Template Function Davidson

Function Documentation

template<typename T, typename HilbertField>
void Davidson(T &hamil, size_t dim, size_t K, vector<double> &val, vector<vector<HilbertField>> &x, double accuracy, bool verb = false)

Davidson algorithm for finding multiple eigenpairs.

Davidson algorithm

conditions on the virtual structure hamil:

  • must contain a method hamil.mult_add(vector<HilbertField> &x, vector<HilbertField> &y) that does y –> y + H.x

  • must contain a method hamil.diag(vector<HilbertField> &d) that provides the diagonal d of H

See “Monster matrices: their eigenvalues and eigenvectors” Davidson, Ernest R and Thompson, William J and others Computers in Physics 7 (519&#8212;522) 1993.

Parameters:

  • hamil – Hamiltonian (templated)

  • dim – dimension of the matrix

  • K – number of states desired

  • val – eigenvalues

  • x – eigenstates (initial vectors)

  • accuracy – desired accuracy