Struct Abs

pub struct Abs {}

A norm that is defined by an absolute value function on a field.

This is used for implementing the norms on types which represent a mathematical field, like the primitive floating point types (representing the field of real numbers) or the num_complex::Complex types (representing the field of complex numbers).

It can be seen as the most primitive kind of norm.

It is the only kind of norm that is used for further generic implementations, i.e. there are impls of the form impl<T: Norm<Abs>> Norm<SomeNorm> for SomeType<T>.

Implementations

impl Abs

pub fn new() -> Self

Creates an Abs norm.

Trait Implementations

impl Clone for Abs

fn clone(&self) -> Abs

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Abs

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

Formats the value using the given formatter.

impl Default for Abs

fn default() -> Abs

Returns the “default value” for a type.

impl<T: Float> Distance<Abs> for Complex<T>

fn distance(&self, other: &Self, _desc: Abs) -> T

Calculates the usual euclidean norm of the complex number.

type Output = T

The resulting type of the distance function.

impl<F: Float, C: FloatChecker<F>> Distance<Abs> for NoisyFloat<F, C>

type Output = NoisyFloat<F, C>

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> Self

Calculates the distance between self and other.

impl Distance<Abs> for f32

type Output = f32

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for f64

type Output = f64

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for i128

type Output = u128

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for i16

type Output = u16

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for i32

type Output = u32

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for i64

type Output = u64

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for i8

type Output = u8

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for isize

type Output = usize

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for u128

type Output = u128

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for u16

type Output = u16

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for u32

type Output = u32

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for u64

type Output = u64

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for u8

type Output = u8

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Distance<Abs> for usize

type Output = usize

The resulting type of the distance function.

fn distance(&self, other: &Self, _desc: Abs) -> <Self as Distance<Abs>>::Output

Calculates the distance between self and other.

impl Hash for Abs

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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T: Float> Norm<Abs> for Complex<T>

fn norm(&self, _desc: Abs) -> T

Calculates the usual euclidean norm of the complex number.

type Output = T

The resulting type of the norm function.

impl<F: Float, C: FloatChecker<F>> Norm<Abs> for NoisyFloat<F, C>

type Output = NoisyFloat<F, C>

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> Self

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for f32

type Output = f32

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for f64

type Output = f64

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for i128

type Output = u128

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for i16

type Output = u16

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for i32

type Output = u32

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for i64

type Output = u64

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for i8

type Output = u8

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for isize

type Output = usize

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for u128

type Output = u128

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for u16

type Output = u16

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for u32

type Output = u32

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for u64

type Output = u64

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for u8

type Output = u8

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl Norm<Abs> for usize

type Output = usize

The resulting type of the norm function.

fn norm(&self, _desc: Abs) -> <Self as Norm<Abs>>::Output

Calculates the norm of self, specified by the descriptor desc.

impl PartialEq for Abs

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

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for Abs

impl Eq for Abs

impl StructuralPartialEq for Abs