doc: chaining_tree

Compute the chaining tree given the canonical distance matrix between point of X

Syntax

[eNet, PiX, DeltaT, U] = chaining_tree(D2, dmax, step, iMin, iMax)
[eNet, PiX, DeltaT, U] = chaining_tree(..., 'Name',Value)

Arguments

• D2 matrix (n, n) of canonical squared distance
• dmax scalar of initial diameter of X
• step scalar > 1 for the geometric decay of $\epsilon_i$
• iMin integer for the first level to consider
• iMax integer for the last level to consider

Name-Value Pair Arguments

• a scalar > 1 power to use for the geometric decay in the union bound, e.g. 2
• lza scalar of logarithm of the Riemann zeta of a, e.g. log(pi^2/6)

Outputs

• eNet vector (1, N) of indices of points in the final $\epsilon$-net
• PiX matrix (h, n) of indices of the closest element of the net for all h=iMax-iMin levels
• DeltaT matrix (h, N) of diameters of the cells of the net for all h levels
• U vector (h, 1) of negative log probabilities w.r.t the union bounds for all h levels