Trait InnerProduct 

pub trait InnerProduct: Vector {
    // Required methods
    fn dot(&self, other: &Self) -> f64;
    fn default_unit() -> Unit<Self>;

    // Provided methods
    fn norm_squared(&self) -> f64 { ... }
    fn norm(&self) -> f64 { ... }
    fn to_unit(self) -> Result<(Unit<Self>, f64), Error> { ... }
    fn to_unit_unchecked(self) -> (Unit<Self>, f64) { ... }
    fn project(&self, b: &Self) -> Self { ... }
}

Operate on elements of an inner product space.

The InnerProduct subtrait defines additional methods that can be performed on any vector in an inner product space, specifically vector norms and inner products.

Required Methods

fn dot(&self, other: &Self) -> f64

Compute the vector dot product between two vectors.

c = \vec{a} \cdot \vec{b}

Example

use hoomd_vector::{Cartesian, InnerProduct};

let a = Cartesian::from([1.0, 2.0]);
let b = Cartesian::from([3.0, 4.0]);
let c = a.dot(&b);
assert_eq!(c, 11.0);

fn default_unit() -> Unit<Self>

Create a unit vector in the space.

Each vector space defines its own default unit vector.

Example

use hoomd_vector::{Cartesian, InnerProduct};

let u = Cartesian::<2>::default_unit();
assert_eq!(*u.get(), [0.0, 1.0].into());

Provided Methods

fn norm_squared(&self) -> f64

Compute the squared norm of the vector.

\left| \vec{v} \right|^2

Example

use hoomd_vector::{Cartesian, InnerProduct};

let v = Cartesian::from([2.0, 4.0]);
let norm_squared = v.norm_squared();
assert_eq!(norm_squared, 20.0);

fn norm(&self) -> f64

Compute the norm of the vector.

\left| \vec{v} \right|

Computing the norm calls sqrt. Prefer norm_squared when possible.

Example

use hoomd_vector::{Cartesian, InnerProduct};

let v = Cartesian::from([3.0, 4.0]);
let norm = v.norm();
assert_eq!(norm, 5.0);

fn to_unit(self) -> Result<(Unit<Self>, f64), Error>

Create a vector of unit length pointing in the same direction as the given vector.

Returns a tuple containing unit vector along with the original vector’s norm:

\frac{\vec{v}}{|\vec{v}|}

Example

use hoomd_vector::{Cartesian, InnerProduct, Unit};

let a = Cartesian::from([3.0, 4.0]);
let (unit, norm) = a.to_unit()?;
assert_eq!(*unit.get(), [3.0 / 5.0, 4.0 / 5.0].into());
assert_eq!(norm, 5.0);

Errors

Error::InvalidVectorMagnitude when self is the 0 vector.

fn to_unit_unchecked(self) -> (Unit<Self>, f64)

Create a vector of unit length pointing in the same direction as the given vector.

Returns a tuple containing unit vector along with the original vector’s norm:

\frac{\vec{v}}{|\vec{v}|}

Example

use hoomd_vector::{Cartesian, InnerProduct, Unit};

let a = Cartesian::from([3.0, 4.0]);
let (unit, norm) = a.to_unit_unchecked();
assert_eq!(*unit.get(), [3.0 / 5.0, 4.0 / 5.0].into());
assert_eq!(norm, 5.0);

Panics

Divide by 0 when self is the 0 vector.

fn project(&self, b: &Self) -> Self

Project one vector onto another.

\left(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2}\right) \vec{b}

where self is $\vec{a}$.

Example

use hoomd_vector::{Cartesian, InnerProduct, Vector};
let a = Cartesian::from([1.0, 2.0]);
let b = Cartesian::from([4.0, 0.0]);
let c = a.project(&b);
assert_eq!(c, [1.0, 0.0].into());

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<const N: usize> InnerProduct for Cartesian<N>