Distance

distance(S::AbstractSingleton, X::LazySet; [p]::Real=2.0)

Compute the distance between the singleton S and the set X with respect to the given p-norm.

Input

• S – singleton, i.e., a set with one element
• X – set
• p – (optional, default: 2.0) the p-norm used; p = 2.0 corresponds to the usual Euclidean norm

Output

A scalar representing the distance between the element wrapped by S and the set X.

distance(H1::AbstractHyperrectangle, H2::AbstractHyperrectangle;
         [p]::Real=2)

Compute the standard distance between two hyperrectangular sets, defined as

\[ \inf_{x ∈ H_1, y ∈ H_2} \{ d(x, y) \}.\]

Input

• H1 – hyperrectangular set
• H2 – hyperrectangular set
• p – (optional; default: 2) value of the $p$-norm

Output

The distance, which is zero if the sets intersect and otherwise the $p$-norm of the shortest line segment between any pair of points.