zero_norm {sparsegl}

Calculate common norms

Description

Calculate different norms of vectors with or without grouping structures.

Usage

zero_norm(x)

one_norm(x)

two_norm(x)

grouped_zero_norm(x, gr)

grouped_one_norm(x, gr)

grouped_two_norm(x, gr)

grouped_sp_norm(x, gr, asparse)

gr_one_norm(x, gr)

gr_two_norm(x, gr)

sp_group_norm(x, gr, asparse = 0.05)

Arguments

x

A numeric vector.

gr

An integer (or factor) vector of the same length as x.

asparse

Scalar. The weight to put on the l1 norm when calculating the group norm.

Value

A numeric scalar or vector

Functions

• zero_norm(): l0-norm (number of nonzero entries).

• one_norm(): l1-norm (Absolute-value norm).

• two_norm(): l2-norm (Euclidean norm).

• grouped_zero_norm(): A vector of group-wise l0-norms.

• grouped_one_norm(): A vector of group-wise l1-norms.

• grouped_two_norm(): A vector of group-wise l2-norms.

• grouped_sp_norm(): A vector of length unique(gr) consisting of the asparse convex combination of the l1 and l2-norm for each group.

• gr_one_norm(): The l1-norm norm of a vector (a scalar).

• gr_two_norm(): The sum of the group-wise l2-norms of a vector (a scalar).

• sp_group_norm(): The sum of the asparse convex combination of group l1 and l2-norms vectors (a scalar).

Examples

x <- c(rep(-1, 5), rep(0, 5), rep(1, 5))
gr <- c(rep(1, 5), rep(2, 5), rep(3, 5))
asparse <- 0.05
grouped_sp_norm(x, gr, asparse)