Wednesday, March 28, 2012

Numerical Methods: Multiplication of two matrices using two dimensional array in C

Let we have two 2 x 2 matrices A and B
\[ A = \begin{bmatrix} a_{00} & a_{01}\\
a_{10} & a_{11}
\end{bmatrix} \text{ and } B = \begin{bmatrix} b_{00} & b_{01} \\
b_{10} & b_{11} \end{bmatrix}\]
The multiplication of $A$ and $B$ works as follows

  1. Multiply $a_{00}$ with $b_{00}$ and $a_{01}$ with $b_{10}$ and sum them together. So the first element $r_{00}$ becomes  $a_{00}$ . $b_{00}$ $a_{01}$ . $b_{10}$
  2. Multiply $a_{00}$ with $b_{01}$ and $a_{01}$ with $b_{11}$ and sum them together. So the first element $r_{01}$ becomes  $a_{00}$ . $b_{01}$ $a_{01}$ . $b_{11}$
  3. Multiply $a_{10}$ with $b_{00}$ and $a_{11}$ with $b_{10}$ and sum them together. So the first element $r_{10}$ becomes  $a_{10}$ . $b_{00}$ $a_{11}$ . $b_{10}$
  4. Multiply $a_{10}$ with $b_{01}$ and $a_{11}$ with $b_{11}$ and sum them together. So the first element $r_{11}$ becomes  $a_{10}$ . $b_{01}$ $a_{11}$ . $b_{11}$
So the resulting matrix $R$ becomes, 
\[ R = \begin{bmatrix} a_{00}.b_{00}+a_{01}.b_{10} &  a_{00}.b_{01} + a_{01}.b_{11} \\ a_{10}.b_{00} + a_{11}.b_{10} & a_{10}.b_{01} + a_{11}.b_{11}\end{bmatrix}\]
Note: In order to multiply two matrices, $A$ and $B$, the number of columns in $A$ must equal the number of rows in $B$. Thus, if $A$ is an $m * n$ matrix and $B$ is an $r * s$ matrix, $n = r$.
Source Code
#include<stdio.h>
int main()
{
    int r1, c1, r2, c2, matrix1[10][10], matrix2[10][10], result[10][10];
    int i, j, k;
    printf("Enter the row and column of the first matrix: ");
    scanf("%d%d",&r1,&c1);
    printf("Enter the row and column of the second matrix: ");
    scanf("%d%d",&r2,&c2);
    if(c1 != r2){
        printf("Matrix multiplication impossible");
    }
    printf("Enter the first matrix: \n");
    for(i = 0; i <r1; i++)
       for(j = 0; j < c1; j++)
            scanf("%d", &matrix1[i][j]);
    printf("Enter the second matrix: \n");
    for(i = 0; i <r2; i++)
       for(j = 0; j < c2; j++)
            scanf("%d", &matrix2[i][j]);
    for(i = 0; i < r1; i++ ){
        for(j = 0; j < c2; j++){
            result[i][j] = 0;
            for(k = 0; k < c1; k++){
                result[i][j] += matrix1[i][k] * matrix2[k][j];
            }
        }
    }
    printf("The multiplication of the matrix is: \n");
    for(i = 0; i < r1; i++){
        for(j = 0; j < c2; j++){
            printf("%d", result[i][j]);
            printf(" ");
        }
        printf("\n");
    }
    return 0;
}

6 comments:

  1. this is wrong.... the multiplication logic is not right....

    ReplyDelete
  2. Shayan thanks for reply ... but i don't think the logic is wrong. Can you prove it?

    ReplyDelete
  3. I think your source code in c/c++ for two Matrix multiplication is correct and not wrong, which Mr Shayan mean, thank you for very nice and in simply way to write your programm about numerical Mathematic, i hope more in analytical Geometrie like point,victor,line,plan in c/c++, my compiler is dev c++ from blood sheet

    ReplyDelete
  4. Bibek, your code for Marixmultiplication is korekt and gut, may be mohr in analytical Geometry source code in c/c++

    ReplyDelete