AdaptiveBoxMap

The above approaches may not necessarily be effective for covering the setwise image of a box. For choosing test points more effectively, we can use some knowledge of the Lipschitz matrix for $f$ in a box Box(c, r), that is, a matrix $L \in \mathbb{R}^{d \times d}$ such that

\[| f(y) - f(z) | \leq L \, | y - z | \quad \text{for all } y, z \in \text{Box}(c, r),\]

where the operations $| \cdot |$ and $\leq$ are to be understood elementwise. The function AdaptiveBoxMap attempts to approximate $L$ before choosing an adaptive grid of test points in each box, as described in [7].

BoxMap(:adaptive, f, domain::Box) -> SampledBoxMap

Example

julia> F = BoxMap(:adaptive, f, domain)SampledBoxMap with 201 sample points
julia> p = plot!(
           p, F(B),
           color=RGBA(1.,0.,1.,0.5),
           lab="adaptive test points"
       )Plot{Plots.GRBackend() n=4}