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[![NPM version][npm-image]][npm-url] [![build status][ci-image]][ci-url] [](https://doi.org/10.5281/zenodo.5644534) [![npm download][download-image]][download-url] ## Installation `$ npm install ml-matrix` ## Usage ### As an ES module ```js import { Matrix } from 'ml-matrix'; const matrix = Matrix.ones(5, 5); ``` ### As a CommonJS module ```js const { Matrix } = require('ml-matrix'); const matrix = Matrix.ones(5, 5); ``` ## [API Documentation](https://mljs.github.io/matrix/) ## Examples ### Standard operations ```js const { Matrix } = require('ml-matrix'); var A = new Matrix([ [1, 1], [2, 2], ]); var B = new Matrix([ [3, 3], [1, 1], ]); var C = new Matrix([ [3, 3], [1, 1], ]); ``` #### Operations ```js const addition = Matrix.add(A, B); // addition = Matrix [[4, 4], [3, 3], rows: 2, columns: 2] const subtraction = Matrix.sub(A, B); // subtraction = Matrix [[-2, -2], [1, 1], rows: 2, columns: 2] const multiplication = A.mmul(B); // multiplication = Matrix [[4, 4], [8, 8], rows: 2, columns: 2] const mulByNumber = Matrix.mul(A, 10); // mulByNumber = Matrix [[10, 10], [20, 20], rows: 2, columns: 2] const divByNumber = Matrix.div(A, 10); // divByNumber = Matrix [[0.1, 0.1], [0.2, 0.2], rows: 2, columns: 2] const modulo = Matrix.mod(B, 2); // modulo = Matrix [[1, 1], [1, 1], rows: 2, columns: 2] const maxMatrix = Matrix.max(A, B); // max = Matrix [[3, 3], [2, 2], rows: 2, columns: 2] const minMatrix = Matrix.min(A, B); // max = Matrix [[1, 1], [1, 1], rows: 2, columns: 2] ``` #### Inplace Operations ```js C.add(A); // => C = C + A C.sub(A); // => C = C - A C.mul(10); // => C = 10 * C C.div(10); // => C = C / 10 C.mod(2); // => C = C % 2 ``` #### Math Operations ```js // Standard Math operations: (abs, cos, round, etc.) var A = new Matrix([ [ 1, 1], [-1, -1], ]); var exponential = Matrix.exp(A); // exponential = Matrix [[Math.exp(1), Math.exp(1)], [Math.exp(-1), Math.exp(-1)], rows: 2, columns: 2]. var cosinus = Matrix.cos(A); // cosinus = Matrix [[Math.cos(1), Math.cos(1)], [Math.cos(-1), Math.cos(-1)], rows: 2, columns: 2]. var absolute = Matrix.abs(A); // absolute = Matrix [[1, 1], [1, 1], rows: 2, columns: 2]. // Note: you can do it inplace too as A.abs() ``` Available Methods: ```js 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 ``` #### Manipulation of the matrix ```js // remember: A = Matrix [[1, 1], [-1, -1], rows: 2, columns: 2] var numberRows = A.rows; // A has 2 rows var numberCols = A.columns; // A has 2 columns var firstValue = A.get(0, 0); // get(rows, columns) var numberElements = A.size; // 2 * 2 = 4 elements var isRow = A.isRowVector(); // false because A has more than 1 row var isColumn = A.isColumnVector(); // false because A has more than 1 column var isSquare = A.isSquare(); // true, because A is 2 * 2 matrix var isSym = A.isSymmetric(); // false, because A is not symmetric A.set(1, 0, 10); // A = Matrix [[1, 1], [10, -1], rows: 2, columns: 2]. We have changed the second row and the first column var diag = A.diag(); // diag = [1, -1] (values in the diagonal) var m = A.mean(); // m = 2.75 var product = A.prod(); // product = -10 (product of all values of the matrix) var norm = A.norm(); // norm = 10.14889156509222 (Frobenius norm of the matrix) var transpose = A.transpose(); // transpose = Matrix [[1, 10], [1, -1], rows: 2, columns: 2] ``` #### Instantiation of matrix ```js var z = Matrix.zeros(3, 2); // z = Matrix [[0, 0], [0, 0], [0, 0], rows: 3, columns: 2] var z = Matrix.ones(2, 3); // z = Matrix [[1, 1, 1], [1, 1, 1], rows: 2, columns: 3] var 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 ``` ### Maths ```js const { Matrix, inverse, solve, linearDependencies, QrDecomposition, LuDecomposition, CholeskyDecomposition, EigenvalueDecomposition, } = require('ml-matrix'); ``` #### Inverse and Pseudo-inverse ```js var A = new Matrix([ [2, 3, 5], [4, 1, 6], [1, 3, 0], ]); var inverseA = inverse(A); var B = A.mmul(inverseA); // B = A * inverse(A), so B ~= Identity // if A is singular, you can use SVD : var A = new Matrix([ [1, 2, 3], [4, 5, 6], [7, 8, 9], ]); // A is singular, so the standard computation of inverse won't work (you can test if you don't trust me^^) var inverseA = inverse(A, (useSVD = true)); // inverseA is only an approximation of the inverse, by using the Singular Values Decomposition var B = A.mmul(inverseA); // B = A * inverse(A), but inverse(A) is only an approximation, so B doesn't really be identity. ``` ```js // if you want the pseudo-inverse of a matrix : var A = new Matrix([ [1, 2], [3, 4], [5, 6], ]); var pseudoInverseA = A.pseudoInverse(); var B = A.mmul(pseudoInverseA).mmul(A); // with pseudo inverse, A*pseudo-inverse(A)*A ~= A. It's the case here ``` #### Least square Least square is the following problem: We search for `x`, such that `A.x = B` (`A`, `x` and `B` are matrix or vectors). Below, how to solve least square with our function ```js // If A is non singular : var A = new Matrix([ [3, 1], [4.25, 1], [5.5, 1], [8, 1], ]); var B = Matrix.columnVector([4.5, 4.25, 5.5, 5.5]); var x = solve(A, B); var error = Matrix.sub(B, A.mmul(x)); // The error enables to evaluate the solution x found. ``` ```js // If A is non singular : var A = new Matrix([ [1, 2, 3], [4, 5, 6], [7, 8, 9], ]); var B = Matrix.columnVector([8, 20, 32]); var 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. var error = Matrix.sub(B, A.mmul(x)); // The error enables to evaluate the solution x found. ``` #### Decompositions ##### QR Decomposition ```js var A = new Matrix([ [2, 3, 5], [4, 1, 6], [1, 3, 0], ]); var QR = new QrDecomposition(A); var Q = QR.orthogonalMatrix; var R = QR.upperTriangularMatrix; // 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 ``` ##### LU Decomposition ```js var A = new Matrix([ [2, 3, 5], [4, 1, 6], [1, 3, 0], ]); var LU = new LuDecomposition(A); var L = LU.lowerTriangularMatrix; var U = LU.upperTriangularMatrix; var P = LU.pivotPermutationVector; // 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. ``` ##### Cholesky Decomposition ```js var A = new Matrix([ [2, 3, 5], [4, 1, 6], [1, 3, 0], ]); var cholesky = new CholeskyDecomposition(A); var L = cholesky.lowerTriangularMatrix; ``` ##### Eigenvalues & eigenvectors ```js var A = new Matrix([ [2, 3, 5], [4, 1, 6], [1, 3, 0], ]); var e = new EigenvalueDecomposition(A); var real = e.realEigenvalues; var imaginary = e.imaginaryEigenvalues; var vectors = e.eigenvectorMatrix; ``` #### Linear dependencies ```js var A = new Matrix([ [2, 0, 0, 1], [0, 1, 6, 0], [0, 3, 0, 1], [0, 0, 1, 0], [0, 1, 2, 0], ]); var dependencies = linearDependencies(A); // 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. ``` ## License [MIT](./LICENSE) [npm-image]: https://img.shields.io/npm/v/ml-matrix.svg [npm-url]: https://npmjs.org/package/ml-matrix [ci-image]: https://github.com/mljs/matrix/workflows/Node.js%20CI/badge.svg?branch=main [ci-url]: https://github.com/mljs/matrix/actions?query=workflow%3A%22Node.js+CI%22 [download-image]: https://img.shields.io/npm/dm/ml-matrix.svg [download-url]: https://npmjs.org/package/ml-matrix