julia>using AppleAccelerate# needed so banded matrices aren't insanely slowjulia>for nin20:20:200                  ax= BlockArrays.BlockedOneTo(ArrayLayouts.RangeCumsum(Base.OneTo(n)))                  D=BandedBlockBandedMatrix{Float64}(I, (ax,ax), (0,0), (0,0))                  x=BlockVector(randn(sum(1:n)), (ax,))                  y=zero(x)@timemy_special_mul_through_data!(y, D, x);@timemy_special_mul!(y, D, x);@timemy_special_mul_with_a_view!(y, D, x);@timemul!(y, D, x);end0.000003 seconds0.000011 seconds (80 allocations:5.938 KiB)0.000003 seconds0.000012 seconds (2 allocations:64 bytes)0.000002 seconds0.000008 seconds (160 allocations:18.219 KiB)0.000002 seconds0.000026 seconds (2 allocations:64 bytes)0.000002 seconds0.000012 seconds (240 allocations:37.188 KiB)0.000003 seconds0.000007 seconds (2 allocations:64 bytes)0.000003 seconds0.000017 seconds (320 allocations:62.438 KiB)0.000006 seconds0.000011 seconds (2 allocations:64 bytes)0.000004 seconds0.000029 seconds (400 allocations:94.500 KiB)0.000009 seconds0.000011 seconds (2 allocations:64 bytes)0.000005 seconds0.000034 seconds (480 allocations:133.469 KiB)0.000013 seconds0.000015 seconds (2 allocations:64 bytes)0.000007 seconds0.000039 seconds (560 allocations:178.156 KiB)0.000013 seconds0.000020 seconds (2 allocations:64 bytes)0.000009 seconds0.000049 seconds (640 allocations:229.531 KiB)0.000022 seconds0.000027 seconds (2 allocations:64 bytes)0.000012 seconds0.000052 seconds (720 allocations:287.469 KiB)0.000059 seconds0.000034 seconds (2 allocations:64 bytes)0.000017 seconds0.000072 seconds (800 allocations:351.938 KiB)0.000029 seconds0.000045 seconds (2 allocations:64 bytes)

julia> n=10_000; D=BandedMatrix(0=>1:n); x=randn(n);@time D*x;0.000042 seconds (3 allocations:78.188 KiB)julia> D=Diagonal(1:n); x=randn(n);@time D*x;0.000010 seconds (3 allocations:78.188 KiB)