Completed draft for version with matrix W

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

diff --git a/pkg/src/functions.c b/pkg/src/functions.c
index 41065bd..8731b9f 100644 (file)
--- a/pkg/src/functions.c
+++ b/pkg/src/functions.c
@@ -1,18 +1,18 @@
 #include <stdlib.h>
 
-//index matrix (by columns)
+// Index matrix (by columns)
 int mi(int i, int j, int d1, int d2)
 {
-       return j*d1+i;
+       return j*d1 + i;
 }
 
-//index 3-tensor (by columns, matrices ordered by last dim)
+// 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;
 }
 
-// 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;
@@ -30,7 +30,7 @@ void Moments_M2(double* X, double* Y, int* pn, int* pd, double* M2)
        }
 }
 
-// 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;
@@ -54,17 +54,49 @@ void Moments_M3(double* X, double* Y, int* pn, int* pd, double* M3)
        }
 }
 
+// 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)
 {
        int n=*pn, d=*pd;
-  //double* W = (double*)calloc(d+d*d+d*d*d,sizeof(double));
-
-  // TODO: formula 1/N sum( t(g(Zi,theta)) g(Zi,theta) )
-  // = 1/N sum( t( (XiYi-...) - M[i] ) ( ... ) )
-  // --> similar to Moments_M2 and M3 above
-  for (int j=0; j<
+  //int dim = d+d*d+d*d*d
+  //double* W = (double*)calloc(dim*dim,sizeof(double));
+  double* g = (double*)malloc(dim * sizeof(double));
   for (int i=0; i<n; i++)
   {
-    W[] += 
+    // Fill gi:
+    for (int j=0; j<d; j++)
+      g[j] = Y[i] * X[mi(i,j,n,d)] - M[i]
+    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)];
+    }
+    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;
+      double tensor_elt = Y[i]*X[mi(i,k,n,d)] / n;
+      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)];
+    }
+    // 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;
+    }
   }
+  free(g);
 }