e41fe3c3f5c3f76a2f7bec23a757904a285e0d2c
[valse.git] / pkg / src / sources / EMGLLF.c
1 #include "utils.h"
2 #include <stdlib.h>
3 #include <gsl/gsl_linalg.h>
4
5 // TODO: don't recompute indexes ai(...) and mi(...) when possible
6 void EMGLLF_core(
7 // IN parameters
8 const Real* phiInit, // parametre initial de moyenne renormalisé
9 const Real* rhoInit, // parametre initial de variance renormalisé
10 const Real* piInit, // parametre initial des proportions
11 const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
12 int mini, // nombre minimal d'itérations dans l'algorithme EM
13 int maxi, // nombre maximal d'itérations dans l'algorithme EM
14 Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
15 Real lambda, // valeur du paramètre de régularisation du Lasso
16 const Real* X, // régresseurs
17 const Real* Y, // réponse
18 Real tau, // seuil pour accepter la convergence
19 // OUT parameters (all pointers, to be modified)
20 Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
21 Real* rho, // parametre de variance renormalisé, calculé par l'EM
22 Real* pi, // parametre des proportions renormalisé, calculé par l'EM
23 Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
24 Real* S,
25 // additional size parameters
26 int n, // nombre d'echantillons
27 int p, // nombre de covariables
28 int m, // taille de Y (multivarié)
29 int k) // nombre de composantes dans le mélange
30 {
31 //Initialize outputs
32 copyArray(phiInit, phi, p*m*k);
33 copyArray(rhoInit, rho, m*m*k);
34 copyArray(piInit, pi, k);
35 zeroArray(LLF, maxi);
36 //S is already allocated, and doesn't need to be 'zeroed'
37
38 //Other local variables: same as in R
39 Real* gam = (Real*)malloc(n*k*sizeof(Real));
40 copyArray(gamInit, gam, n*k);
41 Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
42 Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
43 Real* b = (Real*)malloc(k*sizeof(Real));
44 Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
45 Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
46 Real dist = 0.;
47 Real dist2 = 0.;
48 int ite = 0;
49 Real* pi2 = (Real*)malloc(k*sizeof(Real));
50 Real* ps = (Real*)malloc(m*k*sizeof(Real));
51 Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
52 Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
53 Real* Gam = (Real*)malloc(n*k*sizeof(Real));
54 const Real EPS = 1e-15;
55 // Additional (not at this place, in R file)
56 Real* gam2 = (Real*)malloc(k*sizeof(Real));
57 Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
58 Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
59 gsl_matrix* matrix = gsl_matrix_alloc(m, m);
60 gsl_permutation* permutation = gsl_permutation_alloc(m);
61 Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
62 Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
63 const Real gaussConstM = pow(2.*M_PI,m/2.);
64 Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
65 Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
66 Real* Pi = (Real*)malloc(k*sizeof(Real));
67
68 while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
69 {
70 copyArray(phi, Phi, p*m*k);
71 copyArray(rho, Rho, m*m*k);
72 copyArray(pi, Pi, k);
73
74 // Calculs associés a Y et X
75 for (int r=0; r<k; r++)
76 {
77 for (int mm=0; mm<m; mm++)
78 {
79 //Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
80 for (int u=0; u<n; u++)
81 Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
82 }
83 for (int i=0; i<n; i++)
84 {
85 //X2[i,,r] = sqrt(gam[i,r]) * X[i,]
86 for (int u=0; u<p; u++)
87 X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
88 }
89 for (int mm=0; mm<m; mm++)
90 {
91 //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
92 for (int u=0; u<p; u++)
93 {
94 Real dotProduct = 0.;
95 for (int v=0; v<n; v++)
96 dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
97 ps2[ai(u,mm,r,p,m,k)] = dotProduct;
98 }
99 }
100 for (int j=0; j<p; j++)
101 {
102 for (int s=0; s<p; s++)
103 {
104 //Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
105 Real dotProduct = 0.;
106 for (int u=0; u<n; u++)
107 dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
108 Gram2[ai(j,s,r,p,p,k)] = dotProduct;
109 }
110 }
111 }
112
113 /////////////
114 // Etape M //
115 /////////////
116
117 // Pour pi
118 for (int r=0; r<k; r++)
119 {
120 //b[r] = sum(abs(phi[,,r]))
121 Real sumAbsPhi = 0.;
122 for (int u=0; u<p; u++)
123 for (int v=0; v<m; v++)
124 sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
125 b[r] = sumAbsPhi;
126 }
127 //gam2 = colSums(gam)
128 for (int u=0; u<k; u++)
129 {
130 Real sumOnColumn = 0.;
131 for (int v=0; v<n; v++)
132 sumOnColumn += gam[mi(v,u,n,k)];
133 gam2[u] = sumOnColumn;
134 }
135 //a = sum(gam %*% log(pi))
136 Real a = 0.;
137 for (int u=0; u<n; u++)
138 {
139 Real dotProduct = 0.;
140 for (int v=0; v<k; v++)
141 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
142 a += dotProduct;
143 }
144
145 //tant que les proportions sont negatives
146 int kk = 0;
147 int pi2AllPositive = 0;
148 Real invN = 1./n;
149 while (!pi2AllPositive)
150 {
151 //pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
152 Real pow_01_kk = pow(0.1,kk);
153 for (int r=0; r<k; r++)
154 pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
155 //pi2AllPositive = all(pi2 >= 0)
156 pi2AllPositive = 1;
157 for (int r=0; r<k; r++)
158 {
159 if (pi2[r] < 0)
160 {
161 pi2AllPositive = 0;
162 break;
163 }
164 }
165 kk++;
166 }
167
168 //(pi.^gamma)*b
169 Real piPowGammaDotB = 0.;
170 for (int v=0; v<k; v++)
171 piPowGammaDotB += pow(pi[v],gamma) * b[v];
172 //(pi2.^gamma)*b
173 Real pi2PowGammaDotB = 0.;
174 for (int v=0; v<k; v++)
175 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
176 //transpose(gam2)*log(pi2)
177 Real prodGam2logPi2 = 0.;
178 for (int v=0; v<k; v++)
179 prodGam2logPi2 += gam2[v] * log(pi2[v]);
180 //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
181 while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
182 && kk<1000)
183 {
184 Real pow_01_kk = pow(0.1,kk);
185 //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
186 for (int v=0; v<k; v++)
187 pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
188 //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
189 pi2PowGammaDotB = 0.;
190 for (int v=0; v<k; v++)
191 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
192 prodGam2logPi2 = 0.;
193 for (int v=0; v<k; v++)
194 prodGam2logPi2 += gam2[v] * log(pi2[v]);
195 kk++;
196 }
197 Real t = pow(0.1,kk);
198 //sum(pi + t*(pi2-pi))
199 Real sumPiPlusTbyDiff = 0.;
200 for (int v=0; v<k; v++)
201 sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
202 //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
203 for (int v=0; v<k; v++)
204 pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
205
206 //Pour phi et rho
207 for (int r=0; r<k; r++)
208 {
209 for (int mm=0; mm<m; mm++)
210 {
211 for (int i=0; i<n; i++)
212 {
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 //ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
218 ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
219 nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
220 }
221 //ps[mm,r] = sum(ps1[,mm,r])
222 Real sumPs1 = 0.;
223 for (int u=0; u<n; u++)
224 sumPs1 += ps1[ai(u,mm,r,n,m,k)];
225 ps[mi(mm,r,m,k)] = sumPs1;
226 //nY2[mm,r] = sum(nY21[,mm,r])
227 Real sumNy21 = 0.;
228 for (int u=0; u<n; u++)
229 sumNy21 += nY21[ai(u,mm,r,n,m,k)];
230 nY2[mi(mm,r,m,k)] = sumNy21;
231 //rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r]))) / (2*nY2[mm,r])
232 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)]
233 + 4*nY2[mi(mm,r,m,k)] * gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
234 }
235 }
236 for (int r=0; r<k; r++)
237 {
238 for (int j=0; j<p; j++)
239 {
240 for (int mm=0; mm<m; mm++)
241 {
242 //sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
243 Real dotPhiGram2 = 0.0;
244 for (int u=0; u<p; u++)
245 {
246 if (u != j)
247 dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
248 }
249 //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
250 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;
251 Real pow_pir_gamma = pow(pi[r],gamma);
252 if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow_pir_gamma)
253 phi[ai(j,mm,r,p,m,k)] = 0;
254 else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow_pir_gamma)
255 {
256 phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow_pir_gamma - S[ai(j,mm,r,p,m,k)])
257 / Gram2[ai(j,j,r,p,p,k)];
258 }
259 else
260 {
261 phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow_pir_gamma + S[ai(j,mm,r,p,m,k)])
262 / Gram2[ai(j,j,r,p,p,k)];
263 }
264 }
265 }
266 }
267
268 /////////////
269 // Etape E //
270 /////////////
271
272 int signum;
273 Real sumLogLLF2 = 0.;
274 for (int i=0; i<n; i++)
275 {
276 for (int r=0; r<k; r++)
277 {
278 //compute Y[i,]%*%rho[,,r]
279 for (int u=0; u<m; u++)
280 {
281 YiRhoR[u] = 0.;
282 for (int v=0; v<m; v++)
283 YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
284 }
285
286 //compute X(i,:)*phi(:,:,r)
287 for (int u=0; u<m; u++)
288 {
289 XiPhiR[u] = 0.;
290 for (int v=0; v<p; v++)
291 XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
292 }
293
294 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
295 sqNorm2[r] = 0.;
296 for (int u=0; u<m; u++)
297 sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
298 }
299
300 Real sumLLF1 = 0.;
301 Real sumGamI = 0.;
302 for (int r=0; r<k; r++)
303 {
304 //compute det(rho[,,r]) [TODO: avoid re-computations]
305 for (int u=0; u<m; u++)
306 {
307 for (int v=0; v<m; v++)
308 matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
309 }
310 gsl_linalg_LU_decomp(matrix, permutation, &signum);
311 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
312 Gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRhoR;
313 sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
314 sumGamI += Gam[mi(i,r,n,k)];
315 }
316 sumLogLLF2 += log(sumLLF1);
317 for (int r=0; r<k; r++)
318 {
319 //gam[i,] = Gam[i,] / sumGamI
320 gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
321 }
322 }
323
324 //sumPen = sum(pi^gamma * b)
325 Real sumPen = 0.;
326 for (int r=0; r<k; r++)
327 sumPen += pow(pi[r],gamma) * b[r];
328 //LLF[ite] = -sumLogLLF2/n + lambda*sumPen
329 LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
330 dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1. + fabs(LLF[ite]));
331
332 //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
333 Real Dist1 = 0.;
334 for (int u=0; u<p; u++)
335 {
336 for (int v=0; v<m; v++)
337 {
338 for (int w=0; w<k; w++)
339 {
340 Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
341 / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
342 if (tmpDist > Dist1)
343 Dist1 = tmpDist;
344 }
345 }
346 }
347 //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
348 Real Dist2 = 0.;
349 for (int u=0; u<m; u++)
350 {
351 for (int v=0; v<m; v++)
352 {
353 for (int w=0; w<k; w++)
354 {
355 Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
356 / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
357 if (tmpDist > Dist2)
358 Dist2 = tmpDist;
359 }
360 }
361 }
362 //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
363 Real Dist3 = 0.;
364 for (int u=0; u<n; u++)
365 {
366 for (int v=0; v<k; v++)
367 {
368 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
369 if (tmpDist > Dist3)
370 Dist3 = tmpDist;
371 }
372 }
373 //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
374 dist2 = Dist1;
375 if (Dist2 > dist2)
376 dist2 = Dist2;
377 if (Dist3 > dist2)
378 dist2 = Dist3;
379
380 ite++;
381 }
382
383 //free memory
384 free(b);
385 free(gam);
386 free(Gam);
387 free(Phi);
388 free(Rho);
389 free(Pi);
390 free(ps);
391 free(nY2);
392 free(ps1);
393 free(nY21);
394 free(Gram2);
395 free(ps2);
396 gsl_matrix_free(matrix);
397 gsl_permutation_free(permutation);
398 free(XiPhiR);
399 free(YiRhoR);
400 free(gam2);
401 free(pi2);
402 free(X2);
403 free(Y2);
404 free(sqNorm2);
405 }