forte2.helpers.davidsonliu

Module Contents

class forte2.helpers.davidsonliu.DavidsonLiuSolver(size: int, nroot: int, basis_per_root: int = 4, collapse_per_root: int = 2, maxiter: int = 100, e_tol: float = 1e-12, r_tol: float = 1e-06, eta: float | None = None, log_level: int = logger.get_verbosity_level(), dtype: type = np.float64)

Davidson-Liu solver for iterative diagonalization of Hermitian matrices.

Parameters:

sizeint

Dimension of the matrix / number of basis vectors.

nrootint

Number of roots to find.

basis_per_rootint, optional, default=4

Number of basis vectors to keep per root.

collapse_per_rootint, optional, default=2

Number of vectors to collapse to per root.

maxiterint, optional, default=100

Maximum number of iterations to perform.

e_tolfloat, optional, default=1e-12

Convergence tolerance for eigenvalues.

r_tolfloat, optional, default=1e-6

Convergence tolerance for residuals.

etafloat, optional

Target eigenvalue shift for sorting eigenpairs. If None, no shift is applied.

log_levelint, optional, default=logger.get_verbosity_level()

Logging level for output messages.

dtypetype, optional, default=np.float64

Data type of the matrix to diagonalize. Must be float or complex.

Attributes:

iterint

Current iteration number.

convergedbool

Whether the solver has converged.

size

nroot

collapse_per_root = 2

basis_per_root = 4

maxiter = 100

e_tol = 1e-12

r_tol = 1e-06

eta = None

log_level = 3

dtype

collapse_size

max_subspace_size

b

sigma

r

h_diag = None

G

alpha

lam

lam_old

schmidt_discard_threshold = 1e-07

schmidt_orthogonality_threshold = 1e-12

basis_size = 0

sigma_size = 0

add_sigma_builder(sigma_builder)

Add the function that builds the matrix-vector product.

Parameters:

sigma_buildercallable

This function should have signature sigma_builder(basis_block, sigma_block) -> None, where basis_block.shape == (size, m) and sigma_block.shape == (size, m). and it modifies sigma_block in place, performing the operation sigma_block = matrix @ basis_block.

add_h_diag(h_diag)

add_guesses(guesses)

Add initial guesses for the eigenvectors.

Parameters:

guesses: NDArray

guesses.shape == (size, n_guess), with n_guess between 1 and subspace_size.

add_project_out(project_out)

project_out: list of arrays each shape (size,)

solve()

add_rows_and_orthonormalize(A_existing: numpy.ndarray, B_candidates: numpy.ndarray, A_slots: numpy.ndarray) → int

Add candidate column vectors from B_candidates into A_slots, using iterative orthogonalization per vector. Returns the number of columns added.

orthonormality_check(b: numpy.ndarray, msg: str = 'Orthonormality check failed.')

Check if the columns of b are orthonormal.