Get the number of environmental variables given the number of parameters

Inverts num_par(p) to recover p from n, the number of parameters of the main xsdm model. Uses the closed-form solution of the quadratic: \(2n = p^2 + 5p + 4\), i.e. \(p = (-5 + \sqrt{9 + 8n})/2\). Errors if \(n\) is not a valid value of num_par(p) for some integer \(p \ge 1\).

Usage

num_env_var(n)

Arguments

n

Integerish scalar: total number of parameters.

Value

A single integer p, the number of environmental variables.

Examples

num_env_var(5) # -> 1  (since num_par(1) = 5)
#> [1] 1
num_env_var(9) # -> 2  (since num_par(2) = 9)
#> [1] 2
num_env_var(14) # -> 3  (since num_par(3) = 14)
#> [1] 3
# round-trip check:
p <- 4
stopifnot(num_env_var(num_par(p)) == p)