*(result.matrix+ i*r  + j)

result[i][j]

/**
    Matrix Multiplication
    matrices.c
    Matrix data structure in C.

    @author Michael Asper
    @version 1.0 3/29/17
*/

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

typedef struct Matrix {
    int     rowSize;
    int     columnSize;
    long int*    matrix;
} Matrix;


/**
    Randomizes the elements of a matrix

    @param *m pointer to Matrix to randomize;
*/
void randomize(Matrix *m){
    int i,j;
    for(i = 0; i < m->rowSize ; i++){
        for(j = 0; j < m->columnSize; j++){
            *(m->matrix + i*m->rowSize  + j)= rand() % 5000;
        }
    }
}

/**
    Returns a r x c Matrix with all 0s.

    @param r The row size of the matrix
    @param c The column size of the matrix
    @return r x c Matrix
*/
Matrix createMatrix(int r, int c){
    Matrix temp = {r, c, calloc(r * c, sizeof(long int *))};
    return temp;
}

/**
    Returns a r x c Matrix with random numbers.

    @param r The row size of the matrix
    @param c The column size of the matrix
    @return r x c Matrix
*/
Matrix createRandMatrix(int r, int c){
    Matrix temp = createMatrix(r,c);
    randomize(&temp);
    return temp;
}

/**
    Prints matrix.

    @param *m Pointer to Matrix you want to print
*/
void printMatrix(Matrix *m){

    int i,j;
    for(i = 0; i < m->rowSize ; i++){
        for(j = 0; j < m->columnSize; j++){
            printf("%li ", *(m->matrix + i*m->rowSize  + j));
        }
        printf("n");
    }
}

/**
    Adds two matrices together

    @param *a pointer to first matrix (A);
    @param *b pointer to second matrix (B);
    @return A+B
*/
Matrix add(Matrix *a, Matrix *b){
    //check if matrices are compatible
    if(a->rowSize != b->rowSize || a->columnSize != b->columnSize){
        fprintf(stderr, "Error: Incompatible sizes");
        exit(0);
    }
    //create result matrix
    int r = a->rowSize;
    int c = a->columnSize;
    Matrix result = createMatrix(r,c);
    //add matrices
    int i,j;
    for(i = 0; i < r ; i++){
        for(j = 0; j < c; j++){
            //result[i][j] = a[i][j]+b[i][j]
            *(result.matrix+ i*r  + j) = *(a->matrix + i*r  + j) + *(b->matrix + i*r  + j);
        }
    }
    return result;
}

/**
    Subtracts two matrices together

    @param *a pointer to first matrix (A);
    @param *b pointer to second matrix (B);
    @return A-B
*/
Matrix sub(Matrix *a, Matrix *b){
    //check if matrices are compatible
    if(a->rowSize != b->rowSize || a->columnSize != b->columnSize){
        fprintf(stderr, "Error: Incompatible sizes");
        exit(0);
    }
    //create result matrix
    int r = a->rowSize;
    int c = a->columnSize;
    Matrix result = createMatrix(r,c);
    //subtracts matrix
    int i,j;
    for(i = 0; i < r ; i++){
        for(j = 0; j < c; j++){
            //result[i][j] = a[i][j]-b[i][j]
            *(result.matrix+ i*r  + j) = *(a->matrix + i*r  + j) - *(b->matrix + i*r  + j);
        }
    }
    return result;
}

/**
    Multiplies two matrices together

    @param *a pointer to first matrix (A);
    @param *b pointer to second matrix (B);
    @return A*B
*/
Matrix multiply(Matrix *a, Matrix *b){
    //check if matrices are compatible
    if(a->columnSize != b->rowSize ){
        fprintf(stderr, "Error: Incompatible sizes");
        exit(0);
    }

    //initialize return matrix
    int r = a->rowSize;
    int c = b->columnSize;
    Matrix result = createMatrix(r,c);

    //multiply matrices
    int i,j;
    for(i = 0; i < r ; i++){
        for(j = 0; j < c; j++){
            long int sum = 0;
            int k;
            for(k = 0; k < a->columnSize; k++){
                //sum += a[i][k] * b[k][j]
                sum = sum + (*(a->matrix + i*a->rowSize  + k)**(b->matrix + k*b->rowSize  + j));
            }
            *(result.matrix+ i*r  + j) = sum;
        }
    }
    return result;
}


int main(){
    // seed random with time
    time_t t;
    srand((unsigned) time(&t));

    //setup random matrices and multiply
    Matrix a = createRandMatrix(3,100);
    Matrix b = createRandMatrix(100,3);
    Matrix result = multiply(&a,&b);
    printMatrix(&result);

    return 0;
}