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mutable struct BivariateKDE{Rx<:AbstractRange, Ry<:AbstractRange} <: KernelDensity.AbstractKDE

Store both grid and density for KDE over the real line.

Reading the fields directly is part of the API, and

sum(density) * step(x) * step(y) ≈ 1

Fields

  • x: First coordinate of gridpoints for evaluating the density.

  • y: Second coordinate of gridpoints for evaluating the density.

  • density: Kernel density at corresponding gridpoints Tuple.(x, permutedims(y)).

mutable struct UnivariateKDE{R<:AbstractRange} <: KernelDensity.AbstractKDE

Store both grid and density for KDE over ² .

Reading the fields directly is part of the API, and

sum(density) * step(x) ≈ 1

Fields

  • x: Gridpoints for evaluating the density.

  • density: Kernel density at corresponding gridpoints x.

optimize(f, x_lower, x_upper; iterations=1000, rel_tol=nothing, abs_tol=nothing)

Minimize the function f in the interval x_lower..x_upper, using the golden-section search. Return an approximate minimum x̃ or error if such approximate minimum cannot be found.

This algorithm assumes that -f is unimodal on the interval x_lower..x_upper, that is to say, there exists a unique x in x_lower..x_upper such that f is decreasing on x_lower..x and increasing on x..x_upper.

rel_tol and abs_tol determine the relative and absolute tolerance, that is to say, the returned value x̃ should differ from the actual minimum x at most abs_tol + rel_tol * abs(x̃). If not manually specified, rel_tol and abs_tol default to sqrt(eps(T)) and eps(T) respectively, where T is the floating point type of x_lower and x_upper.

iterations determines the maximum number of iterations allowed before convergence.

This is a private, unexported function, used internally to select the optimal bandwidth automatically.