Hausdorff distance

T hausdorff_distance(const interval<T>& a, const interval<T>& b); 
T hausdorff_distance_error(const interval<T>& a, const interval<T>& b);

hausdorff_distance(const interval<T>&, const interval<T>&): Computes the hausdorff distance between the two given intervals $A,B ∈IR$ , as defined as:
$---- dH(A,B) = max{|b-a-|,|b-a |}$
hausdorff_distance_error(const interval<T>&, const interval<T>&): Computes the hausdorff distance error between the two given intervals $A,B ∈IR$ , as defined as:
$dHe = dH(A,B) a-a--$