scalar_mean_square_error.h

// Description: Mean square-error between scalar sequences
// Documentation: statistics.txt

#ifndef PASTELMATH_SCALAR_MEAN_SQUARE_ERROR_H
#define PASTELMATH_SCALAR_MEAN_SQUARE_ERROR_H

#include "pastel/sys/real/real_concept.h"
#include "pastel/sys/set/set_concept.h"

// Implementation

#include "pastel/sys/math/powers.h"

namespace Pastel
{

    //! Returns the mean square-error between scalar sequences.
    /*!
   Time complexity: 
   O(n)
   where n = min(size(aSet), size(bSet)).

   returns:
   [sum_{i = 1}^n (x_i - y_i)^2] / n, if n > 0,
   0, otherwise.
   */
    template <
        typename Real, 
        typename A_Real_Set, 
        typename B_Real_Set,
        Requires<
            Models<Real, Real_Concept>,
            Models<A_Real_Set, Set_Concept>,
            Models<B_Real_Set, Set_Concept>
        > = 0>
    Real scalarMeanSquareError(
        A_Real_Set aSet,
        B_Real_Set bSet)
    {
        integer n = 0;
        Real result = 0;

        RANGES_FOR(auto&& elements, zipSet(aSet, bSet))
        {
            result += square(elements.first - elements.second);
            ++n;
        }

        if (n == 0)
        {
            return 0;
        }

        return result / n;
    }

}

#endif