Linear algebra library for JavaScript

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

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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.
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Documentation

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

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Usage

`js
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:

`js
// ---------------------------- 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());
`

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Tests

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

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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.