Given two matrices, the task to multiply them. Matrices can either be square or rectangular.
Examples:
Input : mat1[][] = {{1, 2}, {3, 4}} mat2[][] = {{1, 1}, {1, 1}} Output : {{3, 3}, {7, 7}} Input : mat1[][] = {{2, 4}, {3, 4}} mat2[][] = {{1, 2}, {1, 3}} Output : {{6, 16}, {7, 18}}
Multiplication of Square Matrices :
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions.
<script> // Javascript program to multiply // two square matrices. const N = 4; // This function multiplies // mat1[][] and mat2[][], and // stores the result in res[][] function multiply(mat1, mat2, res)
{ let i, j, k;
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++) {
res[i][j] = 0;
for (k = 0; k < N; k++)
res[i][j] += mat1[i][k] * mat2[k][j];
}
}
} // Driver Code let i, j;
// To store result
let res = new Array(N);
for (let k = 0; k < N; k++)
res[k] = new Array(N);
let mat1 = [ [ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
[ 3, 3, 3, 3 ],
[ 4, 4, 4, 4 ] ];
let mat2 = [ [ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
[ 3, 3, 3, 3 ],
[ 4, 4, 4, 4 ] ];
multiply(mat1, mat2, res);
document.write( "Result matrix is <br>" );
for (i = 0; i < N; i++) {
for (j = 0; j < N; j++)
document.write(res[i][j] + " " );
document.write( "<br>" );
}
</script> |
Result matrix is 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(n2)
Multiplication of Rectangular Matrices :
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C?
<script> // Javascript program to multiply two // rectangular matrices // Multiplies two matrices mat1[][] // and mat2[][] and prints result. // (m1) x (m2) and (n1) x (n2) are // dimensions of given matrices. function multiply(m1, m2, mat1, n1, n2, mat2)
{ let x, i, j;
let res = new Array(m1);
for (i = 0; i < m1; i++)
res[i] = new Array(n2);
for (i = 0; i < m1; i++)
{
for (j = 0; j < n2; j++)
{
res[i][j] = 0;
for (x = 0; x < m2; x++)
{
res[i][j] += mat1[i][x] * mat2[x][j];
}
}
}
for (i = 0; i < m1; i++)
{
for (j = 0; j < n2; j++)
{
document.write(res[i][j] + " " );
}
document.write( "<br>" );
}
} // Driver code let mat1 = [ [ 2, 4 ], [ 3, 4 ] ];
let mat2 = [ [ 1, 2 ], [ 1, 3 ] ];
let m1 = 2, m2 = 2, n1 = 2, n2 = 2;
// Function call
multiply(m1, m2, mat1, n1, n2, mat2);
</script> |
6 16 7 18
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(m1 * n2)
Please refer complete article on Program to multiply two matrices for more details!