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
 2000-06-01T00:00:00   6
 2000-07-01T00:00:00   7
 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    0.0275537  0.171798   0.661454       0.580336   0.826641   0.94561
   2    0.455273   0.380872   0.43597        0.312325   0.931262   0.223114
   3    0.333692   0.46747    0.618895       0.808742   0.576437   0.657325
   4    0.5207     0.95715    0.534996       0.25951    0.877483   0.287422
   ⋮                                     ⋱                         ⋮
  97    0.617939   0.980869   0.338072       0.910816   0.657033   0.523385
  98    0.549925   0.340573   0.895484       0.297808   0.518075   0.202221
  99    0.335082   0.14166    0.290357       0.393876   0.177009   0.826134
 100    0.249064   0.0313839  0.0966582  …   0.857851   0.80082    0.547268

A regular broadcast fails:

julia
julia> scaled = data .* month_scalars
ERROR: DimensionMismatch: arrays could not be broadcast to a common size: a has axes DimensionalData.Dimensions.DimUnitRange(Base.OneTo(100), X{Sampled{Int64, UnitRange{Int64}, ForwardOrdered, Regular{Int64}, Points, NoMetadata}}([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])) and b has axes DimensionalData.Dimensions.DimUnitRange(Base.OneTo(12), Ti{Sampled{DateTime, StepRange{DateTime, Month}, ForwardOrdered, Regular{Month}, Points, NoMetadata}}([DateTime("2000-01-01T00:00:00"), DateTime("2000-02-01T00:00:00"), DateTime("2000-03-01T00:00:00"), DateTime("2000-04-01T00:00:00"), DateTime("2000-05-01T00:00:00"), DateTime("2000-06-01T00:00:00"), DateTime("2000-07-01T00:00:00"), DateTime("2000-08-01T00:00:00"), DateTime("2000-09-01T00:00:00"), DateTime("2000-10-01T00:00:00"), DateTime("2000-11-01T00:00:00"), DateTime("2000-12-01T00:00:00")]))

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    0.0275537  0.171798   0.661454       0.580336   0.826641   0.94561
   2    0.455273   0.380872   0.43597        0.312325   0.931262   0.223114
   3    0.333692   0.46747    0.618895       0.808742   0.576437   0.657325
   4    0.5207     0.95715    0.534996       0.25951    0.877483   0.287422
   ⋮                                     ⋱                         ⋮
  97    0.617939   0.980869   0.338072       0.910816   0.657033   0.523385
  98    0.549925   0.340573   0.895484       0.297808   0.518075   0.202221
  99    0.335082   0.14166    0.290357       0.393876   0.177009   0.826134
 100    0.249064   0.0313839  0.0966582  …   0.857851   0.80082    0.547268

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  0.499346
 2000-02-01T00:00:00  0.504421
 2000-03-01T00:00:00  0.500006
 2000-04-01T00:00:00  0.500925
 2000-05-01T00:00:00  0.498882
 2000-06-01T00:00:00  0.509772
 2000-07-01T00:00:00  0.504664
 2000-08-01T00:00:00  0.48904
 2000-09-01T00:00:00  0.501033
 2000-10-01T00:00:00  0.512691
 2000-11-01T00:00:00  0.509249
 2000-12-01T00:00:00  0.504887
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  0.499346
 2000-02-01T00:00:00  1.00884
 2000-03-01T00:00:00  1.50002
 2000-04-01T00:00:00  2.0037
 2000-05-01T00:00:00  2.49441
 2000-06-01T00:00:00  3.05863
 2000-07-01T00:00:00  3.53265
 2000-08-01T00:00:00  3.91232
 2000-09-01T00:00:00  4.50929
 2000-10-01T00:00:00  5.12691
 2000-11-01T00:00:00  5.60174
 2000-12-01T00:00:00  6.05865

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    0.0275537  0.171798   0.661454       0.580336   0.826641   0.94561
   2    0.455273   0.380872   0.43597        0.312325   0.931262   0.223114
   3    0.333692   0.46747    0.618895       0.808742   0.576437   0.657325
   4    0.5207     0.95715    0.534996       0.25951    0.877483   0.287422
   ⋮                                     ⋱                         ⋮
  97    0.617939   0.980869   0.338072       0.910816   0.657033   0.523385
  98    0.549925   0.340573   0.895484       0.297808   0.518075   0.202221
  99    0.335082   0.14166    0.290357       0.393876   0.177009   0.826134
 100    0.249064   0.0313839  0.0966582  …   0.857851   0.80082    0.547268

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  0.0275537      0.549925   0.335082    0.249064
  2000-02-01T00:00:00  1.45622        1.01922    0.269022    1.91317
  2000-03-01T00:00:00  2.12888        2.95191    1.13754     0.411866
  2000-04-01T00:00:00  2.90878        0.952418   2.86682     0.887562
 ⋮                                ⋱                          ⋮
  2000-09-01T00:00:00  7.06221        6.76357    4.42655     7.54669
  2000-10-01T00:00:00  0.524585   …   5.03388    8.99929     1.02435
  2000-11-01T00:00:00  5.58339        7.95765    1.30559     9.12414
  2000-12-01T00:00:00  6.75149        7.79494   11.3744      2.69071

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  0.0275537      0.549925   0.335082    0.249064
  2000-02-01T00:00:00  1.45622        1.01922    0.269022    1.91317
  2000-03-01T00:00:00  2.12888        2.95191    1.13754     0.411866
  2000-04-01T00:00:00  2.90878        0.952418   2.86682     0.887562
 ⋮                                ⋱                          ⋮
  2000-09-01T00:00:00  7.06221        6.76357    4.42655     7.54669
  2000-10-01T00:00:00  0.524585   …   5.03388    8.99929     1.02435
  2000-11-01T00:00:00  5.58339        7.95765    1.30559     9.12414
  2000-12-01T00:00:00  6.75149        7.79494   11.3744      2.69071