Array.Math is a collection of calculation with arrays. You can do all kind of things with arrays. You can see them as data for statistic analysis, you can see them as vectors and matrices for linear algebra, or just use them for calculus like add, subtract and products or more advanced calculus with sequences.

The next steps are Vectors and Matrices. The aim is to be able to calculate eigenvalues and eigenvectors from a given Matrix. Singular Value Decomposition would be nice as well. To do this, JavaScript needs to be extended so it can handle Complex numbers, this can be found in Complex.js

To be sure all the methods work as expected, there is a Specs folder that contains some tests.

Transforms each value of the array to a number.

#JS
['1', '13', '300'].toNumbers(); // [1, 13, 300]

Sorts an array as numbers. The sort method usually transforms each value to a string and lexically compares the values. This will result that '10' will before '2'. This is a quick method to fix that.

#JS
[99, 2, 4, 40, 10].sortNumbers(); [2, 4, 10, 40, 99]

Sum all the entities of the array

#JS
[2, 5, 1, 6].sum(); // 14
[2, 5, 2, 7, 7, 12, 8].sum([start], [length])

Get the product of the array and a number or an array with the same size

#JS
[2, 5, 6, 2].product(3); // [6, 15, 18, 6]
[2, 5, 6, 2].product([3, 7, 1, 5]); // [5, 12, 7, 7]

Get the quotient of the array and a number or an array with the same size

#JS
[9, 12, 15].quotient(3) // [3, 4, 5]
[9, 12, 15].quotient(3, 4, 5) // [3, 3, 3]

Get the power of each entity in the array

#JS
[3, 6, 2].power(3) // [27, 216, 8]
[2, 2, 2].power([3, 4, 5]) // [8, 16, 32]

Add a number to each entity in the array

#JS
[2, 5, 1].add(4) // [6, 9, 5]
[2, 5, 1].add([1, 2, 3]) // [3, 7, 4]

Subtract a number to each entity of the array

#JS
[6, 9, 5].subtract(4) // [2, 5, 1]
[2, 7, 4].subtract([1, 2, 3]) // [1, 5, 1]

Count the number of entities in the array

#JS
[1, 3 , 56, 3, 56].count() // 5

Fill the array with a range of numbers

#JS
[].range(2, 5) // [2, 3, 4, 5]
[].range(1, 8, 2) // [1, 3, 5, 7]

Create a sequence

#JS
//A function with a return
[].sequence(function(n){
	return Math.pow(-1, n);
}, [start], [length]);

// A recursive function without a return
// Fibonacci
[1, 1].sequence(function(n){
	this[n + 2] = this[n] + this[n + 1];
}, [start], [length]);

Find the median of a array of numbers

#JS
[1, 5, 2, 8, 7].median() // 5
[1, 5, 2, 8, 7, 2].median() // 3.5

Find the variance of an array of numbers

#JS
[3, 7, 7, 19].variance() // 36'

Find the standard deviation

#JS
[3, 7, 7, 19].stdDeviation() // 6

Transpose the matrix (swap the rows and columns)

#JS
[ [1, 2, 3], [4, 5, 6], [7, 8, 9] ].transpose() // [ [1, 4, 7], [2, 5, 8], [3, 6, 9] ]

Find the dot product between two vectors

#JS
[1, 2, 3].dot([4, 5, 6]) // 32

Find the cross product between two vectors.

Tip, if you use this in combination with Array.vectorLength(), you will find the magnitude of the vector

#JS
[1, 2, 3].cross([4, 5, 6]) // [-3, 6, -6]

// Find the torque about A with arm r and force F
// M = r x A
var M = [1, 2, 1].cross([100, 145, 106]); // [67, -6, 6]
var Mmagnitude = M.vectorLenght(); // 67.53517601961218

Find the projection of the array on a certain vector For example: you have a vector in a certain direction, and you want to know the vector projected on another vector, for example the vector that describes the x- and the y-axis. This is usefull when you want to devide vector in components (for force analysis).

Tip, if you use this in combination with Array.vectorLength(), you will find the magnitude of the vector

#JS
[3, 3].projection([2, 0]) // [3,0]

// Find the force along the x-axis in this 3d space
[600, 263, 768].projection([1, 0, 0]); // [600, 0, 0]

// Find the force along the line in the xy-area with slope 0.5
[600, 235, 267].projection([1, 0.5, 1]);

Find the determinant of a square matrix

#JS
[[4, 6], [3, 5]].determinant() // 2
[[5, 6, 4], [6, 3, 7], [5, 4, 2]].determinant() // 64
[[5, 3, 2, 2], [9, 5, 2, 9], [6, 8, 9, 4], [0, 6, 3, 4]].determinant() // -692

Find the vector of a vector

#JS
[3, 6, 2].vectorLength() // 7

// Find the magnitude of the force [150, 300, 100] in the 3d space
[150, 300, 100].vectorLength();

Get the normalized vector, so that the vector length is 1

#JS
[8, 6].normalize() // [4/5, 3/5]

Find the angle between two vectors

#JS
[3, 7, 1].angle([3, 3, 6]) / Math.PI // 0.2798476073884561 pi

Get the slope between two points (2d only, there isn't really such thing as a 3d slope)

#JS
[3, 4].slope([5, 8]) // 2

Get the distance between two points (more-dimensional)

#JS
[4, 1].distance([7, 5]) // 5