Mutable addition and substraction of sparse arrays

[blegat]

Turns out broadcast! is well implemented for SparseArrays:

julia> v = sparsevec([1, 3], [π, 2π])
3-element SparseVector{Float64, Int64} with 2 stored entries:
  [1]  =  3.14159
  [3]  =  6.28319

julia> a = copy(v)
3-element SparseVector{Float64, Int64} with 2 stored entries:
  [1]  =  3.14159
  [3]  =  6.28319

julia> b = copy(v)
3-element SparseVector{Float64, Int64} with 2 stored entries:
  [1]  =  3.14159
  [3]  =  6.28319

julia> @btime Broadcast.broadcast!(+, $v, 3, $a, 2, $b)
  38.791 ns (0 allocations: 0 bytes)
3-element SparseVector{Float64, Int64} with 3 stored entries:
  [1]  =  11.2832
  [2]  =  5.0
  [3]  =  17.5664

julia> @btime Broadcast.broadcast!(-, $v, 3, $a)
  27.560 ns (0 allocations: 0 bytes)
3-element SparseVector{Float64, Int64} with 3 stored entries:
  [1]  =  -0.141593
  [2]  =  3.0
  [3]  =  -3.28319

julia> @btime Broadcast.broadcast!(-, $v, $a, $b)
  31.149 ns (0 allocations: 0 bytes)
3-element SparseVector{Float64, Int64} with 0 stored entries

Since what we need exactly matches the definition of broadcast!, we might as well call broadcast! by default for any AbstractArray which is what this PR does.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.80%. Comparing base (e367b37) to head (0166303).
Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #281   +/-   ##
=======================================
  Coverage   91.80%   91.80%           
=======================================
  Files          23       23           
  Lines        2197     2197           
=======================================
  Hits         2017     2017           
  Misses        180      180           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[kalmarek]

@blegat for some reason the tests in StarAlgebras still allocate. Part of this is de-aliasing (I'm fine with this), but there is one additional allocation that happens only while testing, I cannot trace it in REPL:

julia> @test @allocations(MA.operate_to!(YY, +, Y, YY)) == 2
Test Passed

but

FixedBasis caching && allocations: Test Failed at /home/kalmar/.julia/dev/StarAlgebras/test/caching_allocations.jl:54
  Expression: #= /home/kalmar/.julia/dev/StarAlgebras/test/caching_allocations.jl:54 =# @allocations(MA.operate_to!(YY, +, Y, YY)) == 2
   Evaluated: 3 == 2

[blegat]

Testing allocations within the environment of a @testset is usually not easy, wrapping it in a function helps. To solve this issue in MA, we use

MutableArithmetics.jl/test/utilities.jl

Lines 13 to 21 in e303507

	function alloc_test(f, n)
	f() # compile
	@test n == @allocated f()
	end
	function alloc_test_le(f, n)
	f() # compile
	@test n >= @allocated f()
	end

This should be resolved by JuliaAlgebra/StarAlgebras.jl#29