Piecewise constant (step) majorizer for K-Lipschitz functions over an interval (vectorized over the breaks argument).

Return a piecewise constant (step) majorizer for K-Lipschitz functions over an interval. The function is vectorized over the breaks argument. The returned object has the same dimensions as breaks.

Usage

get_step_majorizer(fun, breaks, is_monotone = TRUE, K = 0)

Arguments

fun

A function object with a single argument x. If x is a matrix, fun should be vectorized over it.

breaks

(vector or matrix) The set of M+1 boundaries for the M subintervals in x. If breaks is a matrix, each row is treated as a separate set of breaks.

is_monotone

(boolean) Is the function monotone? (Default is TRUE.)

K

(double) A non-negative number for the Lipschitz cone. (Default is 0.)

Value

A vector of length M with the values of the piecewise constant majorizer

Examples

get_step_majorizer(fun = abs, breaks = -5:5, is_monotone = FALSE, K = 1)
#>  [1] 5.5 4.5 3.5 2.5 1.5 1.5 2.5 3.5 4.5 5.5