Struct maths_traits::analysis::metric::InnerProductMetric

pub struct InnerProductMetric;

A metric on vector-spaces using the inner product of two vectors

For finite dimensional real-vector spaces, this is simply the Euclidean metric, and for functions on measure-spaces, this gives the L2-metric

Trait Implementations

impl<K: ComplexRing, V: InnerProductSpace<K>> SesquilinearForm<K, V> for InnerProductMetric

fn product_of(&self, v1: V, v2: V) -> K

The function that applies the sesquilinear form

fn sigma(&self, x: K) -> K

The mapping on R that factors the second argument of the sesquilinear form

fn sigma_inv(&self, x: K) -> K

The inverse of the σ

fn square(&self, x: M) -> R

An alias for x•x

fn is_null(&self, x: M) -> bool

Returns true if x•x = 0

fn orthogonal(&self, x: M, y: M) -> bool

Returns true if x•y = 0

fn orth_comp(&self, x: M, y: M) -> M where
    R: DivisionRing, 

The orthogonal component of y with respect to x, assuming x is not null

fn par_comp(&self, x: M, y: M) -> M where
    R: DivisionRing, 

The parallel component of y with respect to x, assuming x is not null

impl<K: ComplexRing, V: InnerProductSpace<K>> ReflexiveForm<K, V> for InnerProductMetric

impl<K: ComplexRing, V: InnerProductSpace<K>> SymSesquilinearForm<K, V> for InnerProductMetric

impl<K: Real, V: InnerProductSpace<K>> BilinearForm<K, V> for InnerProductMetric

impl<K: ComplexRing, V: InnerProductSpace<K>> ComplexSesquilinearForm<K, V> for InnerProductMetric

impl<R: Real, V: InnerProductSpace<R>> Metric<V, R> for InnerProductMetric

fn distance(&self, x1: V, x2: V) -> R

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

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

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

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

impl<K: ComplexRing, V: InnerProductSpace<K>> InnerProduct<K, V> for InnerProductMetric

impl Eq for InnerProductMetric

impl Clone for InnerProductMetric

fn clone(&self) -> InnerProductMetric

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl PartialEq<InnerProductMetric> for InnerProductMetric

fn eq(&self, other: &InnerProductMetric) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl Copy for InnerProductMetric

impl Hash for InnerProductMetric

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given [Hasher].

impl Debug for InnerProductMetric

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.