From d08fef424150599b8095727c0f9870ca9535fb65 Mon Sep 17 00:00:00 2001
From: Benjamin Auder <benjamin.auder@somewhere>
Date: Mon, 9 Dec 2019 14:48:50 +0100
Subject: [PATCH] Completed draft for version with matrix W

---
 pkg/R/optimParams.R |  1 +
 pkg/R/utils.R       | 17 --------------
 pkg/src/functions.c | 56 +++++++++++++++++++++++++++++++++++----------
 3 files changed, 45 insertions(+), 29 deletions(-)

diff --git a/pkg/R/optimParams.R b/pkg/R/optimParams.R
index 934a757..c061fcf 100644
--- a/pkg/R/optimParams.R
+++ b/pkg/R/optimParams.R
@@ -190,6 +190,7 @@ setRefClass(
         t( sweep(as.matrix(β2[,km1]), 2, G2[km1], '*') - G2[K] * β2[,K] ),
         t( sweep(as.matrix(β3[,km1]), 2, G3[km1], '*') - G3[K] * β3[,K] )))
 
+      # TODO: understand derivatives order and match the one in optim init param
 			for (i in 1:d)
 			{
 				# i determines the derivated matrix dβ[2,3]
diff --git a/pkg/R/utils.R b/pkg/R/utils.R
index 6ac9bec..6d1c361 100644
--- a/pkg/R/utils.R
+++ b/pkg/R/utils.R
@@ -74,23 +74,6 @@ normalize = function(X)
 computeMoments = function(X, Y)
 	list( colMeans(Y * X), .Moments_M2(X,Y), .Moments_M3(X,Y) )
 
-# Computes the Omega matrix for generalized least square method
-#
-# @param X matrix of covariates (of size n*d)
-# @param Y vector of responses (of size n)
-# @param theta list with p, beta, b
-#
-# @return Matrix of size dimxdim where dim=d+d^2+d^3
-#
-.Moments_M3 = function(X, Y)
-{
-	n = nrow(X)
-	d = ncol(X)
-	M3 = array(0,dim=c(d,d,d))
-	array( .C("Moments_M3", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
-		pd=as.integer(d), M3=as.double(M3), PACKAGE="morpheus")$M3, dim=c(d,d,d) )
-}
-
 # Find the optimal assignment (permutation) between two sets (minimize cost)
 #
 # @param distances The distances matrix, in columns (distances[i,j] is distance between i
diff --git a/pkg/src/functions.c b/pkg/src/functions.c
index 41065bd..8731b9f 100644
--- 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);
 }
-- 
2.44.0