norm_K {FKSUM}

The L2 norm of a kernel

Description

Computes the L2 norm of a kernel implemented in FKSUM, based on its coefficients. NB: the coefficients will first be normalised so that the kernel represents a density function. Equivalent to sqrt(roughness_K())

Usage

norm_K(beta)

Arguments

beta

numeric vector of positive coefficients.

Value

positive numeric representing the L2 norm 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.