pkg/src/functions.c

   1 #include <stdlib.h>
   2
   3 // Index matrix (by columns)
   4 #define mi(i, j, d1, d2) (j*d1 + i)
   5
   6 // Index 3-tensor (by columns, matrices ordered by last dim)
   7 #define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)
   8
   9 // Empirical cross-moment of order 2 between X size nxd and Y size n
  10 void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
  11 {
  12   int n=*pn, d=*pd;
  13   //double* M2 = (double*)calloc(d*d,sizeof(double));
  14
  15   // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
  16   for (int j=0; j<d; j++)
  17   {
  18     for (int i=0; i<n; i++)
  19     {
  20       M2[mi(j,j,d,d)] -= Y[i] / n;
  21       for (int k=0; k<d; k++)
  22         M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
  23     }
  24   }
  25 }
  26
  27 // Empirical cross-moment of order 3 between X size nxd and Y size n
  28 void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
  29 {
  30   int n=*pn, d=*pd;
  31   //double* M3 = (double*)calloc(d*d*d,sizeof(double));
  32
  33   // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
  34   for (int j=0; j<d; j++)
  35   {
  36     for (int k=0; k<d; k++)
  37     {
  38       for (int i=0; i<n; i++)
  39       {
  40         double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
  41         M3[ti(j,k,j,d,d,d)] -= tensor_elt;
  42         M3[ti(j,j,k,d,d,d)] -= tensor_elt;
  43         M3[ti(k,j,j,d,d,d)] -= tensor_elt;
  44         for (int o=0; o<d; o++)
  45           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;
  46       }
  47     }
  48   }
  49 }
  50
  51 // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
  52 // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
  53 void Compute_Omega(double* X, int* Y, double* M, int* pn, int* pd, double* W)
  54 {
  55   int n=*pn, d=*pd;
  56   int dim = d + d*d + d*d*d;
  57   //double* W = (double*)malloc(dim*dim*sizeof(double));
  58
  59   // (Re)Initialize W:
  60   for (int j=0; j<dim; j++)
  61   {
  62     for (int k=0; k<dim; k++)
  63       W[j*dim+k] = 0.0;
  64   }
  65   double* g = (double*)malloc(dim*sizeof(double));
  66   for (int i=0; i<n; i++)
  67   {
  68     // g == gi:
  69     for (int j=0; j<d; j++)
  70       g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
  71     for (int j=d; j<d+(d*d); j++)
  72     {
  73       int idx1 = (j-d) % d; //num row
  74       int idx2 = ((j-d) - idx1) / d; //num col
  75       g[j] = 0.0;
  76       if (idx1 == idx2)
  77         g[j] -= Y[i];
  78       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
  79     }
  80     for (int j=d+d*d; j<dim; j++)
  81     {
  82       int idx1 = (j-d-d*d) % d; //num row
  83       int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
  84       int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
  85       g[j] = 0.0;
  86       if (idx1 == idx2)
  87         g[j] -= Y[i] * X[mi(i,idx3,n,d)];
  88       if (idx1 == idx3)
  89         g[j] -= Y[i] * X[mi(i,idx2,n,d)];
  90       if (idx2 == idx3)
  91         g[j] -= Y[i] * X[mi(i,idx1,n,d)];
  92       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
  93     }
  94     // Add 1/n t(gi) %*% gi to W
  95     for (int j=0; j<dim; j++)
  96     {
  97       for (int k=0; k<dim; k++)
  98         W[j*dim+k] += g[j] * g[k] / n;
  99     }
 100   }
 101   free(g);
 102 }