Matrix

Matrix

Matrix applicative providing standard matrix operations

Constructor

new Matrix()

The Matrix class should not be instantiated with the new keyword. Instead use the Matrix.of syntax to create a new Matrix. Unfortunatly jsdocs does not allow for the constructor to be hidden.

Source:
See:
Example
const m =  Matrix.of([[1,2],[2,3],[4,5]])

Members

precision :Number

Properties:
Name Type Description
precision Number Floating point precision is set to 4 by default
Source:
Type:
  • Number
Example
const m =  Matrix.of([[1,2],[2,3],[4,5]])
m.precision === 4

type :String

Properties:
Name Type Description
type String Returns the string 'Matrix' for all Matrix objects
Source:
Type:
  • String
Example
const m =  Matrix.of([[1,2],[2,3],[4,5]])
m.type === 'Matrix'

Methods

(static) ap(f, M) → {Matrix}

Curried function that applies a function to a Matrix
Source:
Parameters:
Name Type Description
f function Function that accepts a Matrix as input
M Matrix | Array Matrix or Array to apply a function
Returns:
Type:
Matrix
Example
const f = x => x.reduce((prev, next) => prev + next)
Matrix.ap(f, [[1, 2, 3], [4, 5, 6], [7, 8, 9]])
// [[6], [15], [24]

(static) combine(A, A) → {Matrix}

Curried fucntion that combines 2 Matrices
Source:
See:
Parameters:
Name Type Description
A Matrix Left side of the combine operator
A Matrix Right side of the combine operator
Returns:
Type:
Matrix

(static) concat(A, B, fopt) → {Matrix}

A curried function that concatenates 2 Matrices using a function as operator
Source:
Parameters:
Name Type Attributes Default Description
A Matrix Left side Matrix of the concatenation
B Matrix Right side Matrix of the concatenation
f function <optional>
 concat A curried function accepting 2 matrices as input
Returns:
Type:
Matrix
Example
const a = [[0, 1, 1], [2, 3, 4]]
const b = [[2, 2, 2], [3, 3, 3]]
const A = Matrix.of(a)
const B = Matrix.of(b)
const M = Matrix.concat(A, B)
// [[0, 1, 1, 2, 2, 2], [2, 3, 4, 3, 3, 3]]

(static) determinant(A) → {Number}

Calculates the determinant of a square Matrix using Sarrus' rule or LU decomposition
Source:
Parameters:
Name Type Description
A Matrix | Array Matrix as input to calculate the determinant
Returns:
Type:
Number

(static) diag(M) → {Array}

Returns an array containing the values on the diagonal
Source:
Parameters:
Name Type Description
M Matrix | Array Matrix from which to return the diagonal
Returns:
Type:
Array
Example
const diag1 = Matrix.diag([[2, 1], [1, 5]])
// [2, 5]

(static) diagproduct(M) → {Number}

Returns the product of the values on the diagonal
Source:
Parameters:
Name Type Description
M Matrix | Array Matrix from which to return the diagonal
Returns:
Type:
Number
Example
const diag1 = Matrix.diagproduct([[2, 1], [1, 5]])
// 10

(static) dot(A, B) → {Matrix}

Curried fucntion that returns the dot product of 2 matrices
Source:
Parameters:
Name Type Description
A Matrix | Array Left side of the dot product
B Matrix | Array Right side of the dot product
Returns:
Type:
Matrix
Example
const a = [[1, 2, 3], [4, 5, 6]]
const b = [[7, 8], [9, 10], [11, 12]]

const A = Matrix.of(a)
const B = Matrix.of(b)

Matrix.dot(A, B) // [[58, 64], [139, 154]]

(static) empty(rowsopt, colsopt) → {Matrix}

Returns an empty Matrix from an existing Matrix
Source:
Parameters:
Name Type Attributes Default Description
rows Number <optional>
 0 Rows to generate
cols Number <optional>
 0 Cols to generate
Returns:
Type:
Matrix

(static) flatMap(fn, M) → {*}

Runs flatMap on the value of hte Matrix
Source:
Parameters:
Name Type Description
fn function Flatten function
M Matrix | Array
Returns:
Type:
*
Example
const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
const flattenedArray = Matrix.flatMap(x => x, a)  // [1, 2, 3, 4, 5, 6, 7, 8, 9]

(static) flatten() → {Array|*}

Flattens the value of a Matrix into an one dimensional array
Source:
Returns:
  • Type:
    Array
  • Type:
    *
Example
const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
const flattenedArray = Matrix.flatten(a)  // [1, 2, 3, 4, 5, 6, 7, 8, 9]

(static) fold(f, M) → {Matrix}

Static function to reduce the matrix rows using a reduce function
Source:
Parameters:
Name Type Description
f function A reduce/fold function
M Matrix | Array The Matrix to reduce
Returns:
Type:
Matrix
Example
// Sum of all matrix values
const reducer = (prev, next) => Number(prev) + next.reduce((acc, x) => acc + x, 0)
const A = Matrix.of([[1, 1], [1, 1]]
Matrix.fold(reducer, A)
// 4

(static) getColumn(index, M) → {Array}

Returns the values of a Matrix column
Source:
Parameters:
Name Type Description
index Number Index of the column
M Matrix | Array
Returns:
Type:
Array

(static) getRow(index, M) → {Array}

Returns the values of a Matrix row
Source:
Parameters:
Name Type Description
index Number Index of the row
M Matrix | Array
Returns:
Type:
Array

(static) kronecker(A, B) → {Matrix}

The Kronecker product is an operation on two matrices of arbitrary size resulting in a block matrix.
Source:
Parameters:
Name Type Description
A Matrix The left side Matrix of the product (A ⊗ B)
B Matrix The right side Matrix of the product (A ⊗ B)
Returns:
Type:
Matrix

(static) map(f, M) → {Matrix}

Curried function that maps over the rows of the matrix using a map function
Source:
Parameters:
Name Type Description
f function An iterator function
M Matrix | Array Matrix or array to map
Returns:
Type:
Matrix
Example
const m = Matrix.map(x= > x.map(y => y+ 1), [[1, 1], [1, 1]])
// [[2, 2], [2, 2]]

(static) matrixIdentity() → {Matrix}

curried fucntion that returns an matrixIdentity matrix
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.matrixIdentity(3, 2)
// [[1, 0, 0], [0, 1, 0]]

(static) of(val) → {Matrix}

Creates a Matrix object and flattens the Matrix
Source:
Parameters:
Name Type Description
val Array | function An array of arrays
Returns:
Type:
Matrix
Example
const m =  Matrix.of([[1,2],[2,3],[4,5]])

(static) ones(rows, cols) → {Matrix}

Fill up an empty matrix with ones
Source:
Parameters:
Name Type Description
rows Number Defines the rows of the matrix
cols Number Defines the columns of the matrix
Returns:
Type:
Matrix
Example
const A = Matrix.ones(1, 1)
// [[1,1,1], [1,1,1], [1,1,1]]

(static) random(f, rows, cols) → {Matrix}

Fill up an empty matrix with random numbers
Source:
Parameters:
Name Type Description
f function Function which returns random values. Default random values are between -1 and 1
rows Number Defines the rows of the matrix
cols Number Defines the columns of the matrix
Returns:
Type:
Matrix

(static) sum(M) → {Number}

Returns the sum of the values in the Matrix
Source:
Parameters:
Name Type Description
M Matrix | Array Matrix from which to return the diagonal
Returns:
Type:
Number
Example
const diag1 = Matrix.sum([[2, 1], [1, 5]])
// 9

(static) transpose(M) → {Matrix}

Returns a transposed Matrix
Source:
Parameters:
Name Type Description
M Matrix | Array A Matrix or a matrix array
Returns:
Type:
Matrix
Example
const a = [-1, 2], [3, 4], [-8, 2]
const b = Matrix.transpose(a).toArray()
// returns [[-1, 3,-8], [2, 4, 2]]

(static) zeros(rows, cols) → {Matrix}

Fill up an empty matrix with zeros
Source:
Parameters:
Name Type Description
rows Number Defines the rows of the matrix
cols Number Defines the columns of the matrix
Returns:
Type:
Matrix
Example
const A = Matrix.zeros(3, 3)
// [[0,0,0], [0,0,0], [0,0,0]]

add(M) → {Matrix}

Adds a number or a Matrix to this
Source:
Parameters:
Name Type Description
M Matrix | Number Add a Matrix or a number
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5, 4]])
A.add(1) // [[6, 5]]
const B = Matrix.of([[5, 5]])
B.add(B) // [[10, 10]]

additiveinverse() → {Matrix}

Function that returns the matrix obtained by changing the sign of every matrix element. The additive inverse of matrix A is written –A.
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5,-5], [-4, 4]])
const minusA = A.additiveinverse()
// [[-5, 5], [4, -4]]

ap(M) → {Matrix}

Function that applies a function to a Matrix
Source:
Parameters:
Name Type Description
M Matrix | Array Matrix or Array to apply a function
Returns:
Type:
Matrix
Example
const f = x => x.reduce((prev, next) => prev + next)
const A = Matrix.of([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Matrix.of(f).ap(M)
// [[6], [15], [24]

clone() → {Matrix}

Returns a clone of the matrix
Source:
Returns:
Type:
Matrix

combine(M) → {Matrix}

Concatenates 2 Matrices together.
Source:
See:
Parameters:
Name Type Description
M Matrix Right side Matrix of the combine operation
Returns:
Type:
Matrix

concat(M, fopt) → {Matrix}

Concatenates 2 Matrices using a function as operator
Source:
Parameters:
Name Type Attributes Default Description
M Matrix The right side of the concatenation/product
f function <optional>
 concat A curried function accepting 2 matrices as input
Returns:
Type:
Matrix
Example
const a = [[0, 1, 1], [2, 3, 4]]
const b = [[2, 2, 2], [3, 3, 3]]
const A = Matrix.of(a)
const B = Matrix.of(b)
const M = A.concat(B)
// [[0, 1, 1, 2, 2, 2], [2, 3, 4, 3, 3, 3]]

determinant() → {Number}

Calculates the determinant of a square Matrix using Sarrus' rule or LU decomposition
Source:
Returns:
Type:
Number

diag() → {Array}

Returns an array containing the values on the diagonal
Source:
Returns:
Type:
Array
Example
const diag1 = Matrix.ones(3, 3).diag()
// [1, 1, 1]

const diag0 = Matrix.zeros(5, 5).diag()
// [0, 0, 0, 0, 0]

diagproduct() → {Number}

Returns the product of the values on the diagonal
Source:
Returns:
Type:
Number
Example
const diag1 = Matrix.ones(3, 3).diagproduct()
// 1

const diag0 = Matrix.zeros(5, 5).diagproduct()
// 0

dimension() → {Number}

Number indicating the maximum number of linearly independent columns.
Source:
See:
  • Matrix.rank
Returns:
Type:
Number

divide(M) → {Matrix}

Divide a scalar or a matrix by a matrix. Throws an error if the division is not possible.
Source:
Parameters:
Name Type Description
M Matrix | Number A Matrix M or a Number to divide a Matrix
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5, 4]])
A.divide(2) // [[10, 8]]
const B = Matrix.of([[1, 1], [2, 4]])
B.divide(B) // [[1, 0], [0, 1]]

dot(M) → {Matrix}

Returns the dot product between 2 matrices
Source:
Parameters:
Name Type Description
M Matrix | Array Right side of the dot product
Returns:
Type:
Matrix
Example
// Create matrix
const m = Matrix.of([[1, 2], [3, 4]])

// Generate matrixIdentity matrix
const I  = m.matrixIdentity() // [[1, 0], [0, 1]]

if(m.dot(I).equals(m)) {
   console.log('Dot product with matrixIdentity matrix returns the same matrix')
}

empty() → {Matrix}

Returns an empty Matrix from an existing Matrix
Source:
Returns:
Type:
Matrix

equals(M) → {Boolean}

Function returning a boolean testing for equality of the values of a Matrix or Array
Source:
Parameters:
Name Type Description
M Matrix | Array Matrix or Array to compare for equality
Returns:
Type:
Boolean
Example
var a = [[1, 1], [1, 1]]
var A = Matrix.of(a)
var B = Matrix.of(a)
true  === A.equals(B)

fill(f) → {Matrix}

Fill up an empty matrix with the provided map function
Source:
Parameters:
Name Type Description
f function Function that generates a value
Returns:
Type:
Matrix
Example
const A = Matrix.of([[1,2,3], [3,2,1], [4,5,6]]).fill(x => 42)
// [[42,42,42], [42,42,42], [42,42,42]]

flatMap(fn) → {*}

Runs flatMap on the value of hte Matrix
Source:
Parameters:
Name Type Description
fn function Flatten function
Returns:
Type:
*
Example
const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
const A = Matrix.of(a)
const flattenedArray = A.flatMap(x => x)  // [1, 2, 3, 4, 5, 6, 7, 8, 9]

flatten() → {Array}

Flattens the value of a Matrix into an one dimensional array
Source:
Returns:
Type:
Array
Example
const a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
const A = Matrix.of(a)
const flattenedArray = A.flatten()  // [1, 2, 3, 4, 5, 6, 7, 8, 9]

fold(f) → {Matrix}

Reduce the matrix rows using a reduce function
Source:
Parameters:
Name Type Description
f function A reduce/fold function
Returns:
Type:
Matrix
Example
// Flatten Matrix
Matrix.of([[1, 1], [1, 1]]).fold((prev, next) => prev.concat(next))
// [1, 1, 1, 1]

fromArray() → {Array}

Returns a Matrix from an array
Source:
Returns:
Type:
Array

getCols() → {Number}

Number indicating the number of columns in the Matrix
Source:
Returns:
Type:
Number
Example
const A = Matrix.of([[1, 1], [1, 1]])
A.getCols()  === 2

getColumn(index) → {Array}

Returns the values of a Matrix column
Source:
Parameters:
Name Type Description
index Number Index of the column
Returns:
Type:
Array

getRow(index) → {Array}

Returns the values of a Matrix row
Source:
Parameters:
Name Type Description
index Number Index of the row
Returns:
Type:
Array

getRows() → {Number}

Number indicating the number of rows in the Matrix
Source:
Returns:
Type:
Number
Example
const A = Matrix.of([[1, 1], [1, 1]])
A.getRows()  // 2

getShape() → {Array}

Source:
Returns:
Type:
Array
Example
const A = Matrix.of([[1, 1], [1, 1]])
A.getShape()  // [2, 2]

hadamard(M) → {Matrix}

Hadamar is an alias of the multiply function
Source:
See:
  • Matrix.multiply
  • Matrix.hadamard
Parameters:
Name Type Description
M Matrix | Number A Matrix M or a Number to multiply a Matrix
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5, 4]])
A.hadamard(2) // [[10, 8]]
const B = Matrix.of([[5, 5]])
B.hadamard(B) // [[25, 25]]

inverse() → {Matrix}

Returns the inverse of a Matrix
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.of([[1, 1], [2, 4]]).inverse()
// [ [ 2, -0.5 ], [ -1, 0.5 ] ]

isOrthogonal() → {Boolean}

Boolean indicating whether the Matrix is orthogonal by testing for equality between Identity Matrix and the dot product of the Matrix and its transpose.
Source:
Returns:
Type:
Boolean
Example
const result = [[-0.3092, -0.9510], [-0.9510, 0.3092]]
const A = Matrix.fromArray(result)
true  === A.isOrthogonal()

isSquare() → {Boolean}

Boolean indicating whether the Matrix object is square.
Source:
Returns:
Type:
Boolean
Example
const A = Matrix.of([[1, 1], [1, 1]])
true === A.isSquare()

isSymmetric() → {Boolean}

Boolean indicating whether the Matrix is symmetric by testing for equality of the transposed Matrix.
Source:
Returns:
Type:
Boolean
Example
const A = Matrix.of([[1, 1], [1, 1]])
true === A.isSymmetric()

kronecker(M) → {Matrix}

The Kronecker product is an operation on two matrices of arbitrary size resulting in a block matrix.
Source:
Parameters:
Name Type Description
M Matrix The right side Matrix of the product (this ⊗ M)
Returns:
Type:
Matrix

lu() → {Array.<Matrix>}

Calculates LU decomposition of the Matrix
Source:
Returns:
Type:
Array.<Matrix>
Example
const result = [[3, -7, -2, 2], [-3, 5, 1, 0], [6, -4, 0, -5], [-9, 5, -5, 12]]
const A = Matrix.fromArray(result)
const lu = A.lu()
// L.__value = [ [ 1, 0, 0, 0 ], [ -1, 1, 0, 0 ], [ 2, -5, 1, 0 ], [ -3, 8, 3, 1 ] ]
// U.__value =  [ [ 3, -7, -2, 2 ], [ 0, -2, -1, 2 ], [ 0, 0, -1, 1 ], [ 0, 0, 0, -1 ] ]
Matrix.dot(lu[0], lu[1]) // returns clone of A

map(f) → {Matrix}

Maps over the rows of the matrix using a map function
Source:
Parameters:
Name Type Description
f function An iterator function
Returns:
Type:
Matrix
Example
const m = Matrix.of([[1, 1], [1, 1]])
m.map(x => x.map(y => y+ 1))
// [[2, 2], [2, 2]]

matrixIdentity() → {Matrix}

Returns an matrixIdentity matrix
Source:
Returns:
Type:
Matrix
Example
const a = [[1, 2, 3], [4, 5, 6]]
const A = Matrix.of(a)
const Aidentity = A.matrixIdentity()
// [[1, 0, 0], [0, 1, 0]]

max() → {*}

Returns the largest number in the Matrix
Source:
Returns:
Type:
*

min() → {*}

Returns the smallest number in the Matrix
Source:
Returns:
Type:
*

multiply(M) → {Matrix}

Mutliply a scalar or a matrix with a matrix. Throws an error if the multiplication is not possible.
Source:
Parameters:
Name Type Description
M Matrix | Number A Matrix M or a Number to multiply a Matrix
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5, 4]])
A.multiply(2) // [[10, 8]]
const B = Matrix.of([[5, 5]])
B.multiply(B) // [[25, 25]]

ones() → {Matrix}

Fill up an empty matrix with ones
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.of([[1,2,3], [3,2,1], [4,5,6]]).ones()
// [[1,1,1], [1,1,1], [1,1,1]]

random(fopt) → {Matrix}

Fill up an empty matrix with random values
Source:
Parameters:
Name Type Attributes Default Description
f function <optional>
 e => Math.random() * 2 - 1 Function producing random values, can be any type of value
Returns:
Type:
Matrix

rank() → {Number}

Number indicating the maximum number of linearly independent columns.
Source:
Returns:
Type:
Number

rref() → {Matrix}

Returns a Matrix containing the row reduced echelon form
Source:
Returns:
Type:
Matrix
Example
var A = Matrix.of([[-1, 1], [-1, 0], [0, -1], [-1, -2]])
A.rref() //  [ [ 1, 0 ], [ -0, 1 ], [ 0, 0 ], [ 0, 0 ] ]

setPrecision(precisionopt)

The precision is used in floating point calculations for the dot product
Source:
Parameters:
Name Type Attributes Default Description
precision Number <optional>
 4 Set the number of decimals for rounding
Example
const m =  Matrix.of([[1,2],[2,3],[4,5]])
m.setPrecision(10)
m.precision === 10

solve(b) → {Array}

Returns the solution for a system of linear equations
Source:
Parameters:
Name Type Description
b Array The numbers for which to solve the system of linear equations
Returns:
Type:
Array
Example
// Solve xA = b
// 5x + y  = 7
// 3x - 4y = 18
// Solution for x and y:
// x = 2
// y = -3

const A = Matrix.of([[5, 1], [3, -4]])
const solveA = A.solve([7, 18]) // [2, -3]

subtract(M) → {Matrix}

Subtracts a number or a Matrix from this
Source:
Parameters:
Name Type Description
M Matrix | Number Subtract a Matrix or a number
Returns:
Type:
Matrix
Example
const A = Matrix.of([[5, 4]])
A.subtract(1) // [[4, 2]]
const B = Matrix.of([[5, 5]])
B.subtract(B) // [[0, 0]]

sum() → {Number}

Returns the sum of the values in the Matrix
Source:
Returns:
Type:
Number
Example
const diag1 = Matrix.ones(3, 3).sum()
// 9

const diag0 = Matrix.zeros(5, 5).sum()
// 0

toArray() → {Array}

Returns the array from the matrix
Source:
Returns:
Type:
Array

transpose() → {Matrix}

Returns a transposed Matrix
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.of([-1, 2], [3, 4], [-8, 2])
const b = A.transpose().toArray()
// returns [[-1, 3,-8], [2, 4, 2]]

zeros() → {Matrix}

Fill up an empty matrix with zeros
Source:
Returns:
Type:
Matrix
Example
const A = Matrix.of([[1,2,3], [3,2,1], [4,5,6]]).zeros()
// [[0,0,0], [0,0,0], [0,0,0]]