pkg/src/functions.c

   1 #include <stdlib.h>
   2
   3 //index matrix (by columns)
   4 int mi(int i, int j, int d1, int d2)
   5 {
   6     return j*d1+i;
   7 }
   8
   9 //index 3-tensor (by columns, matrices ordered by last dim)
  10 int ti(int i, int j, int k, int d1, int d2, int d3)
  11 {
  12     return k*d1*d2 + j*d1 + i;
  13 }
  14
  15 // Emprical cross-moment of order 2 between X size nxd and Y size n
  16 void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
  17 {
  18     int n=*pn, d=*pd;
  19     //double* M2 = (double*)calloc(d*d,sizeof(double));
  20
  21     // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
  22     for (int j=0; j<d; j++)
  23     {
  24         for (int i=0; i<n; i++)
  25         {
  26             M2[mi(j,j,d,d)] -= Y[i] / n;
  27             for (int k=0; k<d; k++)
  28                 M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
  29         }
  30     }
  31 }
  32
  33 // Emprical cross-moment of order 3 between X size nxd and Y size n
  34 void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
  35 {
  36     int n=*pn, d=*pd;
  37     //double* M3 = (double*)calloc(d*d*d,sizeof(double));
  38
  39     // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
  40     for (int j=0; j<d; j++)
  41     {
  42         for (int k=0; k<d; k++)
  43         {
  44             for (int i=0; i<n; i++)
  45             {
  46                 double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
  47                 M3[ti(j,k,j,d,d,d)] -= tensor_elt;
  48                 M3[ti(j,j,k,d,d,d)] -= tensor_elt;
  49                 M3[ti(k,j,j,d,d,d)] -= tensor_elt;
  50                 for (int o=0; o<d; o++)
  51                     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;
  52             }
  53         }
  54     }
  55 }
  56
  57 void Compute_Omega(double* X, double* Y, int* pn, int* pd, double* W)
  58 {
  59   // TODO: formula 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
  60   // = 1/N sum( t( (XiYi-...) - theta[i] ) ( ... ) )
  61   // --> similar to Moments_M2 and M3 above
  62 }