util::matrix_t
MatrixFactory::build( double E ) const {
// Copy the static elements
util::matrix_t result( static_matrix );
// Generate the dynamic elements
int size = result.size1() / 2;
ublas::range first_half( 0, size );
ublas::range second_half( size, 2*size );
typedef ublas::matrix_range< util::matrix_t > submatrix_t;
submatrix_t A ( result, first_half, first_half );
submatrix_t A_star( result, second_half, second_half );
BOOST_FOREACH( const Term &t, dynamic_terms ) {
A += t( ph_states, E, ENUM_A );
A_star -= t( ph_states, E, ENUM_A_STAR );
}
/*! \fn inline void symmetryBlocking(Eigen::MatrixXd & matrix, int cavitySize, int ntsirr, int nr_irrep)
* \param[out] matrix the matrix to be block-diagonalized
* \param[in] cavitySize the size of the cavity (size of the matrix)
* \param[in] ntsirr the size of the irreducible portion of the cavity (size of the blocks)
* \param[in] nr_irrep the number of irreducible representations (number of blocks)
*/
inline void symmetryBlocking(Eigen::MatrixXd & matrix, size_t cavitySize, int ntsirr,
int nr_irrep)
{
// This function implements the simmetry-blocking of the PCM
// matrix due to point group symmetry as reported in:
// L. Frediani, R. Cammi, C. S. Pomelli, J. Tomasi and K. Ruud, J. Comput.Chem. 25, 375 (2003)
// u is the character table for the group (t in the paper)
Eigen::MatrixXd u = Eigen::MatrixXd::Zero(nr_irrep, nr_irrep);
for (int i = 0; i < nr_irrep; ++i) {
for (int j = 0; j < nr_irrep; ++j) {
u(i, j) = parity(i&j);
}
}
// Naming of indices:
// a, b, c, d run over the total size of the cavity (N)
// i, j, k, l run over the number of irreps (n)
// p, q, r, s run over the irreducible size of the cavity (N/n)
// Instead of forming U (T in the paper) and then perform the dense
// multiplication, we multiply block-by-block using just the u matrix.
// matrix = U * matrix * Ut; U * Ut = Ut * U = id
// First half-transformation, i.e. first_half = matrix * Ut
Eigen::MatrixXd first_half = Eigen::MatrixXd::Zero(cavitySize, cavitySize);
for (int i = 0; i < nr_irrep; ++i) {
int ioff = i * ntsirr;
for (int k = 0; k < nr_irrep; ++k) {
int koff = k * ntsirr;
for (int j = 0; j < nr_irrep; ++j) {
int joff = j * ntsirr;
double ujk = u(j, k) / nr_irrep;
for (int p = 0; p < ntsirr; ++p) {
int a = ioff + p;
for (int q = 0; q < ntsirr; ++q) {
int b = joff + q;
int c = koff + q;
first_half(a, c) += matrix(a, b) * ujk;
}
}
}
}
}
// Second half-transformation, i.e. matrix = U * first_half
matrix.setZero(cavitySize, cavitySize);
for (int i = 0; i < nr_irrep; ++i) {
int ioff = i * ntsirr;
for (int k = 0; k < nr_irrep; ++k) {
int koff = k * ntsirr;
for (int j = 0; j < nr_irrep; ++j) {
int joff = j * ntsirr;
double uij = u(i, j);
for (int p = 0; p < ntsirr; ++p) {
int a = ioff + p;
int b = joff + p;
for (int q = 0; q < ntsirr; ++q) {
int c = koff + q;
matrix(a, c) += uij * first_half(b, c);
}
}
}
}
}
// Traverse the matrix and discard numerical zeros
for (size_t a = 0; a < cavitySize; ++a) {
for (size_t b = 0; b < cavitySize; ++b) {
if (numericalZero(matrix(a, b))) {
matrix(a, b) = 0.0;
}
}
}
}
