/* compute sum and diagonal of covariance matrix of a set of points (v) weighted by probabilities (p) */
static void compute_sum_dcov(int ni,int ki,int di,
const float *v,const float *mu_old,const float *p,
float *mu,float *sigma,float *w) {
long i,j,l;
FINTEGER n=ni,k=ki,d=di;
for (j = 0 ; j < k ; j++) {
double dtmp = 0;
for (i = 0 ; i < n ; i++) dtmp += p[i * k + j];
w[j] = dtmp;
}
float zero=0,one=1;
sgemm_("Not transposed","Transposed",&d,&k,&n,&one,v,&d,p,&k,&zero,mu,&d);
float *v2=fvec_new_cpy(v,n*(long)d);
fvec_sqr(v2,n*(long)d);
sgemm_("Not transposed","Transposed",&d,&k,&n,&one,v2,&d,p,&k,&zero,sigma,&d);
free(v2);
for (j = 0 ; j < k ; j++) {
float *sigma_j=sigma+j*d;
const float *mu_old_j=mu_old+j*d;
const float *mu_j=mu+j*d;
for(l=0; l<d; l++) {
sigma_j[l]+=mu_old_j[l]*(mu_old_j[l]*w[j]-2*mu_j[l]);
}
}
}
void pca_online_project (const pca_online_t * pca, const float * v, float * vo, int d, long n, int dout)
{
const char trmat[2] = {'T', 'N'};
float * vb = fvec_new_cpy (v, n*d);
assert (d == pca->d);
fmat_subtract_from_columns (pca->d, n, vb, pca->mu);
fmat_mul_full (pca->eigvec, vb, dout, n, pca->d, trmat, vo);
free (vb);
}
float *fmat_center_columns(int d,int n,float *v)
{
assert(n>0);
float *accu=fvec_new_cpy(v,d);
long i;
for(i=1;i<n;i++)
fvec_add(accu,v+i*d,d);
fvec_div_by(accu,d,n);
for(i=0;i<n;i++)
fvec_sub(v+i*d,accu,d);
return accu;
}
/* estimate the GMM parameters */
static void gmm_compute_params (int n, const float * v, const float * p,
gmm_t * g,
int flags,
int n_thread)
{
long i, j;
long d=g->d, k=g->k;
float * vtmp = fvec_new (d);
float * mu_old = fvec_new_cpy (g->mu, k * d);
float * w_old = fvec_new_cpy (g->w, k);
fvec_0 (g->w, k);
fvec_0 (g->mu, k * d);
fvec_0 (g->sigma, k * d);
if(0) {
/* slow and simple */
for (j = 0 ; j < k ; j++) {
double dtmp = 0;
for (i = 0 ; i < n ; i++) {
/* contribution to the gaussian weight */
dtmp += p[i * k + j];
/* contribution to mu */
fvec_cpy (vtmp, v + i * d, d);
fvec_mul_by (vtmp, d, p[i * k + j]);
fvec_add (g->mu + j * d, vtmp, d);
/* contribution to the variance */
fvec_cpy (vtmp, v + i * d, d);
fvec_sub (vtmp, mu_old + j * d, d);
fvec_sqr (vtmp, d);
fvec_mul_by (vtmp, d, p[i * k + j]);
fvec_add (g->sigma + j * d, vtmp, d);
}
g->w[j] = dtmp;
}
} else {
/* fast and complicated */
if(n_thread<=1)
compute_sum_dcov(n,k,d,v,mu_old,p,g->mu,g->sigma,g->w);
else
compute_sum_dcov_thread(n,k,d,v,mu_old,p,g->mu,g->sigma,g->w,n_thread);
}
if(flags & GMM_FLAGS_1SIGMA) {
for (j = 0 ; j < k ; j++) {
float *sigma_j=g->sigma+j*d;
double var=fvec_sum(sigma_j,d)/d;
fvec_set(sigma_j,d,var);
}
}
long nz=0;
for(i=0; i<k*d; i++)
if(g->sigma[i]<min_sigma) {
g->sigma[i]=min_sigma;
nz++;
}
if(nz) printf("WARN %ld sigma diagonals are too small (set to %g)\n",nz,min_sigma);
for (j = 0 ; j < k ; j++) {
fvec_div_by (g->mu + j * d, d, g->w[j]);
fvec_div_by (g->sigma + j * d, d, g->w[j]);
}
assert(finite(fvec_sum(g->mu, k*d)));
fvec_normalize (g->w, k, 1);
printf ("w = ");
fvec_print (g->w, k);
double imfac = k * fvec_sum_sqr (g->w, k);
printf (" imfac = %.3f\n", imfac);
free (vtmp);
free (w_old);
free (mu_old);
}