// Find a point in space with high density.
void TChain::find_center(double* const center, gsl_matrix *const cov, gsl_matrix *const inv_cov, double* det_cov, double dmax, unsigned int iterations) const {
// Check that the matrices are the correct size
/*assert(cov->size1 == N);
assert(cov->size2 == N);
assert(inv_cov->size1 == N);
assert(inv_cov->size2 == N);*/
// Choose random point in chain as starting point
gsl_rng *r;
seed_gsl_rng(&r);
long unsigned int index_tmp = gsl_rng_uniform_int(r, length);
const double *x_tmp = get_element(index_tmp);
for(unsigned int i=0; i<N; i++) { center[i] = x_tmp[i]; }
// Iterate
double *sum = new double[N];
double weight;
for(unsigned int i=0; i<iterations; i++) {
// Set mean of nearby points as center
weight = 0.;
for(unsigned int n=0; n<N; n++) { sum[n] = 0.; }
for(unsigned int k=0; k<length; k++) {
x_tmp = get_element(k);
if(metric_dist2(inv_cov, x_tmp, center, N) < dmax*dmax) {
for(unsigned int n=0; n<N; n++) { sum[n] += w[k] * x_tmp[n]; }
weight += w[k];
}
}
for(unsigned int n=0; n<N; n++) { center[n] = sum[n] / (double)weight; }
dmax *= 0.9;
}
//for(unsigned int n=0; n<N; n++) { std::cout << " " << center[n]; }
//std::cout << std::endl;
gsl_rng_free(r);
delete[] sum;
}
// Uses a variant of the bounded harmonic mean approximation to determine the evidence.
// Essentially, the regulator chosen is an ellipsoid with radius nsigma standard deviations
// along each principal axis. The regulator is then 1/V inside the ellipsoid and 0 without,
// where V is the volume of the ellipsoid. In this form, the harmonic mean approximation
// has finite variance. See Gelfand & Dey (1994) and Robert & Wraith (2009) for details.
double TChain::get_ln_Z_harmonic(bool use_peak, double nsigma_max, double nsigma_peak, double chain_frac) const {
// Get the covariance and determinant of the chain
gsl_matrix* Sigma = gsl_matrix_alloc(N, N);
gsl_matrix* invSigma = gsl_matrix_alloc(N, N);
double detSigma;
stats.get_cov_matrix(Sigma, invSigma, &detSigma);
// Determine the center of the prior volume to use
double* mu = new double[N];
if(use_peak) { // Use the peak density as the center
find_center(mu, Sigma, invSigma, &detSigma, nsigma_peak, 5);
//density_peak(mu, nsigma_peak);
} else { // Get the mean from the stats class
for(unsigned int i=0; i<N; i++) { mu[i] = stats.mean(i); }
}
// Sort elements in chain by distance from center, filtering out values of L which are not finite
std::vector<TChainSort> sorted_indices;
sorted_indices.reserve(length);
unsigned int filt_length = 0;
for(unsigned int i=0; i<length; i++) {
if(!(isnan(L[i]) || is_inf_replacement(L[i]))) {
TChainSort tmp_el;
tmp_el.index = i;
tmp_el.dist2 = metric_dist2(invSigma, get_element(i), mu, N);
sorted_indices.push_back(tmp_el);
filt_length++;
}
}
unsigned int npoints = (unsigned int)(chain_frac * (double)filt_length);
std::partial_sort(sorted_indices.begin(), sorted_indices.begin() + npoints, sorted_indices.end());
// Determine <1/L> inside the prior volume
double sum_invL = 0.;
double tmp_invL;
double nsigma = sqrt(sorted_indices[npoints-1].dist2);
unsigned int tmp_index = sorted_indices[0].index;;
double L_0 = L[tmp_index];
//std::cout << "index_0 = " << sorted_indices[0].index << std::endl;
for(unsigned int i=0; i<npoints; i++) {
if(sorted_indices[i].dist2 > nsigma_max * nsigma_max) {
nsigma = nsigma_max;
break;
}
tmp_index = sorted_indices[i].index;
tmp_invL = w[tmp_index] / exp(L[tmp_index] - L_0);
//std::cout << w[tmp_index] << ", " << L[tmp_index] << std::endl;
//if(isnan(tmp_invL)) {
// std::cout << "\t\tL, L_0 = " << L[tmp_index] << ", " << L_0 << std::endl;
//}
if((tmp_invL + sum_invL > 1.e100) && (i != 0)) {
nsigma = sqrt(sorted_indices[i-1].dist2);
break;
}
sum_invL += tmp_invL;
}
// Determine the volume normalization (the prior volume)
double V = sqrt(detSigma) * 2. * pow(SQRTPI * nsigma, (double)N) / (double)(N) / gsl_sf_gamma((double)(N)/2.);
// Return an estimate of ln(Z)
double lnZ = log(V) - log(sum_invL) + log(total_weight) + L_0;
if(isnan(lnZ)) {
std::cout << std::endl;
std::cout << "NaN Error! lnZ = " << lnZ << std::endl;
std::cout << "\tsum_invL = e^(" << -L_0 << ") * " << sum_invL << " = " << exp(-L_0) * sum_invL << std::endl;
std::cout << "\tV = " << V << std::endl;
std::cout << "\ttotal_weight = " << total_weight << std::endl;
std::cout << std::endl;
} else if(is_inf_replacement(lnZ)) {
std::cout << std::endl;
std::cout << "inf Error! lnZ = " << lnZ << std::endl;
std::cout << "\tsum_invL = e^(" << -L_0 << ") * " << sum_invL << " = " << exp(-L_0) * sum_invL << std::endl;
std::cout << "\tV = " << V << std::endl;
std::cout << "\ttotal_weight = " << total_weight << std::endl;
std::cout << "\tnsigma = " << nsigma << std::endl;
std::cout << "\tIndex\tDist^2:" << std::endl;
for(unsigned int i=0; i<10; i++) {
std::cout << sorted_indices[i].index << "\t\t" << sorted_indices[i].dist2 << std::endl;
std::cout << " ";
const double *tmp_x = get_element(sorted_indices[i].index);
for(unsigned int k=0; k<N; k++) { std::cout << " " << tmp_x[k]; }
std::cout << std::endl;
}
std::cout << "mu =";
for(unsigned int i=0; i<N; i++) { std::cout << " " << mu[i]; }
std::cout << std::endl;
}
// Cleanup
gsl_matrix_free(Sigma);
gsl_matrix_free(invSigma);
delete[] mu;
return lnZ;
}
// Find a point in space with high density.
void TChain::find_center(double* const center, gsl_matrix *const cov, gsl_matrix *const inv_cov, double* det_cov, double dmax, unsigned int iterations) const {
// Check that the matrices are the correct size
/*assert(cov->size1 == N);
assert(cov->size2 == N);
assert(inv_cov->size1 == N);
assert(inv_cov->size2 == N);*/
// Choose random point in chain as starting point
gsl_rng *r;
seed_gsl_rng(&r);
long unsigned int index_tmp = gsl_rng_uniform_int(r, length);
const double *x_tmp = get_element(index_tmp);
for(unsigned int i=0; i<N; i++) { center[i] = x_tmp[i]; }
//std::cout << "center #0:";
//for(unsigned int n=0; n<N; n++) { std::cout << " " << center[n]; }
//std::cout << std::endl;
/*double *E_k = new double[N];
double *E_ij = new double[N*N];
for(unsigned int n1=0; n1<N; n1++) {
E_k[n1] = 0.;
for(unsigned int n2=0; n2<N; n2++) { E_ij[n1 + N*n2] = 0.; }
}*/
// Iterate
double *sum = new double[N];
double weight;
for(unsigned int i=0; i<iterations; i++) {
// Set mean of nearby points as center
weight = 0.;
for(unsigned int n=0; n<N; n++) { sum[n] = 0.; }
for(unsigned int k=0; k<length; k++) {
x_tmp = get_element(k);
if(metric_dist2(inv_cov, x_tmp, center, N) < dmax*dmax) {
for(unsigned int n=0; n<N; n++) { sum[n] += w[k] * x_tmp[n]; }
weight += w[k];
// Calculate the covariance
/*if(i == iterations - 1) {
for(unsigned int n1=0; n1<N; n1++) {
E_k[n1] += w[k] * x_tmp[n1];
for(unsigned int n2=0; n2<N; n2++) { E_ij[n1 + N*n2] += w[k] * x_tmp[n1] * x_tmp[n2]; }
}
}*/
}
}
//std::cout << "center #" << i+1 << ":";
for(unsigned int n=0; n<N; n++) { center[n] = sum[n] / (double)weight; }//std::cout << " " << center[n]; }
//std::cout << " (" << weight << ")" << std::endl;
dmax *= 0.9;
}
for(unsigned int n=0; n<N; n++) { std::cout << " " << center[n]; }
std::cout << std::endl;
// Calculate the covariance matrix of the enclosed points
/*double tmp;
for(unsigned int i=0; i<N; i++) {
for(unsigned int j=i; j<N; j++) {
tmp = (E_ij[i + N*j] - E_k[i]*E_k[j]/(double)weight) / (double)weight;
gsl_matrix_set(cov, i, j, tmp);
if(i != j) { gsl_matrix_set(cov, j, i, tmp); }
}
}*/
// Get the inverse of the covariance
/*int s;
gsl_permutation* p = gsl_permutation_alloc(N);
gsl_matrix* LU = gsl_matrix_alloc(N, N);
gsl_matrix_memcpy(LU, cov);
gsl_linalg_LU_decomp(LU, p, &s);
gsl_linalg_LU_invert(LU, p, inv_cov);
// Get the determinant of the covariance
*det_cov = gsl_linalg_LU_det(LU, s);
// Cleanup
gsl_matrix_free(LU);
gsl_permutation_free(p);
delete[] E_k;
delete[] E_ij;*/
gsl_rng_free(r);
delete[] sum;
}
