Scale random-walk penalty strength to account for grid spacing

Rescale lambda across nested equally-spaced grids on [0,1].

Using the common heuristic for RW(q): $$\lambda(h) \propto h^{-(2q-1)}$$ and h = 1/(K-1), we use: $$\lambda_level = \lambda_final * ((K_level-1)/(K_final-1))^{(2q-1)}$$.

lambda_scale_for_spacing(lambda_final, K_final, K_level, q = 2)

Arguments

lambda_final

Scalar lambda used on final grid.

K_final

Number of points on the final grid.

K_level

Number of points on the current level grid.

q

RW order (e.g. 2 for RW2).

Value

Scalar lambda_level.