tangent/lina

Linear algebra for JavaScript (ESM). Browser-first, zero dependencies, runs in Node.js and Deno. The linear algebra leaf of the tangent suite — MIT-licensed infrastructure consumed by tangent/ds and tangent/sem.

Matrices are plain nested row-major arrays (number[][]) at the API boundary; computation runs on flat Float64Array storage internally.

What's in it

• Factorizations: lu (partial pivoting), qr (Householder, reduced/full), cholesky, svd (one-sided Jacobi — high relative accuracy), eigSym (cyclic Jacobi, symmetric matrices)
• Solvers: solve (vector or multi-RHS), choleskySolve, lstsq (QR-based), pinvSolve (minimum-norm, any rank)
• SVD-derived: pinv, rank, cond
• Utilities: matmul, transpose, identity, diag, norm (fro/1/inf), trace, det, inv, isPositiveDefinite

Install

npm install @tangent.to/lina     # npm
deno add jsr:@tangent/lina       # Deno / JSR

Usage

import { cholesky, eigSym, lstsq, solve, svd } from '@tangent.to/lina';

solve([[2, 1], [1, 3]], [3, 5]);            // [0.8, 1.4]

const { values, vectors } = eigSym(covarianceMatrix);  // PCA in two lines
const { U, s, V } = svd(dataMatrix);

const { x } = lstsq(designMatrix, y);        // OLS coefficients
const L = cholesky(spdMatrix);               // throws if not positive definite

Validation against numpy/scipy

tests_compare-to-scipy/ checks every operation against numpy.linalg/scipy.linalg on seeded random matrices — solve/det/inv, Cholesky (entrywise vs numpy), QR and SVD invariants, singular values and symmetric eigenvalues vs numpy, lstsq, pinv (including rank-deficient), rank and cond. Agreement is at machine precision (~1e-15). Requires uv and Node:

npm run test:scipy

Scope

Dense, double-precision, textbook-modern algorithms sized for the suite's workloads (covariance algebra, regression, ordination — n up to a few hundred). Deliberately out of scope: sparse matrices, complex numbers, general nonsymmetric eigenproblems (until a consumer needs them), and BLAS-style micro-optimization — wasm kernels belong in tangent/nd when it lands.

Performance

lina favors simple, unconditionally-stable algorithms (one-sided Jacobi SVD, cyclic Jacobi eigensolver) that hit machine precision on the suite's target sizes. On solve/inv it is competitive with the mature ml-matrix; on matmul and svd it is roughly 1.5–2× slower, and on symmetric eigendecomposition about 5× slower, because those Jacobi methods trade speed for simplicity. If a consumer ever profiles past this, the fix is targeted, not a rewrite: swap the symmetric eigensolver for tridiagonal QL and the SVD for Golub–Reinsch (the JAMA algorithms), and improve matmul cache locality. Until then, correctness and a zero-dependency footprint win. lina is not a general-purpose matrix library — for the rich Matrix API (elementwise arithmetic, broadcasting, views, nonsymmetric eigen), use ml-matrix; lina is the focused linear-algebra leaf the tangent suite's own packages build on.

License

MIT.