scirs2-sparse

Sparse matrix library for Rust, modeled after SciPy's sparse module.

scirs2-sparse provides comprehensive sparse matrix formats, iterative solvers, eigenvalue algorithms, preconditioners, graph algorithms, and advanced sparse linear algebra — all in pure Rust with no C or Fortran dependencies.

Installation

[dependencies]
scirs2-sparse = "0.3.0"

With optional acceleration:

[dependencies]
scirs2-sparse = { version = "0.3.0", features = ["parallel", "simd"] }

Features (v0.3.0)

Sparse Matrix Formats

Additional: SymCsrArray, SymCooArray for symmetric matrices with half-storage.

Iterative Solvers

• Conjugate Gradient (CG) for SPD systems
• BiCG, BiCGSTAB, CGS
• GMRES (restarted) and LGMRES (augmented with deflation vectors)
• MINRES for symmetric indefinite systems
• SYMMLQ
• GCROT, TFQMR
• SOR, SSOR iterative relaxation
• Saddle-point system solver (block preconditioned)
• LSQR and LSMR for least-squares problems

Preconditioners

• Jacobi (diagonal scaling)
• SSOR (symmetric successive over-relaxation)
• Incomplete Cholesky (IC) factorization
• Incomplete LU (ILU) with fill-level control
• SPAI (Sparse Approximate Inverse)
• Block Jacobi preconditioner
• Additive Schwarz (domain decomposition)
• Algebraic Multigrid (AMG) — smoothed aggregation
• Hierarchical matrix (H-matrix) approximation

Eigenvalue Solvers

• LOBPCG (Locally Optimal Block Preconditioned Conjugate Gradient) for extreme eigenvalues
• IRAM (Implicitly Restarted Arnoldi Method) for general sparse matrices
• Shift-and-invert mode for interior eigenvalues
• Generalized eigenvalue problem Ax = λBx
• Lanczos iteration for symmetric matrices
• 2-norm and condition number estimation

Graph Algorithms (csgraph module)

• Shortest paths: Dijkstra (binary heap), Bellman-Ford, Floyd-Warshall
• Connected components (undirected, strongly connected, weakly connected)
• BFS and DFS traversal with path reconstruction
• Minimum spanning tree: Kruskal and Prim
• Graph Laplacian matrices: standard, normalized, random-walk
• Algebraic connectivity (Fiedler value and vector)
• Topological sort
• Spectral clustering via sparse eigensolver

Sparse Linear Algebra Utilities

• SpMV (sparse matrix-vector multiply) and SpMM (sparse-dense matrix multiply)
• Sparse Kronecker product and Kronecker sum
• Block diagonal construction
• Horizontal and vertical stacking
• Matrix norms: Frobenius, 1-norm, infinity-norm, spectral norm (power method)
• Sparse matrix exponential expm and expm_multiply
• Linear operator abstraction with composition, transpose, power

Format Conversions

Bidirectional conversion among all formats: COO, CSR, CSC, BSR, LIL, DOK, DIA, ELLPACK, dense ndarray.

Advanced Formats

• DIA (diagonal format) with efficient matvec for banded matrices
• BCSR (Block CSR) for problems with dense block substructure
• ELLPACK for GPU-friendly uniform-nnz storage

Domain Decomposition

• Additive Schwarz method with overlap
• Restricted Additive Schwarz (RAS)
• Coarse-grid correction (two-level Schwarz)

Neural Adaptive Sparse

• Neural network for adaptive sparsity pattern prediction
• Learned sparse preconditioner
• Data-driven reordering heuristics

Usage Examples

Build a CSR matrix from triplets

use scirs2_sparse::csr_array::CsrArray;

let rows = vec![0usize, 0, 1, 2, 2];
let cols = vec![0usize, 2, 2, 0, 1];
let data = vec![1.0_f64, 2.0, 3.0, 4.0, 5.0];

let a = CsrArray::from_triplets(&rows, &cols, &data, (3, 3), false)?;
println!("nnz = {}", a.nnz());

Sparse matrix-vector multiply

use scirs2_sparse::linalg::spmv;

let b = vec![1.0_f64, 1.0, 1.0];
let x = spmv(&a, &b)?;

Iterative solve with preconditioner

use scirs2_sparse::linalg::solvers::{lgmres, LgmresParams};
use scirs2_sparse::linalg::preconditioners::IluPreconditioner;

let prec = IluPreconditioner::new(&a, 0)?;
let params = LgmresParams { tol: 1e-10, maxiter: 500, inner_m: 30, ..Default::default() };
let x = lgmres(&a, &b, Some(&prec), params)?;

LOBPCG eigenvalue solver

use scirs2_sparse::linalg::eigen::lobpcg;

// Compute 5 smallest eigenvalues
let (eigenvalues, eigenvectors) = lobpcg(&a, 5, None, Some(1e-8), Some(300))?;

Graph algorithms

use scirs2_sparse::csgraph::{shortest_path, connected_components};

let (n_components, labels) = connected_components(&adjacency, false)?;
let dist_matrix = shortest_path(&adjacency, None, false, true)?;

Algebraic multigrid preconditioner

use scirs2_sparse::linalg::algebraic_multigrid::SmoothedAggregationAMG;

let amg = SmoothedAggregationAMG::setup(&a, Default::default())?;
let x = amg.solve(&b, Some(1e-10), Some(100))?;

Feature Flags

Links

• API Documentation
• SciRS2 Repository

License

Licensed under the Apache License 2.0. See LICENSE for details.