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:

using DimensionalData
using Dates
using Statistics

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> 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> 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
   ⋮                                     ⋱                         ⋮
  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> 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> 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
   ⋮                                     ⋱                         ⋮
  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> 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
 ⋮
 2000-08-01T00:00:00  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> 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
 ⋮
 2000-08-01T00:00:00  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> 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
   ⋮                                     ⋱                         ⋮
  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> @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
 ⋮                                ⋱                          ⋮
  2000-09-01T00:00:00  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> @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
 ⋮                                ⋱                          ⋮
  2000-09-01T00:00:00  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