Struct SymmetricMat3 

pub struct SymmetricMat3(/* private fields */);

A memory-efficient 3×3 symmetric matrix for spatial algebra operations.

This structure stores a symmetric 3×3 matrix using only 6 elements instead of 9, exploiting the mathematical property that a_ij = a_ji for symmetric matrices. This provides significant memory savings and computational efficiency for inertia tensors and other symmetric operations in spatial algebra.

Storage Format

The matrix is stored in column-major order, containing the lower triangular elements of the symmetric matrix:

Stored array: [a₀₀, a₁₀, a₂₀, a₁₁, a₂₁, a₂₂]

Full matrix:
| a₀₀  a₀₁  a₀₂ |
| a₁₀  a₁₁  a₁₂ |  where a_ij = a_ji
| a₂₀  a₂₁  a₂₂ |

Applications in Spatial Algebra

• Rotational inertia tensors: Always symmetric, stored efficiently
• Covariance matrices: Common in state estimation and filtering
• Stiffness/damping matrices: Used in compliant dynamics
• Quadratic forms: Energy calculations and optimization

Performance Benefits

• Memory: 33% reduction compared to full 3×3 matrix storage
• Cache efficiency: Compact layout improves memory access patterns
• Computation: Avoids redundant calculations on symmetric elements

Implementations

impl SymmetricMat3

pub const ONE: Self

Identity matrix (diagonal elements are 1, off-diagonal are 0).

Represents the 3×3 identity matrix in symmetric storage format.

pub const ZERO: Self

Zero matrix (all elements are 0).

Useful for initialization and as the additive identity.

pub fn from_array(array: [Real; 6]) -> Self

Create a symmetric matrix from a 6-element array in column-major order.

Input Format

The array should contain the lower triangular elements in column-major order:

array = [a₀₀, a₁₀, a₂₀, a₁₁, a₂₁, a₂₂]

Example

use spatial_math::SymmetricMat3;

// Create matrix |1 2 3|
//               |2 4 5|
//               |3 5 6|
let matrix = SymmetricMat3::from_array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);

pub fn from_iterator(iter: impl IntoIterator<Item = Real>) -> Self

pub fn mat3(&self) -> Mat3

pub fn mul_vec(&self, v: Vec3) -> Vec3

pub fn scale(&self, scalar: Real) -> Self

pub fn add(&self, rhs: Self) -> Self

pub fn sub(&self, rhs: Self) -> Self

pub fn into_array(self) -> [Real; 6]

Trait Implementations

impl Add for SymmetricMat3

type Output = SymmetricMat3

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl Clone for SymmetricMat3

fn clone(&self) -> SymmetricMat3

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SymmetricMat3

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

Formats the value using the given formatter.

impl Default for SymmetricMat3

fn default() -> SymmetricMat3

Returns the “default value” for a type.

impl From<[f32; 6]> for SymmetricMat3

fn from(array: [Real; 6]) -> Self

Converts to this type from the input type.

impl From<Matrix<f32, Const<3>, Const<3>, ArrayStorage<f32, 3, 3>>> for SymmetricMat3

fn from(mat: Mat3) -> Self

Converts to this type from the input type.

impl<RStride, CStride> From<Matrix<f32, Const<3>, Const<3>, ViewStorage<'_, f32, Const<3>, Const<3>, RStride, CStride>>> for SymmetricMat3

where RStride: Dim, CStride: Dim,

fn from(mat: MatrixView3<'_, Real, RStride, CStride>) -> Self

Takes the lower triangle of the matrix and converts it into a SymmetricMat3.

impl Index<(usize, usize)> for SymmetricMat3

type Output = f32

The returned type after indexing.

fn index(&self, (row, col): (usize, usize)) -> &Self::Output

Performs the indexing (container[index]) operation.

impl Mul<Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>> for SymmetricMat3

type Output = Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3) -> Self::Output

Performs the * operation.

impl Mul<f32> for SymmetricMat3

type Output = SymmetricMat3

The resulting type after applying the * operator.

fn mul(self, rhs: Real) -> Self::Output

Performs the * operation.

impl Sub for SymmetricMat3

type Output = SymmetricMat3

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl Copy for SymmetricMat3