codac2_MatrixBase_addons_IntervalVector.h

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template<typename U=Scalar,int R=RowsAtCompileTime,int C=ColsAtCompileTime>
  requires IsIntervalDomain<U> && IsVectorOrRow<R,C>
inline auto complementary() const
{
  return Matrix<codac2::Interval,R,C>((int)this->size()).diff(*this);
}

template<typename OtherDerived,typename U=Scalar,int R=RowsAtCompileTime,int C=ColsAtCompileTime>
  requires IsIntervalDomain<U> && IsVectorOrRow<R,C>
inline std::list<Matrix<codac2::Interval,R,C>> diff(const MatrixBase<OtherDerived>& y, bool compactness = true) const
{
  // This code originates from the ibex-lib
  // See: ibex_TemplateVector.h
  // Author: Gilles Chabert
  // It has been revised with modern C++ and templated types
 
  const Index n = this->size();
  assert_release(y.size() == n);
 
  if(y == *this)
    return { };
 
  Matrix<codac2::Interval,R,C> x = *this;
  Matrix<codac2::Interval,R,C> z = x & y;
 
  if(z.is_empty())
  {
    if(x.is_empty()) return { };
    else return { x };
  }
 
  else
  {
    // Check if in one dimension y is flat and x not,
    // in which case the diff returns also x directly
    if(compactness)
      for(Index i = 0 ; i < n ; i++)
        if(z[i].is_degenerated() && !x[i].is_degenerated())
        {
          if(x.is_empty()) return { };
          else return { x };
        }
  }
 
  std::list<Matrix<codac2::Interval,R,C>> l;
 
  for(Index var = 0 ; var < n ; var++)
  {
    codac2::Interval c1, c2;
    
    for(const auto& ci : x[var].diff(y[var], compactness))
    {
      assert(!ci.is_empty());
 
      Matrix<codac2::Interval,R,C> v(n);
      for(Index i = 0 ; i < var ; i++)
        v[i] = x[i];
      v[var] = ci;
      for(Index i = var+1 ; i < n ; i++)
        v[i] = x[i];
      if(!v.is_empty())
        l.push_back(v);
    }
 
    x[var] = z[var];
  }
 
  return l;
}