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 // Empirical 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 // Empirical 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 // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
  58 // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
  59 void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
  60 {
  61   int n=*pn, d=*pd;
  62   int dim = d + d*d + d*d*d;
  63   //double* W = (double*)malloc(dim*dim*sizeof(double));
  64
  65   // (Re)Initialize W:
  66   for (int j=0; j<dim; j++)
  67   {
  68     for (int k=0; k<dim; k++)
  69       W[j*dim+k] = 0.0;
  70   }
  71   double* g = (double*)malloc(dim*sizeof(double));
  72   for (int i=0; i<n; i++)
  73   {
  74     // g == gi:
  75     for (int j=0; j<d; j++)
  76       g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
  77     for (int j=d; j<d+(d*d); j++)
  78     {
  79       int idx1 = (j-d) % d; //num row
  80       int idx2 = ((j-d) - idx1) / d; //num col
  81       g[j] = 0.0;
  82       if (idx1 == idx2)
  83         g[j] -= Y[i];
  84       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
  85     }
  86     for (int j=d+d*d; j<dim; j++)
  87     {
  88       int idx1 = (j-d-d*d) % d; //num row
  89       int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
  90       int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
  91       g[j] = 0.0;
  92       if (idx1 == idx2)
  93         g[j] -= Y[i] * X[mi(i,idx3,n,d)];
  94       if (idx1 == idx3)
  95         g[j] -= Y[i] * X[mi(i,idx2,n,d)];
  96       if (idx2 == idx3)
  97         g[j] -= Y[i] * X[mi(i,idx1,n,d)];
  98       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
  99     }
 100     // Add 1/n t(gi) %*% gi to W
 101     for (int j=0; j<dim; j++)
 102     {
 103       for (int k=0; k<dim; k++)
 104         W[j*dim+k] += g[j] * g[k] / n;
 105     }
 106   }
 107   free(g);
 108 }