Arrays which also have a label for each element for easy scientific machine learning (SciML)
Author SciML
65 Stars
Updated Last
2 Years Ago
Started In
October 2017


Build Status Coverage Status

LabelledArrays.jl is a package which provides arrays with labels, i.e. they are arrays which map, broadcast, and all of that good stuff, but their components are labelled. Thus for instance you can set that the second component is named :second and retrieve it with A.second.


The SLArray and SLVector macros are for creating static LabelledArrays. First you create the type and then you can use that constructor to generate instances of the labelled array.

ABC = @SLVector (:a,:b,:c)
A = ABC(1,2,3)
A.a == 1

ABCD = @SLArray (2,2) (:a,:b,:c,:d)
B = ABCD(1,2,3,4)
B.c == 3
B[2,2] == B.d

Here we have that A == [1,2,3] and for example A.b == 2. We can create a typed SLArray via:

SVType = @SLVector Float64 (:a,:b,:c)

Alternatively, you can also construct a static labelled array using the SLVector constructor by writing out the entries as keyword arguments:

julia> SLVector(a=1, b=2, c=3)
3-element SLArray{Tuple{3},1,(:a, :b, :c),Int64}:

For general N-dimensional labelled arrays, you need to specify the size (Tuple{dim1,dim2,...}) as the type parameter to the SLArray constructor:

julia> SLArray{Tuple{2,2}}(a=1, b=2, c=3, d=4)
2×2 SLArray{Tuple{2,2},2,(:a, :b, :c, :d),Int64}:
 1  3
 2  4

Constructing copies with some items changed is supported by a keyword constructor whose first argument is the source and additonal keyword arguments change several entries.

julia> v1 = SLVector(a=1.1, b=2.2, c=3.3);
julia> v2 = SLVector(v1; b=20.20, c=30.30 )
3-element SLArray{Tuple{3},Float64,1,3,(:a, :b, :c)}:
julia> ABCD = @SLArray (2,2) (:a,:b,:c,:d);
julia> B = ABCD(1,2,3,4);
julia> B2 = SLArray(B; c=30 )
2×2 SLArray{Tuple{2,2},Int64,2,4,(:a, :b, :c, :d)}:
 1  30
 2   4

One can also specify the indices directly.

julia> EFG = @SLArray (2,2) (e=1:3, f=4, g=2:4);
julia> y = EFG(1.0,2.5,3.0,5.0)
2×2 SLArray{Tuple{2,2},Float64,2,4,(e = 1:3, f = 4, g = 2:4)}:
 1.0  3.0
 2.5  5.0

julia> y.g
3-element view(reshape(::StaticArrays.SArray{Tuple{2,2},Float64,2,4}, 4), 2:4) with eltype Float64:

julia> Arr = @SLArray (2, 2) (a = (2, :), b = 3);
julia> z = Arr(1, 2, 3, 4);
julia> z.a
2-element view(::StaticArrays.SArray{Tuple{2,2},Int64,2,4}, 2, :) with eltype Int64:


The LArrayss are fully mutable arrays with labels. There is no performance loss by using the labelled instead of indexing. Using the macro with values and labels generates the labelled array with the given values:

A = @LArray [1,2,3] (:a,:b,:c)
A.a == 1

One can generate a labelled array with undefined values by instead giving the dimensions:

A = @LArray Float64 (2,2) (:a,:b,:c,:d)
W = rand(2,2)
A .= W
A.d == W[2,2]

or using an @LVector shorthand:

A = @LVector Float64 (:a,:b,:c,:d)
A .= rand(4)

As with SLArray, alternative constructors exist that use the keyword argument form:

julia> LVector(a=1, b=2, c=3)
3-element LArray{Int64,1,(:a, :b, :c)}:

julia> LArray((2,2); a=1, b=2, c=3, d=4) # need to specify size as first argument
2×2 LArray{Int64,2,(:a, :b, :c, :d)}:
 1  3
 2  4

One can also specify the indices directly.

julia> z = @LArray [1.,2.,3.] (a = 1:2, b = 2:3);
julia> z.b
2-element view(::Array{Float64,1}, 2:3) with eltype Float64:
julia> z = @LArray [1 2; 3 4] (a = (2, :), b = 2:3);
julia> z.a
2-element view(::Array{Int64,2}, 2, :) with eltype Int64:

The labels of LArray and SLArray can be accessed by function symbols, which returns a tuple of symbols.

Example: Nice DiffEq Syntax Without A DSL

LabelledArrays.jl are a way to get DSL-like syntax without a macro. In this case, we can solve differential equations with labelled components by making use of labelled arrays, and always refer to the components by name instead of index.

Let's solve the Lorenz equation. Using @LVectors, we can do:

using LabelledArrays, OrdinaryDiffEq

function lorenz_f(du,u,p,t)
  du.x = p.σ*(u.y-u.x)
  du.y = u.x*(p.ρ-u.z) - u.y
  du.z = u.x*u.y - p.β*u.z

u0 = @LArray [1.0,0.0,0.0] (:x,:y,:z)
p = @LArray [10.0, 28.0, 8/3]  (,,)
tspan = (0.0,10.0)
prob = ODEProblem(lorenz_f,u0,tspan,p)
sol = solve(prob,Tsit5())
# Now the solution can be indexed as .x/y/z as well!

We can also make use of @SLVector:

LorenzVector = @SLVector (:x,:y,:z)
LorenzParameterVector = @SLVector (,,)

function f(u,p,t)
  x = p.σ*(u.y-u.x)
  y = u.x*(p.ρ-u.z) - u.y
  z = u.x*u.y - p.β*u.z

u0 = LorenzVector(1.0,0.0,0.0)
p = LorenzParameterVector(10.0,28.0,8/3)
tspan = (0.0,10.0)
prob = ODEProblem(f,u0,tspan,p)
sol = solve(prob,Tsit5())

Relation to NamedTuples

Julia's Base has NamedTuples in v0.7+. They are constructed as:

p == 10.0= 28.0= 8/3)

and they support p[1] and p.σ as well. The LVector, SLVector, LArray and SLArray constructors also support named tuples as their arguments:

julia> LVector((a=1, b=2))
2-element LArray{Int64,1,(:a, :b)}:

julia> SLVector((a=1, b=2))
2-element SLArray{Tuple{2},1,(:a, :b),Int64}:

julia> LArray((2,2), (a=1, b=2, c=3, d=4))
2×2 LArray{Int64,2,(:a, :b, :c, :d)}:
 1  3
 2  4

julia> SLArray{Tuple{2,2}}((a=1, b=2, c=3, d=4))
2×2 SLArray{Tuple{2,2},2,(:a, :b, :c, :d),Int64}:
 1  3
 2  4

Converting to a named tuple from a labelled array x is available using convert(NamedTuple, x). Furthermore, pairs(x) creates an iterator that is functionally the same as pairs(convert(NamedTuple, x)), yielding :label => x.label for each label of the array.

There are some crucial differences between a labelled array and a named tuple. Labelled arrays can have any dimensions while named tuples are always 1D. A named tuple can have different types on each element, while an SLArray can only have one element type and furthermore it has the actions of a static vector. As a result SLArray has less element type information, which improves compilation speed while giving more vector functionality than a NamedTuple. LArray also only has a single element type and, unlike a named tuple, is mutable.

Note: Labelled slices

This functionality has been removed from LabelledArrays.jl, but can replicated with the same compile-time performance and indexing syntax using DimensionalData.jl.