Matrix Multiplication

Matrix Multiplication in C#

Given two matrices A of dimensions M x K and B of dimension K x N, we want to compute their dot product C = A . B, which is also known as matrix multiplication.

The dot product.

\(C += A . B\)

\(1D Array.\)

\(C_{i} = \sum\limits_{i = 0}^{n} (A_{i} . B_{i}) = A_{1}B_{1} + A_{2}B_{2} + ...+ A_{n}B_{n}\)

\(2D Array.\)

\(C_{i , j} = \sum\limits_{k \in [0 ... K) } (A_{i , k} . B_{k , j})\)

\(C_{i , j} = A_{i , k} . B_{k , j}\)

consider:

\(A \in \mathbb{R}^{m \times k} == A \in \mathbb{R}^{rowA \times colA}\)

\(B \in \mathbb{R}^{k \times n} == B \in \mathbb{R}^{rowB \times colB}\)

The main function is the one that calls the dot_product() function.

#include <stdio.h>
#include <stdlib.h>

/*
Note: colA=rowB, A[N][K] . B[K][M]. Hence you will get C[rowA][colB] = C[N][M].
*/

#define rowA 4
#define colA 4
#define rowB 4
#define colB 4
    
//Declaration of dot_product() function.

int** dot_product(int A[][colA], int B[][colB]);

int main(){

    //Initialize and Declare the matrix A[rowA][colA]
    int A[][colA]={ {1,2,3,4},
                    {5,6,7,8}, 
                    {9,10,11,12},
                    {13,14,15,16}};

    //Initialize and Declare the matrix B[rowB][colB]
    int B[][colB]= {{1,2,3,4},
                    {1,2,3,4},
                    {1,2,3,4},
                    {1,2,3,4}};

    //Calling dot_product() function
    int **mult=dot_product(A,B);

    //This is nested for-loop for printing matrix C[rowA][colB]
    for (int i = 0; i < rowA; i++)
    {
        for (int j = 0; j < colB; j++)
        {
            printf("%d\t", mult[i][j]);
        }
        printf("\n");
        
    }

    return 0;
}

This is the dot_product() function.

It takes in two 2D-arrays A[rowA][colA] and B[rowB][colB].

This function returns a pointer-to-pointer variable that points to the 2D-array C[rowA][colB].

int** dot_product (int A[][colA], int B[][colB]){

    int ** mult=(int **)malloc(rowA*sizeof(int *));
    for (int i = 0; i < rowA; i++)
    {  
        mult[i] =(int *)malloc(colB*sizeof(int));
    }

    // Nested for-loop to perform Matrix Multiplication or Dot Product
    for (int i = 0; i < rowA; i++)
    {
        for (int j = 0; j < colB; j++)
        {
            mult[i][j]=0;
            for (int k = 0; k < colA; k++)
            {
                mult[i][j] += A[i][k]*B[k][j];
            }
        }  
    }
return mult;
}