Make an active subspace demonstration

[jiweiqi]

Say LLNL n-heptane mechanism or Aramco mechanism.

[jiweiqi]

Example of sparsedifftools

using SparsityDetection, SparseArrays
using SparseDiffTools

u = @view(pred[:, end])
du = similar(u)
jac_p = jacobian((du, x) -> dudt!(du, x, p, 0.0),
                                du, u)::Array{Float64,2} .* (-idt)
sparsity_pattern = sparse(jac_p)
colors = matrix_colors(sparsity_pattern)

forwarddiff_color_jacobian((du, x) -> dudt!(du, u, x, 0.0),
                                du, p, colorvec = colors)