// Index matrix (by columns)
int mi(int i, int j, int d1, int d2)
{
- return j*d1 + i;
+ return 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;
+ return 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)
{
- int n=*pn, d=*pd;
- //double* M2 = (double*)calloc(d*d,sizeof(double));
+ int n=*pn, d=*pd;
+ //double* M2 = (double*)calloc(d*d,sizeof(double));
- // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
- for (int j=0; j<d; j++)
- {
- for (int i=0; i<n; i++)
- {
- M2[mi(j,j,d,d)] -= Y[i] / n;
- for (int k=0; k<d; k++)
- M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
- }
- }
+ // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
+ for (int j=0; j<d; j++)
+ {
+ for (int i=0; i<n; i++)
+ {
+ M2[mi(j,j,d,d)] -= Y[i] / n;
+ for (int k=0; k<d; k++)
+ M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
+ }
+ }
}
// Empirical cross-moment of order 3 between X size nxd and Y size n
void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
{
- int n=*pn, d=*pd;
- //double* M3 = (double*)calloc(d*d*d,sizeof(double));
+ int n=*pn, d=*pd;
+ //double* M3 = (double*)calloc(d*d*d,sizeof(double));
- // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
- for (int j=0; j<d; j++)
- {
- for (int k=0; k<d; k++)
- {
- for (int i=0; i<n; i++)
- {
- double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
- M3[ti(j,k,j,d,d,d)] -= tensor_elt;
- M3[ti(j,j,k,d,d,d)] -= tensor_elt;
- M3[ti(k,j,j,d,d,d)] -= tensor_elt;
- for (int o=0; o<d; o++)
- M3[ti(j,k,o,d,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)]*X[mi(i,o,n,d)] / n;
- }
- }
- }
+ // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
+ for (int j=0; j<d; j++)
+ {
+ for (int k=0; k<d; k++)
+ {
+ for (int i=0; i<n; i++)
+ {
+ double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
+ M3[ti(j,k,j,d,d,d)] -= tensor_elt;
+ M3[ti(j,j,k,d,d,d)] -= tensor_elt;
+ M3[ti(k,j,j,d,d,d)] -= tensor_elt;
+ for (int o=0; o<d; o++)
+ M3[ti(j,k,o,d,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)]*X[mi(i,o,n,d)] / n;
+ }
+ }
+ }
}
// 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)
{
- int n=*pn, d=*pd;
+ int n=*pn, d=*pd;
int dim = d + d*d + d*d*d;
//double* W = (double*)malloc(dim*dim*sizeof(double));
g[j] = 0.0;
if (idx1 == idx2)
g[j] -= Y[i];
- g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
+ g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
}
for (int j=d+d*d; j<dim; j++)
{