in_bound: Returns whether a vector or each row of a matrix falls inside...

In genscore: Generalized Score Matching Estimators

Returns whether a vector or each row of a matrix falls inside a domain.

Description

Returns whether a vector or each row of a matrix falls inside a domain.

Usage

in_bound(x, domain)

Arguments

x	A vector of length or a matrix of number of columns equal to domain$p if domain$type != "simplex", or either domain$p or domain$p-1 otherwise.
domain	A list returned from make_domain() that represents the domain.

Details

Returns whether a vector or each row of a matrix falls inside a domain. If domain$type == "simplex", if the length/number of columns is domain$p, returns all(x > 0) && abs(sum(x) - 1) < domain$simplex_tol; if the dimension is domain$p-1, returns all(x > 0) && sum(x) < 1.

Value

A logical vector of length equal to the number of rows in x (1 if x is a vector).

Examples

p <- 30
n <- 10

# The 30-dimensional real space R^30, assuming probability of
domain <- make_domain("R", p=p)
in_bound(1:p, domain)
in_bound(matrix(1:(p*n), ncol=p), domain)

# The non-negative orthant of the 30-dimensional real space, R+^30
domain <- make_domain("R+", p=p)
in_bound(matrix(1:(p*n), ncol=p), domain)
in_bound(matrix(1:(p*n) * (2*rbinom(p*n, 1, 0.98)-1), ncol=p), domain)

# x such that sum(x^2) > 10 && sum(x^(1/3)) > 10 with x allowed to be negative
domain <- make_domain("polynomial", p=p, rule="1 && 2",
       ineqs=list(list("expression"="sum(x^2)>10", abs=FALSE, nonnegative=FALSE),
                      list("expression"="sum(x^(1/3))>10", abs=FALSE, nonnegative=FALSE)))
in_bound(rep((5/p)^3, p), domain)
in_bound(rep((10/p)^3, p), domain)
in_bound(rep((15/p)^3, p), domain)
in_bound(rep((5/p)^(1/2), p), domain)
in_bound(rep((10/p)^(1/2), p), domain)
in_bound(rep((15/p)^(1/2), p), domain)

# ([0, 1] v [2,3]) ^ p
domain <- make_domain("uniform", p=p, lefts=c(0,2), rights=c(1,3))
in_bound(c(0.5, 2.5)[rbinom(p, 1, 0.5)+1], domain)
in_bound(c(rep(0.5, p/2), rep(2.5, p/2)), domain)
in_bound(c(rep(0.5, p/2), rep(2.5, p/2-1), 4), domain)

# x such that {x1 > 1 && log(1.3) < x2 < 1 && x3 > log(1.3) && ... && xp > log(1.3)}
domain <- make_domain("polynomial", p=p, rule="1 && 2 && 3",
       ineqs=list(list("expression"="x1>1", abs=FALSE, nonnegative=TRUE),
                      list("expression"="x2<1", abs=FALSE, nonnegative=TRUE),
                      list("expression"="exp(x)>1.3", abs=FALSE, nonnegative=FALSE)))
in_bound(c(1.5, (log(1.3)+1)/2, rep(log(1.3)*2, p-2)), domain)
in_bound(c(0.5, (log(1.3)+1)/2, rep(log(1.3)*2, p-2)), domain)
in_bound(c(1.5, log(1.3)/2, rep(log(1.3)*2, p-2)), domain)
in_bound(c(1.5, (log(1.3)+1)/2, rep(log(1.3)/2, p-2)), domain)

# x in R_+^p such that {sum(log(x))<2 || (x1^(2/3)-1.3x2^(-3)<1 && exp(x1)+2.3*x2>2)}
domain <- make_domain("polynomial", p=p, rule="1 || (2 && 3)",
       ineqs=list(list("expression"="sum(log(x))<2", abs=FALSE, nonnegative=TRUE),
                      list("expression"="x1^(2/3)-1.3x2^(-3)<1", abs=FALSE, nonnegative=TRUE),
                      list("expression"="exp(x1)+2.3*x2^2>2", abs=FALSE, nonnegative=TRUE)))
in_bound(rep(exp(1/p), p), domain)
in_bound(c(1, 1, rep(1e5, p-2)), domain)

# x in R_+^p such that {x in R_+^p: sum_j j * xj <= 1}
domain <- make_domain("polynomial", p=p,
       ineqs=list(list("expression"=paste(paste(sapply(1:p,
                           function(j){paste(j, "x", j, sep="")}), collapse="+"), "<1"),
                     abs=FALSE, nonnegative=TRUE)))
in_bound(0.5/p/1:p, domain)
in_bound(2/p/1:p, domain)
in_bound(rep(1/p, p), domain)
in_bound(rep(1/p^2, p), domain)

# The (p-1)-simplex
domain <- make_domain("simplex", p=p)
x <- abs(matrix(rnorm(p*n), ncol=p))
x <- x / rowSums(x)
in_bound(x, domain) # TRUE
in_bound(x[,1:(p-1)], domain) # TRUE
x2 <- x
x2[,1] <- -x2[,1]
in_bound(x2, domain) # FALSE since the first component is now negative
in_bound(x2[,1:(p-1)], domain) # FALSE since the first component is now negative
x3 <- x
x3[,1] <- x3[,1] + domain$simplex_tol * 10
in_bound(x3, domain) # FALSE since the rows do not sum to 1
in_bound(x3[,1:(p-1)], domain) # TRUE since the first (p-1) elts in each row still sum to < 1
x3[,1] <- x3[,1] + x3[,p]
in_bound(x3[,1:(p-1)], domain) # FALSE since the first (p-1) elts in each row now sum to > 1

# The l-1 ball {sum(|x|) < 1}
domain <- make_domain("polynomial", p=p,
       ineqs=list(list("expression"="sum(x)<1", abs=TRUE, nonnegative=FALSE)))
in_bound(rep(0.5/p, p)*(2*rbinom(p, 1, 0.5)-1), domain)
in_bound(rep(1.5/p, p)*(2*rbinom(p, 1, 0.5)-1), domain)

genscore documentation built on May 31, 2023, 6:28 p.m.