#include <gsl/gsl_linalg.h>
// Compute pseudo-inverse of a square matrix
-static Real* pinv(const Real* matrix, mwSize dim)
+static double* pinv(const double* 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"
+ double EPS = 1e-10; //threshold for singular value "== 0"
//copy matrix into U
- for (mwSize i=0; i<dim*dim; i++)
- U->data[i] = matrix[i];
-
+ 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 (mwSize i=0; i<dim; i++)
+ double* inverse = (double*)malloc(dim*dim*sizeof(double));
+ for (int i=0; i<dim; i++)
{
- for (mwSize ii=0; ii<dim; ii++)
+ for (int ii=0; ii<dim; ii++)
{
- Real dotProduct = 0.0;
- for (mwSize j=0; j<dim; j++)
+ double 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;
}
// TODO: comment EMGrank purpose
void EMGrank(
// 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
+ const double* Pi, // parametre de proportion
+ const double* 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 double* X, // régresseurs
+ const double* Y, // réponse
+ double 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
+ double* phi, // parametre de moyenne renormalisé, calculé par l'EM
+ double* LLF, // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
// additional size parameters
- mwSize n, // taille de l'echantillon
- mwSize p, // nombre de covariables
- mwSize m, // taille de Y (multivarié)
- mwSize k) // nombre de composantes
+ 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));
+ double* Phi = (double*)calloc(p*m*k,sizeof(double));
+ double* hatBetaR = (double*)malloc(p*m*sizeof(double));
int signum;
- Real invN = 1.0/n;
+ double invN = 1.0/n;
int deltaPhiBufferSize = 20;
- Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
- mwSize 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);
+ double* deltaPhi = (double*)malloc(deltaPhiBufferSize*sizeof(double));
+ int ite = 0;
+ double sumDeltaPhi = 0.0;
+ double* YiRhoR = (double*)malloc(m*sizeof(double));
+ double* XiPhiR = (double*)malloc(m*sizeof(double));
+ double* Xr = (double*)malloc(n*p*sizeof(double));
+ double* Yr = (double*)malloc(n*m*sizeof(double));
+ double* tXrXr = (double*)malloc(p*p*sizeof(double));
+ double* tXrYr = (double*)malloc(p*m*sizeof(double));
+ 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* work = gsl_vector_alloc(m);
//Initialize class memberships (all elements in class 0; TODO: randomize ?)
- Int* Z = (Int*)calloc(n, sizeof(Int));
+ int* Z = (int*)calloc(n, sizeof(int));
//Initialize phi to zero, because some M loops might exit before phi affectation
- for (
mwSize i=0; i<p*m*k; i++)
+ for (
int i=0; i<p*m*k; i++)
phi[i] = 0.0;
while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
- {
+ {
/////////////
// Etape M //
/////////////
//M step: Mise à jour de Beta (et donc phi)
- for (mwSize r=0; r<k; r++)
+ for (int r=0; r<k; r++)
{
//Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
- mwSize cardClustR=0;
- for (mwSize i=0; i<n; i++)
+ int cardClustR=0;
+ for (int i=0; i<n; i++)
{
if (Z[i] == r)
{
- for (
mwSize j=0; j<p; j++)
- Xr[cardClustR*p+j] = X[i*p+j];
- for (mwSize j=0; j<m; j++)
- Yr[cardClustR*m+j] = Y[i*m+j];
+ 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)
+ if (cardClustR == 0)
continue;
//Compute tXrXr = t(Xr) * Xr
- for (
mwSize j=0; j<p; j++)
+ for (
int j=0; j<p; j++)
{
- for (
mwSize jj=0; jj<p; jj++)
+ for (
int jj=0; jj<p; jj++)
{
- Real dotProduct = 0.0;
- for (mwSize u=0; u<cardClustR; u++)
- dotProduct += Xr[u*p+j] * Xr[u*p+jj];
- tXrXr[j*p+jj] = dotProduct;
+ double 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);
+ double* invTXrXr = pinv(tXrXr, p);
// Compute tXrYr = t(Xr) * Yr
- for (
mwSize j=0; j<p; j++)
+ for (
int j=0; j<p; j++)
{
- for (mwSize jj=0; jj<m; jj++)
+ for (int jj=0; jj<m; jj++)
{
- Real dotProduct = 0.0;
- for (mwSize u=0; u<cardClustR; u++)
- dotProduct += Xr[u*p+j] * Yr[u*m+jj];
- tXrYr[j*m+jj] = dotProduct;
+ double dotProduct = 0.0;
+ for (int u=0; u<cardClustR; u++)
+ dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,j,n,m)];
+ tXrYr[mi(j,jj,p,m)] = dotProduct;
}
}
//Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
- for (
mwSize j=0; j<p; j++)
+ for (
int j=0; j<p; j++)
{
- for (mwSize jj=0; jj<m; jj++)
+ for (int jj=0; jj<m; jj++)
{
- Real dotProduct = 0.0;
- for (
mwSize u=0; u<p; u++)
- dotProduct += invTXrXr[j*p+u] * tXrYr[u*m+jj];
- matrixM->data[j*m+jj] = dotProduct;
+ double 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
+
+ //Set m-rank(r) singular values to zero, and recompose
//best rank(r) approximation of the initial product
- for (mwSize j=rank[r]; j<m; j++)
+ for (int j=rank[r]; j<m; j++)
S->data[j] = 0.0;
//[intermediate step] Compute hatBetaR = U * S * t(V)
- Real* U = matrixM->data;
- for (
mwSize j=0; j<p; j++)
+ double* U = matrixM->data;
+ for (
int j=0; j<p; j++)
{
- for (mwSize jj=0; jj<m; jj++)
+ for (int jj=0; jj<m; jj++)
{
- Real dotProduct = 0.0;
- for (mwSize u=0; u<m; u++)
+ double dotProduct = 0.0;
+ for (int u=0; u<m; u++)
dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
- hatBetaR[j*m+jj] = dotProduct;
+ hatBetaR[mi(j,jj,p,m)] = dotProduct;
}
}
-
+
//Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
- for (
mwSize j=0; j<p; j++)
+ for (
int j=0; j<p; j++)
{
- for (mwSize jj=0; jj<m; jj++)
+ for (int jj=0; jj<m; jj++)
{
- Real dotProduct=0.0;
- for (mwSize u=0; u<m; u++)
- dotProduct += hatBetaR[j*m+u] * Rho[u*m*k+jj*k+r];
- phi[j*m*k+jj*k+r] = dotProduct;
+ double 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 (mwSize i=0; i<n; i++)
+ double sumLogLLF2 = 0.0;
+ for (int i=0; i<n; i++)
{
- Real sumLLF1 = 0.0;
- Real maxLogGamIR = -INFINITY;
- for (mwSize r=0; r<k; r++)
+ double sumLLF1 = 0.0;
+ double 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) ) );
+ //*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 (mwSize j=0; j<m; j++)
+ for (int j=0; j<m; j++)
{
- for (mwSize jj=0; jj<m; jj++)
- matrixE->data[j*m+jj] = Rho[j*m*k+jj*k+r];
+ 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);
-
+ double detRhoR = gsl_linalg_LU_det(matrixE, signum);
+
//compute Y(i,:)*Rho(:,:,r)
- for (mwSize j=0; j<m; j++)
+ for (int j=0; j<m; j++)
{
YiRhoR[j] = 0.0;
- for (mwSize u=0; u<m; u++)
- YiRhoR[j] += Y[i*m+u] * Rho[u*m*k+j*k+r];
+ 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 (mwSize j=0; j<m; j++)
+ for (int j=0; j<m; j++)
{
XiPhiR[j] = 0.0;
- for (
mwSize u=0; u<p; u++)
- XiPhiR[j] += X[i*p+u] * phi[u*m*k+j*k+r];
+ 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 (mwSize u=0; u<m; u++)
+ double 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;
-
+ double logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
+
//Z(i) = index of max (gam(i,:))
if (logGamIR > maxLogGamIR)
{
}
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 (
mwSize j=0; j<p; j++)
+ double newDeltaPhi = 0.0;
+ for (
int j=0; j<p; j++)
{
- for (mwSize jj=0; jj<m; jj++)
+ for (int jj=0; jj<m; jj++)
{
- for (mwSize r=0; r<k; r++)
+ for (int r=0; r<k; r++)
{
- Real tmpDist = fabs(phi[j*m*k+jj*k+r]-Phi[j*m*k+jj*k+r])
- / (1.0+fabs(phi[j*m*k+jj*k+r]));
+ double 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;
}
sumDeltaPhi += newDeltaPhi;
// update other local variables
- for (mwSize j=0; j<m; j++)
+ for (int j=0; j<m; j++)
{
- for (
mwSize jj=0; jj<p; jj++)
+ for (
int jj=0; jj<p; jj++)
{
- for (mwSize r=0; r<k; r++)
- Phi[j*m*k+jj*k+r] = phi[j*m*k+jj*k+r];
+ for (int r=0; r<k; r++)
+ Phi[ai(j,jj,r,p,m,k)] = phi[ai(j,jj,r,p,m,k)];
}
}
- ite++;
+ ite++;
}
-
+
//free memory
free(hatBetaR);
free(deltaPhi);
free(Yr);
free(tXrXr);
free(tXrYr);
- free(Z);
+ free(Z);
}
projects / valse.git / blobdiff