#include "utils.h"
#include <stdlib.h>
+#include <math.h>
#include <gsl/gsl_linalg.h>
-// TODO: don't recompute indexes every time......
+// TODO: don't recompute indexes ai(...) and mi(...) when possible
void EMGLLF_core(
// IN parameters
const Real* phiInit, // parametre initial de moyenne renormalisé
Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
Real* rho, // parametre de variance renormalisé, calculé par l'EM
Real* pi, // parametre des proportions renormalisé, calculé par l'EM
- Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
+ Real* llh, // (derniere) log vraisemblance associée à cet échantillon,
+ // pour les valeurs estimées des paramètres
Real* S,
+ int* affec,
// additional size parameters
int n, // nombre d'echantillons
int p, // nombre de covariables
copyArray(phiInit, phi, p*m*k);
copyArray(rhoInit, rho, m*m*k);
copyArray(piInit, pi, k);
- zeroArray(LLF, maxi);
//S is already allocated, and doesn't need to be 'zeroed'
- //Other local variables
+ //Other local variables: same as in R
Real* gam = (Real*)malloc(n*k*sizeof(Real));
copyArray(gamInit, gam, n*k);
- Real* b = (Real*)malloc(k*sizeof(Real));
- Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
- Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
- Real* Pi = (Real*)malloc(k*sizeof(Real));
- Real* gam2 = (Real*)malloc(k*sizeof(Real));
- Real* pi2 = (Real*)malloc(k*sizeof(Real));
Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
- Real* ps = (Real*)malloc(m*k*sizeof(Real));
- Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
- Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
- Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
- Real* Gam = (Real*)malloc(n*k*sizeof(Real));
+ Real* b = (Real*)malloc(k*sizeof(Real));
Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
+ *llh = -INFINITY;
+ Real* pi2 = (Real*)malloc(k*sizeof(Real));
+ const Real EPS = 1e-15;
+ // Additional (not at this place, in R file)
+ Real* gam2 = (Real*)malloc(k*sizeof(Real));
Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
+ Real* detRho = (Real*)malloc(k*sizeof(Real));
gsl_matrix* matrix = gsl_matrix_alloc(m, m);
gsl_permutation* permutation = gsl_permutation_alloc(m);
Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
- Real dist = 0.;
- Real dist2 = 0.;
- int ite = 0;
- const Real EPS = 1e-15;
const Real gaussConstM = pow(2.*M_PI,m/2.);
+ Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
+ Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
+ Real* Pi = (Real*)malloc(k*sizeof(Real));
- while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
+ for (int ite=1; ite<=maxi; ite++)
{
copyArray(phi, Phi, p*m*k);
copyArray(rho, Rho, m*m*k);
{
//Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
for (int u=0; u<n; u++)
- Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
+ Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,n,m)];
}
for (int i=0; i<n; i++)
{
}
//tant que les proportions sont negatives
- int kk = 0;
- int pi2AllPositive = 0;
+ int kk = 0,
+ pi2AllPositive = 0;
Real invN = 1./n;
while (!pi2AllPositive)
{
kk++;
}
- //(pi.^gamma)*b
+ //sum(pi^gamma * b)
Real piPowGammaDotB = 0.;
for (int v=0; v<k; v++)
piPowGammaDotB += pow(pi[v],gamma) * b[v];
- //(pi2.^gamma)*b
+ //sum(pi2^gamma * b)
Real pi2PowGammaDotB = 0.;
for (int v=0; v<k; v++)
pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
- //transpose(gam2)*log(pi2)
- Real prodGam2logPi2 = 0.;
+ //sum(gam2 * log(pi2))
+ Real gam2DotLogPi2 = 0.;
for (int v=0; v<k; v++)
- prodGam2logPi2 += gam2[v] * log(pi2[v]);
+ gam2DotLogPi2 += gam2[v] * log(pi2[v]);
+
//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
- while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
+ while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
&& kk<1000)
{
Real pow_01_kk = pow(0.1,kk);
//pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
for (int v=0; v<k; v++)
pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
- //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
+ //pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
pi2PowGammaDotB = 0.;
for (int v=0; v<k; v++)
pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
- prodGam2logPi2 = 0.;
+ gam2DotLogPi2 = 0.;
for (int v=0; v<k; v++)
- prodGam2logPi2 += gam2[v] * log(pi2[v]);
+ gam2DotLogPi2 += gam2[v] * log(pi2[v]);
kk++;
}
Real t = pow(0.1,kk);
{
for (int mm=0; mm<m; mm++)
{
+ Real ps = 0.,
+ nY2 = 0.;
+ // Compute ps, and nY2 = sum(Y2[,mm,r]^2)
for (int i=0; i<n; i++)
{
- //< X2(i,:,r) , phi(:,mm,r) >
+ //< X2[i,,r] , phi[,mm,r] >
Real dotProduct = 0.;
for (int u=0; u<p; u++)
dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
- //ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
- ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
- nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
+ //ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
+ ps += Y2[ai(i,mm,r,n,m,k)] * dotProduct;
+ nY2 += Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
}
- //ps[mm,r] = sum(ps1[,mm,r])
- Real sumPs1 = 0.;
- for (int u=0; u<n; u++)
- sumPs1 += ps1[ai(u,mm,r,n,m,k)];
- ps[mi(mm,r,m,k)] = sumPs1;
- //nY2[mm,r] = sum(nY21[,mm,r])
- Real sumNy21 = 0.;
- for (int u=0; u<n; u++)
- sumNy21 += nY21[ai(u,mm,r,n,m,k)];
- nY2[mi(mm,r,m,k)] = sumNy21;
- //rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r]))) / (2*nY2[mm,r])
- rho[ai(mm,mm,r,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
- + 4*nY2[mi(mm,r,m,k)] * gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
+ //rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2)
+ rho[ai(mm,mm,r,m,m,k)] = (ps + sqrt(ps*ps + 4*nY2 * gam2[r])) / (2*nY2);
}
}
+
for (int r=0; r<k; r++)
{
for (int j=0; j<p; j++)
{
for (int mm=0; mm<m; mm++)
{
- //sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r])
- Real dotPhiGram2 = 0.0;
- for (int u=0; u<j; u++)
- dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
- //sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r])
- for (int u=j+1; u<p; u++)
- dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
- //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
- // (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
- // (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
- S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)] + dotPhiGram2;
- Real pow_pir_gamma = pow(pi[r],gamma);
- if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow_pir_gamma)
- phi[ai(j,mm,r,p,m,k)] = 0;
- else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow_pir_gamma)
+ //sum(phi[-j,mm,r] * Gram2[j,-j,r])
+ Real phiDotGram2 = 0.;
+ for (int u=0; u<p; u++)
{
- phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow_pir_gamma - S[ai(j,mm,r,p,m,k)])
+ if (u != j)
+ phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
+ }
+ //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
+ S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)]
+ + phiDotGram2;
+ Real pirPowGamma = pow(pi[r],gamma);
+ if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
+ phi[ai(j,mm,r,p,m,k)] = 0.;
+ else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
+ {
+ phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - S[ai(j,mm,r,p,m,k)])
/ Gram2[ai(j,j,r,p,p,k)];
}
else
{
- phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow_pir_gamma + S[ai(j,mm,r,p,m,k)])
+ phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pirPowGamma + S[ai(j,mm,r,p,m,k)])
/ Gram2[ai(j,j,r,p,p,k)];
}
}
// Etape E //
/////////////
+ // Precompute det(rho[,,r]) for r in 1...k
int signum;
- Real sumLogLLF2 = 0.0;
- for (int i=0; i<n; i++)
+ for (int r=0; r<k; r++)
{
- Real minSqNorm2 = INFINITY;
+ for (int u=0; u<m; u++)
+ {
+ for (int v=0; v<m; v++)
+ matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
+ }
+ gsl_linalg_LU_decomp(matrix, permutation, &signum);
+ detRho[r] = gsl_linalg_LU_det(matrix, signum);
+ }
+ Real sumLogLLH = 0.;
+ for (int i=0; i<n; i++)
+ {
for (int r=0; r<k; r++)
{
//compute Y[i,]%*%rho[,,r]
for (int u=0; u<m; u++)
{
- YiRhoR[u] = 0.0;
+ YiRhoR[u] = 0.;
for (int v=0; v<m; v++)
YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
}
- //compute X(i,:)*phi(:,:,r)
+ //compute X[i,]%*%phi[,,r]
for (int u=0; u<m; u++)
{
- XiPhiR[u] = 0.0;
+ XiPhiR[u] = 0.;
for (int v=0; v<p; v++)
XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
}
//compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
- sqNorm2[r] = 0.0;
+ sqNorm2[r] = 0.;
for (int u=0; u<m; u++)
sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
- if (sqNorm2[r] < minSqNorm2)
- minSqNorm2 = sqNorm2[r];
}
- Real shift = 0.5*minSqNorm2;
- Real sumLLF1 = 0.0;
- Real sumGamI = 0.0;
+ Real sumGamI = 0.;
for (int r=0; r<k; r++)
{
- //compute det(rho[,,r]) [TODO: avoid re-computations]
- for (int u=0; u<m; u++)
- {
- for (int v=0; v<m; v++)
- matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
- }
- gsl_linalg_LU_decomp(matrix, permutation, &signum);
- Real detRhoR = gsl_linalg_LU_det(matrix, signum);
-
- //FIXME: det(rho[,,r]) too small(?!). See EMGLLF.R
- Gam[mi(i,r,n,k)] = pi[r] * exp(-0.5*sqNorm2[r] + shift) ; //* detRhoR;
- sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
- sumGamI += Gam[mi(i,r,n,k)];
+ gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRho[r];
+ sumGamI += gam[mi(i,r,n,k)];
}
- sumLogLLF2 += log(sumLLF1);
- for (int r=0; r<k; r++)
+
+ sumLogLLH += log(sumGamI) - log(gaussConstM);
+ if (sumGamI > EPS) //else: gam[i,] is already ~=0
{
- //gam[i,] = Gam[i,] / sumGamI
- gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
+ for (int r=0; r<k; r++)
+ gam[mi(i,r,n,k)] /= sumGamI;
}
}
//sumPen = sum(pi^gamma * b)
- Real sumPen = 0.0;
+ Real sumPen = 0.;
for (int r=0; r<k; r++)
sumPen += pow(pi[r],gamma) * b[r];
- //LLF[ite] = -sumLogLLF2/n + lambda*sumPen
- LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
- dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
+ Real last_llh = *llh;
+ //llh = -sumLogLLH/n + lambda*sumPen
+ *llh = -invN * sumLogLLH + lambda * sumPen;
+ Real dist = ite==1 ? *llh : (*llh - last_llh) / (1. + fabs(*llh));
//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
- Real Dist1 = 0.0;
+ Real Dist1 = 0.;
for (int u=0; u<p; u++)
{
for (int v=0; v<m; v++)
{
for (int w=0; w<k; w++)
{
- Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
- / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
+ Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
+ / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
if (tmpDist > Dist1)
Dist1 = tmpDist;
}
}
}
//Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
- Real Dist2 = 0.0;
+ Real Dist2 = 0.;
for (int u=0; u<m; u++)
{
for (int v=0; v<m; v++)
{
for (int w=0; w<k; w++)
{
- Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
- / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
+ Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
+ / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
if (tmpDist > Dist2)
Dist2 = tmpDist;
}
}
}
//Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
- Real Dist3 = 0.0;
+ Real Dist3 = 0.;
for (int u=0; u<n; u++)
{
for (int v=0; v<k; v++)
{
- Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
+ Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
if (tmpDist > Dist3)
Dist3 = tmpDist;
}
}
//dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
- dist2 = Dist1;
+ Real dist2 = Dist1;
if (Dist2 > dist2)
dist2 = Dist2;
if (Dist3 > dist2)
dist2 = Dist3;
- ite++;
+ if (ite >= mini && (dist >= tau || dist2 >= sqrt(tau)))
+ break;
+ }
+
+ //affec = apply(gam, 1, which.max)
+ for (int i=0; i<n; i++)
+ {
+ Real rowMax = 0.;
+ affec[i] = 0;
+ for (int j=0; j<k; j++)
+ {
+ if (gam[mi(i,j,n,k)] > rowMax)
+ {
+ affec[i] = j+1; //R indices start at 1
+ rowMax = gam[mi(i,j,n,k)];
+ }
+ }
}
//free memory
free(b);
free(gam);
- free(Gam);
free(Phi);
free(Rho);
free(Pi);
- free(ps);
- free(nY2);
- free(ps1);
- free(nY21);
free(Gram2);
free(ps2);
+ free(detRho);
gsl_matrix_free(matrix);
gsl_permutation_free(permutation);
free(XiPhiR);
projects / valse.git / blobdiff