roughness_K {FKSUM}

Kernel roughness

Description

Computes the squared L2 norm, also known as the roughness, of a kernel implemented in FKSUM based on its beta coefficients. NB: the coefficients will first be normalised so that the kernel represents a density function. Equivalent to norm_K()^2

Usage

roughness_K(beta)

Arguments

beta

numeric vector of positive coefficients.

Value

positive numeric representing the squared L2 norm, or roughness of the kernel with coefficients beta/norm_const(beta).

References

Hofmeyr, D.P. (2021) "Fast exact evaluation of univariate kernel sums", IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(2), 447-458.