void sample_extremes(T const (&est_p)[A][B][C], T const (&err_p)[A][B][C], T (&out_p)[A][B][C])
{
vector<int> permutation;
for (int i = 0; i < A; ++i)
{
for (int j = 0; j < B; ++j)
{
// use a random ordering to get an extreme point here
sample_permutation(C, permutation);
// first set the elements to the lower bounds to give some leeway
T lsum = 0;
for (int k = 0; k < C; ++k)
{
T lb = max(0.0, est_p[i][j][k] - err_p[i][j][k]);
out_p[i][j][k] = lb;
lsum += lb;
}
// then give as much weight as possible to each of the picks in turn
T leeway = 1 - lsum;
for (int k = 0; k < C; ++k)
{
if (leeway <= 0)
{
break; // done
}
int curr_ix = permutation[k];
T ub = min(1.0, est_p[i][j][curr_ix] + err_p[i][j][curr_ix]);
T avail = min(leeway, ub - out_p[i][j][curr_ix]);
out_p[i][j][curr_ix] += avail;
leeway -= avail;
}
}
}
}
void gr_KL_V_psi2_n (const gsl_vector *v_V_psi2_n, void * null, gsl_vector *df)
{
int i, p=*params->p, j, pe;
int D = *params->D;
double tmp1=0.0, cov=0.0, cov2;
int N = *params->N;
int P_e = *params->P_e;
double KL;
int *sample_non_edges = calloc(*params->NnonE, sizeof(int));
int NC1;
params->V_psi2_n[*params->p] = gsl_vector_get(v_V_psi2_n, 0);
KL = 0.0;
for (i = 0; i < *params->NE; i++) // loop over all edges
{
if (*params->imodel==1)
cov = params->V_xi_n[(params->E[i*2]-1)];
if (*params->imodel==2)
cov = params->V_xi_n[(params->E[i*2+1]-1)];
if (*params->imodel==3)
cov = params->V_xi_n[(params->E[i*2]-1)] + params->V_xi_n[N+(params->E[i*2+1]-1)];
cov2 = params->V_psi2_n[p];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[((params->E[i*2]-1)*N + params->E[i*2+1]-1)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[((params->E[i*2]-1)*N + params->E[i*2+1]-1)* P_e + pe];
}
tmp1 += -0.5/(1.0+exp(-cov + params->dists[((params->E[i*2]-1)*N + params->E[i*2+1]-1)] - 0.5*cov2));
}
sample_permutation(*params->NnonE, sample_non_edges, params->seed);
NC1=MIN(*params->NnonE, (int)(*params->NC* *params->NE));
for (j=0;j<NC1;j++) // loop over a sample of the non-edges
{
i=sample_non_edges[j];
if (*params->imodel==1)
cov = params->V_xi_n[(params->nonE[i*2]-1)];
if (*params->imodel==2)
cov = params->V_xi_n[(params->nonE[i*2+1]-1)];
if (*params->imodel==3)
cov = params->V_xi_n[(params->nonE[i*2]-1)] + params->V_xi_n[N+(params->nonE[i*2+1]-1)];
cov2= params->V_psi2_n[p];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)* P_e + pe];
}
tmp1 += *params->NnonE/NC1*(-0.5/(1.0+exp(-cov + params->dists[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)] - 0.5*cov2)));
}
KL = tmp1 + 0.5 * (D / params->V_psi2_n[*params->p] - D / *params->psi2);
gsl_vector_set(df, 0, -KL);
free(sample_non_edges);
return;
}
void gr_KL_V_xi_e (const gsl_vector *v_V_xi_e, void *null, gsl_vector *df)
{
int i, j, p=*params->p, pn;
int P_e=*params->P_e, P_n=*params->P_n;
params->V_xi_e[p] = gsl_vector_get(v_V_xi_e, 0);
double tmpsum = 0.0, cov, cov2;
int N = *params->N;
double KL;
int *sample_non_edges = calloc(*params->NnonE, sizeof(int));
int NC1;
for (i = 0; i < *params->NE; i++) // loop over all edges
{
cov = params->V_xi_e[p]*params->XX_e[((params->E[i*2]-1)*N + params->E[i*2+1]-1)* P_e + p];
cov2= params->V_psi2_e[p]*params->XX_e[((params->E[i*2]-1)*N + params->E[i*2+1]-1)* P_e + p];
if (*params->imodel==1)
cov += params->V_xi_n[(params->E[i*2]-1)];
if (*params->imodel==2)
cov += params->V_xi_n[(params->E[i*2+1]-1)];
if (*params->imodel==3)
cov += params->V_xi_n[(params->E[i*2]-1)] + params->V_xi_n[N+(params->E[i*2+1]-1)];
for (pn=0;pn<P_n;pn++)
cov2+= params->V_psi2_n[pn];
tmpsum += params->XX_e[((params->E[i*2]-1)*N + params->E[i*2+1]-1)* P_e + p]*
(1.0 - 1.0/(1.0 + exp (-cov + params->dists[((params->E[i*2]-1)*N + params->E[i*2+1]-1)] - 0.5 * cov2)));
}
sample_permutation(*params->NnonE, sample_non_edges, params->seed);
NC1=MIN(*params->NnonE, (int)(*params->NC* *params->NE));
for (j=0;j<NC1;j++) // loop over a sample of the non-edges
{
i=sample_non_edges[j];
cov = params->V_xi_e[p]*params->XX_e[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)* P_e + p];
cov2= params->V_psi2_e[p]*params->XX_e[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)* P_e + p];
if (*params->imodel==1)
cov += params->V_xi_n[(params->nonE[i*2]-1)];
if (*params->imodel==2)
cov += params->V_xi_n[(params->nonE[i*2+1]-1)];
if (*params->imodel==3)
cov += params->V_xi_n[(params->nonE[i*2]-1)] + params->V_xi_n[N+(params->nonE[i*2+1]-1)];
for (pn=0;pn<P_n;pn++)
cov2+= params->V_psi2_n[pn];
tmpsum += *params->NnonE/NC1*(params->XX_e[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)* P_e + p]*
(- 1.0/(1.0 + exp (-cov + params->dists[((params->nonE[i*2]-1)*N + params->nonE[i*2+1]-1)] - 0.5 * cov2))));
}
KL = tmpsum - 0.5*(params->V_xi_e[p] - *params->xi) / *params->psi2;
free(sample_non_edges);
gsl_vector_set(df, 0, -KL);
return;
}
void gr_KL_V_xi_n (const gsl_vector *v_V_xi_n, void *null, gsl_vector *df)
{
int i=*params->i, p=*params->p, P_e=*params->P_e, j, pe;
int N = *params->N;
params->V_xi_n[i+N*p] = gsl_vector_get(v_V_xi_n, 0);
double tmpsum = 0.0, cov=0.0, cov2;
int *sample_nodes, hsum, h, Nnon, k;
double KL;
int diam=*params->diam;
int NC2;
for (j = 2+diam; j < params->hopslist[i*(CONST+diam+N)+1]+2+diam; j++) // loop over all edges
{
// i->j part
cov2 = 0.0;
if (*params->imodel==1)
cov = params->V_xi_n[i];
if (*params->imodel==2)
cov = params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==3)
cov = params->V_xi_n[i] + params->V_xi_n[N+(params->hopslist[i*(CONST+diam+N)+j]-1)];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[(i*N + params->hopslist[i*(CONST+diam+N)+j]-1)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[(i*N + params->hopslist[i*(CONST+diam+N)+j]-1)* P_e + pe];
}
cov2 += params->V_psi2_n[0];
if (*params->imodel==3)
cov2 += params->V_psi2_n[1];
tmpsum += (params->Y[i*N+(params->hopslist[i*(CONST+diam+N)+j]-1)] -
1.0/(1.0 + exp (-cov + params->dists[i*N + (params->hopslist[i*(CONST+diam+N)+j]-1)] - 0.5 * cov2)));
// j->i part
cov2 = 0.0;
if (*params->imodel==1)
cov = params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==2)
cov = params->V_xi_n[i];
if (*params->imodel==3)
cov = params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)] + params->V_xi_n[N+i];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* P_e + pe];
}
cov2 += params->V_psi2_n[0];
if (*params->imodel==3)
cov2 += params->V_psi2_n[1];
tmpsum += (params->Y[(params->hopslist[i*(CONST+diam+N)+j]-1)*N+i] -
1.0/(1.0 + exp (-cov + params->dists[(params->hopslist[i*(CONST+diam+N)+j]-1)*N+i] - 0.5 * cov2)));
}
hsum = 0;
for (h=2;h<1+diam;h++) // <1+diam because we don't sample unknown edges
{
Nnon=params->hopslist[i*(CONST+diam+N)+h];
if (Nnon>0)
{
sample_nodes = calloc(Nnon, sizeof(int));
sample_permutation(Nnon, sample_nodes, params->seed);
NC2=MIN(Nnon, (int)(*params->NC*params->hopslist[i*(CONST+diam+N)+1]));
for (k=0;k<NC2;k++) // loop over some of the non-edges
{
j=params->hopslist[i*(CONST+diam+N)+2+diam+params->hopslist[i*(CONST+diam+N)+1]+hsum+sample_nodes[k]]-1;
// this part for Yij = 0
if (*params->imodel==1)
cov = params->V_xi_n[i];
if (*params->imodel==2)
cov = params->V_xi_n[j];
if (*params->imodel==3)
cov = params->V_xi_n[i] + params->V_xi_n[N+j];
cov2 = params->V_psi2_n[0];
if (*params->imodel==3)
cov2 += params->V_psi2_n[1];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[(i*N + j)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[(i*N + j)* P_e + pe];
}
tmpsum += Nnon/NC2*(- 1.0/(1.0 + exp (-cov + params->dists[i*N + j] - 0.5 * cov2)));
// this part for Yji = 0
if (*params->imodel==1)
cov = params->V_xi_n[j];
if (*params->imodel==2)
cov = params->V_xi_n[i];
if (*params->imodel==3)
cov = params->V_xi_n[N+i] + params->V_xi_n[j];
cov2 = params->V_psi2_n[0];
if (*params->imodel==3)
cov2 += params->V_psi2_n[1];
for (pe=0;pe<P_e;pe++)
{
cov += params->V_xi_e[pe]*params->XX_e[(j*N + i)* P_e + pe];
cov2+= params->V_psi2_e[pe]*params->XX_e[(j*N + i)* P_e + pe];
}
tmpsum += Nnon/NC2*(- 1.0/(1.0 + exp (-cov + params->dists[i*N + j] - 0.5 * cov2)));
}
hsum += Nnon;
free(sample_nodes);
}
}
KL = tmpsum - 0.5*(params->V_xi_n[i+N*p] - *params->xi) / *params->psi2;
gsl_vector_set(df, 0, -KL);
return;
}
void gr_KL_V_sigma2_i (const gsl_vector *v_V_sigma2_i, void *null, gsl_vector *df)
{
int i = *params->i, j, k, d = *params->d;
int D = *params->D;
int g, G = *params->G, hsum, h;
double tmpsum = 0.0, tmp;
int p, N = *params->N;
int diam=*params->diam;
int P_n=*params->P_n;
double KL;
double cov, cov2;
double V_sigma2_i = gsl_vector_get(v_V_sigma2_i, 0);
int Nnon=N-params->hopslist[i*(CONST+diam+N)+1]-params->hopslist[i*(CONST+diam+N)+1+diam];
int *sample_nodes = 0;
int NC2;
for (j = 2+diam; j < params->hopslist[i*(CONST+diam+N)+1]+2+diam; j++) // loop over all edges
{
tmp = 0.0;
for (d = 0; d < D; d++)
tmp += pow (params->V_z[i * D + d] - params->V_z[(params->hopslist[i*(CONST+diam+N)+j]-1) * D + d], 2.0);
cov=0.0; cov2=0.0;
if (params->Y[i*N+(params->hopslist[i*(CONST+diam+N)+j]-1)]>0) // i is sender and j is receiver
{
if (*params->imodel==1)
cov += params->V_xi_n[i];
if (*params->imodel==2)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==3)
cov += params->V_xi_n[i] + params->V_xi_n[N+(params->hopslist[i*(CONST+diam+N)+j]-1)];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[(i*N + (params->hopslist[i*(CONST+diam+N)+j]-1))* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[(i*N + (params->hopslist[i*(CONST+diam+N)+j]-1))* *params->P_e + p];
}
}
if (params->Y[(params->hopslist[i*(CONST+diam+N)+j]-1)*N+i]>0) // j is sender and i is receiver
{
if (*params->imodel==1)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==2)
cov += params->V_xi_n[i];
if (*params->imodel==3)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)] + params->V_xi_n[N+i];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* *params->P_e + p];
}
}
for (p=0;p<P_n;p++)
cov2+= params->V_psi2_n[p];
tmp = SQRT (tmp + D * (V_sigma2_i + params->V_sigma2[(params->hopslist[i*(CONST+diam+N)+j]-1)]));
tmpsum = tmpsum - D + D / (V_sigma2_i * (1.0 + exp (-cov + tmp - 0.5 * cov2)));
}
hsum = 0;
for (h=2;h<1+diam;h++) // <1+diam because we don't sample unknown edges
{
Nnon=params->hopslist[i*(CONST+diam+N)+h];
if (Nnon>0)
{
sample_nodes = calloc(Nnon, sizeof(int));
sample_permutation(Nnon, sample_nodes, params->seed);
NC2=MIN(Nnon, (int)(*params->NC*params->hopslist[i*(CONST+diam+N)+1]));
for (k=0;k<NC2;k++) // loop over some of the non-edges
{
j=params->hopslist[i*(CONST+diam+N)+2+diam+params->hopslist[i*(CONST+diam+N)+1]+hsum+sample_nodes[k]]-1;
tmp = 0.0;
for (d = 0; d < D; d++)
tmp += pow (params->V_z[i * D + d] - params->V_z[j * D + d], 2.0);
cov=0.0; cov2=0.0;
if (*params->imodel==1)
cov += params->V_xi_n[i];
if (*params->imodel==2)
cov += params->V_xi_n[j];
if (*params->imodel==3)
cov += params->V_xi_n[i] + params->V_xi_n[N+j];
for (p=0;p<P_n;p++)
cov2+= params->V_psi2_n[p];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[(i*N + j)* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[(i*N + j)* *params->P_e + p];
}
tmp = SQRT (tmp + D * (V_sigma2_i + params->V_sigma2[j]));
tmpsum = tmpsum + Nnon/NC2*(D / (V_sigma2_i * (1.0 + exp (-cov + tmp - 0.5 * cov2))));
}
hsum += Nnon;
free(sample_nodes);
}
}
tmp = 0.0;
for (g = 0; g < G; g++)
tmp += params->V_lambda[g * N + i] * *params->inv_sigma02 * params->V_alpha[g];
KL = tmpsum - 0.5 * tmp + 0.5 * D / V_sigma2_i;
gsl_vector_set(df, 0, -KL);
return;
}
void gr_KL_V_z_i (const gsl_vector *v_V_z_i, void *null, gsl_vector *df)
{
int i = *params->i, j, k, d;
int D = *params->D;
double tmp;
for (d=0; d<D; d++)
params->V_z[i * D + d] = gsl_vector_get(v_V_z_i, d);
int g, p, G = *params->G;
int N = *params->N, h, Nnon, hsum;
int diam=*params->diam;
int P_n=*params->P_n;
double *KL = calloc(D, sizeof(double));
double *tmpsum = calloc(D, sizeof(double));
double cov, cov2;
int *sample_nodes;
int NC2;
for (j = 2+diam; j < params->hopslist[i*(CONST+diam+N)+1]+2+diam; j++) // loop over all edges
{
tmp = 0.0;
for (d=0; d<D; d++)
tmp += pow(params->V_z[i * D + d] - params->V_z[(params->hopslist[i*(CONST+diam+N)+j]-1) * D + d], 2.0);
tmp = SQRT(tmp + D *(params->V_sigma2[i] + params->V_sigma2[(params->hopslist[i*(CONST+diam+N)+j]-1)]));
cov=0.0; cov2=0.0;
if (params->Y[i*N+(params->hopslist[i*(CONST+diam+N)+j]-1)]>0) // i is sender and j is receiver
{
if (*params->imodel==1)
cov += params->V_xi_n[i];
if (*params->imodel==2)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==3)
cov += params->V_xi_n[i] + params->V_xi_n[N+(params->hopslist[i*(CONST+diam+N)+j]-1)];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[(i*N + (params->hopslist[i*(CONST+diam+N)+j]-1))* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[(i*N + (params->hopslist[i*(CONST+diam+N)+j]-1))* *params->P_e + p];
}
}
if (params->Y[(params->hopslist[i*(CONST+diam+N)+j]-1)*N+i]>0) // j is sender and i is receiver
{
if (*params->imodel==1)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)];
if (*params->imodel==2)
cov += params->V_xi_n[i];
if (*params->imodel==3)
cov += params->V_xi_n[(params->hopslist[i*(CONST+diam+N)+j]-1)] + params->V_xi_n[N+i];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[((params->hopslist[i*(CONST+diam+N)+j]-1)*N+i)* *params->P_e + p];
}
}
for (p=0;p<P_n;p++)
cov2+= params->V_psi2_n[p];
for (d=0; d<D; d++)
tmpsum[d] += (params->V_z[i * D + d] - params->V_z[(params->hopslist[i*(CONST+diam+N)+j]-1) * D + d]) *
(1.0 - 1.0/(1.0+exp(-cov + tmp - 0.5*cov2)));
}
hsum = 0;
for (h=2;h<1+diam;h++) // <1+diam because we don't sample unknown edges
{
Nnon=params->hopslist[i*(CONST+diam+N)+h];
if (Nnon>0)
{
sample_nodes = calloc(Nnon, sizeof(int));
sample_permutation(Nnon, sample_nodes, params->seed);
NC2=MIN(Nnon, (int)(*params->NC*params->hopslist[i*(CONST+diam+N)+1]));
for (k=0;k<NC2;k++) // loop over some of the non-edges
{
j=params->hopslist[i*(CONST+diam+N)+2+diam+params->hopslist[i*(CONST+diam+N)+1]+hsum+sample_nodes[k]]-1;
tmp = 0.0;
for (d=0; d<D; d++)
tmp += pow(params->V_z[i * D + d] - params->V_z[j * D + d], 2.0);
tmp = SQRT(tmp + D *(params->V_sigma2[i] + params->V_sigma2[j]));
cov=0.0; cov2=0.0;
if (*params->imodel==1)
cov += params->V_xi_n[i];
if (*params->imodel==2)
cov += params->V_xi_n[j];
if (*params->imodel==3)
cov += params->V_xi_n[i] + params->V_xi_n[N+j];
for (p=0;p<P_n;p++)
cov2+= params->V_psi2_n[p];
for (p=0;p<*params->P_e;p++)
{
cov += params->V_xi_e[p]*params->XX_e[(i*N + j)* *params->P_e + p];
cov2+= params->V_psi2_e[p]*params->XX_e[(i*N + j)* *params->P_e + p];
}
for (d=0; d<D; d++)
tmpsum[d] += Nnon/NC2*(
(params->V_z[i * D + d] - params->V_z[j * D + d]) *
(- 1.0/(1.0+exp(-cov + tmp - 0.5*cov2))));
}
hsum += Nnon;
free(sample_nodes);
}
}
for (d=0; d<D; d++)
KL[d] = tmpsum[d];
for (d=0; d<D; d++)
tmpsum[d] = 0.0; // there's probably a function for this in C
for (g = 0; g < G; g++)
for (d=0; d<D; d++)
tmpsum[d] = tmpsum[d] + params->V_lambda[g * N + i] *
0.5* *params->inv_sigma02 * params->V_alpha[g] *
fabs(params->V_eta[g * D + d] - params->V_z[i * D + d]);
for (d=0; d<D; d++)
KL[d] -= tmpsum[d];
//KL[d] += tmpsum[d];
for (d=0; d<D; d++)
gsl_vector_set(df, d, -KL[d]);
free(tmpsum);
free(KL);
return;
}
