It's enough to compute half of W (complete by symmetry)

[morpheus.git] / pkg / src / functions.c

diff --git a/pkg/src/functions.c b/pkg/src/functions.c
index c8d51dd..6444b86 100644 (file)
--- a/pkg/src/functions.c
+++ b/pkg/src/functions.c
@@ -1,72 +1,76 @@
 #include <stdlib.h>
+#include <omp.h>
 
 // Index matrix (by columns)
-int mi(int i, int j, int d1, int d2)
-{
-       return j*d1 + i;
-}
+#define mi(i, j, d1, d2) (j*d1 + i)
 
 // Index 3-tensor (by columns, matrices ordered by last dim)
-int ti(int i, int j, int k, int d1, int d2, int d3)
-{
-       return k*d1*d2 + j*d1 + i;
-}
+#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));
+  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;
-               }
-       }
+  // 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));
+  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;
-                       }
-               }
-       }
+  // 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, double* Y, double* M, int* pn, int* pd, double* W)
+void Compute_Omega(double* X, int* Y, double* M, int* pnc, int* pn, int* pd, double* W)
 {
-       int n=*pn, d=*pd;
+  int nc=*pnc, n=*pn, d=*pd;
   int dim = d + d*d + d*d*d;
-  //double* W = (double*)calloc(dim*dim,sizeof(double));
-  double* g = (double*)malloc(dim * sizeof(double));
+  //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));
+  omp_set_num_threads(nc >= 1 ? nc : omp_get_num_procs());
+  #pragma omp parallel for
   for (int i=0; i<n; i++)
   {
-    // Fill gi:
+    // g == gi:
     for (int j=0; j<d; j++)
-      g[j] = Y[i] * X[mi(i,j,n,d)] - M[i];
+      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
@@ -74,7 +78,7 @@ void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
       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[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++)
     {
@@ -88,14 +92,30 @@ void Compute_Omega(double* X, double* Y, double* M, int* pn, int* pd, double* W)
         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[i];
+      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++)
     {
-      for (int k=0; k<dim; k++)
-        W[j*dim+k] += g[j] * g[k] / n;
+      // 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=0; k<=j; k++)
+      W[mi(j,k,dim,dim)] /= n;
+  }
+  // Symmetrize W: W[j,k] = W[k,j] for k > j
+  for (int j=0; j<dim; j++)
+  {
+    for (int k=j+1: k<dim; k++)
+      W[mi(j,k,dim,dim)] = W[mi(k,j,dim,dim)];
+  }
   free(g);
 }