DimensionalData.jl

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Dimensional broadcasts with @d and broadcast_dims ​

Broadcasting over AbstractDimArray works as usual with Base Julia broadcasts, except that dimensions are checked for compatibility with each other, and that values match. Strict checks can be turned off globally with strict_broadcast!(false). To avoid even dimension name checks, broadcast over parent(dimarray).

The @d macro is a dimension-aware extension to regular dot broadcasting. broadcast_dims is analogous to Base Julia's broadcast.

Because we know the names of the dimensions, there is no ambiguity in which ones we mean to broadcast together. This means we can permute and reshape dims so that broadcasts that would fail with a regular Array just work with a DimArray.

As an added bonus, broadcast_dims even works on DimStacks. Currently, @d does not work on DimStack.

Example: scaling along the time dimension ​

Define some dimensions:

julia
using DimensionalData
using Dates
using Statistics
julia
julia> x, y, t = X(1:100), Y(1:25), Ti(DateTime(2000):Month(1):DateTime(2000, 12))
(↓ X 1:100,
→ Y 1:25,
↗ Ti DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00"))

A DimArray from 1:12 to scale with:

julia
julia> month_scalars = DimArray(month, t)
┌ 12-element DimArray{Int64, 1} month(Ti) ┐
├─────────────────────────────────────────┴────────────────────────────── dims ┐
  ↓ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
 2000-01-01T00:00:00   1
 2000-02-01T00:00:00   2
 2000-03-01T00:00:00   3
 2000-04-01T00:00:00   4
 2000-05-01T00:00:00   5
 ⋮
 2000-08-01T00:00:00   8
 2000-09-01T00:00:00   9
 2000-10-01T00:00:00  10
 2000-11-01T00:00:00  11
 2000-12-01T00:00:00  12

And a larger DimArray for example data:

julia
julia> data = rand(x, y, t)
┌ 100×25×12 DimArray{Float64, 3} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ X Sampled{Int64} 1:100 ForwardOrdered Regular Points,
  → Y Sampled{Int64} 1:25 ForwardOrdered Regular Points,
  ↗ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
   ↓ →  1         2         3          …  23         24          25
   1    0.775377  0.59534   0.743848       0.535567   0.991357    0.878324
   2    0.576903  0.637446  0.375855       0.147241   0.637288    0.20265
   3    0.534915  0.982761  0.610407       0.353647   0.0403772   0.886217
   ⋮                                   ⋱                          ⋮
  97    0.165626  0.671548  0.968645       0.793024   0.463557    0.738568
  98    0.507123  0.887135  0.0953293      0.141802   0.905626    0.0460473
  99    0.825027  0.346344  0.951313       0.826774   0.351722    0.12355
 100    0.887804  0.290569  0.048901   …   0.533551   0.590203    0.194993

A regular broadcast fails:

julia
julia> scaled = data .* month_scalars
ERROR: DimensionMismatch: arrays could not be broadcast to a common size: a has axes Base.OneTo(100) and b has axes Base.OneTo(12)

But @d knows to broadcast over the Ti dimension:

julia
julia> scaled = @d data .* month_scalars
┌ 100×25×12 DimArray{Float64, 3} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ X Sampled{Int64} 1:100 ForwardOrdered Regular Points,
  → Y Sampled{Int64} 1:25 ForwardOrdered Regular Points,
  ↗ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
   ↓ →  1         2         3          …  23         24          25
   1    0.775377  0.59534   0.743848       0.535567   0.991357    0.878324
   2    0.576903  0.637446  0.375855       0.147241   0.637288    0.20265
   3    0.534915  0.982761  0.610407       0.353647   0.0403772   0.886217
   ⋮                                   ⋱                          ⋮
  97    0.165626  0.671548  0.968645       0.793024   0.463557    0.738568
  98    0.507123  0.887135  0.0953293      0.141802   0.905626    0.0460473
  99    0.825027  0.346344  0.951313       0.826774   0.351722    0.12355
 100    0.887804  0.290569  0.048901   …   0.533551   0.590203    0.194993

We can see the means of each month are scaled by the broadcast :

julia
julia> mean(eachslice(data; dims=(X, Y)))
┌ 12-element DimArray{Float64, 1} ┐
├─────────────────────────────────┴────────────────────────────────────── dims ┐
  ↓ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
 2000-01-01T00:00:00  0.509149
 2000-02-01T00:00:00  0.50037
 2000-03-01T00:00:00  0.494141
 2000-04-01T00:00:00  0.490035
 2000-05-01T00:00:00  0.499786
 ⋮
 2000-08-01T00:00:00  0.504722
 2000-09-01T00:00:00  0.500603
 2000-10-01T00:00:00  0.49601
 2000-11-01T00:00:00  0.503478
 2000-12-01T00:00:00  0.489599
julia
julia> mean(eachslice(scaled; dims=(X, Y)))
┌ 12-element DimArray{Float64, 1} ┐
├─────────────────────────────────┴────────────────────────────────────── dims ┐
  ↓ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
 2000-01-01T00:00:00  0.509149
 2000-02-01T00:00:00  1.00074
 2000-03-01T00:00:00  1.48242
 2000-04-01T00:00:00  1.96014
 2000-05-01T00:00:00  2.49893
 ⋮
 2000-08-01T00:00:00  4.03778
 2000-09-01T00:00:00  4.50543
 2000-10-01T00:00:00  4.9601
 2000-11-01T00:00:00  5.53826
 2000-12-01T00:00:00  5.87519

You can also use broadcast_dims the same way:

julia
julia> broadcast_dims(*, data, month_scalars)
┌ 100×25×12 DimArray{Float64, 3} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ X Sampled{Int64} 1:100 ForwardOrdered Regular Points,
  → Y Sampled{Int64} 1:25 ForwardOrdered Regular Points,
  ↗ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
   ↓ →  1         2         3          …  23         24          25
   1    0.775377  0.59534   0.743848       0.535567   0.991357    0.878324
   2    0.576903  0.637446  0.375855       0.147241   0.637288    0.20265
   3    0.534915  0.982761  0.610407       0.353647   0.0403772   0.886217
   ⋮                                   ⋱                          ⋮
  97    0.165626  0.671548  0.968645       0.793024   0.463557    0.738568
  98    0.507123  0.887135  0.0953293      0.141802   0.905626    0.0460473
  99    0.825027  0.346344  0.951313       0.826774   0.351722    0.12355
 100    0.887804  0.290569  0.048901   …   0.533551   0.590203    0.194993

And with the @d macro you can set the dimension order and other properties of the output array, by passing a single assignment or a NamedTuple argument to @d after the broadcast:

julia
julia> @d data .* month_scalars dims=(Ti, X, Y)
┌ 12×100×25 DimArray{Float64, 3} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points,
  → X Sampled{Int64} 1:100 ForwardOrdered Regular Points,
  ↗ Y Sampled{Int64} 1:25 ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
 ↓ →                   1         …  98           99          100
  2000-01-01T00:00:00  0.775377      0.507123     0.825027     0.887804
  2000-02-01T00:00:00  0.573513      1.09029      0.0156437    1.92325
  2000-03-01T00:00:00  0.700354      0.486974     2.57895      0.963306
 ⋮                               ⋱                             ⋮
  2000-09-01T00:00:00  8.75144       0.00175277   1.86087      2.1219
  2000-10-01T00:00:00  6.09013   …   5.58649      5.7329       6.64644
  2000-11-01T00:00:00  8.74168       0.851296     8.57574      1.27239
  2000-12-01T00:00:00  3.69662       7.31219      0.810321     6.09965

Or

julia
julia> @d data .* month_scalars (dims=(Ti, X, Y), name=:scaled)
┌ 12×100×25 DimArray{Float64, 3} scaled ┐
├───────────────────────────────────────┴──────────────────────────────── dims ┐
  ↓ Ti Sampled{DateTime} DateTime("2000-01-01T00:00:00"):Month(1):DateTime("2000-12-01T00:00:00") ForwardOrdered Regular Points,
  → X Sampled{Int64} 1:100 ForwardOrdered Regular Points,
  ↗ Y Sampled{Int64} 1:25 ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
[:, :, 1]
 ↓ →                   1         …  98           99          100
  2000-01-01T00:00:00  0.775377      0.507123     0.825027     0.887804
  2000-02-01T00:00:00  0.573513      1.09029      0.0156437    1.92325
  2000-03-01T00:00:00  0.700354      0.486974     2.57895      0.963306
 ⋮                               ⋱                             ⋮
  2000-09-01T00:00:00  8.75144       0.00175277   1.86087      2.1219
  2000-10-01T00:00:00  6.09013   …   5.58649      5.7329       6.64644
  2000-11-01T00:00:00  8.74168       0.851296     8.57574      1.27239
  2000-12-01T00:00:00  3.69662       7.31219      0.810321     6.09965