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Adjustments for CRAN upload
[valse.git] / pkg / src / EMGLLF.c
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1#include "utils.h"
2#include <stdlib.h>
3#include <math.h>
4#include <gsl/gsl_linalg.h>
5
6// TODO: don't recompute indexes ai(...) and mi(...) when possible
7void EMGLLF_core(
8 // IN parameters
9 const Real* phiInit, // parametre initial de moyenne renormalise
10 const Real* rhoInit, // parametre initial de variance renormalise
11 const Real* piInit, // parametre initial des proportions
12 const Real* gamInit, // parametre initial des probabilites a posteriori de chaque echantillon
13 int mini, // nombre minimal d'iterations dans l'algorithme EM
14 int maxi, // nombre maximal d'iterations dans l'algorithme EM
15 Real gamma, // puissance des proportions dans la penalisation pour un Lasso adaptatif
16 Real lambda, // valeur du parametre de regularisation du Lasso
17 const Real* X, // regresseurs
18 const Real* Y, // reponse
19 Real eps, // seuil pour accepter la convergence
20 // OUT parameters (all pointers, to be modified)
21 Real* phi, // parametre de moyenne renormalise, calcule par l'EM
22 Real* rho, // parametre de variance renormalise, calcule par l'EM
23 Real* pi, // parametre des proportions renormalise, calcule par l'EM
24 Real* llh, // (derniere) log vraisemblance associee a cet echantillon,
25 // pour les valeurs estimees des parametres
26 Real* S,
27 int* affec,
28 // additional size parameters
29 int n, // nombre d'echantillons
30 int p, // nombre de covariables
31 int m, // taille de Y (multivarie)
32 int k) // nombre de composantes dans le melange
33{
34 //Initialize outputs
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'
39
40 //Other local variables: same as in R
41 Real* gam = (Real*)malloc(n*k*sizeof(Real));
42 Real* logGam = (Real*)malloc(k*sizeof(Real));
43 copyArray(gamInit, gam, n*k);
44 Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
45 Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
46 Real* b = (Real*)malloc(k*sizeof(Real));
47 Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
48 Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
49 *llh = -INFINITY;
50 Real* pi2 = (Real*)malloc(k*sizeof(Real));
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));
63
64 for (int ite=1; ite<=maxi; ite++)
65 {
66 copyArray(phi, Phi, p*m*k);
67 copyArray(rho, Rho, m*m*k);
68 copyArray(pi, Pi, k);
69
70 // Calculs associes a Y et X
71 for (int r=0; r<k; r++)
72 {
73 for (int mm=0; mm<m; mm++)
74 {
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)];
78 }
79 for (int i=0; i<n; i++)
80 {
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)];
84 }
85 for (int mm=0; mm<m; mm++)
86 {
87 //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
88 for (int u=0; u<p; u++)
89 {
90 Real dotProduct = 0.;
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;
94 }
95 }
96 for (int j=0; j<p; j++)
97 {
98 for (int s=0; s<p; s++)
99 {
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;
105 }
106 }
107 }
108
109 /////////////
110 // Etape M //
111 /////////////
112
113 // Pour pi
114 for (int r=0; r<k; r++)
115 {
116 //b[r] = sum(abs(phi[,,r]))
117 Real sumAbsPhi = 0.;
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)]);
121 b[r] = sumAbsPhi;
122 }
123 //gam2 = colSums(gam)
124 for (int u=0; u<k; u++)
125 {
126 Real sumOnColumn = 0.;
127 for (int v=0; v<n; v++)
128 sumOnColumn += gam[mi(v,u,n,k)];
129 gam2[u] = sumOnColumn;
130 }
131 //a = sum(gam %*% log(pi))
132 Real a = 0.;
133 for (int u=0; u<n; u++)
134 {
135 Real dotProduct = 0.;
136 for (int v=0; v<k; v++)
137 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
138 a += dotProduct;
139 }
140
141 //tant que les proportions sont negatives
142 int kk = 0,
143 pi2AllPositive = 0;
144 Real invN = 1./n;
145 while (!pi2AllPositive)
146 {
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)
152 pi2AllPositive = 1;
153 for (int r=0; r<k; r++)
154 {
155 if (pi2[r] < 0)
156 {
157 pi2AllPositive = 0;
158 break;
159 }
160 }
161 kk++;
162 }
163
164 //sum(pi^gamma * b)
165 Real piPowGammaDotB = 0.;
166 for (int v=0; v<k; v++)
167 piPowGammaDotB += pow(pi[v],gamma) * b[v];
168 //sum(pi2^gamma * b)
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]);
176
177 //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit decroissante ou constante
178 while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
179 && kk<1000)
180 {
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];
189 gam2DotLogPi2 = 0.;
190 for (int v=0; v<k; v++)
191 gam2DotLogPi2 += gam2[v] * log(pi2[v]);
192 kk++;
193 }
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;
202
203 //Pour phi et rho
204 for (int r=0; r<k; r++)
205 {
206 for (int mm=0; mm<m; mm++)
207 {
208 Real ps = 0.,
209 nY2 = 0.;
210 // Compute ps, and nY2 = sum(Y2[,mm,r]^2)
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 //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)];
220 }
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);
223 }
224 }
225
226 for (int r=0; r<k; r++)
227 {
228 for (int j=0; j<p; j++)
229 {
230 for (int mm=0; mm<m; mm++)
231 {
232 //sum(phi[-j,mm,r] * Gram2[j,-j,r])
233 Real phiDotGram2 = 0.;
234 for (int u=0; u<p; u++)
235 {
236 if (u != j)
237 phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
238 }
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)]
241 + phiDotGram2;
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)
246 {
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)];
249 }
250 else
251 {
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)];
254 }
255 }
256 }
257 }
258
259 /////////////
260 // Etape E //
261 /////////////
262
263 // Precompute det(rho[,,r]) for r in 1...k
264 int signum;
265 for (int r=0; r<k; r++)
266 {
267 for (int u=0; u<m; u++)
268 {
269 for (int v=0; v<m; v++)
270 matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
271 }
272 gsl_linalg_LU_decomp(matrix, permutation, &signum);
273 detRho[r] = gsl_linalg_LU_det(matrix, signum);
274 }
275
276 Real sumLogLLH = 0.;
277 for (int i=0; i<n; i++)
278 {
279 for (int r=0; r<k; r++)
280 {
281 //compute Y[i,]%*%rho[,,r]
282 for (int u=0; u<m; u++)
283 {
284 YiRhoR[u] = 0.;
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)];
287 }
288
289 //compute X[i,]%*%phi[,,r]
290 for (int u=0; u<m; u++)
291 {
292 XiPhiR[u] = 0.;
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)];
295 }
296
297 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
298 sqNorm2[r] = 0.;
299 for (int u=0; u<m; u++)
300 sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
301 }
302
303 // Update gam[,]; use log to avoid numerical problems
304 Real maxLogGam = -INFINITY;
305 for (int r=0; r<k; r++)
306 {
307 logGam[r] = log(pi[r]) - .5 * sqNorm2[r] + log(detRho[r]);
308 if (maxLogGam < logGam[r])
309 maxLogGam = logGam[r];
310 }
311 Real norm_fact = 0.;
312 for (int r=0; r<k; r++)
313 {
314 logGam[r] = logGam[r] - maxLogGam; //adjust without changing proportions
315 gam[mi(i,r,n,k)] = exp(logGam[r]); //gam[i, ] <- exp(logGam)
316 norm_fact += gam[mi(i,r,n,k)]; //norm_fact <- sum(gam[i, ])
317 }
318 // gam[i, ] <- gam[i, ] / norm_fact
319 for (int r=0; r<k; r++)
320 gam[mi(i,r,n,k)] /= norm_fact;
321
322 sumLogLLH += log(norm_fact) - log(gaussConstM);
323 }
324
325 //sumPen = sum(pi^gamma * b)
326 Real sumPen = 0.;
327 for (int r=0; r<k; r++)
328 sumPen += pow(pi[r],gamma) * b[r];
329 Real last_llh = *llh;
330 //llh = -sumLogLLH/n #+ lambda*sumPen
331 *llh = -invN * sumLogLLH; //+ lambda * sumPen;
332 Real dist = ( ite==1 ? *llh : (*llh - last_llh) / (1. + fabs(*llh)) );
333
334 //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
335 Real Dist1 = 0.;
336 for (int u=0; u<p; u++)
337 {
338 for (int v=0; v<m; v++)
339 {
340 for (int w=0; w<k; w++)
341 {
342 Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
343 / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
344 if (tmpDist > Dist1)
345 Dist1 = tmpDist;
346 }
347 }
348 }
349 //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
350 Real Dist2 = 0.;
351 for (int u=0; u<m; u++)
352 {
353 for (int v=0; v<m; v++)
354 {
355 for (int w=0; w<k; w++)
356 {
357 Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
358 / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
359 if (tmpDist > Dist2)
360 Dist2 = tmpDist;
361 }
362 }
363 }
364 //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
365 Real Dist3 = 0.;
366 for (int u=0; u<n; u++)
367 {
368 for (int v=0; v<k; v++)
369 {
370 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
371 if (tmpDist > Dist3)
372 Dist3 = tmpDist;
373 }
374 }
375 //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
376 Real dist2 = Dist1;
377 if (Dist2 > dist2)
378 dist2 = Dist2;
379 if (Dist3 > dist2)
380 dist2 = Dist3;
381
382 if (ite >= mini && (dist >= eps || dist2 >= sqrt(eps)))
383 break;
384 }
385
386 //affec = apply(gam, 1, which.max)
387 for (int i=0; i<n; i++)
388 {
389 Real rowMax = 0.;
390 affec[i] = 0;
391 for (int j=0; j<k; j++)
392 {
393 if (gam[mi(i,j,n,k)] > rowMax)
394 {
395 affec[i] = j+1; //R indices start at 1
396 rowMax = gam[mi(i,j,n,k)];
397 }
398 }
399 }
400
401 //free memory
402 free(b);
403 free(gam);
404 free(logGam);
405 free(Phi);
406 free(Rho);
407 free(Pi);
408 free(Gram2);
409 free(ps2);
410 free(detRho);
411 gsl_matrix_free(matrix);
412 gsl_permutation_free(permutation);
413 free(XiPhiR);
414 free(YiRhoR);
415 free(gam2);
416 free(pi2);
417 free(X2);
418 free(Y2);
419 free(sqNorm2);
420}
Variable selection with mixtures of models