Accelerate initialization through the use of undefined arrays

[JanJereczek]

The initialization is not the performance-critical step of our code but accelerating it can improve the user experience. To achieve this, we could initialize any array with undef, in alignment with the results of following benchmark:

julia> @btime zeros(10,10)
  47.559 ns (2 allocations: 944 bytes)
10×10 Matrix{Float64}:
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 ⋮                        ⋮                   
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0

julia> @btime Matrix{Float64}(undef,10,10)
  23.417 ns (2 allocations: 944 bytes)
10×10 Matrix{Float64}:
 6.9109e-310  6.9109e-310  6.9109e-310  …  6.9109e-310  6.9109e-310  6.9109e-310
 6.9109e-310  6.9109e-310  6.9109e-310     6.9109e-310  6.9109e-310  6.9109e-310
 6.9109e-310  6.9109e-310  6.9109e-310     6.9109e-310  6.9109e-310  6.9109e-310
 ⋮                                      ⋱                            
 6.9109e-310  6.9109e-310  6.9109e-310     6.9109e-310  6.9109e-310  6.9109e-310
 6.9109e-310  6.9109e-310  6.9109e-310     6.9109e-310  6.9109e-310  6.9109e-310

[JanJereczek]

Additionally, consider following benchmark:

@btime A = copy($Omega.null)
  5.639 μs (2 allocations: 128.05 KiB)

@btime A = Matrix{Float64}(undef, $Omega.Nx, $Omega.Ny)
  439.170 ns (2 allocations: 128.05 KiB)

Speed-up factor is about 10 for this example.