tril

[ArnoStrouwen]

the symmetry of the hessian is exploited for extra compression (casadi also does this):
https://github.com/JuliaDiff/SparseDiffTools.jl/blob/master/test/test_sparse_hessian.jl#L12
But I don't immediately see how that extra compression is then later recovered:
https://github.com/JuliaDiff/SparseDiffTools.jl/blob/master/src/differentiation/compute_hessian_ad.jl#L142

using Pkg; Pkg.activate(".")
using SparsityDetection
using SparseDiffTools
function f(x)
    y = zero(eltype(x))
    for i in firstindex(x):lastindex(x)-1
        y += x[i]*x[i+1]
    end
    return y
end
f(rand(10))

x = randn(5)
sparsity = hessian_sparsity(f, x)

colors = matrix_colors(tril(sparsity))
colors2 = matrix_colors(sparsity)

ncolors = maximum(colors)
ncolors2 = maximum(colors2)

hescache = ForwardAutoColorHesCache(f, x, colors, sparsity)
hescache2 = ForwardAutoColorHesCache(f, x, colors2, sparsity)

H = SparseDiffTools.autoauto_color_hessian(f, x, hescache)
H2 = SparseDiffTools.autoauto_color_hessian(f, x, hescache2)
H3 = SparseDiffTools.autoauto_color_hessian(f, x)

Also, H3 is not really sparse.