DimensionalData

DimensionalData.jl provides tools and abstractions for working with datasets that have named dimensions. It's a pluggable, generalised version of AxisArrays.jl with a cleaner syntax, and additional functionality found in NamedDims.jl. It has similar goals to pythons xarray, and is primarily written for use with spatial data in GeoData.jl.

Dimensions

Dimensions are just wrapper types. They store the dimension index and define details about the grid and other metadata, and are also used to index into the array, wrapping a value or a Selector. X, Y, Z and Ti are the exported defaults.

A generalised Dim type is available to use arbitrary symbols to name dimensions. Custom dimensions can be defined using the @dim macro.

We can use dim wrappers for indexing, so that the dimension order in the underlying array does not need to be known:

julia> using DimensionalData

julia> A = DimArray(rand(40, 50), (X, Y));

julia> A[Y(1), X(1:10)]
DimArray with dimensions:
 X: 1:10 (NoIndex)
and referenced dimensions:
 Y: 1 (NoIndex)
and data: 10-element Array{Float64,1}
[0.515774, 0.575247, 0.429075, 0.234041, 0.4484, 0.302562, 0.911098, 0.541537, 0.267234, 0.370663]

And this has no runtime cost:

julia> A = DimArray(rand(40, 50), (X, Y));

julia> @btime $A[X(1), Y(2)]
  2.092 ns (0 allocations: 0 bytes)
0.27317596504655417

julia> @btime parent($A)[1, 2]
  2.092 ns (0 allocations: 0 bytes)
0.27317596504655417

Dims can be used for indexing and views without knowing dimension order:

julia> A[X(10)]
DimArray with dimensions:
 Y (type Y): Base.OneTo(50) (NoIndex)
and referenced dimensions:
 X (type X): 10 (NoIndex)
and data: 50-element Array{Float64,1}
[0.0850249, 0.313408, 0.0762157, 0.549103, 0.297763, 0.309075, 0.854535, 0.659537, 0.392969, 0.89998  …  0.63791, 0.875881, 0.437688, 0.925918, 0.291636, 0.358024, 0.692283, 0.606932, 0.629122, 0.284592]

julia> view(A, Y(30:40), X(1:5))
DimArray with dimensions:
 X (type X): 1:5 (NoIndex)
 Y (type Y): 30:40 (NoIndex)
and data: 5×11 view(::Array{Float64,2}, 1:5, 30:40) with eltype Float64
 0.508793   0.721117  0.558849  …  0.505518   0.532322
 0.869126   0.754219  0.328315     0.0148934  0.778308
 0.0596468  0.458492  0.250458     0.980508   0.524938
 0.446838   0.659638  0.632399     0.33478    0.549402
 0.292962   0.995038  0.26026      0.526124   0.589176

And for indicating dimensions to reduce or permute in julia Base and Statistics functions that have dims arguments:

julia> using Statistics

julia> A = DimArray(rand(3, 4, 5), (X, Y, Ti));

julia> mean(A, dims=Ti)
DimArray with dimensions:
 X (type X): Base.OneTo(3) (NoIndex)
 Y (type Y): Base.OneTo(4) (NoIndex)
 Time (type Ti): 1 (NoIndex)
and data: 3×4×1 Array{Float64,3}
[:, :, 1]
 0.495295  0.650432  0.787521  0.502066
 0.576573  0.568132  0.770812  0.504983
 0.39432   0.5919    0.498638  0.337065
[and 0 more slices...]

julia> permutedims(A, [Ti, Y, X])
DimArray with dimensions:
 Time (type Ti): Base.OneTo(5) (NoIndex)
 Y (type Y): Base.OneTo(4) (NoIndex)
 X (type X): Base.OneTo(3) (NoIndex)
and data: 5×4×3 Array{Float64,3}
[:, :, 1]
 0.401374  0.469474  0.999326  0.265688
 0.439387  0.57274   0.493883  0.88678
 0.425845  0.617372  0.998552  0.650999
 0.852777  0.954702  0.928367  0.0045136
 0.357095  0.637873  0.517476  0.702351
[and 2 more slices...]

You can also use symbols to create Dim{X} dimensions:

julia> A = DimArray(rand(10, 20, 30), (:a, :b, :c));

julia> A[a=2:5, c=9]

DimArray with dimensions:
 Dim{:a}: 2:5 (NoIndex)
 Dim{:b}: Base.OneTo(20) (NoIndex)
and referenced dimensions:
 Dim{:c}: 9 (NoIndex)
and data: 4×20 Array{Float64,2}
 0.868237   0.528297   0.32389   …  0.89322   0.6776    0.604891
 0.635544   0.0526766  0.965727     0.50829   0.661853  0.410173
 0.732377   0.990363   0.728461     0.610426  0.283663  0.00224321
 0.0849853  0.554705   0.594263     0.217618  0.198165  0.661853

Selectors

Selectors find indices in the dimension based on values At, Near, or Between the index value(s). They can be used in getindex, setindex! and view to select indices matching the passed in value(s)

• At(x): get indices exactly matching the passed in value(s)
• Near(x): get the closest indices to the passed in value(s)
• Where(f::Function): filter the array axis by a function of dimension index values.
• Between(a, b): get all indices between two values (inclusive)
• Contains(x): get indices where the value x falls in the interval. Only used for Sampled Intervals, for Points us At.

We can use selectors with dim wrappers:

using Dates, DimensionalData
timespan = DateTime(2001,1):Month(1):DateTime(2001,12)
A = DimArray(rand(12,10), (Ti(timespan), X(10:10:100)))

julia> A[X(Near(35)), Ti(At(DateTime(2001,5)))]
0.658404535807791

julia> A[Near(DateTime(2001, 5, 4)), Between(20, 50)]
DimArray with dimensions:
 X: 20:10:50
and referenced dimensions:
 Time (type Ti): 2001-05-01T00:00:00
and data: 4-element Array{Float64,1}
[0.456175, 0.737336, 0.658405, 0.520152]

Without dim wrappers selectors must be in the right order:

using Unitful

julia> A = DimArray(rand(10, 20), (X((1:10:100)u"m"), Ti((1:5:100)u"s")))

julia> A[Between(10.5u"m", 50.5u"m"), Near(23u"s")]
DimArray with dimensions:
 X: (11:10:41) m (Sampled: Ordered Regular Points)
and referenced dimensions:
 Time (type Ti): 21 s (Sampled: Ordered Regular Points)
and data: 4-element Array{Float64,1}
[0.819172, 0.418113, 0.461722, 0.379877]

For values other than Int/AbstractArray/Colon (which are set aside for regular indexing) the At selector is assumed, and can be dropped completely:

julia> A = DimArray(rand(3, 3), (X(Val((:a, :b, :c))), Y([25.6, 25.7, 25.8])));

julia> A[:b, 25.8]
0.61839141062599

Compile-time selectors

Using all Val indexes (only recommended for small arrays) you can index with named dimensions At arbitrary values with no runtime cost:

julia> A = DimArray(rand(3, 3), (cat=Val((:a, :b, :c)),
                                 val=Val((5.0, 6.0, 7.0))));

julia> @btime $A[:a, 7.0]
  2.094 ns (0 allocations: 0 bytes)
0.25620608873275397

julia> @btime $A[cat=:a, val=7.0]
  2.091 ns (0 allocations: 0 bytes)
0.25620608873275397

Methods where dims can be used containing indices or Selectors

getindex, setindex! view

Methods where dims can be used

• size, axes, firstindex, lastindex
• cat
• reverse
• dropdims
• reduce, mapreduce
• sum, prod, maximum, minimum,
• mean, median, extrema, std, var, cor, cov
• permutedims, adjoint, transpose, Transpose
• mapslices, eachslice
• fill

Warnings

Indexing with unordered or reverse order arrays has undefined behaviour. It will trash the dimension index, break searchsorted and nothing will make sense any more. So do it at you own risk. However, indexing with sorted vectors of Int can be useful. So it's allowed. But it will still do strange things to your interval sizes if the dimension span is Irregular.

Alternate Packages

There are a lot of similar Julia packages in this space. AxisArrays.jl, NamedDims.jl, NamedArrays.jl are registered alternative that each cover some of the functionality provided by DimensionalData.jl. DimensionalData.jl should be able to replicate most of their syntax and functionality.

AxisKeys.jl and AbstractIndices.jl are some other interesting developments. For more detail on why there are so many similar options and where things are headed, read this thread.