[]Struct lumol::Matrix3

pub struct Matrix3(_);

A 3x3 square matrix type.

Matrix3 implements all the usual arithmetic operations:

use lumol_core::types::{Matrix3, Vector3D};

let one = Matrix3::one();
let a = Matrix3::new([
    [1.0, 0.0, 3.0],
    [0.0, 2.0, 5.6],
    [0.0, 0.0, 8.0]
]);

let v = Vector3D::new(3.0, 2.0, 1.0);

// Indexing
assert_eq!(a[0][0], 1.0);
assert_eq!(a[1][2], 5.6);

// Addition
let c = a + one;
assert_eq!(c, Matrix3::new([
    [2.0, 0.0, 3.0],
    [0.0, 3.0, 5.6],
    [0.0, 0.0, 9.0]
]));

// Subtraction
let c = a - one;
assert_eq!(c, Matrix3::new([
    [0.0, 0.0, 3.0],
    [0.0, 1.0, 5.6],
    [0.0, 0.0, 7.0]
]));

// Multiplication
let c = a * one;  // matrix - matrix
assert_eq!(c, a);

let c = a * v;  // matrix - vector
assert_eq!(c, Vector3D::new(6.0, 9.6, 8.0));

let c = 42.0 * one;  // matrix - scalar
assert_eq!(c, Matrix3::new([
    [42., 0.0, 0.0],
    [0.0, 42., 0.0],
    [0.0, 0.0, 42.]
]));

// Division
let c = a / 2.0;
assert_eq!(c, Matrix3::new([
    [0.5, 0.0, 1.5],
    [0.0, 1.0, 2.8],
    [0.0, 0.0, 4.0]
]));

Implementations

impl Matrix3

pub fn new(data: [[f64; 3]; 3]) -> Matrix3

Create a new Matrix3 specifying all its components

Examples

let matrix = Matrix3::new([
    [0.0, 0.0, 3.0],
    [0.0, 1.0, 5.6],
    [0.0, 0.0, 7.0],
]);
assert_eq!(matrix[0][2], 3.0);

pub fn zero() -> Matrix3

Create a new Matrix3 with components set to 0

Examples

let matrix = Matrix3::zero();

for i in 0..3 {
    for j in 0..3 {
        assert_eq!(matrix[i][j], 0.0);
    }
}

pub fn one() -> Matrix3

Create a new Vector3D with components all components set to 0, except the diagonal components set to 1.

Examples

let matrix = Matrix3::one();

for i in 0..3 {
    for j in 0..3 {
        if i == j {
            assert_eq!(matrix[i][j], 1.0);
        } else {
            assert_eq!(matrix[i][j], 0.0);
        }
    }
}

pub fn rotation(axis: &Vector3D, angle: f64) -> Matrix3

Returns rotation matrix given a rotation angle and an axis.

Examples

let e1 = Vector3D::new(1.0f64, 0.0, 0.0);
let e3 = Vector3D::new(0.0f64, 0.0, 1.0);
let angle = 90f64.to_radians();

let rotation = Matrix3::rotation(&(e1 * 2.0), angle);
let mut rot_vec = rotation * e3;
for i in 0..3 {
    rot_vec[i] = (rot_vec[i] * 1.0e8).round() / 1.0e8
};
assert_eq!(rot_vec, Vector3D::new(0.0, 1.0, 0.0));

pub fn trace(&self) -> f64

Compute the trace of the matrix

Examples

let matrix = Matrix3::new([
    [0.0, 0.0, 3.0],
    [0.0, 1.0, 5.6],
    [0.0, 0.0, 7.0]
]);
assert_eq!(matrix.trace(), 8.0);

pub fn inverse(&self) -> Matrix3

Computes the inverse of a matrix

Examples

// A diagonal matrix is trivially invertible
let matrix = Matrix3::new([
    [4.0, 0.0, 0.0],
    [0.0, 1.0, 0.0],
    [0.0, 0.0, 7.0]
]);

let inverted = Matrix3::new([
    [1.0/4.0, 0.0, 0.0],
    [0.0, 1.0, 0.0],
    [0.0, 0.0, 1.0/7.0]
]);

assert_eq!(matrix.inverse(), inverted);
assert_eq!(matrix * matrix.inverse(), Matrix3::one());

Panics

If the matrix is not invertible, i.e. if the matrix determinant equals zero.

pub fn determinant(&self) -> f64

Computes the determinant of a matrix

Examples

let matrix = Matrix3::new([
    [4.0, 0.0, 0.0],
    [0.0, 1.5, 0.0],
    [0.0, 0.0, 7.0]
]);

assert_eq!(matrix.determinant(), 4.0 * 1.5 * 7.0);

pub fn transposed(&self) -> Matrix3

Transpose this matrix into a new matrix

Examples

let matrix = Matrix3::new([
    [1.0, 2.0, 4.0],
    [0.0, 1.0, 3.0],
    [0.0, 0.0, 1.0]
]);

let transposed = Matrix3::new([
    [1.0, 0.0, 0.0],
    [2.0, 1.0, 0.0],
    [4.0, 3.0, 1.0]
]);

assert_eq!(matrix.transposed(), transposed);

pub fn norm(&self) -> f64

Compute the (Frobenius) norm of the matrix

Examples

let matrix = Matrix3::new([
    [1.0, 2.0, 4.0],
    [0.0, 1.0, 3.0],
    [0.0, 0.0, 1.0]
]);

assert_eq!(matrix.norm(), 5.656854249492381);

Methods from Deref<Target = [[f64; 3]; 3]>

Trait Implementations

impl<'a, 'b> Add<&'a Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a, 'b> Add<&'a Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a> Add<&'a Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a, 'b> Add<&'a mut Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a, 'b> Add<&'a mut Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a> Add<&'a mut Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a> Add<Matrix3> for &'a Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a> Add<Matrix3> for &'a mut Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl Add<Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

impl<'a> AddAssign<&'a Matrix3> for Matrix3

impl<'a> AddAssign<&'a mut Matrix3> for Matrix3

impl<'a> AddAssign<Matrix3> for Matrix3

impl Clone for Matrix3

impl Copy for Matrix3

impl Debug for Matrix3

impl Deref for Matrix3

type Target = [[f64; 3]; 3]

The resulting type after dereferencing.

impl DerefMut for Matrix3

impl<'a> Div<f64> for &'a Matrix3

type Output = Matrix3

The resulting type after applying the / operator.

impl Div<f64> for Matrix3

type Output = Matrix3

The resulting type after applying the / operator.

impl<'a> Div<f64> for &'a mut Matrix3

type Output = Matrix3

The resulting type after applying the / operator.

impl<'a> DivAssign<&'a f64> for Matrix3

impl<'a> DivAssign<&'a mut f64> for Matrix3

impl<'a> DivAssign<f64> for Matrix3

impl From<[[f64; 3]; 3]> for Matrix3

impl<'a> Mul<&'a Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a Vector3D> for &'b Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a Vector3D> for &'b mut Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a> Mul<&'a Vector3D> for Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a mut Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> Mul<&'a mut Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a mut Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a mut Vector3D> for &'b mut Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a, 'b> Mul<&'a mut Vector3D> for &'b Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a> Mul<&'a mut Vector3D> for Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl Mul<Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> Mul<Matrix3> for &'a mut Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> Mul<Matrix3> for &'a Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> Mul<Vector3D> for &'a Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a> Mul<Vector3D> for &'a mut Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl Mul<Vector3D> for Matrix3

type Output = Vector3D

The resulting type after applying the * operator.

impl<'a> Mul<f64> for &'a mut Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl Mul<f64> for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> Mul<f64> for &'a Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

impl<'a> MulAssign<&'a Matrix3> for Matrix3

impl<'a> MulAssign<&'a f64> for Matrix3

impl<'a> MulAssign<&'a mut Matrix3> for Matrix3

impl<'a> MulAssign<&'a mut f64> for Matrix3

impl<'a> MulAssign<Matrix3> for Matrix3

impl<'a> MulAssign<f64> for Matrix3

impl One for Matrix3

fn one() -> Matrix3

Create an identity matrix

impl PartialEq<Matrix3> for Matrix3

impl StructuralPartialEq for Matrix3

impl<'a> Sub<&'a Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a, 'b> Sub<&'a Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a, 'b> Sub<&'a Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a, 'b> Sub<&'a mut Matrix3> for &'b mut Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a> Sub<&'a mut Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a, 'b> Sub<&'a mut Matrix3> for &'b Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a> Sub<Matrix3> for &'a Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a> Sub<Matrix3> for &'a mut Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl Sub<Matrix3> for Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

impl<'a> SubAssign<&'a Matrix3> for Matrix3

impl<'a> SubAssign<&'a mut Matrix3> for Matrix3

impl<'a> SubAssign<Matrix3> for Matrix3

impl Sum<Matrix3> for Matrix3

impl Zero for Matrix3

Auto Trait Implementations

impl RefUnwindSafe for Matrix3

impl Send for Matrix3

impl Sync for Matrix3

impl Unpin for Matrix3

impl UnwindSafe for Matrix3

Blanket Implementations

impl<T> Any for T where
    T: 'static + ?Sized
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impl<T> Borrow<T> for T where
    T: ?Sized
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impl<T> BorrowMut<T> for T where
    T: ?Sized
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impl<T> From<T> for T[src]

impl<T, U> Into<U> for T where
    U: From<T>, 
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impl<T> Pointable for T

type Init = T

The type for initializers.

impl<T> ToOwned for T where
    T: Clone
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type Owned = T

The resulting type after obtaining ownership.

impl<T, U> TryFrom<U> for T where
    U: Into<T>, 
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type Error = Infallible

The type returned in the event of a conversion error.

impl<T, U> TryInto<U> for T where
    U: TryFrom<T>, 
[src]

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.

impl<V, T> VZip<V> for T where
    V: MultiLane<T>,