Matrix multiplication using 1Dimensional arrays

[IsNull]

hi, I need to multiply two NxN matrices without using 2Dimentional Arrays.... any Ideas of how to do it with only 1D arrays.? (i.e. A 2x2 matrix should look like this: M1[4]={1,1,0,1} ). Thanks for any help.

[jonnin]

Well you can hack on it... the malloc/free thing should probably use some sort of allocated (passed in, or whatever) swap space for speed, you can do calloc instead to zero the memory, but this covers the technique pretty well even if its sloppy C code.

double*multiply(double *a,int ar,int ac,double*b,int br,int bc)
/*ar = a's rows, ac = a's cols, etc*/
{/*returns null for bad dimensions and ab for good ones.*/

double *product;
int i,j,k,dx;

if(ac != br)/*then its not valid.*/
return(NULL);

product = (double*)malloc(sizeof(double)*ar*bc);
memset(product,0,sizeof(double)*ar*bc);
/*set up zeros to use += later.*/
dx = 0;/*index into 1d array...*/
for(i = 0; i<ar;i++)
for(j = 0; j<bc;j++)
{
for(k = 0; k<ac;k++)
{
product[dx]+= a[i*ac+k]*b[k*bc+j];
}
dx++;
}
return(product);
}

[jonnin]

theoretically, you can do a multiply in N^2.XX instead of the N^3 but the method is messy, and so bloated (its recursive, for one thing) that you have to have a pretty big matrix to justify it, as in thousands of entries.

You can also toss out whole (value * row or value * col depending on how you look at it) if you find a zero, but you will have to re-order the loops to do that. All in all this is just the brute force method.

Note that an x,y pair for a 2d array is really
desired_row * Max_cols + desired_col (in c, because memory is rows of columns)
-- thats what the index magic is doing.

[jonnin]

That was so bad I decided to fix it myself. I had never bothered to fix it because I don't use it much.

double *multiply(const double *a, const int ar, const int ac, const double *b, const int br, const int bc)
{
/*skips inner loop if the constant is zero
returns null for bad dimensions*/

static double * product = swap_space; /*provide a place for the result*/
static int bcols;
static int brows;
register int arows;

memset(product,0,ar*bc*sizeof(double));
if(ac != br) return 0;
for(brows = 0; brows < br; brows++)
{
for(bcols = 0; bcols < bc; bcols++)
{
register double con;
if(con = b[brows*bc+bcols]); /*if con != 0.0*/
{
for(arows = 0; arows < ar; arows++)
{
product[ arows*bc+bcols] += a[arows*ac + brows] * con;
}
}
}
}
return product;
}