pbat::math::CLinearOperator Concept Reference

Concept for operator that satisfies linearity in the mathematical sense. More...

#include <LinearOperator.h>

Concept definition

template<class T>
concept pbat::math::CLinearOperator =  requires(T t)
{
    {
        t.OutputDimensions()
    } -> std::convertible_to<int>;
    {
        t.InputDimensions()
    } -> std::convertible_to<int>;
    {t.Apply(VectorX{}, std::declval<VectorX&>())};
    {t.Apply(MatrixX{}, std::declval<MatrixX&>())};
    {
        t.ToMatrix()
    } -> std::convertible_to<CSCMatrix>;
}

Detailed Description

Concept for operator that satisfies linearity in the mathematical sense.

Linear operators satisfy \( L(ax+bz) = a*L(x) + b*L(z) \), hence simply scale and add the input (1st parameter of Apply) prior to the Apply member function to obtain the desired result. Often, the user wishes to obtain the result of multiple applications of linear operators, hence we should not overwrite the out variable (2nd parameter of Apply), but simply add to it. To subtract from it, simply negate the input x, i.e. \( L(-x) = -L(x) \) by linearity.