dxx::math::norms Namespace Reference

Built-in norms. More...

Variables
constexpr Norm	dxx::math::norms::euclidean
	Euclidean norm (2-norm)
constexpr Norm	dxx::math::norms::p_one
	1-norm (sum of absolute values of elements)
constexpr Norm	dxx::math::norms::infinity
	Infinity norm (max absolute value across elements)

Detailed Description

Built-in norms.

Variable Documentation

euclidean

Norm dxx::math::norms::euclidean

inlineconstexprexport

Initial value:

{
    .norm = [] (const vector auto& v) static {
        return std::sqrt(detail::euclidean_squared(v));
    },
    .sq_norm = detail::euclidean_squared,
}

Euclidean norm (2-norm)

infinity

Norm dxx::math::norms::infinity

inlineconstexprexport

Initial value:

{
    .norm = [] <vector V> (const V& v) static {
        RealOf<V> ret{};
        for (const auto& ve : v) {
            const auto ave = std::abs(ve);
            if (ave > ret) {
                ret = ave;
            }
        }
        return ret;
    },
}

Infinity norm (max absolute value across elements)

p_one

Norm dxx::math::norms::p_one

inlineconstexprexport

Initial value:

{
    .norm = [] <vector V> (const V& v) static {
        RealOf<V> ret{};
        for (const auto& ve : v) {
            ret += std::abs(ve);
        }
        return ret;
    },
}

1-norm (sum of absolute values of elements)