[WIP] added definitions for lp-distances. Faster than just using norm

src/LinearAlgebra.jl

@@ -130,6 +130,10 @@ export
     lyap,
     mul!,
     norm,
+    lpdist,
+    l1dist,
+    euclidean,
+    l2dist,
     normalize!,
     normalize,
     nullspace,

src/generic.jl

@@ -892,6 +892,89 @@
 
 norm(v::AdjOrTrans, p::Real) = norm(v.parent, p)
 
+"""
+    lpdist(x::T, y::T, p::Int) where {T <: AbstractVector}
+    lpdist(x::T, y::T, p::Real) where {T <: AbstractVector}
+
+    Computes the Lₚ distance between two vectors `x` and `y`, defined as:
+    for 0 < p < Inf: Lₚ dist = ᵖ√(Σ|xᵢ - yᵢ|ᵖ)
+    for p = 0: count of mismatches for p = 0
+    for p + Inf: L_∞ = maxᵢ(abs(xᵢ - yᵢ))
+"""
+
+function _lpunnorm(x::T, y::T, fn) where {T}
+    r = 0.0
+    for i in eachindex(x,y)
+        @inbounds r += fn(x[i] - y[i])
+    end
+
+    return r
+end
+
+
+function lpdist(x::T, y::T, p::Int) where {T <: AbstractVector}
+    p < 0 && throw(DomainError("p must be non-negative"))
+    length(x) == length(y) || throw(DimensionMismatch("x and y have different lenghts"))
+    if p == 0
+        @warn("Technically not a distance metric for p = 0")
+        fn = !iszero # simply count number of nonzeros
+    elseif p == 1
+        fn = abs
+    elseif p == 2
+        fn = abs2
+    else
+        fn = u -> abs(u)^p
+    end
+    r = _lpunnorm(x, y, fn)
+
+    p <= 1 && return r
+    p == 2 && return √r
+
+    return r^(1/p)
+end
+
+function lpdist(x::T, y::T, p::Real) where {T <: AbstractVector}
+    length(x) == length(y) || throw(DimensionMismatch("x and y have different lenghts"))
+    p < 0 && throw(DomainError("p must be non-negative"))
+    p < 1 && @warn("Technically not a distance metric for 0 < p < 1")
+
+    # handle inf norm separatey
+    if p == Inf
+        r = 0.0
+        for i in eachindex(x,y)
+            @inbounds r = max(abs(x[i] - y[i]), r)
+        end
+        return r
+    elseif iszero(p)
+        return lpdist(x, y, 0)
+    else
+        fn = u -> abs(u)^p
+    end
+    r = _lpunnorm(x, y, fn)
+
+    return r^(1/p)
+end
+
+"""
+    euclidean(x::T, y::T)
+    l2dist(x::T, y::T)
+
+    Compute the L₂ distance between vectors x and y.
+    Basically just aliases for lpdist(x, y, 2)
+"""
+euclidean(x::T, y::T) where {T <: AbstractVector} = lpdist(x, y, 2)
+l2dist(x::T, y::T) where {T <: AbstractVector} = lpdist(x, y, 2)
+
+"""
+    l1dist(x::T, y::T)
+
+    Compute the L₁ distance between vectors x and y.
+    Basically just an alias for lpdist(x, y, 1)
+"""
+l1dist(x::T, y::T) where {T <: AbstractVector} = lpdist(x, y, 1)
+
+
+## dot products
 """
     dot(x, y)
     x ⋅ y

test/generic.jl

@@ -837,4 +837,20 @@ end
     end
 end
 
+@testset "distance functions" begin
+    x = [1., 2., 3.]; y = [1., 2.1, 3.4]
+    @test lpdist(x, y, 1) ≈ norm(x .- y, 1)
+    @test lpdist(x, y, 2) ≈ norm(x .- y, 2)
+    @test lpdist(x, y, 4) ≈ norm(x .- y, 4)
+    @test lpdist(x, y, 3.5) ≈ norm(x .- y, 3.5)
+    @test euclidean(x, y) ≈ norm(x .- y, 2)
+    @test l2dist(x, y) ≈ norm(x .- y, 2)
+    @test l1dist(x, y) ≈ norm(x .- y, 1)
+    @test lpdist(x, y, 0) ≈ norm(x .- y, 0)
+    @test lpdist(x, y, Inf) ≈ norm(x .- y, Inf)
+    @test_throws DomainError lpdist(x, y, -1)
+    @test_throws DomainError lpdist(x, y, -0.5)
+    @test_throws DimensionMismatch lpdist(x, [1.5, 2.0, 2.0, 3.1], 1)
+end
+
 end # module TestGeneric