scirs2-linalg

High-performance linear algebra for Rust, modeled after SciPy/NumPy linalg.

scirs2-linalg provides a comprehensive linear algebra library with SciPy-compatible APIs, pure-Rust BLAS/LAPACK via OxiBLAS (no C or Fortran dependencies), SIMD acceleration, randomized methods, tensor decompositions, and iterative solvers suitable for large-scale scientific computing and machine learning.

Installation

[dependencies]
scirs2-linalg = "0.3.4"

With optional acceleration:

[dependencies]
scirs2-linalg = { version = "0.3.4", features = ["simd", "parallel"] }

Features (v0.3.4)

Core Decompositions

• LU (with partial/rook/complete pivoting), QR, SVD, Cholesky, LDL^T
• Eigendecomposition: eig, eigh (symmetric), generalized eigenproblem
• Schur decomposition (real and complex), QZ decomposition
• Polar decomposition, complete orthogonal decomposition
• Tall-and-Skinny QR (TSQR), LQ decomposition for wide matrices
• Randomized SVD (Halko, Martinsson, Tropp), Nystrom approximation

Iterative Solvers

• GMRES (restarted, deflated, recycled/GCRO-DR style)
• Preconditioned Conjugate Gradient (PCG)
• BiCGStab (stabilized bi-conjugate gradient)
• MINRES, SYMMLQ
• Arnoldi iteration, Lanczos iteration (with thick restarts)
• SOR, SSOR, Gauss-Seidel, Jacobi

Matrix Functions

• Matrix exponential expm (Pade approximant + scaling/squaring)
• Matrix logarithm logm (inverse scaling/squaring)
• Matrix square root sqrtm (Schur-based)
• Matrix sign function signm
• Matrix trigonometric functions (sin, cos, tan, sinh, cosh via Schur)
• Polar decomposition
• Matrix polynomial evaluation

Control Theory

• Algebraic Riccati equations (CARE, DARE): Newton iteration, Hamiltonian Schur
• Lyapunov equations (continuous and discrete)
• Sylvester equations (Bartels-Stewart, Hessenberg-Schur)
• Controllability and observability Gramians

Tensor Operations

• CP decomposition (Canonical Polyadic via ALS)
• Tucker decomposition (Higher-Order SVD / HOOI)
• Tensor contractions and mode-n products
• Einstein summation (einsum)
• Hierarchical Tucker (HT) decomposition
• Tensor-train format basics

Randomized Linear Algebra

• Randomized SVD with power iteration and oversampling
• Nystrom extension for kernel matrices
• Randomized eigensolvers (subspace iteration)
• Sketching: CountSketch, Gaussian sketch, SRHT

Structured and Specialized Matrices

• Toeplitz, Hankel, Circulant (FFT-based O(n log n) matvec)
• Cauchy matrix, companion matrix
• Banded matrices (tridiagonal, pentadiagonal), block tridiagonal
• Block diagonal, block sparse row
• Indefinite systems (symmetric indefinite factorization)

Matrix Completion and Low-Rank

• Nuclear norm minimization via alternating projections
• Soft-impute algorithm for matrix completion
• CUR decomposition (column-row factorization)
• Sparse-dense hybrid operations

Numerical Analysis

• Perturbation theory: condition number bounds, backward error analysis
• Numerical range (field of values) computation
• Matrix pencil problems (regular and singular pencils)
• Error analysis for linear systems and least squares

ML / AI Support

• Scaled dot-product attention, multi-head attention
• Flash attention (memory-efficient)
• Sparse attention patterns
• Positional encodings: RoPE, ALiBi
• Quantization-aware matrix multiply (4-bit, 8-bit, 16-bit)
• Mixed-precision operations with iterative refinement
• Batch matrix operations for mini-batch processing

Usage Examples

Basic operations

use scirs2_linalg::{det, inv, solve, svd, eigh};
use scirs2_core::ndarray::array;

let a = array![[4.0_f64, 2.0], [2.0, 3.0]];
let b = array![6.0_f64, 7.0];

let d = det(&a.view(), None)?;
let a_inv = inv(&a.view(), None)?;
let x = solve(&a.view(), &b.view(), None)?;

let (u, s, vt) = svd(&a.view(), true, None)?;
let (eigenvals, eigenvecs) = eigh(&a.view(), None)?;

Iterative solvers

use scirs2_linalg::iterative::{gmres, pcg, bicgstab};

// GMRES for a general non-symmetric system
let x = gmres(&a.view(), &b.view(), None, Some(30), Some(200), Some(1e-10))?;

// PCG for symmetric positive definite
let x = pcg(&a_spd.view(), &b.view(), None, Some(500), Some(1e-12))?;

// BiCGStab for non-symmetric
let x = bicgstab(&a.view(), &b.view(), None, Some(500), Some(1e-10))?;

Matrix functions

use scirs2_linalg::matrix_functions::{expm, logm, sqrtm};

let exp_a = expm(&a.view())?;
let log_a = logm(&a.view())?;
let sqrt_a = sqrtm(&a.view())?;

Tensor decompositions

use scirs2_linalg::tensor::{cp_als, tucker_hooi};

// CP decomposition with 5 components, 200 ALS iterations
let cp = cp_als(&tensor, 5, Some(200), Some(1e-8))?;

// Tucker decomposition with rank [3, 3, 3]
let tucker = tucker_hooi(&tensor, &[3, 3, 3], Some(100), Some(1e-8))?;

Control theory

use scirs2_linalg::control::{solve_care, solve_dare, solve_lyapunov};

// Continuous algebraic Riccati equation: A^T X + X A - X B R^{-1} B^T X + Q = 0
let x = solve_care(&a.view(), &b.view(), &q.view(), &r.view())?;

// Discrete algebraic Riccati equation
let x = solve_dare(&a.view(), &b.view(), &q.view(), &r.view())?;

// Lyapunov equation: A X + X A^T + Q = 0
let x = solve_lyapunov(&a.view(), &q.view())?;

Feature Flags

Links

• API Documentation
• SciRS2 Repository

License

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