Struct SymmetricMatrix 

pub struct SymmetricMatrix<A>
where
    A: Float + NumAssign + Zero + Sum + One + ScalarOperand + Send + Sync + Debug,
{ /* private fields */ }

Symmetric matrix representation

A symmetric matrix has the property that A = A^T, meaning the element at position (i, j) is equal to the element at position (j, i). This allows storing only the lower or upper triangular part of the matrix, saving almost half the memory.

Examples

use scirs2_core::ndarray::array;
use scirs2_linalg::specialized::SymmetricMatrix;
use scirs2_linalg::SpecializedMatrix;

// Create a 3x3 symmetric matrix
let a = array![
    [1.0, 2.0, 3.0],
    [2.0, 4.0, 5.0],
    [3.0, 5.0, 6.0]
];

let sym = SymmetricMatrix::frommatrix(&a.view()).unwrap();

// Get elements
assert_eq!(sym.get(0, 0).unwrap(), 1.0);
assert_eq!(sym.get(0, 1).unwrap(), 2.0);
assert_eq!(sym.get(1, 0).unwrap(), 2.0); // Equal to (0, 1)
assert_eq!(sym.get(2, 1).unwrap(), 5.0);

// Matrix-vector multiplication
let x = array![1.0, 2.0, 3.0];
let y = sym.matvec(&x.view()).unwrap();

Implementations

impl<A> SymmetricMatrix<A>

where A: Float + NumAssign + Zero + Sum + One + ScalarOperand + Send + Sync + Debug,

pub fn new(lower: ArrayView2<'_, A>) -> LinalgResult<Self>

Create a new symmetric matrix from the lower triangular part

Arguments

• lower - Lower triangular part of the matrix (including the diagonal)

Returns

• SymmetricMatrix if the input is valid
• LinalgError if the input is not a valid lower triangular part

pub fn frommatrix(a: &ArrayView2<'_, A>) -> LinalgResult<Self>

Create a new symmetric matrix from a general matrix

Arguments

• a - Input matrix, expected to be symmetric

Returns

• SymmetricMatrix if the input is symmetric
• LinalgError if the input is not symmetric

pub fn cholesky(&self) -> LinalgResult<Array2<A>>

Perform a Cholesky decomposition of the symmetric matrix

The Cholesky decomposition of a symmetric positive-definite matrix A is a lower triangular matrix L such that A = L * L^T.

Returns

• Lower triangular matrix L such that A = L * L^T
• LinalgError if the matrix is not positive definite

pub fn solve(&self, b: &ArrayView1<'_, A>) -> LinalgResult<Array1<A>>

Solve a symmetric system of equations Ax = b using Cholesky decomposition

Arguments

• b - Right-hand side vector

Returns

• Solution vector x
• LinalgError if the matrix is not positive definite or dimensions are incompatible

Trait Implementations

impl<A> Clone for SymmetricMatrix<A>

where A: Float + NumAssign + Zero + Sum + One + ScalarOperand + Send + Sync + Debug + Clone,

fn clone(&self) -> SymmetricMatrix<A>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<A> Debug for SymmetricMatrix<A>

where A: Float + NumAssign + Zero + Sum + One + ScalarOperand + Send + Sync + Debug + Debug,

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

Formats the value using the given formatter.

impl<A> SpecializedMatrix<A> for SymmetricMatrix<A>

where A: Float + NumAssign + Zero + Sum + One + ScalarOperand + Send + Sync + Debug,

fn nrows(&self) -> usize

Return the number of rows in the matrix

fn ncols(&self) -> usize

Return the number of columns in the matrix

fn get(&self, i: usize, j: usize) -> LinalgResult<A>

Get the element at position (i, j)

fn matvec(&self, x: &ArrayView1<'_, A>) -> LinalgResult<Array1<A>>

Perform matrix-vector multiplication: A * x

fn matvec_transpose(&self, x: &ArrayView1<'_, A>) -> LinalgResult<Array1<A>>

Perform transposed matrix-vector multiplication: A^T * x

fn to_dense(&self) -> LinalgResult<Array2<A>>

Convert to a dense matrix representation

fn to_operator(&self) -> LinalgResult<LinearOperator<A>>

where Self: Sync + 'static + Sized,

Convert to a matrix-free operator