Trait lowdim::Vector

pub trait Vector<S> where
    S: Integer,
    Self: Clone + Copy + Eq + Hash,
    Self: Index<usize, Output = S>,
    Self: FromIterator<S>,
    Self: VectorOps<S, Self>,
    Self: for<'a> VectorOps<S, &'a Self>,
    Self: Div<S, Output = Self>,
    Self: for<'a> Div<&'a S, Output = Self>,
    Self: Sum<Self> + for<'a> Sum<&'a Self>, {
    type DefaultLayout: Layout<S, Self>;

    const DIM: usize;

    fn with<F>(f: F) -> Self
    where
        F: Fn(usize) -> S;
    fn as_slice(&self) -> &[S];
    fn as_mut_slice(&mut self) -> &mut [S];
    fn norm_l1(&self) -> S;
    fn norm_l_infty(&self) -> S;
    fn norm_l2_squared(&self) -> S;
    fn componentwise_cmp(&self, other: &Self) -> Option<Ordering>;
    fn lex_cmp(&self, other: &Self) -> Ordering;

    fn zero() -> Self { ... }
    fn ones() -> Self { ... }
    fn is_zero(&self) -> bool { ... }
    fn min(&self, other: Self) -> Self { ... }
    fn max(&self, other: Self) -> Self { ... }
    fn signum(&self) -> Self { ... }
    fn unit_vecs() -> UnitVecs<S, Self> { ... }
    fn unit_vecs_l1() -> UnitVecsL1<S, Self> { ... }
    fn unit_vecs_l_infty() -> UnitVecsLInfty<S, Self> { ... }
}

Required traits and operations for vectors.

Associated Types

type DefaultLayout: Layout<S, Self>

The default layout to use with this vector.

Associated Constants

const DIM: usize

The dimension of the vectors in this type.

Required methods

fn with<F>(f: F) -> Self where
    F: Fn(usize) -> S, 

Create a vector from a function which computes the coordinates.

The function must return a scalar value for each possible coordinate index.

Example

assert_eq!(v4d(0, 1, 2, 3), Vec4d::with(|i| i64::try_from(i).unwrap()));

fn as_slice(&self) -> &[S]

Returns a slice containing the coordinates of the vector.

fn as_mut_slice(&mut self) -> &mut [S]

Returns a mutable slice containing the coordinates of the vector.

fn norm_l1(&self) -> S

Returns the L1 norm of the vector.

This is also called the taxicab, Manhatten or city block norm.

fn norm_l_infty(&self) -> S

Returns the L∞ norm of the vector.

This is also called the maximum or Chebychev norm.

fn norm_l2_squared(&self) -> S

Returns the square of the L2-norm of the vector.

The L2-norm is also called the Euclidean norm and is the standard notion of the length of a vector.

fn componentwise_cmp(&self, other: &Self) -> Option<Ordering>

Returns the partial ordering by component of two vectors.

fn lex_cmp(&self, other: &Self) -> Ordering

Returns the lexicographic total ordering for this and another vector.

That is, the first different coordinate decides the ordering. This is useful as an arbitrary total ordering for sorting, but is not intended to be otherwise meaningful.

Provided methods

fn zero() -> Self

Creates the zero vector.

fn ones() -> Self

Creates a vector of ones.

fn is_zero(&self) -> bool

Returns true if a vector is the zero vector.

fn min(&self, other: Self) -> Self

Apply min by component

fn max(&self, other: Self) -> Self

Apply max by component

fn signum(&self) -> Self

Signum by component.

Maps a vector to a unit step in the L∞ norm. This is a step on a shortest path w.r.t. L∞ along the vector.

fn unit_vecs() -> UnitVecs<S, Self>

Returns an iterator that yields the unit vectors.

fn unit_vecs_l1() -> UnitVecsL1<S, Self>

Returns an iterator that yields the vectors to orthogonal neighbours.

These are the vectors with L1 norm equal to 1.

fn unit_vecs_l_infty() -> UnitVecsLInfty<S, Self>

Creates a vector of the vectors with L∞ norm equal to 1.

These correspond to a single orthogonal or diagonal step.

Implementors

impl<S: Integer> Vector<S> for Vec2d<S>

const DIM: usize

type DefaultLayout = Layout2d<S>

impl<S: Integer> Vector<S> for Vec3d<S>

const DIM: usize

type DefaultLayout = Layout3d<S>

impl<S: Integer> Vector<S> for Vec4d<S>

const DIM: usize

type DefaultLayout = Layout4d<S>