Struct TridiagonalMatrix 

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

Tridiagonal matrix representation

A tridiagonal matrix stores only the three diagonals, giving O(n) storage instead of O(n²) for dense matrices.

Examples

use scirs2_core::ndarray::{array, Array1};
use scirs2_linalg::specialized::TridiagonalMatrix;
use scirs2_linalg::SpecializedMatrix;

// Create a 4x4 tridiagonal matrix
let a = array![1.0, 2.0, 3.0, 4.0]; // Main diagonal
let b = array![5.0, 6.0, 7.0];      // Superdiagonal
let c = array![8.0, 9.0, 10.0];     // Subdiagonal

let tri = TridiagonalMatrix::new(a.view(), b.view(), c.view()).unwrap();

// The matrix is equivalent to:
// [[ 1.0, 5.0, 0.0, 0.0 ],
//  [ 8.0, 2.0, 6.0, 0.0 ],
//  [ 0.0, 9.0, 3.0, 7.0 ],
//  [ 0.0, 0.0, 10.0, 4.0 ]]

// Get elements
assert_eq!(tri.get(0, 0).unwrap(), 1.0);
assert_eq!(tri.get(0, 1).unwrap(), 5.0);
assert_eq!(tri.get(1, 0).unwrap(), 8.0);
assert_eq!(tri.get(2, 3).unwrap(), 7.0);
assert_eq!(tri.get(0, 2).unwrap(), 0.0); // Off-tridiagonal element

// Matrix-vector multiplication
let x = array![1.0, 2.0, 3.0, 4.0];
let y = tri.matvec(&x.view()).unwrap();

Implementations

impl<A> TridiagonalMatrix<A>

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

pub fn new( diag: ArrayView1<'_, A>, superdiag: ArrayView1<'_, A>, subdiag: ArrayView1<'_, A>, ) -> LinalgResult<Self>

Create a new tridiagonal matrix from the three diagonals

Arguments

• diag - Main diagonal of length n
• superdiag - Superdiagonal of length n-1
• subdiag - Subdiagonal of length n-1

Returns

• TridiagonalMatrix if the diagonals have compatible lengths
• LinalgError if the diagonal lengths are incompatible

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

Create a new tridiagonal matrix from a general matrix, extracting the three diagonals

Arguments

• a - Input square matrix to extract tridiagonal structure from

Returns

• TridiagonalMatrix representation of the input matrix
• LinalgError if the input matrix is not square

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

Solve a tridiagonal system of equations Ax = b using the Thomas algorithm

Arguments

• b - Right-hand side vector

Returns

• Solution vector x
• LinalgError if the matrix is singular or dimensions are incompatible

Trait Implementations

impl<A> Clone for TridiagonalMatrix<A>

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

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<A> Debug for TridiagonalMatrix<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 TridiagonalMatrix<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