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, double* 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
  66 //printf("X: \n");
  67 //for (int kk=0; kk<d*n; kk++) printf("%f ",X[kk]);
  68 //printf("\n");
  69 //printf("Y: \n");
  70 //for (int kk=0; kk<n; kk++) printf("%f ",Y[kk]);
  71 //printf("\n");
  72 //printf("M: \n");
  73 //for (int kk=0; kk<dim; kk++) printf("%f ",M[kk]);
  74 //printf("\n");
  75
  76   // (Re)Initialize W:
  77   for (int j=0; j<dim; j++)
  78   {
  79     for (int k=0; k<dim; k++)
  80       W[j*dim+k] = 0.0;
  81   }
  82
  83   //double* W = (double*)calloc(dim*dim,sizeof(double));
  84   double* g = (double*)malloc(dim*sizeof(double));
  85   for (int i=0; i<n; i++)
  86   {
  87     // Fill gi:
  88     for (int j=0; j<d; j++)
  89       g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
  90     for (int j=d; j<d+(d*d); j++)
  91     {
  92       int idx1 = (j-d) % d; //num row
  93       int idx2 = ((j-d) - idx1) / d; //num col
  94       g[j] = 0.0;
  95       if (idx1 == idx2)
  96         g[j] -= Y[i];
  97             g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
  98     }
  99     for (int j=d+d*d; j<dim; j++)
 100     {
 101       int idx1 = (j-d-d*d) % d; //num row
 102       int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
 103       int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
 104       g[j] = 0.0;
 105       if (idx1 == idx2)
 106         g[j] -= Y[i] * X[mi(i,idx3,n,d)];
 107       if (idx1 == idx3)
 108         g[j] -= Y[i] * X[mi(i,idx2,n,d)];
 109       if (idx2 == idx3)
 110         g[j] -= Y[i] * X[mi(i,idx1,n,d)];
 111       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
 112     }
 113
 114 //printf("i=%i, g=: \n", i);
 115 //for (int kk=0; kk<d; kk++) printf("%f ",g[kk]);
 116 //printf("\n");
 117
 118     // Add 1/n t(gi) %*% gi to W
 119     for (int j=0; j<dim; j++)
 120     {
 121       for (int k=0; k<dim; k++)
 122         W[j*dim+k] += g[j] * g[k] / n;
 123     }
 124   }
 125   free(g);
 126
 127 //  for (int j=0; j<dim; j++)
 128 //  {
 129 //    printf("\n");
 130 //    for (int k=0; k<dim; k++)
 131 //      printf("%f ",W[j*dim+k]);
 132 //  }
 133 }