Dimensional defines a generic type Matrix that is parameterized by the type of element it holds.
let myBoolMatrix: Matrix = [[true, false], [false, true]]
let myStringMatrix: Matrix = [["hello", "hi", "howdy"], ["goodbye", "bye", "see ya"]]
print(myBoolMatrix.map{ $0 ? 1 : 0 }) // -> [[1, 0], [0, 1]]
print(myStringMatrix.transpose) // -> [["hello", "goodbye"], ["hi", "bye"], ["howdy", "see ya"]]Note that matrices can be initialized from 2-dimensional array literals, and that each inner-array represents a row in the constructed Matrix.
While a Matrix can be parameterized by any type, it is most useful if it is parameterized by some numeric type since it gains tons of special abilities!
let a: Matrix = [[1, 2], [3, 4]]
let b: Matrix = [[5, 10], [-5, 0]]
print(a.determinant) // -> -2
print(a.dot(b) * (a + b)) // -> [[60, 120], [-20, 40]]
print(a * b) // -> [[-5, 10], [-5, 30]]Matrices composed of floating point types gain even more amazing powers, such as the ability to take an inverse!
Not only does Matrix conform to MutableCollectionType, but it exposes two views RowView and ColumnView each of which conform to RangeReplaceableCollectionType allowing for complex manipulations.
var x: Matrix = [[1, 2], [3, 4]]
x.rows.append([5, 6])
x.columns.insert([3, 6, 9], atIndex: 2)
print(x) // -> [[1, 2, 3], [3, 4, 6], [5, 6, 9]]I want to reiterate how cool this is! The properties rows and columns provide collections that not only allow you to inspect a Matrix, but also allow you to modify it in really familiar ways. Its interface is nearly identical to that of Array since both conform to the same protocols.
A Matrix can be initialized in many different novel ways.
let a: Matrix = Matrix([[1, 2], [3, 4]] as RowView)
let b: Matrix = Matrix([[1, 3], [2, 4]] as ColumnView)
print(a == b) // -> true
let c = Matrix(dimensions: (width: 3, height: 2), repeatedValue: 7)
print(c) // -> [[7, 7, 7], [7, 7, 7]]
let d = Matrix.identity(size: 3)
print(d) // [[1, 0, 0], [0, 1, 0], [0, 0, 1]]