Redesign to support slicing

[mtfishman]

Here is a brief demonstration of some of the newly supported functionality:

julia> using NamedDimsArrays: namedoneto

julia> i, j, k = namedoneto.(4, ("i", "j", "k"))
(named(Base.OneTo(4), "i"), named(Base.OneTo(4), "j"), named(Base.OneTo(4), "k"))

julia> a = randn(i, j)
named(4, named(Base.OneTo(4), "i"))×named(4, named(Base.OneTo(4), "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}}} with indices named(Base.OneTo(4), named(Base.OneTo(4), "i"))×named(Base.OneTo(4), named(Base.OneTo(4), "j"))
4×4 Matrix{Float64}:
  0.34339     0.31337    1.26852    -1.40212
  0.795976   -0.50429   -0.0727511  -0.916328
 -2.11173     0.305251  -1.28703    -0.0885537
 -0.0745913   0.145892   0.0768396   0.949534

julia> b = randn(j, k)
named(4, named(Base.OneTo(4), "j"))×named(4, named(Base.OneTo(4), "k")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}}} with indices named(Base.OneTo(4), named(Base.OneTo(4), "j"))×named(Base.OneTo(4), named(Base.OneTo(4), "k"))
4×4 Matrix{Float64}:
 -0.626989   0.601241   0.267535   0.445796
 -1.06342   -0.300968   0.614928   1.17934
 -0.395963  -0.221125   0.462799   0.309347
  0.960161  -0.608346  -1.02573   -0.874405

julia> a[i[2:3], j[2:3]] # Get a slice (copy)
named(2, named(2:3, "i"))×named(2, named(2:3, "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}}} with indices named(Base.OneTo(2), named(2:3, "i"))×named(Base.OneTo(2), named(2:3, "j"))
2×2 Matrix{Float64}:
 -0.50429   -0.0727511
  0.305251  -1.28703

julia> @view a[i[2:3], j[2:3]] # Get a slice (view)
named(2, named(2:3, "i"))×named(2, named(2:3, "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, SubArray{Float64, 2, Matrix{Float64}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}}} with indices named(Base.OneTo(2), named(2:3, "i"))×named(Base.OneTo(2), named(2:3, "j"))
2×2 view(::Matrix{Float64}, 2:3, 2:3) with eltype Float64:
 -0.50429   -0.0727511
  0.305251  -1.28703

julia> a[i[2:3], j[2:3]] = fill(1, (2, 2)) # Set a slice
2×2 Matrix{Int64}:
 1  1
 1  1

julia> a
named(4, named(Base.OneTo(4), "i"))×named(4, named(Base.OneTo(4), "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}}} with indices named(Base.OneTo(4), named(Base.OneTo(4), "i"))×named(Base.OneTo(4), named(Base.OneTo(4), "j"))
4×4 Matrix{Float64}:
  0.34339    0.31337   1.26852    -1.40212
  0.795976   1.0       1.0        -0.916328
 -2.11173    1.0       1.0        -0.0885537
 -0.0745913  0.145892  0.0768396   0.949534

julia> a[i[[2, 4]], j[[2, 4]]] # Get a non-contiguous slice
named(2, named([2, 4], "i"))×named(2, named([2, 4], "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedArray{Int64, 1, Vector{Int64}, String}, NamedDimsArrays.NamedArray{Int64, 1, Vector{Int64}, String}}} with indices named(Base.OneTo(2), named([2, 4], "i"))×named(Base.OneTo(2), named([2, 4], "j"))
2×2 Matrix{Float64}:
 1.0       -0.916328
 0.145892   0.949534

julia> a[i[2:3], j[2:3]] = a[i[2:3], j[2:3]] + fill(2, (i[2:3], j[2:3])) # Add over a slice
named(2, named(2:3, "i"))×named(2, named(2:3, "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, UnitRange{Int64}, String}}} with indices named(Base.OneTo(2), named(2:3, "i"))×named(Base.OneTo(2), named(2:3, "j"))
2×2 Matrix{Float64}:
 3.0  3.0
 3.0  3.0

julia> a
named(4, named(Base.OneTo(4), "i"))×named(4, named(Base.OneTo(4), "j")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}}} with indices named(Base.OneTo(4), named(Base.OneTo(4), "i"))×named(Base.OneTo(4), named(Base.OneTo(4), "j"))
4×4 Matrix{Float64}:
  0.34339    0.31337   1.26852    -1.40212
  0.795976   3.0       3.0        -0.916328
 -2.11173    3.0       3.0        -0.0885537
 -0.0745913  0.145892  0.0768396   0.949534

julia> a[i, j[[2, 4]]] * b[j[[2, 4]], k] # Contract over a sliced dimension (slices must match)
named(4, named(Base.OneTo(4), "i"))×named(4, named(Base.OneTo(4), "k")) NamedDimsArrays.NamedDimsArray{Float64, 2, Matrix{Float64}, Tuple{NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}, NamedDimsArrays.NamedUnitRange{Int64, Base.OneTo{Int64}, String}}} with indices named(Base.OneTo(4), named(Base.OneTo(4), "i"))×named(Base.OneTo(4), named(Base.OneTo(4), "k"))
4×4 Matrix{Float64}:
 -1.67951    0.758661   1.6309     1.59559
 -4.07009   -0.34546    2.78469    4.33926
 -3.27529   -0.849033   1.93562    3.61545
  0.756561  -0.621553  -0.884253  -0.658221

The new design principle in this PR idea is that the NamedDimsArray stores an unnamed array that it is wrapping, dimension names, and slice indices those dimensions run over. Operations like addition and contraction check that the dimension names and slice indices match (up to permutations).

Note that you can also use the Pair syntax:

julia> a[i[2:3], j[2:3]] == a[i => 2:3, j => 2:3]

like you can with scalar indexing.

[codecov]

Codecov Report

Attention: Patch coverage is 36.46724% with 223 lines in your changes missing coverage. Please review.

Project coverage is 33.56%. Comparing base (a8caa48) to head (bef1cc4).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/abstractnameddimsarray.jl	41.20%	147 Missing ⚠️
src/abstractnamedarray.jl	27.27%	24 Missing ⚠️
src/tensoralgebra.jl	8.69%	21 Missing ⚠️
...aysBlockArraysExt/NamedDimsArraysBlockArraysExt.jl	0.00%	12 Missing ⚠️
src/abstractnamedunitrange.jl	43.75%	9 Missing ⚠️
src/abstractnamedinteger.jl	0.00%	5 Missing ⚠️
src/nameddimsarray.jl	50.00%	4 Missing ⚠️
src/adapt.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main      #10       +/-   ##
===========================================
+ Coverage   14.28%   33.56%   +19.28%     
===========================================
  Files          11       14        +3     
  Lines         343      566      +223     
===========================================
+ Hits           49      190      +141     
- Misses        294      376       +82     

Flag	Coverage Δ
docs	33.45% <36.46%> (+20.00%)	⬆️

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