2020-10-12 17:06:56 -05:00
// Wikipedia URL for General Matrix Multiplication Concepts: https://en.wikipedia.org/wiki/Matrix_multiplication
2020-10-12 17:23:23 -05:00
// This algorithm has multiple functions that ultimately check if the inputs are actually matrices and if two Matrices (that can be different sizes) can be multiplied together.
2020-10-12 17:17:58 -05:00
// matrices that are of the same size [2x2]x[2x2], and the second is the multiplication of two matrices that are not the same size [2x3]x[3x2].
2020-10-12 16:35:28 -05:00
// MatrixCheck tests to see if all of the rows of the matrix inputted have similar size columns
2020-10-12 16:54:50 -05:00
const matrixCheck = ( matrix ) => {
let columnNumb
for ( let index = 0 ; index < matrix . length ; index ++ ) {
if ( index === 0 ) {
columnNumb = matrix [ index ] . length
} else if ( matrix [ index ] . length !== columnNumb ) {
2021-10-10 17:55:08 +02:00
// The columns in this array are not equal
2020-10-12 16:35:28 -05:00
} else {
2020-10-12 16:54:50 -05:00
return columnNumb
2020-10-12 16:35:28 -05:00
}
}
}
2025-09-04 07:02:03 +03:00
// tests to see if the matrices have a like side, i.e., the row length on the first matrix matches the column length on the second matrix, or vice versa.
2020-10-12 16:54:50 -05:00
const twoMatricesCheck = ( first , second ) => {
2023-10-03 23:08:19 +02:00
const [ firstRowLength , secondRowLength , firstColLength , secondColLength ] = [
first . length ,
second . length ,
matrixCheck ( first ) ,
matrixCheck ( second )
]
2023-08-21 15:06:43 -03:00
// These matrices do not have a common side
2023-10-03 23:08:19 +02:00
return (
firstRowLength === secondColLength && secondRowLength === firstColLength
)
2020-10-12 16:35:28 -05:00
}
// returns an empty array that has the same number of rows as the left matrix being multiplied.
2020-10-12 16:54:50 -05:00
// Uses Array.prototype.map() to loop over the first (or left) matrix and returns an empty array on each iteration.
const initiateEmptyArray = ( first , second ) => {
if ( twoMatricesCheck ( first , second ) ) {
const emptyArray = first . map ( ( ) => {
return [ '' ]
2020-10-12 16:35:28 -05:00
} )
2020-10-12 16:54:50 -05:00
return emptyArray
} else {
return false
2020-10-12 16:35:28 -05:00
}
}
// Finally, `matrixMult` uses `Array.prototype.push()`, multiple layers of nested `for` loops, the addition assignment `+=` operator and multiplication operator `*` to perform the dot product between two matrices of differing sizes.
2020-10-12 16:54:50 -05:00
// Dot product, takes the row of the first matrix and multiplies it by the column of the second matrix, the `twoMatricesCheck` tested to see if they were the same size already.
// The dot product for each iteration is then saved to its respective index into `multMatrix`.
2021-10-10 17:55:08 +02:00
export const matrixMult = ( firstArray , secondArray ) => {
2020-10-12 16:54:50 -05:00
const multMatrix = initiateEmptyArray ( firstArray , secondArray )
for ( let rm = 0 ; rm < firstArray . length ; rm ++ ) {
const rowMult = [ ]
for ( let col = 0 ; col < firstArray [ 0 ] . length ; col ++ ) {
rowMult . push ( firstArray [ rm ] [ col ] )
2020-10-12 16:35:28 -05:00
}
2020-10-12 16:54:50 -05:00
for ( let cm = 0 ; cm < firstArray . length ; cm ++ ) {
const colMult = [ ]
for ( let row = 0 ; row < secondArray . length ; row ++ ) {
colMult . push ( secondArray [ row ] [ cm ] )
2020-10-12 16:35:28 -05:00
}
2020-10-12 16:54:50 -05:00
let newNumb = 0
for ( let index = 0 ; index < rowMult . length ; index ++ ) {
newNumb += rowMult [ index ] * colMult [ index ]
2020-10-12 16:35:28 -05:00
}
2020-10-12 16:54:50 -05:00
multMatrix [ rm ] [ cm ] = newNumb
2020-10-12 16:35:28 -05:00
}
}
2020-10-12 16:54:50 -05:00
return multMatrix
2020-10-12 16:35:28 -05:00
}
2021-10-10 17:55:08 +02:00
// const firstMatrix = [
// [1, 2],
// [3, 4]
// ]
2020-10-12 16:35:28 -05:00
2021-10-10 17:55:08 +02:00
// const secondMatrix = [
// [5, 6],
// [7, 8]
// ]
2020-10-12 16:35:28 -05:00
2021-10-10 17:55:08 +02:00
// matrixMult(firstMatrix, secondMatrix) // [ [ 19, 22 ], [ 43, 50 ] ]
2020-10-12 16:35:28 -05:00
2021-10-10 17:55:08 +02:00
// const thirdMatrix = [
// [-1, 4, 1],
// [7, -6, 2]
// ]
// const fourthMatrix = [
// [2, -2],
// [5, 3],
// [3, 2]
// ]
2020-10-12 16:35:28 -05:00
2021-10-10 17:55:08 +02:00
// matrixMult(thirdMatrix, fourthMatrix) // [ [ 21, 16 ], [ -10, -28 ] ]
