matrix_mult.c

/**
 ** Howto multiply two matrixes in C using one dimensional arrays
 ** Explanation at the end of the code....
 **/

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

void print_mx(int *mx, int x, int y)
{
  int i,j;
  for(i = 0; i < x; i++)
  {
    for(j = 0; j < y; j++)
    {
      printf("%4d ", mx[y * i + j]);
    }
    printf("\n");
  }
}

//  test ranks:             2       3               3       4
int * mx_mult(int *A, int ax, int ay, int *B, int bx, int by)
{
  // check matrix ranks
  if (ay != bx)
  {
    fprintf(stderr,"Wrong matrix ranks: Cannot multiply!\n");
    exit(-1);
  }

  // allocate memory
  int *ret = (int *) malloc(sizeof(int) * ay * bx);
  if (ret == NULL)
  {
    fprintf(stderr,"Memory allocation error!\n");
    exit(-2);
  }

  // generate
  int i,j,k;
  for (i = 0; i < ax; i++) // 2
  {
    for (j = 0; j < by; j++) // 4
    {
      int sum = 0;
      for (k = 0; k < ay; k++) // 3
      {
        sum += A[i * ay + k] * B[k * by + j];
      }
      // debug: // printf("C[%d,%d] = %d\n", i,j,sum);
      ret[i * by + j] = sum;
    }
  }

  return ret;
}

int main(int argc, char * argv[])
{

  int mx1[] = {2,3,4, 2,5,6};
  int mx1_x = 2, mx1_y = 3;

  int mx2[] = {6,7,7,8, 8,9,-1,-2, -2,3,-4,1};
  int mx2_x = 3, mx2_y = 4;

  print_mx(mx2, mx2_x, mx2_y);
  printf("\n");
  print_mx(mx1, mx1_x, mx1_y);
  printf("\n");

  // we should pass the ranks to know where the array ends.
  int *mul = mx_mult(mx1, mx1_x, mx1_y,  mx2, mx2_x, mx2_y);
  int mul_x = mx1_x, mul_y = mx2_y;

  printmx(mul, mul_x, mul_y);
  printf("\n");
  return 0;
}



/**
 ** Let's take 2 matrixes A and B. Rank of A = 2x3. Rank of B = 3x4.
 **
 ** A * B = C
 **
 ** Criterions of multiplication is: columns of A == lines of B
 **
 ** Lines   of C will be equal to lines   of A
 ** Columns of C will be equal to columns of B
 **
 ** Running vars will be
 **   i:  lines   of C  ==  lines   of A  | 0 .. 1  (2)
 **   j:  columns of C  ==  columns of B  | 0 .. 3  (4)
 **   k:  columns of A  ==  lines   of B  | 0 .. 2  (3)
 **
 **               B
 **
 **               g  h  i  j    3 x 4
 **               k  l  m  n
 **    A          o  p  q  r
 **
 **    a  b  c    S  T  U  V    S = a*g + b*k + c*o
 **    d  e  f    W  X  Y  Z    1st line 1st item = 1..3 SUM (A_1,k * B_k,1)
 **
 **    2 x 3           2 x 4
 **
 ** Howto define A?        Howto define B?
 **   A = {a,b,c,d,e,f};   B = {g,h,i,j,k,l,m,n,o,p,q,r};
 **   Ax = 2;              Bx = 3;
 **   Ay = 3;              By = 4;
 **
 ** Howto refer to an individual item in the matrix
 ** when we use single dimensional arrays?
 **
 ** Well we should add the rank of a line (the number of columns)
 ** as many times as the line number (- 1) is.
 ** Eg: the M matrix has 4 lines and 7 columns. Then rank(M) = 4x7
 ** The item in the 3rd line and the 5th column will be: M[3,5]
 ** In C we start the enumeration from 0, not from 1,
 ** that's why we should say  M[3,5]  is actually the  M[2,4].
 **
 ** M[2,4] = M[ (2 * 7) + 4 ];
 **
 **   A[i,k] = (i * Ay) + k;
 **   B[k,j] = (k * By) + j;
 **   C[i,j] = (i * Cy) + j;
 **
 ** To calculate the individual items in matrix C, we apply the followings
 **   C[i,j] = 0;
 **   for(..k..) { C[i,j] += A[i,k] * B[k,j]; }
 **
 **/