Linear algebra library for JavaScript

This library contains some useful classes and functions for dealing with linear algebra in 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

    const LinearAlgebra = require('jsalgebra')

    var x = LinearAlgebra.Vector(size, [.......]);

    var k = LinearAlgebra.Matrix(row, col);

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)

// set 1 at provided index rest fill with zero
console.log(x.createUnitBasis(1).toString()); // ==> (0,1,0,0,0)

// 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 Integer vectors
console.log(LinearAlgebra.randomVectorInt(3, 0, 5).toString());

// creates random Float vectors
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.