adjointDualFactors.jl

using DualNumbers, LinearAlgebra, SparseArrays, SuiteSparse

n = 10
A = randn(n, n)            # a real-valued matrix
B = randn(n, n)            # another real-valued matrix

# Create a dual-valued matrix
M = A + ε * B

# And a sparse version of it
spM = sparse(M)

# Create the DualFactors type
struct DualFactors
    Af # the factors of the real part
    B  # the ε part
end

# Overload the factorize
function LinearAlgebra.factorize(M::AbstractArray{Dual128,2})
    return DualFactors(factorize(realpart.(M)), dualpart.(M))
end

# And break things
spMf = factorize(spM)