pkg/src/functions.c

   1 #include <stdlib.h>
   2 #include <omp.h>
   3
   4 // Index matrix (by columns)
   5 #define mi(i, j, d1, d2) (j*d1 + i)
   6
   7 // Index 3-tensor (by columns, matrices ordered by last dim)
   8 #define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)
   9
  10 // Empirical cross-moment of order 2 between X size nxd and Y size n
  11 void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
  12 {
  13   int n=*pn, d=*pd;
  14   //double* M2 = (double*)calloc(d*d,sizeof(double));
  15
  16   // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
  17   for (int j=0; j<d; j++)
  18   {
  19     for (int i=0; i<n; i++)
  20     {
  21       M2[mi(j,j,d,d)] -= Y[i] / n;
  22       for (int k=0; k<d; k++)
  23         M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
  24     }
  25   }
  26 }
  27
  28 // Empirical cross-moment of order 3 between X size nxd and Y size n
  29 void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
  30 {
  31   int n=*pn, d=*pd;
  32   //double* M3 = (double*)calloc(d*d*d,sizeof(double));
  33
  34   // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
  35   for (int j=0; j<d; j++)
  36   {
  37     for (int k=0; k<d; k++)
  38     {
  39       for (int i=0; i<n; i++)
  40       {
  41         double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
  42         M3[ti(j,k,j,d,d,d)] -= tensor_elt;
  43         M3[ti(j,j,k,d,d,d)] -= tensor_elt;
  44         M3[ti(k,j,j,d,d,d)] -= tensor_elt;
  45         for (int o=0; o<d; o++)
  46           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;
  47       }
  48     }
  49   }
  50 }
  51
  52 // W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
  53 // with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
  54 void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
  55 {
  56   int nc=*pnc, n=*pn, d=*pd;
  57   int dim = d + d*d + d*d*d;
  58   //double* W = (double*)malloc(dim*dim*sizeof(double));
  59
  60   // (Re)Initialize W:
  61   for (int j=0; j<dim; j++)
  62   {
  63     for (int k=0; k<dim; k++)
  64       W[j*dim+k] = 0.0;
  65   }
  66   double* g = (double*)malloc(dim*sizeof(double));
  67   omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
  68   #pragma omp parallel for
  69   for (int i=0; i<n; i++)
  70   {
  71     // g == gi:
  72     for (int j=0; j<d; j++)
  73       g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
  74     for (int j=d; j<d+(d*d); j++)
  75     {
  76       int idx1 = (j-d) % d; //num row
  77       int idx2 = ((j-d) - idx1) / d; //num col
  78       g[j] = 0.0;
  79       if (idx1 == idx2)
  80         g[j] -= Y[i];
  81       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
  82     }
  83     for (int j=d+d*d; j<dim; j++)
  84     {
  85       int idx1 = (j-d-d*d) % d; //num row
  86       int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
  87       int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
  88       g[j] = 0.0;
  89       if (idx1 == idx2)
  90         g[j] -= Y[i] * X[mi(i,idx3,n,d)];
  91       if (idx1 == idx3)
  92         g[j] -= Y[i] * X[mi(i,idx2,n,d)];
  93       if (idx2 == idx3)
  94         g[j] -= Y[i] * X[mi(i,idx1,n,d)];
  95       g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
  96     }
  97     // Add 1/n t(gi) %*% gi to W
  98     for (int j=0; j<dim; j++)
  99     {
 100       // This final nested loop is very costly. Some basic optimisations:
 101       double gj = g[j];
 102       int baseIdx = j * dim;
 103       #pragma GCC unroll 32
 104       for (int k=j; k>=0; k--)
 105         W[baseIdx+k] += gj * g[k];
 106     }
 107   }
 108   // Normalize W: x 1/n
 109   for (int j=0; j<dim; j++)
 110   {
 111     for (int k=j; k<dim; k++)
 112       W[mi(j,k,dim,dim)] /= n;
 113   }
 114   // Symmetrize W: W[k,j] = W[j,k] for k > j
 115   for (int j=0; j<dim; j++)
 116   {
 117     for (int k=j+1; k<dim; k++)
 118       W[mi(k,j,dim,dim)] = W[mi(j,k,dim,dim)];
 119   }
 120   free(g);
 121 }