Struct BlockTridiagonalMatrix 

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

Block tridiagonal matrix representation

A block tridiagonal matrix stores blocks on the main diagonal, superdiagonal, and subdiagonal, giving O(n) storage for the blocks instead of O(n²) for dense matrices.

Each matrix in the structure is stored as a square matrix using ndarray’s Array2.

Examples

use scirs2_core::ndarray::{array, Array2};
use scirs2_linalg::specialized::BlockTridiagonalMatrix;
use scirs2_linalg::SpecializedMatrix;

// Create 2×2 blocks for a block tridiagonal matrix
let a1 = array![[1.0, 2.0], [3.0, 4.0]];
let a2 = array![[5.0, 6.0], [7.0, 8.0]];
let a3 = array![[9.0, 10.0], [11.0, 12.0]];

let b1 = array![[13.0, 14.0], [15.0, 16.0]];
let b2 = array![[17.0, 18.0], [19.0, 20.0]];

let c1 = array![[21.0, 22.0], [23.0, 24.0]];
let c2 = array![[25.0, 26.0], [27.0, 28.0]];

// Create a block tridiagonal matrix with 3 diagonal blocks
let diag = vec![a1.clone(), a2.clone(), a3.clone()];
let super_diag = vec![b1.clone(), b2.clone()];
let sub_diag = vec![c1.clone(), c2.clone()];

let block_tri = BlockTridiagonalMatrix::new(diag, super_diag, sub_diag).unwrap();

// Get block dimensions and total dimensions
assert_eq!(block_tri.block_count(), 3);
assert_eq!(block_tri.nrows(), 6); // 3 blocks of size 2×2
assert_eq!(block_tri.ncols(), 6);

// Get element at position (1,3) which is in block (0,1) at position (1,1)
assert_eq!(block_tri.get(1, 3).unwrap(), 16.0);

// Matrix-vector multiplication with a 6-element vector
let x = array![1.0, 2.0, 3.0, 4.0, 5.0, 6.0];
let y = block_tri.matvec(&x.view()).unwrap();

Implementations

impl<A> BlockTridiagonalMatrix<A>

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

pub fn new( diagonal: Vec<Array2<A>>, superdiagonal: Vec<Array2<A>>, subdiagonal: Vec<Array2<A>>, ) -> LinalgResult<Self>

Create a new block tridiagonal matrix from blocks

Arguments

• diagonal - Vector of diagonal blocks
• superdiagonal - Vector of superdiagonal blocks (one fewer than diagonal)
• subdiagonal - Vector of subdiagonal blocks (one fewer than diagonal)

Returns

• LinalgResult<BlockTridiagonalMatrix<A>> - New block tridiagonal matrix

Errors

• If any diagonal block is not square
• If the number of superdiagonal or subdiagonal blocks is not one fewer than diagonal
• If the dimensions of adjacent blocks are incompatible

pub fn block_count(&self) -> usize

Get the number of diagonal blocks

pub fn diagonal_block(&self, i: usize) -> Option<&Array2<A>>

Get a reference to a diagonal block

pub fn superdiagonal_block(&self, i: usize) -> Option<&Array2<A>>

Get a reference to a superdiagonal block

pub fn subdiagonal_block(&self, i: usize) -> Option<&Array2<A>>

Get a reference to a subdiagonal block

Trait Implementations

impl<A> Clone for BlockTridiagonalMatrix<A>

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

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<A> Debug for BlockTridiagonalMatrix<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 BlockTridiagonalMatrix<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