I am a complete newbie to c++ and programming in general. I need to write something for scientific purposes and as such, performance is crucial. I introduced two types, matrices and vectors with intervals as entries, and now want to make them “able to work with”, i.e. define basic operations. The type definitions:

#include <eigen3/Eigen/Dense> #include <boost/numeric/interval.hpp>  namespace bn = boost::numeric; namespace bi = bn::interval_lib;  // Interval typedefs using Interval = bn::interval<         double,         bi::policies<             bi::save_state<bi::rounded_transc_std<double> >,             bi::checking_base<double>         >     >;  using Matrix = Eigen::Matrix<Interval, 3, 3>; using Vector = Eigen::Matrix<Interval, 3, 1>; 

Luckily, matrix products work without extra definitions (although I need to call a.lazyProduct(b), otherwise I receive an “operator unambiguous” error, which I don’t understand), but inner products and multiplications with constants do not. It seems that I have to manually overload the multiplications, which I did as follows:

Interval operator* (const double& x, const Interval& y)   {     double lower(x*y.lower());     double upper(x*y.upper());     if(x>0){       return Interval(lower,upper);     }     else{       return Interval(upper,lower);     }   }  Vector operator* (const double& x, const Vector& y)   {   Vector res;   for(int i = 0; i<3;i++) {     res[i] = x*y[i];   }   return res;   }  Matrix operator* (const double& x, const Matrix& y)   {   Matrix res;   for(int i = 0; i<3; i++) {     for(int j = 0; j<3; j++){       res(i,j) = x* y(i,j);     }   }   return res;   }  Interval inner_prod(const Vector& x, const Vector& y){   Interval res;   for(int i = 0; i<3; i++){     res += x[i]*y[i];   }   return res; }  Interval inner_prod(const std::vector<double>& x, const Vector& y){   Interval res;   for(int i = 0; i<3; i++){     res += x[i] * y[i];   }   return res; } 

sizes are hard-coded as I will not be working with any others. I would love to have some feedback and improvement suggestions that focus on performance. Also for the inner product, I was hoping there was a way to make use of std::inner_product for possible better performance, but I can’t figure out how.