Vectorious

Vectorious is a generalized n-dimensional matrix and vector library written in JavaScript, which can be used both in node.js and the browser.

Clone or install with

$ npm install vectorious

Extensions

• vectorious-solve - Solves linear systems of equations of the form Ax = B.
• vectorious-plot - Generates a two-dimensional SVG plot from two input vectors.

Usage

The constructors of both Matrix and Vector are designed to be flexible, so they can be initialized using several different arguments.

var vectorious = require('vectorious');

var vector,
    matrix;

vector = new vectorious.Vector();
// { values: [], length: 0 }

matrix = new vectorious.Matrix();
// { rows: [] }

vector = new vectorious.Vector().zeros(5);
// { values: [0, 0, 0, 0, 0], length: 5 }

vector = new vectorious.Vector(1, 2, 3, 4, 5);
// { values: [1, 2, 3, 4, 5], length: 5 }

matrix = new vectorious.Matrix(vector);
// { rows: [ { values: [1, 2, 3, 4, 5], length: 5 } ] }

matrix = new vectorious.Matrix().zeros(2, 2);
/* {
  rows: [
    { values: [0, 0], length: 2 },
    { values: [0, 0], length: 2 }
  ]
} */

var input = [
  [1, 2],
  [3, 4]
];

matrix = new vectorious.Matrix(input);
/* {
  rows: [
    { values: [1, 2], length: 2 },
    { values: [3, 4], length: 2 }
  ]
} */

Now that you've got a hang of the basics, let me show you a useful application example.

var time = new vectorious.Vector().range(0, Math.PI / 12, Math.PI);
/* {
  values: 
   [ 0,
     0.2617993877991494,
     0.5235987755982988,
     0.7853981633974483,
     1.0471975511965976,
     1.308996938995747,
     1.5707963267948963,
     1.8325957145940457,
     2.0943951023931953,
     2.356194490192345,
     2.6179938779914944,
     2.879793265790644 ],
  length: 12 } */

var sine = time.map(Math.sin);
/* {
  values: 
   [ 0,
     0.25881904510252074,
     0.49999999999999994,
     0.7071067811865475,
     0.8660254037844386,
     0.9659258262890682,
     1,
     0.9659258262890684,
     0.8660254037844387,
     0.7071067811865476,
     0.49999999999999994,
     0.2588190451025206 ],
  length: 12 } */

Matrix

The following matrix operations and methods are implemented in matrix.js.

• add
• subtract
• scale
• multiply
• transpose
• gauss
• diag
• augment
• trace
• identity
• zeros
• ones
• equals
• get
• set
• swap
• map
• each
• toString
• toArray

// (Matrix, Matrix) => (Matrix)
Matrix.prototype.add = function(matrix)

Add two matrices together.

// (Matrix, Matrix) => (Matrix)
Matrix.prototype.subtract = function(matrix)

Subtract two matrices.

// (Matrix, Number) => (Matrix)
Matrix.prototype.scale = function(scalar)

Multiply all elements in matrix with a scalar.

// (Matrix, Matrix) => (Matrix)
Matrix.prototype.multiply = function(matrix)

Multiply two matrices together.

// (Matrix) => (Matrix)
Matrix.prototype.transpose = function()

Transpose a matrix.

// (Matrix, Boolean) => (Matrix)
Matrix.prototype.gauss = function(reduce)

Convert a matrix to (reduced) row echelon form.

// (Matrix) => (Vector)
Matrix.prototype.diag = function()

Get matrix diagonal as a Vector.

// (Matrix, Matrix) => (Matrix)
Matrix.prototype.augment = function(matrix)

Create an augmented matrix.

// (Matrix) => (Number)
Matrix.prototype.trace = function()

Get matrix trace (the sum of the diagonal).

// (Matrix, Number) => (Matrix)
Matrix.prototype.identity = function(size)

Create an identity matrix.

// (Matrix, Number, Number) => (Matrix)
Matrix.prototype.zeros = function(i, j)

Create an i x j matrix of zeros.

// (Matrix, Number, Number) => (Matrix)
Matrix.prototype.ones = function(i, j)

Create an i x j matrix of ones.

// (Matrix, Matrix) => (Boolean)
Matrix.prototype.equals = function(matrix)

Compare two matrices.

// (Matrix, Number, Number) => (Number)
Matrix.prototype.get = function(i, j)

Get element at row i, column j.

// (Matrix, Number, Number, Number) => (Matrix)
Matrix.prototype.set = function(i, j, value)

Set the value of an element at row i, column j.

// (Matrix, Number, Number) => (Matrix)
Matrix.prototype.swap = function(i, j)

Swaps the position of rows i and j.

// (Matrix, Function) => (Matrix)
Matrix.prototype.map = function(callback)

Maps a function callback to all elements of the matrix.

// (Matrix, Function) => (Matrix)
Matrix.prototype.each = function(callback)

Calls callback(row, index) for each row in the matrix.

// (Matrix) => (String)
Matrix.prototype.toString = function()

Convert matrix to string.

// (Matrix) => (Array)
Matrix.prototype.toArray = function()

Convert matrix to array.

Vector

The following vector operations and methods are implemented in vector.js.

• add
• subtract
• scale
• normalize
• dot
• magnitude
• angle
• project
• zeros
• ones
• range
• equals
• get
• min
• max
• set
• combine
• push
• map
• each
• toString
• toArray

// (Vector, Vector) => (Vector)
Vector.prototype.add = function(vector)

Add two vectors together.

// (Vector, Vector) => (Vector)
Vector.prototype.subtract = function(vector)

Subtract two vectors.

// (Vector, Number) => (Vector)
Vector.prototype.scale = function(scalar)

Multiply a vector by a scalar.

// (Vector) => (Vector)
Vector.prototype.normalize = function()

Normalize a vector.

// (Vector, Vector) => (Number)
Vector.prototype.dot = function(vector)

Get dot product of two vectors.

// (Vector) => (Number)
Vector.prototype.magnitude = function()

Get magnitude of vector (Pythagoras).

// (Vector, Vector) => (Angle)
Vector.prototype.angle = function(vector)

Get the angle (in radians) between two vectors.

// (Vector, Vector) => (Vector)
Vector.prototype.project = function(vector)

Project a vector onto another vector.

// (Vector, Number) => (Vector)
Vector.prototype.zeros = function(count)

Create a vector of count zeros.

// (Vector, Number) => (Vector)
Vector.prototype.ones = function(count)

Create a vector of count ones.

// (Vector, Number, [Number], Number) => (Vector)
Vector.prototype.range = function(start, [step], end)

Create a vector containing the range from start to end in steps of step (optional).

// (Vector, Vector) => (Boolean)
Vector.prototype.equals = function(vector)

Compare two vectors.

// (Vector, Number) => (Number)
Vector.prototype.get = function(index)

Get value of an element at index.

// (Vector, Number) => (Number)
Vector.prototype.min = function()

Get the minimum value of a vector.

// (Vector, Number) => (Number)
Vector.prototype.max = function()

Get the maximum value of a vector.

// (Vector, Number, Number) => (Vector)
Vector.prototype.set = function(index, value)

Set value of an element at index.

// (Vector, Vector) => (Vector)
Vector.prototype.combine = function(vector)

Combines two vectors.

// (Vector, Number) => (Vector)
Vector.prototype.push = function(value)

Pushes value into the vector.

// (Vector, Function) => (Vector)
Vector.prototype.map = function(callback)

Maps a function callback to all elements of the vector.

// (Vector, Function) => (Vector)
Vector.prototype.each = function(callback)

Calls callback(value, index) for each element in the vector.

// (Vector) => (String)
Vector.prototype.toString = function()

Convert vector to string.

// (Vector) => (Array)
Vector.prototype.toArray = function()

Convert vector to array.

Todo

• Add testing suite
• Add more useful operations :)

Contribute

Feel free to fork and commit pull requests. If you have any problems just submit an issue or send me an email.