Linear algebra library for JavaScript

This library contains some useful classes and functions for dealing with linear algebra in JavaScript.
The library was orginal written in TypeScript and then compiles into pure JavaScript.

---

Overview

• class Vector : This class represents a vector of arbitray size and operations on it.

  • constructor Vector(N) : creates a zero vector of size N
  • constructor Vector(N, components) : creates a vector of size N with the given components.
  • createUnitBasis(pos) : converts this vector in a unit basis vector and returns it.
  • component(pos) : returns the specified component (indexing at 0)
  • changeComponent(pos, value) : change the specified component.
  • toString() : returns a string representation of this vector.
  • size() : returns the size of the vector. (not the eulidean length!)
  • eulideanLength() : computes the eulidean length of this vector.
  • add(other) : vector addition, returns the rersult.
  • sub(other) : vector subtraction, returns the rersult.
  • dot(other) : computes the dot-product and returns it.
  • scalar(s) : scalar (s) multiplication. returns the result.
  • norm() : normalizes this vector and returns it.
  • equal(other) : returns true if the vectors are equal, otherwise false.

• function unitBasisVector(N,pos) : returns a unit basis vector of size N with a One on position 'pos'

• function randomVectorInt(N,a,b) : returns a random vector with integer components (between 'a' and 'b') of size N.

• function randomVectorFloat(N,a,b) : returns a random vector with floating point components (between 'a' and 'b') of size N.

• class Matrix : This class represents a matrix of arbitrary size and operations on it.

  • constructor(rows, cols) : creates a zero matrix of dimension rows x cols.
  • constructor(rows, cols, components) : creates a matrix with fix numbers of dimension rows x cols.
  • component(x,y) : returns the specified component.
  • changeComponent(x,y,value) : changes the specified component with the new value 'value'.
  • toString() : returns a string representation of this matrix.
  • dimension() : returns the dimension of this matrix as number arras [rows,cols].
  • add(other) : returns the result of the matrix addition.
  • equal(other) : returns true if the matrices are equal, otherwise false.
  • scalar(c) : returns the result of the matrix-scalar multiplication.

---

Documentation

The module is well documented in its source code. Look in the TypeScript file la_lib.ts.

---

Usage

You will find the library in the src directory its called la_lib.js. You simply need to
include this library in your project (you don't install anything). After that:

    var x = LinearAlgebra.Vector(...);

The namespace LinearAlgebra contains useful classes and functions for dealing with linear algebra under JavaScript.

Some examples:

// ---------------------------- Examples ------------------------------------------

// creates vectors 
var x = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);
var y = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);

// prints size of the vector
console.log(x.size()); // ==> 5

// changes the 2-th component with 7
//x.changeComponent(2,7);

// print the 2-th component.
console.log(x.component(2)); // ==> 3

// prints the full vector as string.
console.log(x.toString()); // ==> (1,2,3,4,5)

// vector addition
console.log(x.add(y).toString()); // ==> (2,3,6,8,10)

//console.log(x.createUnitBasis(1).toString());

// computes the dot-product
console.log(x.dot(y)); // ==> 55

// computes and prints the scalar-product
console.log(x.scalar(5).toString()); // ==> (5,10,15,20,25)

// creates a unit basis vector
console.log(LinearAlgebra.unitBasisVector(3, 0).toString()); // ==> (1,0,0)

// creates random vectors
console.log(LinearAlgebra.randomVectorInt(3, 0, 5).toString());
console.log(LinearAlgebra.randomVectorFloat(3, 0, 5).toString());

---

Tests

Go in the directory of the project and type in:
npm install
npm test
The test-suite use the JavaScript test-framework mocha.

---

Contributing

You can contribute to this project. Feel free and pull request some new features or documention.
TODO: Global functions for special matrices.
TODO: Documention of the classes and functions.