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\n \n\n \n \n\n \n Maintained by Zakodium\n
\n\n[![NPM version][npm-image]][npm-url]\n[![build status][ci-image]][ci-url]\n[](https://doi.org/10.5281/zenodo.5644534)\n[![npm download][download-image]][download-url]\n\n\n\n## Installation\n\n`$ npm install ml-matrix`\n\n## Usage\n\n### As an ES module\n\n```js\nimport { Matrix } from 'ml-matrix';\n\nconst matrix = Matrix.ones(5, 5);\n```\n\n### As a CommonJS module\n\n```js\nconst { Matrix } = require('ml-matrix');\n\nconst matrix = Matrix.ones(5, 5);\n```\n\n## [API Documentation](https://mljs.github.io/matrix/)\n\n## Examples\n\n### Standard operations\n\n```js\nconst { Matrix } = require('ml-matrix');\n\nvar A = new Matrix([\n [1, 1],\n [2, 2],\n]);\n\nvar B = new Matrix([\n [3, 3],\n [1, 1],\n]);\n\nvar C = new Matrix([\n [3, 3],\n [1, 1],\n]);\n```\n\n#### Operations\n```js\nconst addition = Matrix.add(A, B); // addition = Matrix [[4, 4], [3, 3], rows: 2, columns: 2]\nconst subtraction = Matrix.sub(A, B); // subtraction = Matrix [[-2, -2], [1, 1], rows: 2, columns: 2]\nconst multiplication = A.mmul(B); // multiplication = Matrix [[4, 4], [8, 8], rows: 2, columns: 2]\nconst mulByNumber = Matrix.mul(A, 10); // mulByNumber = Matrix [[10, 10], [20, 20], rows: 2, columns: 2]\nconst divByNumber = Matrix.div(A, 10); // divByNumber = Matrix [[0.1, 0.1], [0.2, 0.2], rows: 2, columns: 2]\nconst modulo = Matrix.mod(B, 2); // modulo = Matrix [[1, 1], [1, 1], rows: 2, columns: 2]\nconst maxMatrix = Matrix.max(A, B); // max = Matrix [[3, 3], [2, 2], rows: 2, columns: 2]\nconst minMatrix = Matrix.min(A, B); // max = Matrix [[1, 1], [1, 1], rows: 2, columns: 2]\n```\n\n#### Inplace Operations\n```js\nC.add(A); // => C = C + A\nC.sub(A); // => C = C - A\nC.mul(10); // => C = 10 * C\nC.div(10); // => C = C / 10\nC.mod(2); // => C = C % 2\n```\n\n#### Math Operations\n```js\n// Standard Math operations: (abs, cos, round, etc.)\nvar A = new Matrix([\n [ 1, 1],\n [-1, -1],\n]);\n\nvar exponential = Matrix.exp(A); // exponential = Matrix [[Math.exp(1), Math.exp(1)], [Math.exp(-1), Math.exp(-1)], rows: 2, columns: 2].\nvar cosinus = Matrix.cos(A); // cosinus = Matrix [[Math.cos(1), Math.cos(1)], [Math.cos(-1), Math.cos(-1)], rows: 2, columns: 2].\nvar absolute = Matrix.abs(A); // absolute = Matrix [[1, 1], [1, 1], rows: 2, columns: 2].\n// Note: you can do it inplace too as A.abs()\n```\nAvailable Methods:\n```js\nabs, 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\n```\n#### Manipulation of the matrix\n```js\n// remember: A = Matrix [[1, 1], [-1, -1], rows: 2, columns: 2]\n\nvar numberRows = A.rows; // A has 2 rows\nvar numberCols = A.columns; // A has 2 columns\nvar firstValue = A.get(0, 0); // get(rows, columns)\nvar numberElements = A.size; // 2 * 2 = 4 elements\nvar isRow = A.isRowVector(); // false because A has more than 1 row\nvar isColumn = A.isColumnVector(); // false because A has more than 1 column\nvar isSquare = A.isSquare(); // true, because A is 2 * 2 matrix\nvar isSym = A.isSymmetric(); // false, because A is not symmetric\nA.set(1, 0, 10); // A = Matrix [[1, 1], [10, -1], rows: 2, columns: 2]. We have changed the second row and the first column\nvar diag = A.diag(); // diag = [1, -1] (values in the diagonal)\nvar m = A.mean(); // m = 2.75\nvar product = A.prod(); // product = -10 (product of all values of the matrix)\nvar norm = A.norm(); // norm = 10.14889156509222 (Frobenius norm of the matrix)\nvar transpose = A.transpose(); // transpose = Matrix [[1, 10], [1, -1], rows: 2, columns: 2]\n```\n\n#### Row and column wise reductions\n```js\nvar M = new Matrix([\n [1, 2, 3],\n [4, 5, 6],\n]);\n\nvar sumOf = (vector) => vector.reduce((total, value) => total + value, 0);\n\nvar rowSums = M.applyAlongAxis(sumOf, 'row'); // rowSums = [6, 15]\nvar columnSums = M.applyAlongAxis(sumOf, 'column'); // columnSums = [5, 7, 9]\n```\nThe callback receives each row or column as a plain array along with its index, so any reduction can be expressed with it.\n\n#### Instantiation of matrix\n```js\nvar z = Matrix.zeros(3, 2); // z = Matrix [[0, 0], [0, 0], [0, 0], rows: 3, columns: 2]\nvar z = Matrix.ones(2, 3); // z = Matrix [[1, 1, 1], [1, 1, 1], rows: 2, columns: 3]\nvar z = Matrix.eye(3, 4); // z = Matrix [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], rows: 3, columns: 4]. there are 1 only in the diagonal\n```\n\n#### Concatenation of matrices\n```js\nvar M = new Matrix([\n [1, 2],\n [3, 4],\n]);\n\nvar stacked = M.concat([[5, 6]]); // stacked = Matrix [[1, 2], [3, 4], [5, 6], rows: 3, columns: 2]\nvar widened = M.concat(Matrix.columnVector([5, 6]), 'column'); // widened = Matrix [[1, 2, 5], [3, 4, 6], rows: 2, columns: 3]\n```\nConcatenating by row needs the same number of columns on both sides, concatenating by column needs the same number of rows. The two operands are left untouched.\n\n### Maths\n```js\nconst {\n Matrix,\n inverse,\n solve,\n linearDependencies,\n QrDecomposition,\n LuDecomposition,\n CholeskyDecomposition,\n EigenvalueDecomposition,\n} = require('ml-matrix');\n```\n#### Inverse and Pseudo-inverse\n```js\nvar A = new Matrix([\n [2, 3, 5],\n [4, 1, 6],\n [1, 3, 0],\n]);\n\nvar inverseA = inverse(A);\nvar B = A.mmul(inverseA); // B = A * inverse(A), so B ~= Identity\n\n\n// if A is singular, you can use SVD :\nvar A = new Matrix([\n [1, 2, 3],\n [4, 5, 6],\n [7, 8, 9],\n]); \n// A is singular, so the standard computation of inverse won't work (you can test if you don't trust me^^)\n\nvar inverseA = inverse(A, (useSVD = true)); // inverseA is only an approximation of the inverse, by using the Singular Values Decomposition\nvar B = A.mmul(inverseA); // B = A * inverse(A), but inverse(A) is only an approximation, so B doesn't really be identity.\n```\n```js\n// if you want the pseudo-inverse of a matrix :\nvar A = new Matrix([\n [1, 2],\n [3, 4],\n [5, 6],\n]);\n\nvar pseudoInverseA = A.pseudoInverse();\nvar B = A.mmul(pseudoInverseA).mmul(A); // with pseudo inverse, A*pseudo-inverse(A)*A ~= A. It's the case here\n```\n#### Least square\nLeast square is the following problem: We search for `x`, such that `A.x = B` (`A`, `x` and `B` are matrix or vectors).\nBelow, how to solve least square with our function\n```js\n// If A is non singular :\nvar A = new Matrix([\n [3, 1],\n [4.25, 1],\n [5.5, 1],\n [8, 1],\n]);\n\nvar B = Matrix.columnVector([4.5, 4.25, 5.5, 5.5]);\nvar x = solve(A, B);\nvar error = Matrix.sub(B, A.mmul(x)); // The error enables to evaluate the solution x found.\n```\n```js\n// If A is non singular :\nvar A = new Matrix([\n [1, 2, 3],\n [4, 5, 6],\n [7, 8, 9],\n]);\n\nvar B = Matrix.columnVector([8, 20, 32]);\nvar x = solve(A, B, (useSVD = true)); // there are many solutions. x can be [1, 2, 1].transpose(), or [1.33, 1.33, 1.33].transpose(), etc.\nvar error = Matrix.sub(B, A.mmul(x)); // The error enables to evaluate the solution x found.\n```\n#### Decompositions\n\n##### QR Decomposition\n```js\nvar A = new Matrix([\n [2, 3, 5],\n [4, 1, 6],\n [1, 3, 0],\n]);\n\nvar QR = new QrDecomposition(A);\nvar Q = QR.orthogonalMatrix;\nvar R = QR.upperTriangularMatrix;\n// So you have the QR decomposition. If you multiply Q by R, you'll see that A = Q.R, with Q orthogonal and R upper triangular\n```\n##### LU Decomposition\n```js\nvar A = new Matrix([\n [2, 3, 5],\n [4, 1, 6],\n [1, 3, 0],\n]);\n\nvar LU = new LuDecomposition(A);\nvar L = LU.lowerTriangularMatrix;\nvar U = LU.upperTriangularMatrix;\nvar P = LU.pivotPermutationVector;\n// So you have the LU decomposition. P includes the permutation of the matrix. Here P = [1, 2, 0], i.e the first row of LU is the second row of A, the second row of LU is the third row of A and the third row of LU is the first row of A.\n```\n##### Cholesky Decomposition\n```js\nvar A = new Matrix([\n [2, 3, 5],\n [4, 1, 6],\n [1, 3, 0],\n]);\n\nvar cholesky = new CholeskyDecomposition(A);\nvar L = cholesky.lowerTriangularMatrix;\n```\n##### Eigenvalues & eigenvectors\n```js\nvar A = new Matrix([\n [2, 3, 5],\n [4, 1, 6],\n [1, 3, 0],\n]);\n\nvar e = new EigenvalueDecomposition(A);\nvar real = e.realEigenvalues;\nvar imaginary = e.imaginaryEigenvalues;\nvar vectors = e.eigenvectorMatrix;\n```\n#### Linear dependencies\n```js\nvar A = new Matrix([\n [2, 0, 0, 1],\n [0, 1, 6, 0],\n [0, 3, 0, 1],\n [0, 0, 1, 0],\n [0, 1, 2, 0],\n]);\n\nvar dependencies = linearDependencies(A);\n// dependencies is a matrix with the dependencies of the rows. When we look row by row, we see that the first row is [0, 0, 0, 0, 0], so it means that the first row is independent, and the second row is [ 0, 0, 0, 4, 1 ], i.e the second row = 4 times the 4th row + the 5th row.\n```\n\n## License\n\n[MIT](./LICENSE)\n\n[npm-image]: https://img.shields.io/npm/v/ml-matrix.svg\n[npm-url]: https://npmjs.org/package/ml-matrix\n[ci-image]: https://github.com/mljs/matrix/workflows/Node.js%20CI/badge.svg?branch=main\n[ci-url]: https://github.com/mljs/matrix/actions?query=workflow%3A%22Node.js+CI%22\n[download-image]: https://img.shields.io/npm/dm/ml-matrix.svg\n[download-url]: https://npmjs.org/package/ml-matrix\n","readmeFilename":"README.md","users":{"maasencioh":true}}