broadcasted_mul(A, tail(b))...)
_broadcasted_mul(A::AbstractQuasiMatrix, b::Tuple{Union{AbstractVector,AbstractQuasiVector},Vararg{Any}}) = (size(first(b),1) == 1 ? (sum(A; dims=2)*first(b)[1]) : (A*first(b)), _broadcasted_mul(A, tail(b))...)
_broadcasted_mul(A::AbstractQuasiMatrix, B::Tuple{Union{AbstractMatrix,AbstractQuasiMatrix},Vararg{Any}}) = (size(first(B),1) == 1 ? (sum(A; dims=2) * first(B)) : (A * first(B)), _broadcasted_mul(A, tail(B))...)
_broadcasted_mul(A::AbstractQuasiMatrix, b::Tuple{AbstractQuasiOrVector,Vararg{Any}}) = (size(first(b),1) == 1 ? (sum(A; dims=2)*first(b)[1]) : (A*first(b)), _broadcasted_mul(A, tail(b))...)
_broadcasted_mul(A::AbstractQuasiMatrix, B::Tuple{AbstractQuasiOrMatrix,Vararg{Any}}) = (size(first(B),1) == 1 ? (sum(A; dims=2) * first(B)) : (A * first(B)), _broadcasted_mul(A, tail(B))...)



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22 changes: 18 additions & 4 deletions test/test_calculus.jl
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Expand Up @@ -30,19 +30,25 @@ using QuasiArrays, IntervalSets, Test

@testset "Diff" begin
x = range(0, 1; length=10_000)
@test diff(Inclusion(x)) == ones(Inclusion(x[1:end-1]))
@test diff(ones(Inclusion(x))) == zeros(Inclusion(x[1:end-1]))
@test diff(Inclusion(x)) == diff(Inclusion(x),1) == ones(Inclusion(x[1:end-1]))
@test diff(Inclusion(x),2) == diff(diff(Inclusion(x))) == zeros(Inclusion(x[1:end-2]))
@test diff(ones(Inclusion(x))) == diff(ones(Inclusion(x)),1) == zeros(Inclusion(x[1:end-1]))
@test diff(ones(Inclusion(x)),2) == diff(diff(ones(Inclusion(x)))) == zeros(Inclusion(x[1:end-2]))

@test diff(ones(Inclusion(x), Inclusion(x))) == zeros(Inclusion(x[1:end-1]), Inclusion(x))
@test diff(ones(Inclusion(x), Inclusion(x)), 2) == zeros(Inclusion(x[1:end-2]), Inclusion(x))
@test diff(ones(Inclusion(x), Inclusion(x)); dims=2) == zeros(Inclusion(x), Inclusion(x[1:end-1]))
@test diff(ones(Inclusion(x), Inclusion(x)), 2; dims=2) == zeros(Inclusion(x), Inclusion(x[1:end-2]))

b = QuasiVector(exp.(x), x)

@test diff(b) ≈ b[Inclusion(x[1:end-1])] atol=1E-2
@test diff(b,2) ≈ b[Inclusion(x[1:end-2])] atol=1E-1


A = QuasiArray(randn(3,2), (1:0.5:2,0:0.5:0.5))
@test diff(A; dims=1)[:,0] == diff(A[:,0])
@test diff(A,2; dims=1)[:,0] == diff(diff(A[:,0]))
@test diff(A; dims=2)[1,:] == diff(A[1,:])

@testset "* diff" begin
Expand All @@ -57,10 +63,18 @@ using QuasiArrays, IntervalSets, Test

@testset "Interval" begin
@test diff(Inclusion(0.0..1)) ≡ ones(Inclusion(0.0..1))
@test diff(ones(Inclusion(0.0..1))) ≡ zeros(Inclusion(0.0..1))
@test diff(ones(Inclusion(0.0..1), Base.OneTo(3))) ≡ zeros(Inclusion(0.0..1), Base.OneTo(3))
@test diff(Inclusion(0.0..1),1) ≡ fill(1.0,Inclusion(0.0..1))
@test diff(Inclusion(0.0..1),2) ≡ fill(0.0,Inclusion(0.0..1))
@test diff(ones(Inclusion(0.0..1))) ≡ diff(ones(Inclusion(0.0..1)),1) ≡ diff(ones(Inclusion(0.0..1)),2) ≡ zeros(Inclusion(0.0..1))
@test diff(ones(Inclusion(0.0..1), Base.OneTo(3))) ≡ diff(ones(Inclusion(0.0..1), Base.OneTo(3)),2) ≡ zeros(Inclusion(0.0..1), Base.OneTo(3))
@test diff(ones(Inclusion(0.0..1), Base.OneTo(3)); dims=2) ≡ zeros(Inclusion(0.0..1), Base.OneTo(2))
@test diff(ones(Base.OneTo(3), Inclusion(0.0..1))) ≡ zeros(Base.OneTo(2), Inclusion(0.0..1))
@test diff(ones(Base.OneTo(3), Inclusion(0.0..1)); dims=2) ≡ zeros(Base.OneTo(3), Inclusion(0.0..1))
end

@testset "Incomplete" begin
struct IncompleteQuasiArray <: AbstractQuasiVector{Int} end
Base.axes(::IncompleteQuasiArray) = (Base.OneTo(3),)
@test_throws ErrorException diff(IncompleteQuasiArray())
end
end

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Registration pull request created: JuliaRegistries/General/123859

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Release notes:

## Breaking changes

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Release notes:

Breaking changes

  • Adds order argument to diff

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Registration pull request updated: JuliaRegistries/General/123859

Tagging

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.12.0 -m "<description of version>" 538c66f70df20faeb9318c655af5c5b2cfd21fad
git push origin v0.12.0

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