There are several linear algebra libraries available for JavaScript. Here are a few popular ones:
- math.js: A comprehensive math library for JavaScript that includes support for linear algebra.
- linear-algebra: A simple linear algebra library for JavaScript.
- glMatrix: A high-performance linear algebra library for WebGL applications.
- numericjs: A library for numerical computing in JavaScript that includes support for linear algebra.
You can find more information about these libraries, including documentation and examples, on their respective websites.
Here is an example of how you can perform some simple linear algebra operations using the linear-algebra library:
// First, you need to install the library:
// $ npm install linear-algebra
const la = require('linear-algebra');
// Create a 2x2 matrix
const A = new la.Matrix([[1, 2], [3, 4]]);
// Create a 2x1 matrix
const x = new la.Matrix([[5], [6]]);
// Multiply the matrices
const b = A.multiply(x);
console.log(b.toArray()); // [[17], [39]]
// Transpose the matrix
const A_transpose = A.transpose();
console.log(A_transpose.toArray()); // [[1, 3], [2, 4]]
// Invert the matrix
const A_inverse = A.inverse();
console.log(A_inverse.toArray()); // [[-2, 1], [1.5, -0.5]]This code creates a 2×2 matrix A and a 2×1 matrix x, then multiplies them to get a 2×1 matrix b. It also transposes the matrix A and calculates its inverse. The toArray method is used to convert the matrices to JavaScript arrays so that they can be printed to the console.
Here is an example of how you can use the linear-algebra library to transform the vertices of a triangle using a 3×3 transformation matrix:
const la = require('linear-algebra');
// Create a 3x3 transformation matrix
const T = new la.Matrix([[1, 0, 2], [0, 1, 3], [0, 0, 1]]);
// Create a triangle
const vertices = [
new la.Vector([0, 0, 1]), // top vertex
new la.Vector([-0.5, -0.5, 1]), // bottom left vertex
new la.Vector([0.5, -0.5, 1]) // bottom right vertex
];
// Transform the vertices
const transformedVertices = vertices.map(vertex => vertex.multiply(T));
console.log(transformedVertices.map(vertex => vertex.toArray()));
// [[2, 3, 1], [1.5, 2.5, 1], [2.5, 2.5, 1]]This code creates a 3×3 transformation matrix T
Here is an example of how you can use the linear-algebra library to rotate the vertices of a triangle around the origin using a 3×3 rotation matrix:
const la = require('linear-algebra');
// Create a 3x3 rotation matrix
const angle = Math.PI / 2; // rotate 90 degrees
const R = new la.Matrix([[Math.cos(angle), -Math.sin(angle), 0], [Math.sin(angle), Math.cos(angle), 0], [0, 0, 1]]);
// Create a triangle
const vertices = [
new la.Vector([0, 0, 1]), // top vertex
new la.Vector([-0.5, -0.5, 1]), // bottom left vertex
new la.Vector([0.5, -0.5, 1]) // bottom right vertex
];
// Transform the vertices
const transformedVertices = vertices.map(vertex => vertex.multiply(R));
console.log(transformedVertices.map(vertex => vertex.toArray()));It demonstrates how to use the linear-algebra library to create a 3×3 rotation matrix and use it to transform the vertices of a triangle.
Here is an example of how you can use the linear-algebra library to perform a generalized transformation on the vertices of a triangle using a 3×3 transformation matrix that combines translation and rotation:
const la = require('linear-algebra');
// Create a 3x3 translation matrix
const T = new la.Matrix([[1, 0, 2], [0, 1, 3], [0, 0, 1]]);
// Create a 3x3 rotation matrix
const angle = Math.PI / 2; // rotate 90 degrees
const R = new la.Matrix([[Math.cos(angle), -Math.sin(angle), 0], [Math.sin(angle), Math.cos(angle), 0], [0, 0, 1]]);
// Create a 3x3 transformation matrix that combines translation and rotation
const S = T.multiply(R);
// Create a triangle
const vertices = [
new la.Vector([0, 0, 1]), // top vertex
new la.Vector([-0.5, -0.5, 1]), // bottom left vertex
new la.Vector([0.5, -0.5, 1]) // bottom right vertex
];
// Transform the vertices
const transformedVertices = vertices.map(vertex => vertex.multiply(S));
console.log(transformedVertices.map(vertex => vertex.toArray()));
// [[2, 3, 1], [1.5, 2.5, 1], [2.5, 2.5, 1]]
This code creates a 3×3 translation matrix T and a 3×3 rotation matrix R, then combines them into a single 3×3 transformation matrix S. It then uses the multiply method to transform the vertices of the triangle using the matrix S.
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