void IEFSolver::buildIsotropicMatrix(const Cavity & cav, const IGreensFunction & gf_i, const IGreensFunction & gf_o)
{
// The total size of the cavity
size_t cavitySize = cav.size();
// The number of irreps in the group
int nrBlocks = cav.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cav.irreducible_size();
// Compute SI and DI on the whole cavity, regardless of symmetry
Eigen::MatrixXd SI = gf_i.singleLayer(cav.elements());
Eigen::MatrixXd DI = gf_i.doubleLayer(cav.elements());
// Perform symmetry blocking
// If the group is C1 avoid symmetry blocking, we will just pack the fullPCMMatrix
// into "block diagonal" when all other manipulations are done.
if (cav.pointGroup().nrGenerators() != 0) {
symmetryBlocking(DI, cavitySize, dimBlock, nrBlocks);
symmetryBlocking(SI, cavitySize, dimBlock, nrBlocks);
}
Eigen::MatrixXd a = cav.elementArea().asDiagonal();
Eigen::MatrixXd aInv = Eigen::MatrixXd::Zero(cavitySize, cavitySize);
aInv = a.inverse();
// Tq = -Rv -> q = -(T^-1 * R)v = -Kv
// T = (2 * M_PI * fact * aInv - DI) * a * SI; R = (2 * M_PI * aInv - DI)
// fullPCMMatrix_ = K = T^-1 * R * a
// 1. Form T
double epsilon = profiles::epsilon(gf_o.permittivity());
double fact = (epsilon + 1.0)/(epsilon - 1.0);
fullPCMMatrix_ = (2 * M_PI * fact * aInv - DI) * a * SI;
// 2. Invert T using LU decomposition with full pivoting
// This is a rank-revealing LU decomposition, this allows us
// to test if T is invertible before attempting to invert it.
Eigen::FullPivLU<Eigen::MatrixXd> T_LU(fullPCMMatrix_);
if (!(T_LU.isInvertible()))
PCMSOLVER_ERROR("T matrix is not invertible!");
fullPCMMatrix_ = T_LU.inverse();
// 3. Multiply T^-1 and R
fullPCMMatrix_ *= (2 * M_PI * aInv - DI);
// 4. Multiply by a
fullPCMMatrix_ *= a;
// 5. Symmetrize K := (K + K+)/2
if (hermitivitize_) {
hermitivitize(fullPCMMatrix_);
}
// Pack into a block diagonal matrix
// For the moment just packs into a std::vector<Eigen::MatrixXd>
symmetryPacking(blockPCMMatrix_, fullPCMMatrix_, dimBlock, nrBlocks);
std::ofstream matrixOut("PCM_matrix");
matrixOut << "fullPCMMatrix" << std::endl;
matrixOut << fullPCMMatrix_ << std::endl;
for (int i = 0; i < nrBlocks; ++i) {
matrixOut << "Block number " << i << std::endl;
matrixOut << blockPCMMatrix_[i] << std::endl;
}
built_ = true;
}
void IEFSolver::buildIsotropicMatrix(const Cavity & cav, const IGreensFunction & gf_i, const IGreensFunction & gf_o)
{
fullPCMMatrix_ = isotropicIEFMatrix(cav, gf_i, profiles::epsilon(gf_o.permittivity()));
// Symmetrize K := (K + K+)/2
if (hermitivitize_) {
hermitivitize(fullPCMMatrix_);
}
// Pack into a block diagonal matrix
// The number of irreps in the group
int nrBlocks = cav.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cav.irreducible_size();
// For the moment just packs into a std::vector<Eigen::MatrixXd>
symmetryPacking(blockPCMMatrix_, fullPCMMatrix_, dimBlock, nrBlocks);
built_ = true;
}
void CPCMSolver::buildSystemMatrix_impl(const Cavity & cavity, const IGreensFunction & gf_i, const IGreensFunction & gf_o)
{
if (!isotropic_) PCMSOLVER_ERROR("C-PCM is defined only for isotropic environments!");
// The total size of the cavity
size_t cavitySize = cavity.size();
// The number of irreps in the group
int nrBlocks = cavity.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cavity.irreducible_size();
// Compute SI on the whole cavity, regardless of symmetry
Eigen::MatrixXd SI = gf_i.singleLayer(cavity.elements());
// Perform symmetry blocking only for the SI matrix as the DI matrix is not used.
// If the group is C1 avoid symmetry blocking, we will just pack the fullPCMMatrix
// into "block diagonal" when all other manipulations are done.
if (cavity.pointGroup().nrGenerators() != 0) {
symmetryBlocking(SI, cavitySize, dimBlock, nrBlocks);
}
double epsilon = profiles::epsilon(gf_o.permittivity());
double fact = (epsilon - 1.0)/(epsilon + correction_);
// Invert SI using LU decomposition with full pivoting
// This is a rank-revealing LU decomposition, this allows us
// to test if SI is invertible before attempting to invert it.
Eigen::FullPivLU<Eigen::MatrixXd> SI_LU(SI);
if (!(SI_LU.isInvertible()))
PCMSOLVER_ERROR("SI matrix is not invertible!");
fullPCMMatrix_ = fact * SI_LU.inverse();
// 5. Symmetrize K := (K + K+)/2
if (hermitivitize_) {
hermitivitize(fullPCMMatrix_);
}
symmetryPacking(blockPCMMatrix_, fullPCMMatrix_, dimBlock, nrBlocks);
built_ = true;
}
void CPCMSolver::buildSystemMatrix_impl(const ICavity & cavity,
const IGreensFunction & gf_i,
const IGreensFunction & gf_o,
const IBoundaryIntegralOperator & op) {
if (!isotropic_)
PCMSOLVER_ERROR("C-PCM is defined only for isotropic environments!");
TIMER_ON("Computing S");
double epsilon = gf_o.permittivity();
S_ = op.computeS(cavity, gf_i);
S_ /= (epsilon - 1.0) / (epsilon + correction_);
// Get in Hermitian form
if (hermitivitize_)
utils::hermitivitize(S_);
TIMER_OFF("Computing S");
// Symmetry-pack
// The number of irreps in the group
int nrBlocks = cavity.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cavity.irreducible_size();
utils::symmetryPacking(blockS_, S_, dimBlock, nrBlocks);
built_ = true;
}