GMMExpectationMaximization::Real GMMExpectationMaximization::gauss(const VectorX & mean,
const MatrixX & cov,const VectorX & pt) const
{
Real det = cov.determinant();
uint dim = mean.size();
// check that the covariance matrix is invertible
if (std::abs(det) < std::pow(m_epsilon,dim) * 0.1)
return 0.0; // the gaussian has approximately zero width: the probability of any point falling into it is approximately 0.
// else, compute pdf
MatrixX inverse_cov = cov.inverse();
VectorX dist = pt - mean;
Real exp = - (dist.dot(inverse_cov * dist)) / 2.0;
Real den = std::sqrt(std::pow(2.0 * M_PI,dim) * std::abs(det));
return std::exp(exp) / den;
}
void SlaterSet::initCalculation()
{
if (m_initialized)
return;
m_normalized.resize(m_overlap.cols(), m_overlap.rows());
SelfAdjointEigenSolver<MatrixX> s(m_overlap);
MatrixX p = s.eigenvectors();
MatrixX m = p * s.eigenvalues().array().inverse().array().sqrt()
.matrix().asDiagonal() * p.inverse();
m_normalized = m * m_eigenVectors;
if (!(m_overlap * m * m).eval().isIdentity())
cout << "Identity test FAILED - do you need a newer version of Eigen?\n";
m_factors.resize(m_zetas.size());
m_PQNs = m_pqns;
// Calculate the normalizations of the orbitals.
for (size_t i = 0; i < m_zetas.size(); ++i) {
switch (m_slaterTypes[i]) {
case S:
m_factors[i] = pow(2.0 * m_zetas[i], m_pqns[i] + 0.5)
* sqrt(1.0 / (4.0 * M_PI) / factorial(2 * m_pqns[i]));
m_PQNs[i] -= 1;
break;
case PX:
case PY:
case PZ:
m_factors[i] = pow(2.0 * m_zetas[i], m_pqns[i] + 0.5)
* sqrt(3.0 / (4.0 * M_PI) / factorial(2 * m_pqns[i]));
m_PQNs[i] -= 2;
break;
case X2:
m_factors[i] = 0.5 * pow(2.0 * m_zetas[i], m_pqns[i] + 0.5)
* sqrt(15.0 / (4.0 * M_PI) / factorial(2 * m_pqns[i]));
m_PQNs[i] -= 3;
break;
case XZ:
m_factors[i] = pow(2.0 * m_zetas[i], m_pqns[i] + 0.5)
* sqrt(15.0 / (4.0 * M_PI) / factorial(2 * m_pqns[i]));
m_PQNs[i] -= 3;
break;
case Z2:
m_factors[i] = (0.5 / sqrt(3.0)) * pow(2.0 * m_zetas[i], m_pqns[i] + 0.5)
* sqrt(15.0 / (4.0 * M_PI) / factorial(2 * m_pqns[i]));
m_PQNs[i] -= 3;
break;
case YZ:
case XY:
m_factors[i] = pow(2.0 * m_zetas[i], m_pqns[i] + 0.5) *
sqrt(15.0 / (4.0*M_PI) / factorial(2*m_pqns[i]));
m_PQNs[i] -= 3;
break;
default:
cout << "Orbital " << i << " not handled, type " << m_slaterTypes[i]
<< endl;
}
}
// Convert the exponents into Angstroms
for (size_t i = 0; i < m_zetas.size(); ++i)
m_zetas[i] = m_zetas[i] / BOHR_TO_ANGSTROM;
m_initialized = true;
}