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fix arrays reading in C, add type Real for double or float
[valse.git] / src / sources / EMGLLF.c
... / ...
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1#include "utils.h"
2#include <stdlib.h>
3#include <gsl/gsl_linalg.h>
4
5// TODO: don't recompute indexes every time......
6void 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
39 //NOTE: variables order is always [maxi],n,p,m,k
40 Real* gam = (Real*)malloc(n*k*sizeof(Real));
41 copyArray(gamInit, gam, n*k);
42 Real* b = (Real*)malloc(k*sizeof(Real));
43 Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
44 Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
45 Real* Pi = (Real*)malloc(k*sizeof(Real));
46 Real* gam2 = (Real*)malloc(k*sizeof(Real));
47 Real* pi2 = (Real*)malloc(k*sizeof(Real));
48 Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
49 Real* ps = (Real*)malloc(m*k*sizeof(Real));
50 Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
51 Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
52 Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
53 Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
54 Real* Gam = (Real*)malloc(n*k*sizeof(Real));
55 Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
56 Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
57 gsl_matrix* matrix = gsl_matrix_alloc(m, m);
58 gsl_permutation* permutation = gsl_permutation_alloc(m);
59 Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
60 Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
61 Real dist = 0.;
62 Real dist2 = 0.;
63 int ite = 0;
64 Real EPS = 1e-15;
65 Real* dotProducts = (Real*)malloc(k*sizeof(Real));
66
67 while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
68 {
69 copyArray(phi, Phi, p*m*k);
70 copyArray(rho, Rho, m*m*k);
71 copyArray(pi, Pi, k);
72
73 // Calculs associés a Y et X
74 for (int r=0; r<k; r++)
75 {
76 for (int mm=0; mm<m; mm++)
77 {
78 //Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
79 for (int u=0; u<n; u++)
80 Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
81 }
82 for (int i=0; i<n; i++)
83 {
84 //X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
85 for (int u=0; u<p; u++)
86 X2[ai(i,u,r,n,m,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
87 }
88 for (int mm=0; mm<m; mm++)
89 {
90 //ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
91 for (int u=0; u<p; u++)
92 {
93 Real dotProduct = 0.;
94 for (int v=0; v<n; v++)
95 dotProduct += X2[ai(v,u,r,n,m,k)] * Y2[ai(v,mm,r,n,m,k)];
96 ps2[ai(u,mm,r,n,m,k)] = dotProduct;
97 }
98 }
99 for (int j=0; j<p; j++)
100 {
101 for (int s=0; s<p; s++)
102 {
103 //Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
104 Real dotProduct = 0.;
105 for (int u=0; u<n; u++)
106 dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
107 Gram2[ai(j,s,r,p,p,k)] = dotProduct;
108 }
109 }
110 }
111
112 /////////////
113 // Etape M //
114 /////////////
115
116 // Pour pi
117 for (int r=0; r<k; r++)
118 {
119 //b(r) = sum(sum(abs(phi(:,:,r))));
120 Real sumAbsPhi = 0.;
121 for (int u=0; u<p; u++)
122 for (int v=0; v<m; v++)
123 sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
124 b[r] = sumAbsPhi;
125 }
126 //gam2 = sum(gam,1);
127 for (int u=0; u<k; u++)
128 {
129 Real sumOnColumn = 0.;
130 for (int v=0; v<n; v++)
131 sumOnColumn += gam[mi(v,u,n,k)];
132 gam2[u] = sumOnColumn;
133 }
134 //a=sum(gam*transpose(log(pi)));
135 Real a = 0.;
136 for (int u=0; u<n; u++)
137 {
138 Real dotProduct = 0.;
139 for (int v=0; v<k; v++)
140 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
141 a += dotProduct;
142 }
143
144 //tant que les proportions sont negatives
145 int kk = 0;
146 int pi2AllPositive = 0;
147 Real invN = 1./n;
148 while (!pi2AllPositive)
149 {
150 //pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
151 for (int r=0; r<k; r++)
152 pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
153 pi2AllPositive = 1;
154 for (int r=0; r<k; r++)
155 {
156 if (pi2[r] < 0)
157 {
158 pi2AllPositive = 0;
159 break;
160 }
161 }
162 kk++;
163 }
164
165 //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
166 //(pi.^gamma)*b
167 Real piPowGammaDotB = 0.;
168 for (int v=0; v<k; v++)
169 piPowGammaDotB += pow(pi[v],gamma) * b[v];
170 //(pi2.^gamma)*b
171 Real pi2PowGammaDotB = 0.;
172 for (int v=0; v<k; v++)
173 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
174 //transpose(gam2)*log(pi2)
175 Real prodGam2logPi2 = 0.;
176 for (int v=0; v<k; v++)
177 prodGam2logPi2 += gam2[v] * log(pi2[v]);
178 while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
179 && kk<1000)
180 {
181 //pi2=pi+0.1^kk*(1/n*gam2-pi);
182 for (int v=0; v<k; v++)
183 pi2[v] = pi[v] + pow(0.1,kk) * (invN*gam2[v] - pi[v]);
184 //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
185 pi2PowGammaDotB = 0.;
186 for (int v=0; v<k; v++)
187 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
188 prodGam2logPi2 = 0.;
189 for (int v=0; v<k; v++)
190 prodGam2logPi2 += gam2[v] * log(pi2[v]);
191 kk++;
192 }
193 Real t = pow(0.1,kk);
194 //sum(pi+t*(pi2-pi))
195 Real sumPiPlusTbyDiff = 0.;
196 for (int v=0; v<k; v++)
197 sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
198 //pi=(pi+t*(pi2-pi))/sum(pi+t*(pi2-pi));
199 for (int v=0; v<k; v++)
200 pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
201
202 //Pour phi et rho
203 for (int r=0; r<k; r++)
204 {
205 for (int mm=0; mm<m; mm++)
206 {
207 for (int i=0; i<n; i++)
208 {
209 //< X2(i,:,r) , phi(:,mm,r) >
210 Real dotProduct = 0.0;
211 for (int u=0; u<p; u++)
212 dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,n,m,k)];
213 //ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
214 ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
215 nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
216 }
217 //ps(mm,r)=sum(ps1(:,mm,r));
218 Real sumPs1 = 0.0;
219 for (int u=0; u<n; u++)
220 sumPs1 += ps1[ai(u,mm,r,n,m,k)];
221 ps[mi(mm,r,m,k)] = sumPs1;
222 //nY2(mm,r)=sum(nY21(:,mm,r));
223 Real sumNy21 = 0.0;
224 for (int u=0; u<n; u++)
225 sumNy21 += nY21[ai(u,mm,r,n,m,k)];
226 nY2[mi(mm,r,m,k)] = sumNy21;
227 //rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
228 rho[ai(mm,mm,k,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
229 + 4*nY2[mi(mm,r,m,k)] * (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
230 }
231 }
232 for (int r=0; r<k; r++)
233 {
234 for (int j=0; j<p; j++)
235 {
236 for (int mm=0; mm<m; mm++)
237 {
238 //sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r)
239 // .*transpose(Gram2(j,j+1:p,r)))
240 Real dotPhiGram2 = 0.0;
241 for (int u=0; u<j; u++)
242 dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
243 for (int u=j+1; u<p; u++)
244 dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
245 //S(j,r,mm)=-rho(mm,mm,r)*ps2(j,mm,r)+sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))
246 // +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
247 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;
248 if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow(pi[r],gamma))
249 phi[ai(j,mm,r,p,m,k)] = 0;
250 else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow(pi[r],gamma))
251 phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow(pi[r],gamma) - S[ai(j,mm,r,p,m,k)])
252 / Gram2[ai(j,j,r,p,p,k)];
253 else
254 phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)])
255 / Gram2[ai(j,j,r,p,p,k)];
256 }
257 }
258 }
259
260 /////////////
261 // Etape E //
262 /////////////
263
264 int signum;
265 Real sumLogLLF2 = 0.0;
266 for (int i=0; i<n; i++)
267 {
268 Real sumLLF1 = 0.0;
269 Real sumGamI = 0.0;
270 Real minDotProduct = INFINITY;
271
272 for (int r=0; r<k; r++)
273 {
274 //Compute
275 //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
276 // *phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
277 //split in several sub-steps
278
279 //compute Y(i,:)*rho(:,:,r)
280 for (int u=0; u<m; u++)
281 {
282 YiRhoR[u] = 0.0;
283 for (int v=0; v<m; v++)
284 YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
285 }
286
287 //compute X(i,:)*phi(:,:,r)
288 for (int u=0; u<m; u++)
289 {
290 XiPhiR[u] = 0.0;
291 for (int v=0; v<p; v++)
292 XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
293 }
294
295 //compute dotProduct
296 // < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
297 dotProducts[r] = 0.0;
298 for (int u=0; u<m; u++)
299 dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
300 if (dotProducts[r] < minDotProduct)
301 minDotProduct = dotProducts[r];
302 }
303 Real shift = 0.5*minDotProduct;
304 for (int r=0; r<k; r++)
305 {
306 //compute det(rho(:,:,r)) [TODO: avoid re-computations]
307 for (int u=0; u<m; u++)
308 {
309 for (int v=0; v<m; v++)
310 matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
311 }
312 gsl_linalg_LU_decomp(matrix, permutation, &signum);
313 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
314
315 Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
316 sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
317 sumGamI += Gam[mi(i,r,n,k)];
318 }
319 sumLogLLF2 += log(sumLLF1);
320 for (int r=0; r<k; r++)
321 {
322 //gam(i,r)=Gam(i,r)/sum(Gam(i,:));
323 gam[mi(i,r,n,k)] = sumGamI > EPS
324 ? Gam[mi(i,r,n,k)] / sumGamI
325 : 0.0;
326 }
327 }
328
329 //sum(pen(ite,:))
330 Real sumPen = 0.0;
331 for (int r=0; r<k; r++)
332 sumPen += pow(pi[r],gamma) * b[r];
333 //LLF(ite)=-1/n*sum(log(LLF2(ite,:)))+lambda*sum(pen(ite,:));
334 LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
335 if (ite == 0)
336 dist = LLF[ite];
337 else
338 dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
339
340 //Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
341 Real Dist1 = 0.0;
342 for (int u=0; u<p; u++)
343 {
344 for (int v=0; v<m; v++)
345 {
346 for (int w=0; w<k; w++)
347 {
348 Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
349 / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
350 if (tmpDist > Dist1)
351 Dist1 = tmpDist;
352 }
353 }
354 }
355 //Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
356 Real Dist2 = 0.0;
357 for (int u=0; u<m; u++)
358 {
359 for (int v=0; v<m; v++)
360 {
361 for (int w=0; w<k; w++)
362 {
363 Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
364 / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
365 if (tmpDist > Dist2)
366 Dist2 = tmpDist;
367 }
368 }
369 }
370 //Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
371 Real Dist3 = 0.0;
372 for (int u=0; u<n; u++)
373 {
374 for (int v=0; v<k; v++)
375 {
376 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
377 if (tmpDist > Dist3)
378 Dist3 = tmpDist;
379 }
380 }
381 //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
382 dist2 = Dist1;
383 if (Dist2 > dist2)
384 dist2 = Dist2;
385 if (Dist3 > dist2)
386 dist2 = Dist3;
387
388 ite++;
389 }
390
391 //free memory
392 free(b);
393 free(gam);
394 free(Gam);
395 free(Phi);
396 free(Rho);
397 free(Pi);
398 free(ps);
399 free(nY2);
400 free(ps1);
401 free(nY21);
402 free(Gram2);
403 free(ps2);
404 gsl_matrix_free(matrix);
405 gsl_permutation_free(permutation);
406 free(XiPhiR);
407 free(YiRhoR);
408 free(gam2);
409 free(pi2);
410 free(X2);
411 free(Y2);
412 free(dotProducts);
413}
Variable selection with mixtures of models