mljs
ml-matrix
Matrix manipulation and computation library.
Maintained by Zakodium
Installation
$ npm install ml-matrix
Usage
As an ES module
import { Matrix } from 'ml-matrix';
const matrix = Matrix.ones(5, 5);As a CommonJS module
const { Matrix } = require('ml-matrix');
const matrix = Matrix.ones(5, 5);API Documentation
Examples
Standard operations
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
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
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 % 2Math Operations
// 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:
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, truncManipulation of the matrix
// 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
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 diagonalMaths
const {
Matrix,
inverse,
solve,
linearDependencies,
QrDecomposition,
LuDecomposition,
CholeskyDecomposition,
EigenvalueDecomposition,
} = require('ml-matrix');Inverse and Pseudo-inverse
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.// 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 hereLeast 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
// 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.// 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
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 triangularLU Decomposition
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
var A = new Matrix([
[2, 3, 5],
[4, 1, 6],
[1, 3, 0],
]);
var cholesky = new CholeskyDecomposition(A);
var L = cholesky.lowerTriangularMatrix;Eigenvalues & eigenvectors
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
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.