matrixflow-js

Dense matrix computation and linear algebra for JavaScript.

matrixflow-js is a typed library for building, transforming, and decomposing dense matrices in Node.js and the browser. Create matrices, run element-wise and linear-algebra operations, and factorize with SVD, EVD, LU, QR, Cholesky, and NIPALS — all from one package.

Homepage: https://matrixflow-js.github.io/matrixflow-js/

Features

• Dense Matrix with Float64-backed storage and a full operator surface
• Views that slice, transpose, or flip without copying data
• SymmetricMatrix and DistanceMatrix for structured data
• Decompositions: SVD, EVD, LU, QR, Cholesky, NIPALS
• Solvers: inverse, pseudo-inverse, least squares
• Statistics: mean, variance, covariance, correlation, center, scale
• ESM, CommonJS, and a minified UMD build
• TypeScript definitions included

Install

npm install matrixflow-js

Quick start

ES modules

import { Matrix } from 'matrixflow-js';

const matrix = Matrix.ones(5, 5);

CommonJS

const { Matrix } = require('matrixflow-js');

const matrix = Matrix.ones(5, 5);

Browser (CDN)

<script src="https://cdn.jsdelivr.net/npm/matrixflow-js/matrix.umd.js"></script>
<script>
  const { Matrix } = matrixflow;
  console.log(Matrix.eye(3).toString());
</script>

Usage

Create matrices

import { Matrix } from 'matrixflow-js';

const A = new Matrix([
  [1, 1],
  [2, 2],
]);

const zeros = Matrix.zeros(3, 2);
const ones = Matrix.ones(2, 3);
const identity = Matrix.eye(3, 4);
const diagonal = Matrix.diag([1, 2, 3]);

Arithmetic

import { Matrix } from 'matrixflow-js';

const A = new Matrix([
  [1, 1],
  [2, 2],
]);
const B = new Matrix([
  [3, 3],
  [1, 1],
]);

Matrix.add(A, B); // [[4, 4], [3, 3]]
Matrix.sub(A, B); // [[-2, -2], [1, 1]]
A.mmul(B); // matrix product
Matrix.mul(A, 10); // scalar multiply
Matrix.div(A, 10); // scalar divide
Matrix.max(A, B);
Matrix.min(A, B);

In-place variants mutate the receiver:

const C = B.clone();
C.add(A);
C.mul(10);

Math functions

const A = new Matrix([
  [1, 1],
  [-1, -1],
]);

Matrix.exp(A);
Matrix.cos(A);
Matrix.abs(A);
A.clone().abs(); // in place

Available: abs, acos, acosh, asin, asinh, atan, atanh, cbrt, ceil, clz32, cos, cosh, exp, expm1, floor, fround, log, log1p, log10, log2, round, sign, sin, sinh, sqrt, tan, tanh, trunc.

Inspect and reshape

A.rows;
A.columns;
A.size;
A.get(0, 0);
A.set(1, 0, 10);
A.diag();
A.mean();
A.prod();
A.norm();
A.transpose();
A.isSquare();
A.isSymmetric();

Rows, columns, and concatenation

const M = new Matrix([
  [1, 2, 3],
  [4, 5, 6],
]);

const sumOf = (vector) => vector.reduce((total, value) => total + value, 0);

M.applyAlongAxis(sumOf, 'row'); // [6, 15]
M.applyAlongAxis(sumOf, 'column'); // [5, 7, 9]

M.concat([[7, 8, 9]]);
M.concat(Matrix.columnVector([7, 8]), 'column');

Linear algebra

import {
  Matrix,
  inverse,
  solve,
  linearDependencies,
  QrDecomposition,
  LuDecomposition,
  CholeskyDecomposition,
  EigenvalueDecomposition,
  SingularValueDecomposition,
} from 'matrixflow-js';

Inverse and pseudo-inverse

const A = new Matrix([
  [2, 3, 5],
  [4, 1, 6],
  [1, 3, 0],
]);

const inverseA = inverse(A);
A.mmul(inverseA); // ~ identity

const singular = new Matrix([
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
]);
inverse(singular, true); // SVD-based inverse

const tall = new Matrix([
  [1, 2],
  [3, 4],
  [5, 6],
]);
tall.pseudoInverse();

Least squares

Solve A · x = B:

const A = new Matrix([
  [3, 1],
  [4.25, 1],
  [5.5, 1],
  [8, 1],
]);
const B = Matrix.columnVector([4.5, 4.25, 5.5, 5.5]);
const x = solve(A, B);

Pass true as the third argument to use SVD when A is singular.

Decompositions

const A = new Matrix([
  [2, 3, 5],
  [4, 1, 6],
  [1, 3, 0],
]);

const QR = new QrDecomposition(A);
QR.orthogonalMatrix;
QR.upperTriangularMatrix;

const LU = new LuDecomposition(A);
LU.lowerTriangularMatrix;
LU.upperTriangularMatrix;
LU.pivotPermutationVector;

const cholesky = new CholeskyDecomposition(A);
cholesky.lowerTriangularMatrix;

const evd = new EigenvalueDecomposition(A);
evd.realEigenvalues;
evd.imaginaryEigenvalues;
evd.eigenvectorMatrix;

const svd = new SingularValueDecomposition(A);
svd.diagonal;
svd.leftSingularVectors;
svd.rightSingularVectors;

Linear dependencies

const A = new Matrix([
  [2, 0, 0, 1],
  [0, 1, 6, 0],
  [0, 3, 0, 1],
  [0, 0, 1, 0],
  [0, 1, 2, 0],
]);

linearDependencies(A);

Documentation

Full homepage, live playground, and API overview:

https://matrixflow-js.github.io/matrixflow-js/

The homepage deploys automatically on every push to main. In the GitHub repository, set Settings → Pages → Source to GitHub Actions.

TypeScript definitions ship with the package (matrix.d.ts).

License

MIT © LinNianPing ([email protected])