c 中的二维矩阵乘法

Question

I have written a code in C language for matrix multiplication. There is no error, but the desired output is not coming, which part of my code is wrong or had I miss something.

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

int main() {
    int r1, c1, r2, c2;
    int a[r1][c1];
    int b[r2][c2];
    int c[r1][c2];
    int i, j;
    printf("enter row1 and col1:\n");
    scanf("%d%d", &r1, &c1);
    printf("enter row2 and col2:\n");
    scanf("%d%d", &r2, &c2);
    if (c1 == r2) {
        printf("enter element of 1st matrix:");
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c1; j++) {
                scanf("%d", &a[i][j]);
            }
        }
        printf("\n-----------------");
        printf("enter element of 2nd matrix:");
        for (i = 0; i < r2; i++) {
            for (j = 0; j < c2; j++) {
                scanf("%d", &b[i][j]);
            }
        }
    
        printf("the resultant matrix is:\n");
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c2; j++) {
                c[i][j] += a[i][j] * b[j][i];
            }
        }
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c2; j++) {
                printf("%d\t", c[i][j]);
            }
            printf("\n\n");
        }
    }
    return 0;
}

Answer 1

There are multiple problems in the code:

• the arrays int a[r1][c1]; , int b[r2][c2]; , int c[r1][c2]; are defined before r1 and c1 have been read from the user: the code has potential undefined behavior as r1 and c1 are uninitialized, thus have indeterminate values: the allocation of the arrays may fail or cause undefined behavior if the sizes happen to be negative and accessing them with index values iterating up to different boundary values entered by the user will have undefined behavior.

• you verify that the number of columns of a is equal to the number of rows of b , but you should also check that all dimensions are positive to avoid potential undefined behavior.

• Defining the matrices as variable length arrays with automatic storage is risky: large sizes may cause a stack overflow . Allocating the matrices from the heap is recommended.

• the multiplication algorithm is incorrect: you must implement a triple loop and initialize the target element at c1[i][j] before the inner loop.

Here is a modified version:

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

int main() {
    int r1, c1, r2, c2;
    printf("enter row1 and col1:\n");
    if (scanf("%d%d", &r1, &c1) != 2)
        return 1;
    printf("enter row2 and col2:\n");
    if (scanf("%d%d", &r2, &c2) != 2)
        return 1;
    if (r1 <= 0 || c1 <= 0 || r2 <= 0 || c2 <= 0 || c1 != r2) {
        printf("invalid matrix sizes\n");
        return 1;
    } else {
#if !defined ALLOCATE_MATRICES_FROM_THE_HEAP
        // if the dimensions are small, you can define the matrices as
        int a[r1][c1], b[r2][c2], c[r1][c2];
#else
        // for large sizes, you can allocate the matrices from the heap this way:
        int (*a)[c1] = calloc(sizeof(*a), r1);
        int (*b)[c2] = calloc(sizeof(*b), r2);
        int (*c)[c2] = calloc(sizeof(*c), r1);
        if (a == NULL || b == NULL || c == NULL) {
            printf("out of memory\n");
            return 1;
        }
#endif
        printf("enter elements of 1st matrix:");
        for (int i = 0; i < r1; i++) {
            for (int j = 0; j < c1; j++) {
                a[i][j] = 0;
                scanf("%d", &a[i][j]);
            }
        }
        printf("\n-----------------");
        printf("enter elements of 2nd matrix:");
        for (int i = 0; i < r2; i++) {
            for (int j = 0; j < c2; j++) {
                b[i][j] = 0;
                scanf("%d", &b[i][j]);
            }
        }
    
        printf("the resultant matrix is:\n");
        for (int i = 0; i < r1; i++) {
            for (int j = 0; j < c2; j++) {
                int v = 0;
                for (int k = 0; k < c1; k++) {
                    v += a[i][k] * b[k][j];
                }
                c[i][j] = v;
            }
        }
        for (int i = 0; i < r1; i++) {
            for (int j = 0; j < c2; j++) {
                printf("%5d\t", c[i][j]);
            }
            printf("\n\n");
        }
#if defined ALLOCATE_MATRICES_FROM_THE_HEAP
        free(a);
        free(b);
        free(c);
#endif
        return 0;
    }
}

Answer 2

The problem is here:

int r1, c1, r2, c2;
int a[r1][c1];   // at this point r1 c1, r2, c2 etc.
int b[r2][c2];   // are not yet initialized and their
int c[r1][c2];   // content is undetermined. Therefore
                 // the size of the arrays a, b and C are
                 // undetermined leading to the problem you encounter

You want this:

int r1,c1,r2,c2;
int i,j;
printf("enter row1 and col1:\n");
scanf("%d%d",&r1,&c1);
printf("enter row2 and col2:\n");
scanf("%d%d",&r2,&c2);

int a[r1][c1];  // here r1, c1, r2, c2 etc.
int b[r2][c2];  // have determined values
int c[r1][c2];

There might be more problems further in your code, I didn't check.

Answer 3

The program you post dimensions the three matrices with undefined values coming from uninitialized variables. You can, at least, dimension those variables once you know the values of the dimensions, as in (please, read my comments in your code, as they state problems in your code you have not realized):

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

int main()
{
    int r1, c1, r2, c2;
    int i, j;
    printf("enter row1 and col1:\n");
    scanf("%d%d", &r1, &c1);
    printf("enter row2 and col2:\n");
    scanf("%d%d", &r2, &c2);
    int a[r1][c1];  /* declare the dimensions <<<after>>> you know what values are */
    int b[r2][c2];  /* to be given. */
    int c[r1][c2];

    if (c1 == r2) { /* put an else statement to this if indicating the cause of */
            /* not making any calculation in case r2 and c1 not being equal */
        printf("enter element of 1st matrix:");
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c1; j++) {
                scanf("%d", &a[i][j]);
            }
        }
        printf("\n-----------------");
        printf("enter element of 2nd matrix:");
        for (i = 0; i < r2; i++) {
            for (j = 0; j < c2; j++) {
                scanf("%d", &b[i][j]);
            }
        }
    
        printf("the resultant matrix is:\n");
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c2; j++) { /* you need three nested loops, not two */
                /* ALL YOUR CODE HERE IS BAD, USE THIS INSTEAD */
                int k;
                c[i][j] = 0; /* initialize c[i][j] to zero or you'll get weird values */
                for (k = 0; k < c1; k++) { /* YOU NEED ANOTHER LOOP */
                    c[i][j] += a[i][k] * b[k][j];
                }
            }
        }
        for (i = 0; i < r1; i++) {
            for (j = 0; j < c2; j++) {
                printf("%d\t", c[i][j]);
            }
            printf("\n\n");
        }
    }
    return 0;
}

but it is more portable to give your matrices maximum dimensions and work only in the subbox delimited by the values of r1 , c1 , r2 , c2 , r3 and c3 . As in:

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

#define MAX_DIM 10

int main()
{
    int r1, c1, r2, c2;
    int i, j; /* why didn't you call these r and c (for row and column resp.)? */

    /* this will loop on input until you give correct values for all dimensions, */
    do {
        printf("enter row1 and col1:\n");
        scanf("%d%d", &r1, &c1);
        printf("enter row2 and col2:\n");
        scanf("%d%d", &r2, &c2);
    } while (r1 <= 0 || r1 > MAX_DIM || c1 <= 0 || c1 > MAX_DIM ||
             r2 <= 0 || r2 > MAX_DIM || c2 <= 0 || c2 > MAX_DIM ||
             c1 != r2);

    int a[MAX_DIM][MAX_DIM]; /* more portable this way, as variable dimensioning */
    int b[MAX_DIM][MAX_DIM]; /* is not present in all standard editions */
    /* there's no need to have matrix c as we are not doing anything with it. 
     * (see below why)*/

    printf("enter element of 1st matrix:");
    for (i = 0; i < r1; i++) {
        for (j = 0; j < c1; j++) {
            scanf("%d", &a[i][j]);
        }
    }

    printf("\n-----------------");

    printf("enter element of 2nd matrix:");
    for (i = 0; i < r2; i++) {
        for (j = 0; j < c2; j++) {
            scanf("%d", &b[i][j]);
        }
    }
    
    printf("the resultant matrix is:\n");
    for (i = 0; i < r1; i++) {
        for (j = 0; j < c2; j++) {
            int k;
            int cell_value = 0;
            for (k = 0; k < c1 /* or k < r2, both are the same */; k++) {
                    cell_value += a[i][k] * b[k][j];
            }
            /* cell_value is the value of product matrix at [i][j] */
            printf("%d\t", cell_value);
        }
        printf("\n\n"); /* new line for each row */
    }
    return 0;
}

As you see, this last sample doesn't require to have stored the product matrix c , as you can print the elements (which are generated per rows, then per columns) as they are calculated.

Answer 4

#include<stdio.h>
#include<stdlib.h>
int main(){
    int r1,c1,r2,c2;
   
    int i,j;
    printf("enter row1 and col1:\n");
    scanf("%d%d",&r1,&c1);
    printf("enter row2 and col2:\n");
    scanf("%d%d",&r2,&c2);
     int a[r1][c1];
    int b[r2][c2];
    int c[r1][c2];
    if(c1==r2){
        printf("enter element of 1st matrix:");
        for(i=0;i<r1;i++){
            for(j=0;j<c1;j++){
                scanf("%d",&a[i][j]);
            }
        }
        printf("\n-----------------");
        printf("enter element of 2st matrix:");
        for(i=0;i<r2;i++){
            for(j=0;j<c2;j++){
                scanf("%d",&b[i][j]);
            }
    }
    
    printf("the resultant matrix is:\n");
    for(i=0;i<r1;i++){
        
        for(j=0;j<c2;j++){
            c[i][j]=0;
            for(int k=0;k<c1;k++)    
              {    
           c[i][j]+=a[i][k]*b[k][j];    
              } 
        }
    }
    for(i=0;i<r1;i++){
        for(j=0;j<c2;j++){
            printf("%d\t",c[i][j]);
        }
        printf("\n\n");
    }
    
    
}
return 0;
    
    
}