linear-algebra

Luna-Flow/linear-algebra is the linear-algebra layer of Luna Flow for MoonBit. It provides dense matrices and vectors in two execution models (immutable values and in-place buffers), numerical routines for floating-point matrices, exact algorithms for integer matrices, and small capability layers so that generic algorithms run on any matrix type that implements them. Every operation that can fail at runtime has a checked form returning a structured LinearAlgebraError.

Install

moon add Luna-Flow/linear-algebra@0.5.0

import {
  "Luna-Flow/linear-algebra/immut",
  "Luna-Flow/linear-algebra/mutable",
}

Example

///|
test "linear-algebra in a few lines" {
  let a = @immut.Matrix::from_2d_array([[1, 1], [1, 0]])
  inspect(a.pow(10).unwrap(), content="|89, 55|\n|55, 34|")
  let m = @mutable.Matrix::from_2d_array([[4.0, 2.0], [2.0, 3.0]])
  inspect(m.determinant().unwrap(), content="8")
  inspect(m.inverse().unwrap(), content="|0.375, -0.25|\n|-0.25, 0.5|")
  inspect(m.cholesky_decomposition().unwrap(), content="|2, 0|\n|1, 1.4142135623730951|")
}

Packages

Package	Purpose
immut	immutable Matrix, Vector and lazy MatrixFn; Bareiss determinants for integers, pivoted LU for floating point, and powers
mutable	in-place Matrix and Vector, row/column/transpose views; LU, inverse, rank, Cholesky, symmetric eigenvalues, power method, statistics
error	LinearAlgebraError and LinearAlgebraErrorKind for every checked API
arithmetic	scalar operation traits (Abs, ApproxEq, checked division, square root and comparison) and upstream re-exports
algebra	structure traits for whole vectors and matrices, from MatrixShape to MatMulMatrix (experimental)
backends/default	dense wrappers implementing the algebra traits over immut and mutable
container	storage-independent read/build/edit dictionaries and generic map, convert and transpose (experimental)
container/adapters	dictionaries for every vector and matrix type of this repository
internal, consistency	shared shape guards and cross-package agreement tests
perf, perf_runner, perf_support	benchmark subsystem (see bench/README.md)

The native OpenBLAS backend is not part of this release: its upstream binding does not compile with MoonBit 0.10. The source and re-enable steps are kept in contrib/openblas_backend.

Toolchain

MoonBit with moonc 0.10 or newer. The module builds without warnings with moon check --target all and is tested on wasm-gc, js, wasm and native. It depends on Luna-Flow/luna-generic 0.4.0 and Luna-Flow/arithmetic 0.5.0.

Documentation

The manual (API, tutorials and design notes for every package, in English, Chinese and Japanese) is published at https://lunaflow.cn/en/linear-algebra/. Its English source is doc/manual; every example in it is compiled and run as a test by src/doc_en_us. The design pages derive the algorithms (LU, Cholesky, the symmetric eigensolver, Bareiss elimination) and state their accuracy; the numerical routines of mutable use an absolute tolerance of 1e-11, so scale data to order one, and read the numerical caveats before relying on @immut.Matrix::determinant for floating-point data. Release history is in CHANGELOG.md.

Development

moon check --target all
./run_test.sh                               # default gate on all targets
LINEAR_ALGEBRA_TEST_BENCH=1 ./run_test.sh   # also the benchmark packages
just bench                                  # full benchmark report

Contributing

See CONTRIBUTING.md. Commits follow Conventional Commits.

License

Apache-2.0. See LICENSE.