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 #include <stdio.h>
  58
  59 // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
  60 // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
  61 //void Compute_Omega(double* X, int* Y, double* M, int* pn, int* pd, double* W)
  62 //{
  63 //  int n=*pn, d=*pd;
  64 //  int dim = d + d*d + d*d*d;
  65 //  //double* W = (double*)malloc(dim*dim*sizeof(double));
  66 //
  67 //  // (Re)Initialize W:
  68 //  for (int j=0; j<dim; j++)
  69 //  {
  70 //    for (int k=0; k<dim; k++)
  71 //      W[j*dim+k] = 0.0;
  72 //  }
  73 //  double* g = (double*)malloc(dim*sizeof(double));
  74 //  for (int i=0; i<n; i++)
  75 //  {
  76 //    // g == gi:
  77 //    for (int j=0; j<d; j++)
  78 //      g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
  79 //    for (int j=d; j<d+(d*d); j++)
  80 //    {
  81 //      int idx1 = (j-d) % d; //num row
  82 //      int idx2 = ((j-d) - idx1) / d; //num col
  83 //      g[j] = 0.0;
  84 //      if (idx1 == idx2)
  85 //        g[j] -= Y[i];
  86 //      g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
  87 //    }
  88 //    for (int j=d+d*d; j<dim; j++)
  89 //    {
  90 //      int idx1 = (j-d-d*d) % d; //num row
  91 //      int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
  92 //      int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
  93 //      g[j] = 0.0;
  94 //      if (idx1 == idx2)
  95 //        g[j] -= Y[i] * X[mi(i,idx3,n,d)];
  96 //      if (idx1 == idx3)
  97 //        g[j] -= Y[i] * X[mi(i,idx2,n,d)];
  98 //      if (idx2 == idx3)
  99 //        g[j] -= Y[i] * X[mi(i,idx1,n,d)];
 100 //      g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
 101 //    }
 102 //    // Add 1/n t(gi) %*% gi to W
 103 //    for (int j=0; j<dim; j++)
 104 //    {
 105 //      for (int k=0; k<dim; k++)
 106 //        W[j*dim+k] += g[j] * g[k] / n;
 107 //    }
 108 //  }
 109 //  free(g);
 110 //}
 111
 112 // Optimisation attempt:
 113 void Compute_Omega(double* X, int* Y, double* M, int* pn, int* pd, double* W)
 114 {
 115   int n=*pn, d=*pd;
 116   int dim = d + d*d + d*d*d;
 117   //double* W = (double*)malloc(dim*dim*sizeof(double));
 118
 119   // (Re)Initialize W:
 120   for (int j=0; j<dim; j++)
 121   {
 122     for (int k=0; k<dim; k++)
 123       W[j*dim+k] = 0.0;
 124   }
 125   double* g = (double*)malloc(dim*sizeof(double));
 126   for (int i=0; i<n; i++)
 127   {
 128     printf("i: %i\n",i);
 129     // g == gi:
 130     for (int j=0; j<d; j++)
 131       g[j] = (Y[i] ? X[mi(i,j,n,d)] - M[j] : 0.0);
 132     for (int j=d; j<d+(d*d); j++)
 133     {
 134       int idx1 = (j-d) % d; //num row
 135       int idx2 = ((j-d) - idx1) / d; //num col
 136       g[j] = 0.0;
 137       if (Y[i])
 138       {
 139         if (idx1 == idx2)
 140           g[j]--;
 141         g[j] += X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
 142       }
 143     }
 144     for (int j=d+d*d; j<dim; j++)
 145     {
 146       int idx1 = (j-d-d*d) % d; //num row
 147       int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
 148       int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
 149       g[j] = 0.0;
 150       if (Y[i])
 151       {
 152         if (idx1 == idx2)
 153           g[j] -= X[mi(i,idx3,n,d)];
 154         if (idx1 == idx3)
 155           g[j] -= X[mi(i,idx2,n,d)];
 156         if (idx2 == idx3)
 157           g[j] -= X[mi(i,idx1,n,d)];
 158         g[j] += X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
 159       }
 160     }
 161     // Add 1/n t(gi) %*% gi to W
 162     for (int j=0; j<dim; j++)
 163     {
 164       for (int k=0; k<dim; k++)
 165         W[j*dim+k] += g[j] * g[k] / n;
 166     }
 167   }
 168   free(g);
 169 }