#include <stdlib.h>
-//index matrix (by columns)
-int mi(int i, int j, int d1, int d2)
+// Index matrix (by columns)
+int inline 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)
+// Index 3-tensor (by columns, matrices ordered by last dim)
+int inline 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;
}
-// Emprical cross-moment of order 2 between X size nxd and Y size n
+// 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));
-
- // 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;
- }
- }
+ 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;
+ }
+ }
}
-// Emprical cross-moment of order 3 between X size nxd and Y size 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));
-
- // 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;
- }
- }
- }
+ 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;
+ }
+ }
+ }
}
-void Compute_Omega(double* X, double* Y, int* pn, int* pd, double* W)
+// 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, int* Y, double* M, int* pn, int* pd, double* W)
{
- // TODO: formula 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
- // = 1/N sum( t( (XiYi-...) - theta[i] ) ( ... ) )
- // --> similar to Moments_M2 and M3 above
+ int n=*pn, d=*pd;
+ int dim = d + d*d + d*d*d;
+ //double* W = (double*)malloc(dim*dim*sizeof(double));
+
+ // (Re)Initialize W:
+ for (int j=0; j<dim; j++)
+ {
+ for (int k=0; k<dim; k++)
+ W[j*dim+k] = 0.0;
+ }
+ double* g = (double*)malloc(dim*sizeof(double));
+ for (int i=0; i<n; i++)
+ {
+ // g == gi:
+ for (int j=0; j<d; j++)
+ g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
+ for (int j=d; j<d+(d*d); j++)
+ {
+ int idx1 = (j-d) % d; //num row
+ int idx2 = ((j-d) - idx1) / d; //num col
+ 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];
+ }
+ for (int j=d+d*d; j<dim; j++)
+ {
+ int idx1 = (j-d-d*d) % d; //num row
+ int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
+ int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
+ g[j] = 0.0;
+ if (idx1 == idx2)
+ g[j] -= Y[i] * X[mi(i,idx3,n,d)];
+ if (idx1 == idx3)
+ g[j] -= Y[i] * X[mi(i,idx2,n,d)];
+ if (idx2 == idx3)
+ g[j] -= Y[i] * X[mi(i,idx1,n,d)];
+ g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
+ }
+ // 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;
+ }
+ }
+ free(g);
}
projects / morpheus.git / blobdiff