Store both an Array A and a scale s together in a ScaledArray SA = s*A, such that for example SA1*SA2 = (s1*s2)*A1*A2. The arrays are supposed to have elements O(1), whereas the scale s is supposed to carry the magnitude.
Use unscale to unscale SA (i.e. s=1) and rescale to change s.
julia> using ScaledArrays
julia> SA = ScaledArray(rand(3,3),100)
3×3 ScaledArray{Float64,2}:
0.354352 0.360733 0.0441772
0.39473 0.499311 0.560835
0.392939 0.245807 0.0387673
julia> unscale(SA)
3×3 ScaledArray{Float64,2}:
35.4352 36.0733 4.41772
39.473 49.9311 56.0835
39.2939 24.5807 3.87673
julia> rescale(SA,2)
3×3 ScaledArray{Float64,2}:
17.7176 18.0367 2.20886
19.7365 24.9655 28.0417
19.647 12.2903 1.93837
julia> SA² = SA*SA
3×3 ScaledArray{Float64,2}:
0.285316 0.318804 0.219679
0.55734 0.529561 0.319211
0.251499 0.27401 0.156719
julia> SA².s
10000.0
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