#include <stdlib.h>
//#include <omp.h>

// Index matrix (by columns)
#define mi(i, j, d1, d2) (j*d1 + i)

// Index 3-tensor (by columns, matrices ordered by last dim)
#define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)

// Empirical cross-moment of order 2 between X size nxd and Y size n
void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
{
  int n=*pn, d=*pd;
  //double* M2 = (double*)calloc(d*d,sizeof(double));

  // M2 = E[Y*X^*2] - E[Y*e^*2] = E[Y (X^*2 - I)]
  for (int j=0; j<d; j++)
  {
    for (int i=0; i<n; i++)
    {
      M2[mi(j,j,d,d)] -= Y[i] / n;
      for (int k=0; k<d; k++)
        M2[mi(j,k,d,d)] += Y[i] * X[mi(i,j,n,d)]*X[mi(i,k,n,d)] / n;
    }
  }
}

// Empirical cross-moment of order 3 between X size nxd and Y size n
void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
{
  int n=*pn, d=*pd;
  //double* M3 = (double*)calloc(d*d*d,sizeof(double));

  // M3 = E[Y*X^*3] - E[Y*e*X*e] - E[Y*e*e*X] - E[Y*X*e*e]
  for (int j=0; j<d; j++)
  {
    for (int k=0; k<d; k++)
    {
      for (int i=0; i<n; i++)
      {
        double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
        M3[ti(j,k,j,d,d,d)] -= tensor_elt;
        M3[ti(j,j,k,d,d,d)] -= tensor_elt;
        M3[ti(k,j,j,d,d,d)] -= tensor_elt;
        for (int o=0; o<d; o++)
          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;
      }
    }
  }
}

// W = 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
// with g(Zi, theta) = i-th contribution to all moments (size dim) - real moments
void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
{
  int n=*pn, d=*pd; //,nc=*pnc
  int dim = d + d*d + d*d*d;
  //double* W = (double*)malloc(dim*dim*sizeof(double));

  // (Re)Initialize W:
  for (int j=0; j<dim; j++)
  {
    for (int k=0; k<dim; k++)
      W[j*dim+k] = 0.0;
  }
  double* g = (double*)malloc(dim*sizeof(double));
  // TODO: stabilize this (for now, random result)
//  omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
//  #pragma omp parallel for
  for (int i=0; i<n; i++)
  {
    // g == gi:
    for (int j=0; j<d; j++)
      g[j] = Y[i] * X[mi(i,j,n,d)] - M[j];
    for (int j=d; j<d+(d*d); j++)
    {
      int idx1 = (j-d) % d; //num row
      int idx2 = ((j-d) - idx1) / d; //num col
      g[j] = 0.0;
      if (idx1 == idx2)
        g[j] -= Y[i];
      g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)] - M[j];
    }
    for (int j=d+d*d; j<dim; j++)
    {
      int idx1 = (j-d-d*d) % d; //num row
      int idx2 = ((j-d-d*d - idx1) / d) %d; //num col
      int idx3 = (((j-d-d*d - idx1) / d) - idx2) / d; //num "depth"
      g[j] = 0.0;
      if (idx1 == idx2)
        g[j] -= Y[i] * X[mi(i,idx3,n,d)];
      if (idx1 == idx3)
        g[j] -= Y[i] * X[mi(i,idx2,n,d)];
      if (idx2 == idx3)
        g[j] -= Y[i] * X[mi(i,idx1,n,d)];
      g[j] += Y[i] * X[mi(i,idx1,n,d)]*X[mi(i,idx2,n,d)]*X[mi(i,idx3,n,d)] - M[j];
    }
    // Add 1/n t(gi) %*% gi to W
    for (int j=0; j<dim; j++)
    {
      // This final nested loop is very costly. Some basic optimisations:
      double gj = g[j];
      int baseIdx = j * dim;
//      #pragma GCC unroll 32
      for (int k=j; k>=0; k--)
        W[baseIdx+k] += gj * g[k];
    }
  }
  // Normalize W: x 1/n
  for (int j=0; j<dim; j++)
  {
    for (int k=j; k<dim; k++)
      W[mi(j,k,dim,dim)] /= n;
  }
  // Symmetrize W: W[k,j] = W[j,k] for k > j
  for (int j=0; j<dim; j++)
  {
    for (int k=j+1; k<dim; k++)
      W[mi(k,j,dim,dim)] = W[mi(j,k,dim,dim)];
  }
  free(g);
}