/* Update the group and model sufficient statistics based on assignments qZj.
*
* mutable: the clusters (add sufficient stats).
* returns: the number of observations in each cluster for this groups.
*/
template <class C> ArrayXd updateSS (
const MatrixXd& Xj, // Observations in group j
const MatrixXd& qZj, // Observations to group mixture assignments
vector<C>& clusters, // Cluster Distributions
const bool sparse // Do sparse updates to groups
)
{
const unsigned int K = qZj.cols();
const ArrayXd Njk = qZj.colwise().sum(); // count obs. in this group
ArrayXi Kful = ArrayXi::Zero(1), // Initialise and set K = 1 defaults
Kemp = ArrayXi::Zero(0);
// Find empty clusters if sparse
if ( (sparse == false) && (K > 1) )
Kful = ArrayXi::LinSpaced(Sequential, K, 0, K-1);
else if (sparse == true)
arrfind((Njk >= ZEROCUTOFF), Kful, Kemp);
const unsigned int nKful = Kful.size();
// Sufficient statistics - with observations
for (unsigned int k = 0; k < nKful; ++k)
{
#ifdef WITH_OMP
#pragma omp critical
#endif
clusters[Kful(k)].addobs(qZj.col(Kful(k)), Xj);
}
return Njk;
}
ArrayXi perm_nodes_2_locations(const PermutationMatrix<Dynamic, Dynamic, int> &_perm_nodes)
{
ArrayXi indices = _perm_nodes.indices().array();
for (unsigned int i = 0; i<indices.size(); i++)
indices = (indices > indices(i)).select(indices + nodes_.at(i).dim-1, indices);
return indices;
}
void nodePermutation2VariablesPermutation(const PermutationMatrix<Dynamic, Dynamic, int> &_perm_nodes, PermutationMatrix<Dynamic, Dynamic, int> &perm_variables)
{
ArrayXi locations = perm_nodes_2_locations(_perm_nodes);
int last_idx = 0;
for (unsigned int i = 0; i<locations.size(); i++)
{
perm_variables.indices().segment(last_idx, nodes_.at(i).dim) = VectorXi::LinSpaced(nodes_.at(i).dim, locations(i), locations(i)+nodes_.at(i).dim-1);
last_idx += nodes_.at(i).dim;
}
}
BlockMatrixXcd random_hermitian(ArrayXi sizes) {
if (log) std::cout << "A random hermitian matrix is made!" << std::endl;
const long full_size = sizes.sum();
if (log) std::cout << "We initialize with zeros." << std::endl;
BlockMatrixXcd result = MatrixXcd::Zero(full_size,full_size);
if (log) std::cout << "We define blocks." << std::endl;
result.setBlocks(sizes);
if (log) std::cout << "We randomly set the diagonal as well as lower and upper diagonal blocks." << std::endl;
for(int i = 0; i < sizes.size(); i++)
{
if (log) std::cout << "Diagonal block " << i << " is set." << std::endl;
result.block(i, i) = MatrixXcd::Random(sizes[i],sizes[i]);
if( i < sizes.size() - 1)
{
if (log) std::cout << "Upper diagonal block " << i << " is set." << std::endl;
result.block(i + 1, i) = MatrixXcd::Random(sizes[i + 1], sizes[i]);
if (log) std::cout << "Lower diagonal block " << i << " is set." << std::endl;
result.block(i, i + 1) = MatrixXcd::Random(sizes[i], sizes[i + 1]);
}
}
if (log) std::cout << "The matrix is added to its adjoint." << std::endl;
result += result.adjoint().eval();
if (log) std::cout << "The matrix is finished." << std::endl;
return result;
}
/* The Variational Bayes Expectation step for each group.
*
* mutable: Group assignment probabilities, qZj
* returns: The complete-data (X,Z) free energy E[log p(X,Z)/q(Z)] for group j.
* throws: invalid_argument rethrown from other functions.
*/
template <class W, class C> double vbexpectation (
const MatrixXd& Xj, // Observations in group J
const W& weights, // Group Weight parameter distribution
const vector<C>& clusters, // Cluster parameter distributions
MatrixXd& qZj, // Observations to group mixture assignments
const bool sparse // Do sparse updates to groups
)
{
const int K = clusters.size(),
Nj = Xj.rows();
// Get log marginal weight likelihoods
const ArrayXd E_logZ = weights.Elogweight();
// Initialise and set K = 1 defaults for cluster counts
ArrayXi Kful = ArrayXi::Zero(1), Kemp = ArrayXi::Zero(0);
// Find empty clusters if sparse
if ( (sparse == false) && (K > 1) )
Kful = ArrayXi::LinSpaced(Sequential, K, 0, K-1);
else if (sparse == true)
arrfind((weights.getNk() >= ZEROCUTOFF), Kful, Kemp);
const int nKful = Kful.size(),
nKemp = Kemp.size();
// Find Expectations of log joint observation probs -- allow sparse evaluation
MatrixXd logqZj(Nj, nKful);
for (int k = 0; k < nKful; ++k)
logqZj.col(k) = E_logZ(Kful(k)) + clusters[Kful(k)].Eloglike(Xj).array();
// Log normalisation constant of log observation likelihoods
const VectorXd logZzj = logsumexp(logqZj);
// Make sure qZ is the right size, this is a nop if it is
qZj.resize(Nj, K);
// Normalise and Compute Responsibilities -- again allow sparse evaluation
for (int k = 0; k < nKful; ++k)
qZj.col(Kful(k)) = ((logqZj.col(k) - logZzj).array().exp()).matrix();
// Empty Cluster Responsabilities
for (int k = 0; k < nKemp; ++k)
qZj.col(Kemp(k)).setZero();
return -logZzj.sum();
}
