4 #include <gsl/gsl_linalg.h>
6 // TODO: don't recompute indexes ai(...) and mi(...) when possible
9 const Real* phiInit, // parametre initial de moyenne renormalisé
10 const Real* rhoInit, // parametre initial de variance renormalisé
11 const Real* piInit, // parametre initial des proportions
12 const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
13 int mini, // nombre minimal d'itérations dans l'algorithme EM
14 int maxi, // nombre maximal d'itérations dans l'algorithme EM
15 Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
16 Real lambda, // valeur du paramètre de régularisation du Lasso
17 const Real* X, // régresseurs
18 const Real* Y, // réponse
19 Real tau, // seuil pour accepter la convergence
20 // OUT parameters (all pointers, to be modified)
21 Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
22 Real* rho, // parametre de variance renormalisé, calculé par l'EM
23 Real* pi, // parametre des proportions renormalisé, calculé par l'EM
24 Real* llh, // (derniere) log vraisemblance associée à cet échantillon,
25 // pour les valeurs estimées des paramètres
28 // additional size parameters
29 int n, // nombre d'echantillons
30 int p, // nombre de covariables
31 int m, // taille de Y (multivarié)
32 int k) // nombre de composantes dans le mélange
35 copyArray(phiInit, phi, p*m*k);
36 copyArray(rhoInit, rho, m*m*k);
37 copyArray(piInit, pi, k);
38 //S is already allocated, and doesn't need to be 'zeroed'
40 //Other local variables: same as in R
41 Real* gam = (Real*)malloc(n*k*sizeof(Real));
42 copyArray(gamInit, gam, n*k);
43 Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
44 Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
45 Real* b = (Real*)malloc(k*sizeof(Real));
46 Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
47 Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
49 Real* pi2 = (Real*)malloc(k*sizeof(Real));
50 const Real EPS = 1e-15;
51 // Additional (not at this place, in R file)
52 Real* gam2 = (Real*)malloc(k*sizeof(Real));
53 Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
54 Real* detRho = (Real*)malloc(k*sizeof(Real));
55 gsl_matrix* matrix = gsl_matrix_alloc(m, m);
56 gsl_permutation* permutation = gsl_permutation_alloc(m);
57 Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
58 Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
59 const Real gaussConstM = pow(2.*M_PI,m/2.);
60 Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
61 Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
62 Real* Pi = (Real*)malloc(k*sizeof(Real));
64 for (int ite=1; ite<=maxi; ite++)
66 copyArray(phi, Phi, p*m*k);
67 copyArray(rho, Rho, m*m*k);
70 // Calculs associés a Y et X
71 for (int r=0; r<k; r++)
73 for (int mm=0; mm<m; mm++)
75 //Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
76 for (int u=0; u<n; u++)
77 Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,n,m)];
79 for (int i=0; i<n; i++)
81 //X2[i,,r] = sqrt(gam[i,r]) * X[i,]
82 for (int u=0; u<p; u++)
83 X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
85 for (int mm=0; mm<m; mm++)
87 //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
88 for (int u=0; u<p; u++)
91 for (int v=0; v<n; v++)
92 dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
93 ps2[ai(u,mm,r,p,m,k)] = dotProduct;
96 for (int j=0; j<p; j++)
98 for (int s=0; s<p; s++)
100 //Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
101 Real dotProduct = 0.;
102 for (int u=0; u<n; u++)
103 dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
104 Gram2[ai(j,s,r,p,p,k)] = dotProduct;
114 for (int r=0; r<k; r++)
116 //b[r] = sum(abs(phi[,,r]))
118 for (int u=0; u<p; u++)
119 for (int v=0; v<m; v++)
120 sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
123 //gam2 = colSums(gam)
124 for (int u=0; u<k; u++)
126 Real sumOnColumn = 0.;
127 for (int v=0; v<n; v++)
128 sumOnColumn += gam[mi(v,u,n,k)];
129 gam2[u] = sumOnColumn;
131 //a = sum(gam %*% log(pi))
133 for (int u=0; u<n; u++)
135 Real dotProduct = 0.;
136 for (int v=0; v<k; v++)
137 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
141 //tant que les proportions sont negatives
145 while (!pi2AllPositive)
147 //pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
148 Real pow_01_kk = pow(0.1,kk);
149 for (int r=0; r<k; r++)
150 pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
151 //pi2AllPositive = all(pi2 >= 0)
153 for (int r=0; r<k; r++)
165 Real piPowGammaDotB = 0.;
166 for (int v=0; v<k; v++)
167 piPowGammaDotB += pow(pi[v],gamma) * b[v];
169 Real pi2PowGammaDotB = 0.;
170 for (int v=0; v<k; v++)
171 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
172 //sum(gam2 * log(pi2))
173 Real gam2DotLogPi2 = 0.;
174 for (int v=0; v<k; v++)
175 gam2DotLogPi2 += gam2[v] * log(pi2[v]);
177 //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
178 while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
181 Real pow_01_kk = pow(0.1,kk);
182 //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
183 for (int v=0; v<k; v++)
184 pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
185 //pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
186 pi2PowGammaDotB = 0.;
187 for (int v=0; v<k; v++)
188 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
190 for (int v=0; v<k; v++)
191 gam2DotLogPi2 += gam2[v] * log(pi2[v]);
194 Real t = pow(0.1,kk);
195 //sum(pi + t*(pi2-pi))
196 Real sumPiPlusTbyDiff = 0.;
197 for (int v=0; v<k; v++)
198 sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
199 //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
200 for (int v=0; v<k; v++)
201 pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
204 for (int r=0; r<k; r++)
206 for (int mm=0; mm<m; mm++)
210 // Compute ps, and nY2 = sum(Y2[,mm,r]^2)
211 for (int i=0; i<n; i++)
213 //< X2[i,,r] , phi[,mm,r] >
214 Real dotProduct = 0.;
215 for (int u=0; u<p; u++)
216 dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
217 //ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
218 ps += Y2[ai(i,mm,r,n,m,k)] * dotProduct;
219 nY2 += Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
221 //rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2)
222 rho[ai(mm,mm,r,m,m,k)] = (ps + sqrt(ps*ps + 4*nY2 * gam2[r])) / (2*nY2);
226 for (int r=0; r<k; r++)
228 for (int j=0; j<p; j++)
230 for (int mm=0; mm<m; mm++)
232 //sum(phi[-j,mm,r] * Gram2[j,-j,r])
233 Real phiDotGram2 = 0.;
234 for (int u=0; u<p; u++)
237 phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
239 //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
240 S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)]
242 Real pirPowGamma = pow(pi[r],gamma);
243 if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
244 phi[ai(j,mm,r,p,m,k)] = 0.;
245 else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
247 phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - S[ai(j,mm,r,p,m,k)])
248 / Gram2[ai(j,j,r,p,p,k)];
252 phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pirPowGamma + S[ai(j,mm,r,p,m,k)])
253 / Gram2[ai(j,j,r,p,p,k)];
263 // Precompute det(rho[,,r]) for r in 1...k
265 for (int r=0; r<k; r++)
267 for (int u=0; u<m; u++)
269 for (int v=0; v<m; v++)
270 matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
272 gsl_linalg_LU_decomp(matrix, permutation, &signum);
273 detRho[r] = gsl_linalg_LU_det(matrix, signum);
277 for (int i=0; i<n; i++)
279 for (int r=0; r<k; r++)
281 //compute Y[i,]%*%rho[,,r]
282 for (int u=0; u<m; u++)
285 for (int v=0; v<m; v++)
286 YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
289 //compute X[i,]%*%phi[,,r]
290 for (int u=0; u<m; u++)
293 for (int v=0; v<p; v++)
294 XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
297 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
299 for (int u=0; u<m; u++)
300 sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
304 for (int r=0; r<k; r++)
306 gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRho[r];
307 sumGamI += gam[mi(i,r,n,k)];
310 sumLogLLH += log(sumGamI) - log(gaussConstM);
311 if (sumGamI > EPS) //else: gam[i,] is already ~=0
313 for (int r=0; r<k; r++)
314 gam[mi(i,r,n,k)] /= sumGamI;
318 //sumPen = sum(pi^gamma * b)
320 for (int r=0; r<k; r++)
321 sumPen += pow(pi[r],gamma) * b[r];
322 Real last_llh = *llh;
323 //llh = -sumLogLLH/n + lambda*sumPen
324 *llh = -invN * sumLogLLH + lambda * sumPen;
325 Real dist = ite==1 ? *llh : (*llh - last_llh) / (1. + fabs(*llh));
327 //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
329 for (int u=0; u<p; u++)
331 for (int v=0; v<m; v++)
333 for (int w=0; w<k; w++)
335 Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
336 / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
342 //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
344 for (int u=0; u<m; u++)
346 for (int v=0; v<m; v++)
348 for (int w=0; w<k; w++)
350 Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
351 / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
357 //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
359 for (int u=0; u<n; u++)
361 for (int v=0; v<k; v++)
363 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
368 //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
375 if (ite >= mini && (dist >= tau || dist2 >= sqrt(tau)))
379 //affec = apply(gam, 1, which.max)
380 for (int i=0; i<n; i++)
384 for (int j=0; j<k; j++)
386 if (gam[mi(i,j,n,k)] > rowMax)
388 affec[i] = j+1; //R indices start at 1
389 rowMax = gam[mi(i,j,n,k)];
403 gsl_matrix_free(matrix);
404 gsl_permutation_free(permutation);