I was looking for an implementation of Strassen's Algorithm in C, and I've found this code at the end.
To use the multiply
function:
void multiply(int n, matrix a, matrix b, matrix c, matrix d);
which multiplies two matrices a
, b
and puts the result in c
(d
is a intermediary matrix). Matrices a
and b
should have the following type:
typedef union _matrix
{
double **d;
union _matrix **p;
} *matrix;
I have allocated dynamically four matrices a
, b
, c
, d
(two-dimensional arrays of doubles) and have assigned their addresses to the field _matrix.d
:
#include "strassen.h"
#define SIZE 50
int main(int argc, char *argv[])
{
double ** matA, ** matB, ** matC, ** matD;
union _matrix ma, mb, mc, md;
int i = 0, j = 0, n;
matA = (double **) malloc(sizeof(double *) * SIZE);
for (i = 0; i < SIZE; i++)
matA[i] = (double *) malloc(sizeof(double) * SIZE);
// Do the same for matB, matC, matD.
ma.d = matA;
mb.d = matB;
mc.d = matC;
md.d = matD;
// Initialize matC and matD to 0.
// Read n.
// Read matA and matB.
multiply(n, &ma, &mb, &mc, &md);
return 0;
}
This code successfully compiles but crashes with n
> BREAK
.
strassen.c :
#include "strassen.h"
/* c = a * b */
void multiply(int n, matrix a, matrix b, matrix c, matrix d)
{
if (n <= BREAK) {
double sum, **p = a->d, **q = b->d, **r = c->d;
int i, j, k;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++) {
for (sum = 0., k = 0; k < n; k++)
sum += p[i][k] * q[k][j];
r[i][j] = sum;
}
} else {
n /= 2;
sub(n, a12, a22, d11);
add(n, b21, b22, d12);
multiply(n, d11, d12, c11, d21);
sub(n, a21, a11, d11);
add(n, b11, b12, d12);
multiply(n, d11, d12, c22, d21);
add(n, a11, a12, d11);
multiply(n, d11, b22, c12, d12);
sub(n, c11, c12, c11);
sub(n, b21, b11, d11);
multiply(n, a22, d11, c21, d12);
add(n, c21, c11, c11);
sub(n, b12, b22, d11);
multiply(n, a11, d11, d12, d21);
add(n, d12, c12, c12);
add(n, d12, c22, c22);
add(n, a21, a22, d11);
multiply(n, d11, b11, d12, d21);
add(n, d12, c21, c21);
sub(n, c22, d12, c22);
add(n, a11, a22, d11);
add(n, b11, b22, d12);
multiply(n, d11, d12, d21, d22);
add(n, d21, c11, c11);
add(n, d21, c22, c22);
}
}
/* c = a + b */
void add(int n, matrix a, matrix b, matrix c)
{
if (n <= BREAK) {
double **p = a->d, **q = b->d, **r = c->d;
int i, j;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
r[i][j] = p[i][j] + q[i][j];
} else {
n /= 2;
add(n, a11, b11, c11);
add(n, a12, b12, c12);
add(n, a21, b21, c21);
add(n, a22, b22, c22);
}
}
/* c = a - b */
void sub(int n, matrix a, matrix b, matrix c)
{
if (n <= BREAK) {
double **p = a->d, **q = b->d, **r = c->d;
int i, j;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
r[i][j] = p[i][j] - q[i][j];
} else {
n /= 2;
sub(n, a11, b11, c11);
sub(n, a12, b12, c12);
sub(n, a21, b21, c21);
sub(n, a22, b22, c22);
}
}
strassen.h:
#define BREAK 8
typedef union _matrix {
double **d;
union _matrix **p;
} *matrix;
/* Notational shorthand to access submatrices for matrices named a, b, c, d */
#define a11 a->p[0]
#define a12 a->p[1]
#define a21 a->p[2]
#define a22 a->p[3]
#define b11 b->p[0]
#define b12 b->p[1]
#define b21 b->p[2]
#define b22 b->p[3]
#define c11 c->p[0]
#define c12 c->p[1]
#define c21 c->p[2]
#define c22 c->p[3]
#define d11 d->p[0]
#define d12 d->p[1]
#define d21 d->p[2]
#define d22 d->p[3]
My question is how to use the function multiply
(how to implement the matrix).
When n > BREAK, the matrix multiplication algorithm uses a hierarchical matrix representation (the field p
of union _matrix
, not the field d
).
You need to adjust your code for the hierarchical representation when allocating memory and when initializing matrices a
and b
.