get_g0 {genscore}

Calculates the l2 distance to the boundary of the domain and its gradient for some domains.

Description

Calculates the l2 distance to the boundary of the domain and its gradient for some domains.

Usage

get_g0(domain, C)

Arguments

domain

A list returned from make_domain() that represents the domain.

C

A positive number, cannot be Inf if domain$type == "R". If not Inf, the l2 distance will be truncated to C, i.e. the function returns pmin(g0(x), C) and its gradient.

Details

Calculates the l2 distance to the boundary of the domain, with the distance truncated above by a constant C. Matches the g0 function and its gradient from Liu (2019) if C == Inf and domain is bounded. Currently only R, R+, simplex, uniform and polynomial-type domains of the form sum(x^2) <= d or sum(x^2) >= d or sum(abs(x)) <= d are implemented.

Value

A function that takes x and returns a list of a vector g0 and a matrix g0d.

Examples

n <- 15
p <- 5
K <- diag(p)
eta <- numeric(p)

domain <- make_domain("R", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("R+", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("uniform", p=p, lefts=c(-Inf,-3,3), rights=c(-5,1,Inf))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("simplex", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
max(abs(get_g0(domain, 1)(x)$g0 - get_g0(domain, 1)(x[,-p])$g0))
max(abs(get_g0(domain, 1)(x)$g0d - get_g0(domain, 1)(x[,-p])$g0d))

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)>1.3", "nonnegative"=FALSE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)>1.3", "nonnegative"=TRUE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)<1.3", "nonnegative"=FALSE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)<1.3", "nonnegative"=TRUE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x)<1.3", "nonnegative"=FALSE, "abs"=TRUE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x)<1.3", "nonnegative"=TRUE, "abs"=TRUE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0(domain, 1)(x)