Javascript :Matrix Multiplication

A matrix in arrangement of numbers into rows and columns.In JS a matrix can be

represented with arrays and multi dimensional arrays can be created by nesting

arrays. So in this problem we can use the terms matrices and arrays

interchangeably.

e.g. suppose we want to represent a 2 row 2 column matrix in javascript then it

will look like

let twoDimArr = [

[1,2],

[3, 4]

];

Matrix Multiplication:

Given two matrices say matrixA having m rows & n columns i.e. m x n matrix and

other matrix say matrixB having p rows & q columns i.e. p x q matrix their

multplication is possible only where number of columns of first matrix i.e n

here equals the number of rows of second matrix i.e. p.

How the addition is done

let matrixA =[

[ a[0][0], a[0][1] ],

[ a[1][0], a[1][1] ]

]

let matrixB =[

[ b[0][0], b[0][1] ],

[ b[1][0], b[1][1] ]

]

let multiMatrix =[

[ c[0][0], c[0][1] ],

[ c[1][0], c[1][1] ]

]

where

c[0][0] = (a[0][0] * b[0][0] )+ (a[0][1] * b[1][0])

c[0][1] = (a[0][0] * b[0][1] )+ (a[0][1] * b[1][1])

c[1][0] = (a[1][0] * b[0][0] )+ (a[1][1] * b[1][0])

c[1][1] = (a[1][0] * b[0][1] )+ (a[1][1] * b[1][1])

In General

c[i][j] = ( a[i][0] * b[0][j] ) + (a[i][1] * b[1][j])

Here both matrices we are doing sum are of size 2 x 2 the matrix after there

multiplication will be off size 2x2. w.r.t. our generic matrices matrixA (size m

x n) & matrixB (size p x q) if n = p then their muplication matrix will be of

size m x q.

In matrix of size say m x n either m & n can be same or different if same

matrix is called square matrix else rectangular matrix.

Here is Javascript Implementation:

//5 x 4 matrix

let matrixA = [

[1, 2, 3, 4],

[5, 6, 7, 8],

[9, 10, 11, 12],

[13, 14, 15, 16],

[17, 18, 19, 20],

];

//4 x 6 matrix

let matrixB = [

[21, 22, 23, 24, 25, 26],

[27, 28, 29, 30, 31, 32],

[33, 34, 35, 36, 37, 38],

[39, 40, 41, 42, 43, 44],

];

let element = 0;

let result = [];

//loop 5 times

for (let i = 0; i < matrixA.length; i++) {

let row = matrixA[i];

//loops 6 time

let resultArrayIthRow=[]

for (let k = 0; k < matrixB[0].length; k++) {

let column = [];

//loop 4 times

let resultArrayIthRowKthColumnElement=0;

for (let j = 0; j < matrixB.length; j++) {

resultArrayIthRowKthColumnElement

= resultArrayIthRowKthColumnElement + row[j] * matrixB[j][k]

}

resultArrayIthRow.push(resultArrayIthRowKthColumnElement)

}

result.push(resultArrayIthRow)

}

console.log(result)

Output:

[

[ 330, 340, 350, 360, 370, 380 ],

[ 810, 836, 862, 888, 914, 940 ],

[ 1290, 1332, 1374, 1416, 1458, 1500 ],

[ 1770, 1828, 1886, 1944, 2002, 2060 ],

[ 2250, 2324, 2398, 2472, 2546, 2620 ]

]

Generic Matrix Multiplication function:

function matrixMultiplication(matrixA, matrixB) {

let matrixARowCount = matrixA.length; //5

let matrixAColumnCount = matrixA[0].length; //4

//size of matrixA is matrixARowCount x matrixAColumnCount i.e. 5 x 4

let matrixBRowCount = matrixB.length; //4

let matrixBColumnCount = matrixB[0].length; //6

//size of matrixB is matrixBRowCount x matrixBColumnCount i.e. 4 x 6

if (matrixAColumnCount == matrixBRowCount) {

//create matrixARowCount x matrixBColumnCount i.e. 5 x 6 matrix

let matrixC = Array(matrixARowCount)

.fill()

.map(() => Array(6).fill());

for (let i = 0; i < matrixC.length; i++) {

for (let j = 0; j < matrixC[0].length; j++) {

matrixC[i][j] = 0;

for (let k = 0; k < matrixB.length; k++) {

//4

matrixC[i][j] = matrixC[i][j] + matrixA[i][k] * matrixB[k][j];

}

}

}

return matrixC;

} else {

throw "Matrix Multiplication is not Possible for

given matrices as per their order";

}

}

let matrixA = [

[1, 2, 3, 4],

[5, 6, 7, 8],

[9, 10, 11, 12],

[13, 14, 15, 16],

[17, 18, 19, 20],

];

//4 x 6 matrix

let matrixB = [

[21, 22, 23, 24, 25, 26],

[27, 28, 29, 30, 31, 32],

[33, 34, 35, 36, 37, 38],

[39, 40, 41, 42, 43, 44],

];

let matrixC = matrixMultiplication(matrixA,matrixB)

console.log("Result:", matrixC);

Output:

Result: [

[ 330, 340, 350, 360, 370, 380 ],

[ 810, 836, 862, 888, 914, 940 ],

[ 1290, 1332, 1374, 1416, 1458, 1500 ],

[ 1770, 1828, 1886, 1944, 2002, 2060 ],

[ 2250, 2324, 2398, 2472, 2546, 2620 ]

]