Hyperrectangle

Hyperrectangle{N, VNC<:AbstractVector{N}, VNR<:AbstractVector{N}
              } <: AbstractHyperrectangle{N}

Type that represents a hyperrectangle.

A hyperrectangle is the Cartesian product of one-dimensional intervals.

Fields

• center – center of the hyperrectangle as a real vector
• radius – radius of the ball as a real vector, i.e., half of its width along each coordinate direction

Examples

The Hyperrectangle type stores a vector representing the center and another vector representing the radius. The default constructor Hyperrectangle(c, r) receives the center and radius, in that order. For instance,

julia> c = [-1.0, 1.0];

julia> r = [2.0, 1.0];

julia> H = Hyperrectangle(c, r)
Hyperrectangle{Float64,Array{Float64,1},Array{Float64,1}}([-1.0, 1.0], [2.0, 1.0])

Which creates the hyperrectangle with vertices:

julia> vertices_list(H)
4-element Array{Array{Float64,1},1}:
 [1.0, 2.0]
 [-3.0, 2.0]
 [1.0, 0.0]
 [-3.0, 0.0]

The getter functions for the center and the radius are center and radius_hyperrectangle (since radius corresponds to the radius of the enclosing ball of minimal volume):

julia> center(H)
2-element Array{Float64,1}:
 -1.0
  1.0

julia> radius_hyperrectangle(H)
2-element Array{Float64,1}:
 2.0
 1.0

There is also a constructor from lower and upper bounds with keyword arguments high and low. The following construction results in the same hyperrectangle as in the previous paragraph:

julia> l = [-3.0, 0.0];

julia> h = [1.0, 2.0];

julia> Hyperrectangle(low=l, high=h)
Hyperrectangle{Float64,Array{Float64,1},Array{Float64,1}}([-1.0, 1.0], [2.0, 1.0])

By default, the constructor checks that that radius of the hyperrecatangle is nonnegative. To supress this check, use the check_bounds optional flag in the constructor. Note that if check_bounds is set to false, the behavior of a set with contradictory bounds is undefined.

rand(::Type{Hyperrectangle}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
     [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing)

Create a random hyperrectangle.

Input

• Hyperrectangle – type for dispatch
• N – (optional, default: Float64) numeric type
• dim – (optional, default: 2) dimension
• rng – (optional, default: GLOBAL_RNG) random number generator
• seed – (optional, default: nothing) seed for reseeding

Output

A random hyperrectangle.

Algorithm

All numbers are normally distributed with mean 0 and standard deviation 1. Additionally, the radius is nonnegative.

center(H::Hyperrectangle)

Return the center of a hyperrectangle.

Input

• H – hyperrectangle

Output

The center of the hyperrectangle.

radius_hyperrectangle(H::Hyperrectangle)

Return the box radius of a hyperrectangle in every dimension.

Input

• H – hyperrectangle

Output

The box radius of the hyperrectangle.

radius_hyperrectangle(H::Hyperrectangle, i::Int)

Return the box radius of a hyperrectangle in a given dimension.

Input

• H – hyperrectangle
• i – dimension of interest

Output

The radius in the given dimension.

translate(H::Hyperrectangle, v::AbstractVector; [share]::Bool=false)

Translate (i.e., shift) a hyperrectangle by a given vector.

Input

• H – hyperrectangle
• v – translation vector
• share – (optional, default: false) flag for sharing unmodified parts of the original set representation

Output

A translated hyperrectangle.

Notes

The radius vector is shared with the original hyperrectangle if share == true.

Algorithm

We add the vector to the center of the hyperrectangle.