Complex Hausdorff Distance RC

6.5 Complex Hausdorff Distance $RC$

std::complex<T> hausdorff_distance(const rc_interval<T>& a, const rc_interval<T>& b); 
std::complex<T> hausdorff_distance_error(const rc_interval<T>& a, const rc_interval<T>& b);

The complex Hausdorff distance is the normal Hausdorff distance applied to the real and imaginary components individually.

hausdorff_distance(const rc_interval<T>&, const rc_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 |}

For $X,Y ∈ RC$ this becomes:

dH(X,Y )=dH(ℜi(X),ℜi(Y ))+ idH(ℑi(X),ℑi(Y))

hausdorff_distance_error(const rc_interval<T>&, const rc_interval<T>&)

Computes the hausdorff distance error between the two given intervals $A,B ∈IR$ , as defined as:

dHe = dH(A,B) a-a--

So in the case of $X,Y ∈RC$ :

dHe(X,Y)= dHe(ℜi(X),ℜi(Y))+idHe(ℑi(X),ℑi(Y))

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