Add RecursiveArrayToolsExt to support ArrayPartitions

[hakkelt]

Summary

• Adds a package extension (RecursiveArrayToolsExt) that lets SeparableSum and PrecomposedSlicedSeparableSum operate directly on RecursiveArrayTools.ArrayPartition, avoiding the need to manually convert to/from tuples.
• Extension is triggered by RecursiveArrayTools as a weak dependency (Project.toml [weakdeps]/[extensions]), so it adds no dependency unless the user already has RecursiveArrayTools loaded.

Test plan

• test/test_recursivearraytools.jl exercises prox, prox!, gradient, gradient!, and function evaluation on ArrayPartitions for both SeparableSum and PrecomposedSlicedSeparableSum.
• test/runtests.jl updated to run the new test file and load RecursiveArrayTools in a Julia version that supports it.
• Aqua tests updated/passing for the new extension.

Marking as draft to get early feedback on the extension's API surface before finalizing.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	6596794...	master / 6596794...
IndBallL1/Float32	3.73 ± 3.5 μs	3.79 ± 3.4 μs	0.984 ± 1.3
IndBallL1/Float64	4.19 ± 1.6 μs	4.16 ± 1.6 μs	1.01 ± 0.55
IndBox/Float32	8.18 ± 0.47 μs	8.13 ± 0.45 μs	1.01 ± 0.08
IndBox/Float64	8.61 ± 1.7 μs	9.23 ± 1.5 μs	0.933 ± 0.24
IndExpPrimal/Float32	0.158 ± 0.0089 ms	0.155 ± 0.0088 ms	1.02 ± 0.081
IndExpPrimal/Float64	0.159 ± 0.0095 ms	0.156 ± 0.0093 ms	1.02 ± 0.086
IndNonnegative/Float32	2.69 ± 1.2 μs	2.71 ± 1.1 μs	0.992 ± 0.6
IndNonnegative/Float64	3.68 ± 2.7 μs	4.5 ± 2.1 μs	0.818 ± 0.72
IndPSD/("ComplexF64", 10)	15 ± 0.67 μs	15 ± 0.66 μs	1 ± 0.063
IndPSD/("ComplexF64", 20)	0.0557 ± 0.00071 ms	0.0556 ± 0.00071 ms	1 ± 0.018
IndPSD/("ComplexF64", 50)	0.462 ± 0.012 ms	0.463 ± 0.012 ms	0.999 ± 0.037
IndPSD/("Float64", 10)	12.2 ± 0.47 μs	12.2 ± 0.47 μs	0.999 ± 0.055
IndPSD/("Float64", 20)	0.039 ± 0.00092 ms	0.0391 ± 0.00091 ms	0.997 ± 0.033
IndPSD/("Float64", 50)	0.24 ± 0.0079 ms	0.24 ± 0.0073 ms	0.999 ± 0.045
IndSimplex/Float32	20.6 ± 0.49 μs	20.2 ± 0.5 μs	1.02 ± 0.035
IndSimplex/Float64	24 ± 2.6 μs	23.7 ± 2.7 μs	1.01 ± 0.16
LeastSquares/("ComplexF64", "(11, 5)", 0, 0)	0.932 ± 0.03 μs	0.942 ± 0.03 μs	0.989 ± 0.045
LeastSquares/("ComplexF64", "(11, 5)", 0, 1)	1.28 ± 0.13 μs	1.26 ± 0.14 μs	1.02 ± 0.15
LeastSquares/("ComplexF64", "(11, 5)", 1, 0)	7.69 ± 0.37 μs	7.79 ± 0.4 μs	0.987 ± 0.07
LeastSquares/("ComplexF64", "(11, 5)", 1, 1)	1.28 ± 0.14 μs	1.27 ± 0.14 μs	1.01 ± 0.16
LeastSquares/("ComplexF64", "(5, 11)", 0, 0)	1.05 ± 0.031 μs	1.05 ± 0.04 μs	0.999 ± 0.048
LeastSquares/("ComplexF64", "(5, 11)", 0, 1)	1.38 ± 0.13 μs	1.38 ± 0.14 μs	1 ± 0.14
LeastSquares/("ComplexF64", "(5, 11)", 1, 0)	7.9 ± 0.37 μs	7.95 ± 0.36 μs	0.994 ± 0.065
LeastSquares/("ComplexF64", "(5, 11)", 1, 1)	1.41 ± 0.15 μs	1.43 ± 0.16 μs	0.986 ± 0.15
LeastSquares/("Float64", "(11, 5)", 0, 0)	0.771 ± 0.02 μs	0.761 ± 0.03 μs	1.01 ± 0.048
LeastSquares/("Float64", "(11, 5)", 0, 1)	1.04 ± 0.14 μs	1.06 ± 0.13 μs	0.981 ± 0.18
LeastSquares/("Float64", "(11, 5)", 1, 0)	7.52 ± 0.34 μs	7.49 ± 0.32 μs	1 ± 0.063
LeastSquares/("Float64", "(11, 5)", 1, 1)	1.06 ± 0.15 μs	1.06 ± 0.16 μs	0.999 ± 0.21
LeastSquares/("Float64", "(5, 11)", 0, 0)	0.891 ± 0.021 μs	0.891 ± 0.021 μs	1 ± 0.033
LeastSquares/("Float64", "(5, 11)", 0, 1)	1.17 ± 0.12 μs	1.16 ± 0.12 μs	1.01 ± 0.15
LeastSquares/("Float64", "(5, 11)", 1, 0)	7.64 ± 0.31 μs	7.7 ± 0.28 μs	0.992 ± 0.054
LeastSquares/("Float64", "(5, 11)", 1, 1)	1.16 ± 0.16 μs	1.16 ± 0.15 μs	1 ± 0.19
NormL2/Float32	3.5 ± 0.32 μs	3.48 ± 0.31 μs	1.01 ± 0.13
NormL2/Float64	9.19 ± 1.9 μs	9.23 ± 1.8 μs	0.996 ± 0.28
time_to_load	0.876 ± 0.0038 s	0.887 ± 0.01 s	0.987 ± 0.012

Memory benchmarks

	master	6596794...	master / 6596794...
IndBallL1/Float32	10 allocs: 10.4 kB	10 allocs: 10.4 kB	1
IndBallL1/Float64	10 allocs: 20.5 kB	10 allocs: 20.5 kB	1
IndBox/Float32	1 allocs: 16 B	1 allocs: 16 B	1
IndBox/Float64	1 allocs: 16 B	1 allocs: 16 B	1
IndExpPrimal/Float32	11 k allocs: 0.179 MB	11 k allocs: 0.179 MB	1
IndExpPrimal/Float64	11 k allocs: 0.179 MB	11 k allocs: 0.179 MB	1
IndNonnegative/Float32	1 allocs: 16 B	1 allocs: 16 B	1
IndNonnegative/Float64	1 allocs: 16 B	1 allocs: 16 B	1
IndPSD/("ComplexF64", 10)	19 allocs: 11.9 kB	19 allocs: 11.9 kB	1
IndPSD/("ComplexF64", 20)	22 allocs: 29.2 kB	22 allocs: 29.2 kB	1
IndPSD/("ComplexF64", 50)	23 allocs: 0.116 MB	23 allocs: 0.116 MB	1
IndPSD/("Float64", 10)	16 allocs: 5.88 kB	16 allocs: 5.88 kB	1
IndPSD/("Float64", 20)	18 allocs: 14 kB	18 allocs: 14 kB	1
IndPSD/("Float64", 50)	19 allocs: 0.0564 MB	19 allocs: 0.0564 MB	1
IndSimplex/Float32	24 allocs: 0.0344 MB	24 allocs: 0.0344 MB	1
IndSimplex/Float64	26 allocs: 0.0685 MB	26 allocs: 0.0685 MB	1
LeastSquares/("ComplexF64", "(11, 5)", 0, 0)	7 allocs: 1.05 kB	7 allocs: 1.05 kB	1
LeastSquares/("ComplexF64", "(11, 5)", 0, 1)	17 allocs: 1.14 kB	17 allocs: 1.14 kB	1
LeastSquares/("ComplexF64", "(11, 5)", 1, 0)	0.059 k allocs: 4.6 kB	0.059 k allocs: 4.6 kB	1
LeastSquares/("ComplexF64", "(11, 5)", 1, 1)	17 allocs: 1.17 kB	17 allocs: 1.17 kB	1
LeastSquares/("ComplexF64", "(5, 11)", 0, 0)	7 allocs: 1.05 kB	7 allocs: 1.05 kB	1
LeastSquares/("ComplexF64", "(5, 11)", 0, 1)	17 allocs: 1.14 kB	17 allocs: 1.14 kB	1
LeastSquares/("ComplexF64", "(5, 11)", 1, 0)	0.059 k allocs: 4.6 kB	0.059 k allocs: 4.6 kB	1
LeastSquares/("ComplexF64", "(5, 11)", 1, 1)	17 allocs: 1.17 kB	17 allocs: 1.17 kB	1
LeastSquares/("Float64", "(11, 5)", 0, 0)	7 allocs: 0.609 kB	7 allocs: 0.609 kB	1
LeastSquares/("Float64", "(11, 5)", 0, 1)	17 allocs: 0.984 kB	17 allocs: 0.984 kB	1
LeastSquares/("Float64", "(11, 5)", 1, 0)	0.059 k allocs: 3.96 kB	0.059 k allocs: 3.96 kB	1
LeastSquares/("Float64", "(11, 5)", 1, 1)	17 allocs: 1.02 kB	17 allocs: 1.02 kB	1
LeastSquares/("Float64", "(5, 11)", 0, 0)	7 allocs: 0.609 kB	7 allocs: 0.609 kB	1
LeastSquares/("Float64", "(5, 11)", 0, 1)	17 allocs: 0.984 kB	17 allocs: 0.984 kB	1
LeastSquares/("Float64", "(5, 11)", 1, 0)	0.059 k allocs: 3.96 kB	0.059 k allocs: 3.96 kB	1
LeastSquares/("Float64", "(5, 11)", 1, 1)	17 allocs: 1.02 kB	17 allocs: 1.02 kB	1
NormL2/Float32	1 allocs: 16 B	1 allocs: 16 B	1
NormL2/Float64	1 allocs: 16 B	1 allocs: 16 B	1
time_to_load	0.149 k allocs: 11.2 kB	0.149 k allocs: 11.2 kB	1