X-Git-Url: https://git.auder.net/?p=valse.git;a=blobdiff_plain;f=pkg%2Fsrc%2Fsources%2FEMGrank.c;fp=pkg%2Fsrc%2Fsources%2FEMGrank.c;h=3a9bf94b23a05c443d7cb6f32dd835d19667274f;hp=0000000000000000000000000000000000000000;hb=f87ff0f5116c0c1c59c5608e46563ff0f79e5d43;hpb=53fa233d8fbeaf4d51a4874ba69d8472d01d04ba

diff --git a/pkg/src/sources/EMGrank.c b/pkg/src/sources/EMGrank.c
new file mode 100644
index 0000000..3a9bf94
--- /dev/null
+++ b/pkg/src/sources/EMGrank.c
@@ -0,0 +1,307 @@
+#include <stdlib.h>
+#include <gsl/gsl_linalg.h>
+#include "utils.h"
+
+// Compute pseudo-inverse of a square matrix
+static Real* pinv(const Real* matrix, int dim)
+{
+	gsl_matrix* U = gsl_matrix_alloc(dim,dim);
+	gsl_matrix* V = gsl_matrix_alloc(dim,dim);
+	gsl_vector* S = gsl_vector_alloc(dim);
+	gsl_vector* work = gsl_vector_alloc(dim);
+	Real EPS = 1e-10; //threshold for singular value "== 0"
+	
+	//copy matrix into U
+	copyArray(matrix, U->data, dim*dim);
+
+	//U,S,V = SVD of matrix
+	gsl_linalg_SV_decomp(U, V, S, work);
+	gsl_vector_free(work);
+
+	// Obtain pseudo-inverse by V*S^{-1}*t(U)
+	Real* inverse = (Real*)malloc(dim*dim*sizeof(Real));
+	for (int i=0; i<dim; i++)
+	{
+		for (int ii=0; ii<dim; ii++)
+		{
+			Real dotProduct = 0.0;
+			for (int j=0; j<dim; j++)
+				dotProduct += V->data[i*dim+j] * (S->data[j] > EPS ? 1.0/S->data[j] : 0.0) * U->data[ii*dim+j];
+			inverse[i*dim+ii] = dotProduct;
+		}
+	}
+	
+	gsl_matrix_free(U);
+	gsl_matrix_free(V);
+	gsl_vector_free(S);
+	return inverse;
+}
+
+// TODO: comment EMGrank purpose
+void EMGrank_core(
+	// IN parameters
+	const Real* Pi, // parametre de proportion
+	const Real* Rho, // parametre initial de variance renormalisé
+	int mini, // nombre minimal d'itérations dans l'algorithme EM
+	int maxi, // nombre maximal d'itérations dans l'algorithme EM
+	const Real* X, // régresseurs
+	const Real* Y, // réponse
+	Real tau, // seuil pour accepter la convergence
+	const int* rank, // vecteur des rangs possibles
+	// OUT parameters
+	Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
+	Real* LLF, // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
+	// additional size parameters
+	int n, // taille de l'echantillon
+	int p, // nombre de covariables
+	int m, // taille de Y (multivarié)
+	int k) // nombre de composantes
+{
+	// Allocations, initializations
+	Real* Phi = (Real*)calloc(p*m*k,sizeof(Real));
+	Real* hatBetaR = (Real*)malloc(p*m*sizeof(Real));
+	int signum;
+	Real invN = 1.0/n;
+	int deltaPhiBufferSize = 20;
+	Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
+	int ite = 0;
+	Real sumDeltaPhi = 0.0;
+	Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
+	Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
+	Real* Xr = (Real*)malloc(n*p*sizeof(Real));
+	Real* Yr = (Real*)malloc(n*m*sizeof(Real));
+	Real* tXrXr = (Real*)malloc(p*p*sizeof(Real));
+	Real* tXrYr = (Real*)malloc(p*m*sizeof(Real));
+	gsl_matrix* matrixM = gsl_matrix_alloc(p, m);
+	gsl_matrix* matrixE = gsl_matrix_alloc(m, m);
+	gsl_permutation* permutation = gsl_permutation_alloc(m);
+	gsl_matrix* V = gsl_matrix_alloc(m,m);
+	gsl_vector* S = gsl_vector_alloc(m);
+	gsl_vector* work = gsl_vector_alloc(m);
+
+	//Initialize class memberships (all elements in class 0; TODO: randomize ?)
+	int* Z = (int*)calloc(n, sizeof(int));
+
+	//Initialize phi to zero, because some M loops might exit before phi affectation
+	zeroArray(phi, p*m*k);
+
+	while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
+	{
+		/////////////
+		// Etape M //
+		/////////////
+		
+		//M step: Mise à jour de Beta (et donc phi)
+		for (int r=0; r<k; r++)
+		{
+			//Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
+			int cardClustR=0;
+			for (int i=0; i<n; i++)
+			{
+				if (Z[i] == r)
+				{
+					for (int j=0; j<p; j++)
+						Xr[mi(cardClustR,j,n,p)] = X[mi(i,j,n,p)];
+					for (int j=0; j<m; j++)
+						Yr[mi(cardClustR,j,n,m)] = Y[mi(i,j,n,m)];
+					cardClustR++;
+				}
+			}
+			if (cardClustR == 0)
+				continue;
+
+			//Compute tXrXr = t(Xr) * Xr
+			for (int j=0; j<p; j++)
+			{
+				for (int jj=0; jj<p; jj++)
+				{
+					Real dotProduct = 0.0;
+					for (int u=0; u<cardClustR; u++)
+						dotProduct += Xr[mi(u,j,n,p)] * Xr[mi(u,jj,n,p)];
+					tXrXr[mi(j,jj,p,p)] = dotProduct;
+				}
+			}
+
+			//Get pseudo inverse = (t(Xr)*Xr)^{-1}
+			Real* invTXrXr = pinv(tXrXr, p);
+			
+			// Compute tXrYr = t(Xr) * Yr
+			for (int j=0; j<p; j++)
+			{
+				for (int jj=0; jj<m; jj++)
+				{
+					Real dotProduct = 0.0;
+					for (int u=0; u<cardClustR; u++)
+						dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,jj,n,m)];
+					tXrYr[mi(j,jj,p,m)] = dotProduct;
+				}
+			}
+
+			//Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
+			for (int j=0; j<p; j++)
+			{
+				for (int jj=0; jj<m; jj++)
+				{
+					Real dotProduct = 0.0;
+					for (int u=0; u<p; u++)
+						dotProduct += invTXrXr[mi(j,u,p,p)] * tXrYr[mi(u,jj,p,m)];
+					matrixM->data[j*m+jj] = dotProduct;
+				}
+			}
+			free(invTXrXr);
+
+			//U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
+			gsl_linalg_SV_decomp(matrixM, V, S, work);
+
+			//Set m-rank(r) singular values to zero, and recompose
+			//best rank(r) approximation of the initial product
+			for (int j=rank[r]; j<m; j++)
+				S->data[j] = 0.0;
+			
+			//[intermediate step] Compute hatBetaR = U * S * t(V)
+			double* U = matrixM->data; //GSL require double precision
+			for (int j=0; j<p; j++)
+			{
+				for (int jj=0; jj<m; jj++)
+				{
+					Real dotProduct = 0.0;
+					for (int u=0; u<m; u++)
+						dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
+					hatBetaR[mi(j,jj,p,m)] = dotProduct;
+				}
+			}
+
+			//Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
+			for (int j=0; j<p; j++)
+			{
+				for (int jj=0; jj<m; jj++)
+				{
+					Real dotProduct=0.0;
+					for (int u=0; u<m; u++)
+						dotProduct += hatBetaR[mi(j,u,p,m)] * Rho[ai(u,jj,r,m,m,k)];
+					phi[ai(j,jj,r,p,m,k)] = dotProduct;
+				}
+		}
+		}
+
+		/////////////
+		// Etape E //
+		/////////////
+		
+		Real sumLogLLF2 = 0.0;
+		for (int i=0; i<n; i++)
+		{
+			Real sumLLF1 = 0.0;
+			Real maxLogGamIR = -INFINITY;
+			for (int r=0; r<k; r++)
+			{
+				//Compute
+				//Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
+				//*phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
+				//split in several sub-steps
+				
+				//compute det(Rho(:,:,r)) [TODO: avoid re-computations]
+				for (int j=0; j<m; j++)
+				{
+					for (int jj=0; jj<m; jj++)
+						matrixE->data[j*m+jj] = Rho[ai(j,jj,r,m,m,k)];
+				}
+				gsl_linalg_LU_decomp(matrixE, permutation, &signum);
+				Real detRhoR = gsl_linalg_LU_det(matrixE, signum);
+
+				//compute Y(i,:)*Rho(:,:,r)
+				for (int j=0; j<m; j++)
+				{
+					YiRhoR[j] = 0.0;
+					for (int u=0; u<m; u++)
+						YiRhoR[j] += Y[mi(i,u,n,m)] * Rho[ai(u,j,r,m,m,k)];
+				}
+
+				//compute X(i,:)*phi(:,:,r)
+				for (int j=0; j<m; j++)
+				{
+					XiPhiR[j] = 0.0;
+					for (int u=0; u<p; u++)
+						XiPhiR[j] += X[mi(i,u,n,p)] * phi[ai(u,j,r,p,m,k)];
+				}
+
+				//compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
+				Real dotProduct = 0.0;
+				for (int u=0; u<m; u++)
+					dotProduct += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+				Real logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
+
+				//Z(i) = index of max (gam(i,:))
+				if (logGamIR > maxLogGamIR)
+				{
+					Z[i] = r;
+					maxLogGamIR = logGamIR;
+				}
+				sumLLF1 += exp(logGamIR) / pow(2*M_PI,m/2.0);
+			}
+
+			sumLogLLF2 += log(sumLLF1);
+		}
+
+		// Assign output variable LLF
+		*LLF = -invN * sumLogLLF2;
+
+		//newDeltaPhi = max(max((abs(phi-Phi))./(1+abs(phi))));
+		Real newDeltaPhi = 0.0;
+		for (int j=0; j<p; j++)
+		{
+			for (int jj=0; jj<m; jj++)
+			{
+				for (int r=0; r<k; r++)
+				{
+					Real tmpDist = fabs(phi[ai(j,jj,r,p,m,k)]-Phi[ai(j,jj,r,p,m,k)])
+						/ (1.0+fabs(phi[ai(j,jj,r,p,m,k)]));
+					if (tmpDist > newDeltaPhi)
+						newDeltaPhi = tmpDist;
+				}
+			}
+		}
+
+		//update distance parameter to check algorithm convergence (delta(phi, Phi))
+		//TODO: deltaPhi should be a linked list for perf.
+		if (ite < deltaPhiBufferSize)
+			deltaPhi[ite] = newDeltaPhi;
+		else
+		{
+			sumDeltaPhi -= deltaPhi[0];
+			for (int u=0; u<deltaPhiBufferSize-1; u++)
+				deltaPhi[u] = deltaPhi[u+1];
+			deltaPhi[deltaPhiBufferSize-1] = newDeltaPhi;
+		}
+		sumDeltaPhi += newDeltaPhi;
+
+		// update other local variables
+		for (int j=0; j<m; j++)
+		{
+			for (int jj=0; jj<p; jj++)
+			{
+				for (int r=0; r<k; r++)
+					Phi[ai(jj,j,r,p,m,k)] = phi[ai(jj,j,r,p,m,k)];
+			}
+		}
+		ite++;
+	}
+
+	//free memory
+	free(hatBetaR);
+	free(deltaPhi);
+	free(Phi);
+	gsl_matrix_free(matrixE);
+	gsl_matrix_free(matrixM);
+	gsl_permutation_free(permutation);
+	gsl_vector_free(work);
+	gsl_matrix_free(V);
+	gsl_vector_free(S);
+	free(XiPhiR);
+	free(YiRhoR);
+	free(Xr);
+	free(Yr);
+	free(tXrXr);
+	free(tXrYr);
+	free(Z);
+}