Matrix Multiplication: Four Loops vs Three Loops

Question

While my code is running without error, my resultant matrix (ie. C) is incorrect. What C should be:[6, 20, 3, 5],[-3, 3,-2, 0],[30, 27, 5, 12],[9, 13, 8, 4].

What C currently is, based on my code:[35,45,25,15],[14,18,10,6],[-14,-18,-10,-6],[14,18,10,6]

I have a feeling this is from mismatching my loops for my resultant matrix, but I can't seem to figure out the issue.

I've also noticed that other matrix multiplication threads on this forum use 3 loops, as opposed to my 4 loops. If this is the reason for my error, could you please explain why? Shouldn't there be an iteration for the 2 separate rows and 2 separate columns?

const A = [  [-4,0,5],
            [-3,-1,2],
            [6,7,-2],
            [1, 1, 2]
         ];

const B = [ [1, 0, 3, 0],
            [4,5,-1, 2],
            [2, 4, 3, 1]
         ];

C = [];

for (var i =0; i< A.length; i++){
    C[i] = [];
    for (var j =0 ; j< A[j].length; j++){
        //console.log(A[i][j]);
        for (var y = 0 ; y < B[0].length ; y++){
                C[i][y] = 0;
            for (var x = 0 ; x < B.length ; x++){
                //console.log(B[x][y]+ "["+x+","+y+"]");
                //console.log(C[i][y]+ "["+i+","+y+"]"); 
                C[i][y] += A[i][j] * B[x][y];
            }
            console.log(C[i][y] + "[" + i + "," +y+"] is the resultant matrix");
        }
    }
}
console.log(JSON.stringify(C)); //to print out resultant matrix in array format

Maheer Ali · Accepted Answer · 2019-07-02T16:09:41.557

1

You don't need to use four loops. You need only three loops that is the problem. The no of nested loops to use for a problem are not your choice.

This problem needs only three nested loops. To multiply matrices. We multiple each element of each row of the first matrix with corresponding element of each column of second matrix.

Now the thing which you need to understand is that the third nested loop will generate -4,0,5. At this point we don't need another loop because we add them to corresponding value. Not each value is added to all.

const A = [  [-4,0,5],
            [-3,-1,2],
            [6,7,-2],
            [1, 1, 2]
         ];

const B = [ [1, 0, 3, 0],
            [4,5,-1, 2],
            [2, 4, 3, 1]
         ];
const C = [];

for(let i = 0; i < A.length; i++){
  C[i] = []
  for(let j = 0; j < B[0].length; j++){
    C[i][j] = 0
    for(let k = 0; k < A[0].length; k++){    
      C[i][j] += A[i][k] * B[k][j];
    }  
  }
  
}
//[6, 20, 3, 5],[-3, 3,-2, 0],[30, 27, 5, 12],[9, 13, 8, 4]
console.log(C);

edited Jul 02 '19 at 16:09

answered Jul 02 '19 at 16:01

Maheer Ali

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Thank you! The issue now is that the resultant matrix from your suggestion prints out 3 columns instead of four... – S K Jul 02 '19 at 16:18
@SK Try refreshing I have updated the code a while ago. For me its giving correct result. – Maheer Ali Jul 02 '19 at 16:23
Yes it is! Thank you so much. – S K Jul 02 '19 at 17:48
@SK Consider accepting the answer if you think it helped you. – Maheer Ali Jul 02 '19 at 17:53
Done! (I hope I did correctly though; still relatively new to Stack.) – S K Jul 02 '19 at 18:44

Matrix Multiplication: Four Loops vs Three Loops

1 Answers1