X-Git-Url: https://git.auder.net/?p=morpheus.git;a=blobdiff_plain;f=pkg%2Fsrc%2Ffunctions.c;h=6444b8649875ef2022fb5151aa77207743c48740;hp=42bb1343c8fdb7b47c663fd4869ff65a4fa2149f;hb=9fdd3e5f57aa1fd0f839214d9cbfac022a8739a8;hpb=4263503b0fbe45a6fa5b353c8405e30557b3dd70

diff --git a/pkg/src/functions.c b/pkg/src/functions.c
index 42bb134..6444b86 100644
--- a/pkg/src/functions.c
+++ b/pkg/src/functions.c
@@ -1,62 +1,121 @@
 #include <stdlib.h>
+#include <omp.h>
 
-//index matrix (by columns)
-int mi(int i, int j, int d1, int d2)
-{
-	return j*d1+i;
-}
+// Index matrix (by columns)
+#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;
-}
+// Index 3-tensor (by columns, matrices ordered by last dim)
+#define ti(i, j, k, d1, d2, d3) (k*d1*d2 + j*d1 + i)
 
-// Emprical cross-moment of order 2 between X size nxd and Y size n
+// 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;
-		}
-	}
+  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;
+    }
+  }
 }
 
-// Emprical cross-moment of order 3 between X size nxd and Y size 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;
-			}
-		}
-	}
+  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;
+      }
+    }
+  }
 }
 
-void Compute_Omega(double* X, double* Y, int* pn, int* pd, double* W)
+// 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)
 {
-  // TODO: formula 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
-  // = 1/N sum( t( (XiYi-...) - theta[i] ) ( ... ) )
-  // --> similar to Moments_M2 and M3 above
+  int nc=*pnc, n=*pn, d=*pd;
+  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));
+  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=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);
 }