#include <stdlib.h>
+#include <omp.h>
// Index matrix (by columns)
-int mi(int i, int j, int d1, int d2)
-{
- return j*d1 + i;
-}
+#define mi(i, j, d1, d2) (j*d1 + i)
// Index 3-tensor (by columns, matrices ordered by last dim)
-int ti(int i, int j, int k, int d1, int d2, int d3)
-{
- return k*d1*d2 + j*d1 + i;
-}
+#define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)
// Empirical cross-moment of order 2 between X size nxd and Y size n
void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
// W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
// with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
-void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
+void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
{
- int n=*pn, d=*pd;
+ int nc=*pnc, n=*pn, d=*pd;
int dim = d + d*d + d*d*d;
//double* W = (double*)malloc(dim*dim*sizeof(double));
W[j*dim+k] = 0.0;
}
double* g = (double*)malloc(dim*sizeof(double));
+ omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
+ #pragma omp parallel for
for (int i=0; i<n; i++)
{
// g == gi:
// Add 1/n t(gi) %*% gi to W
for (int j=0; j<dim; j++)
{
- for (int k=0; k<dim; k++)
- W[j*dim+k] += g[j] * g[k] / n;
+ // This final nested loop is very costly. Some basic optimisations:
+ double gj = g[j];
+ int baseIdx = j * dim;
+ #pragma GCC unroll 32
+ for (int k=j; k>=0; k--)
+ W[baseIdx+k] += gj * g[k];
}
}
+ // Normalize W: x 1/n
+ for (int j=0; j<dim; j++)
+ {
+ for (int k=j; k<dim; k++)
+ W[mi(j,k,dim,dim)] /= n;
+ }
+ // Symmetrize W: W[k,j] = W[j,k] for k > j
+ for (int j=0; j<dim; j++)
+ {
+ for (int k=j+1; k<dim; k++)
+ W[mi(k,j,dim,dim)] = W[mi(j,k,dim,dim)];
+ }
free(g);
}