lina

tangent/lina validated against numpy / scipy.linalg

Dense linear algebra on plain JavaScript arrays: solving systems, the standard factorizations (LU, QR, Cholesky, SVD, symmetric eigendecomposition), least squares, and the everyday matrix operations. Matrices are nested arrays (number[][]) and vectors are flat arrays (number[]); flat Float64Array storage is used internally for the numerics.

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

Run the example notebook

Solving systems

Direct solves for square systems, plus the least-squares and pseudo-inverse routes for over- or under-determined ones.

Signature	Description
`solve(A, b)`	Solve `A x = b` for a square `A` via LU with partial pivoting.
`lstsq(A, b)`	Least-squares solution of `A x = b`. Returns `{x, residualNorm}`.
`pinvSolve(A, b)`	Minimum-norm least-squares solution through the pseudo-inverse (SVD).

Factorizations

Signature	Description
`lu(A)`	LU decomposition with partial pivoting. Returns `{L, U, P}`.
`qr(A)`	QR decomposition. Returns `{Q, R}`.
`cholesky(A)`	Cholesky factor of a symmetric positive-definite `A`.
`choleskySolve(A, b)`	Solve `A x = b` using the Cholesky factor.
`svd(A)`	Singular value decomposition. Returns `{U, s, V}` with singular values `s`.
`eigSym(A)`	Eigendecomposition of a symmetric `A`. Returns `{values, vectors}`.

Matrix operations

Signature	Description
`matmul(A, B)`	Matrix product `A B`.
`transpose(A)`	Matrix transpose.
`inv(A)`	Inverse of a square `A`.
`det(A)`	Determinant.
`identity(n)`	`n`-by-`n` identity matrix.
`diag(v)`	Diagonal matrix from a vector (or the diagonal of a matrix).
`norm(x, ord?)`	Vector or matrix norm.
`trace(A)`	Sum of the diagonal entries.

Properties

Signature	Description
`rank(A)`	Numerical rank from the singular values.
`cond(A)`	Condition number (ratio of largest to smallest singular value).
`isPositiveDefinite(A)`	Tests symmetric positive-definiteness via an attempted Cholesky.

Verified against numpy

The comparison suite runs each routine against numpy and scipy.linalg on shared matrices: solve and lstsq match to tolerance, the factorizations reconstruct their inputs (Q R, L U, U diag(s) Vᵀ) and satisfy their defining properties, and eigSym recovers the same values and vectors up to sign and ordering. cond and rank agree on the singular-value spectrum.