dyson.solvers.static.davidson

Davidson algorithm [1] [2].

[1]

Davidson, E. R. (1975). The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. Journal of Computational Physics, 17(1), 87–94. https://doi.org/10.1016/0021-9991(75)90065-0

[2]

Morgan, R. B. (1990). Davidson’s method and preconditioning for generalized eigenvalue problems. Journal of Computational Physics, 89(1), 241–245. https://doi.org/10.1016/0021-9991(90)90124-j

Classes

Davidson(*args, **kwargs)

Davidson algorithm for diagonalisation of the supermatrix form of the self-energy.

class dyson.solvers.static.davidson.Davidson(*args: Any, **kwargs: Any)

Bases: StaticSolver

Davidson algorithm for diagonalisation of the supermatrix form of the self-energy.

Parameters:

• matvec – The matrix-vector operation for the self-energy supermatrix.

• diagonal – The diagonal of the self-energy supermatrix.

• bra – The bra excitation vector mapping the supermatrix to the physical space.

• ket – The ket excitation vector mapping the supermatrix to the physical space.

hermitian: bool = True

nroots: int = 1

max_cycle: int = 100

max_space: int = 16

conv_tol: float = 1e-08

conv_tol_residual: float = 1e-05

converged: Array | None = None

classmethod from_self_energy(static: Array, self_energy: Lehmann, overlap: Array | None = None, **kwargs: Any) → Davidson

Create a solver from a self-energy.

Parameters:

• static – Static part of the self-energy.

• self_energy – Self-energy.

• overlap – Overlap matrix for the physical space.

• kwargs – Additional keyword arguments for the solver.

Returns:

Solver instance.

classmethod from_expression(expression: BaseExpression, **kwargs: Any) → Davidson

Create a solver from an expression.

Parameters:

• expression – Expression to be solved.

• kwargs – Additional keyword arguments for the solver.

Returns:

Solver instance.

get_guesses() → list[Array]

Get the initial guesses for the eigenvectors.

Returns:

Initial guesses for the eigenvectors.

kernel(*args: Any, **kwargs: Any) → Any

Run the solver.

property matvec: Callable[[Array], Array]

Get the matrix-vector operation for the self-energy supermatrix.

property diagonal: Array

Get the diagonal of the self-energy supermatrix.

property bra: Array

Get the bra excitation vector mapping the supermatrix to the physical space.

property ket: Array

Get the ket excitation vector mapping the supermatrix to the physical space.

property nphys: int

Get the number of physical degrees of freedom.