Trait maths_traits::analysis::metric::Seminorm

pub trait Seminorm<K: UnitalRing, X: RingModule<K>, R: Real> {
    fn norm(&self, x: X) -> R;

    fn normalize(&self, x: X) -> X
    where
        K: From<R>,
    { ... }
}

A real-valued function from a ring module that quantifies it's length, allowing for null-vectors

Specifically, a seminorm ‖•‖ is a function from a ring module X over K to the reals such that:

• K has a seminorm |•|
• ‖x‖ >= 0
• ‖cx‖ = |c|‖x‖
• ‖x+y‖ <= ‖x‖ + ‖y‖

This is distinct from a NormedMetric in that it is allowed to be 0 for non-zero vectors

Required methods

fn norm(&self, x: X) -> R

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Provided methods

fn normalize(&self, x: X) -> X where
    K: From<R>, 

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Implementors

impl<K: ComplexRing, V: InnerProductSpace<K>> Seminorm<K, V, <K as ComplexSubset>::Real> for InnerProductMetric

fn norm(&self, x: V) -> K::Real

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