base: make diff() use views and broadcasting

Author: stev47

base/multidimensional.jl

@@ -659,17 +659,15 @@ end
     end
 end
 
-function diff(a::AbstractVector)
-    @assert !has_offset_axes(a)
-    [ a[i+1] - a[i] for i=1:length(a)-1 ]
-end
+diff(a::AbstractVector) = diff(a, dims=1)
 
 """
     diff(A::AbstractVector)
-    diff(A::AbstractMatrix; dims::Integer)
+    diff(A::AbstractArray; dims::Integer)
 
-Finite difference operator of matrix or vector `A`. If `A` is a matrix,
-specify the dimension over which to operate with the `dims` keyword argument.
+Finite difference operator on a vector or a multidimensional array `A`. In the
+latter case the dimension to operate on needs to be specified with the `dims`
+keyword argument.
 
 # Examples
 ```jldoctest
@@ -690,14 +688,15 @@ julia> diff(vec(a))
  12
 ```
 """
-function diff(A::AbstractMatrix; dims::Integer)
-    if dims == 1
-        [A[i+1,j] - A[i,j] for i=1:size(A,1)-1, j=1:size(A,2)]
-    elseif dims == 2
-        [A[i,j+1] - A[i,j] for i=1:size(A,1), j=1:size(A,2)-1]
-    else
-        throw(ArgumentError("dimension must be 1 or 2, got $dims"))
-    end
+function diff(a::AbstractArray{T,N}; dims::Integer) where {T,N}
+    has_offset_axes(a) && throw(ArgumentError("offset axes unsupported"))
+    1 <= dims <= N || throw(ArgumentError("dimension $dims out of range (1:$N)"))
+
+    r = axes(a)
+    r0 = ntuple(i -> i == dims ? UnitRange(1, last(r[i]) - 1) : UnitRange(r[i]), N)
+    r1 = ntuple(i -> i == dims ? UnitRange(2, last(r[i])) : UnitRange(r[i]), N)
+
+    return view(a, r1...) .- view(a, r0...)
 end
 
 ### from abstractarray.jl

test/arrayops.jl

@@ -2283,6 +2283,9 @@ end
 
 @testset "diff" begin
     # test diff, throw ArgumentError for invalid dimension argument
+    v = [7, 3, 5, 1, 9]
+    @test diff(v) == [-4, 2, -4, 8]
+    @test diff(v,dims=1) == [-4, 2, -4, 8]
     X = [3  9   5;
          7  4   2;
          2  1  10]
@@ -2292,6 +2295,9 @@ end
     @test diff(view(X, 1:2, 1:2),dims=2) == reshape([6; -3], (2,1))
     @test diff(view(X, 2:3, 2:3),dims=1) == [-3 8]
     @test diff(view(X, 2:3, 2:3),dims=2) == reshape([-2; 9], (2,1))
+    Y = cat([1 3; 4 3], [6 5; 1 4], dims=3)
+    @test diff(Y, dims=3) == reshape([5 2; -3 1], (2, 2, 1))
+    @test_throws UndefKeywordError diff(X)
     @test_throws ArgumentError diff(X,dims=3)
     @test_throws ArgumentError diff(X,dims=-1)
 end