davidson_solver

psi4.driver.p4util.davidson_solver(engine, guess, *, nroot, r_convergence=0.0001, max_ss_size=100, maxiter=60, verbose=1)[source]

Solves for the lowest few eigenvalues and eigenvectors of a large problem emulated through an engine.

If the large matrix A has dimension {NxN} and N is very large, and only a small number of roots, k are desired this algorithm is preferable to standard methods as uses on the order of N * k memory. One only needs to have the ability to compute the product of a times a vector.

For non-hermitan A the basis of the algorithm breaks down. However in practice, for strongly diagonally-dominant A such as the similarity-transformed Hamiltonian in EOM-CC this algorithm is commonly still used.

Parameters:
  • engine (Type[SolverEngine]) – The engine drive all operations involving data structures that have at least one “large” dimension. See SolverEngine for requirements

  • guess (List) – list {engine dependent} At least nroot initial expansion vectors

  • nroot (int) – Number of roots desired

  • r_convergence (float) – Convergence tolerance for residual vectors

  • max_ss_size (int) – The maximum number of trial vectors in the iterative subspace that will be stored before a collapse is done.

  • maxiter (int) – The maximum number of iterations

  • verbose (int) – The amount of logging info to print (0 -> none, 1 -> some, >1 -> everything)

Return type:

Dict[str, Any]

Returns:

  • best_values (numpy.ndarray) – (nroots, ) The best approximation of the eigenvalues of A, computed on the last iteration of the solver

  • best_vectors (List[vector]) – (nroots) The best approximation of the eigenvectors of A, computed on the last iteration of the solver

  • stats (List[Dict]) – Statistics collected on each iteration

    • count : int, iteration number

    • res_norm : np.ndarray (nroots, ), the norm of residual vector for each roots

    • val : np.ndarray (nroots, ), the eigenvalue corresponding to each root

    • delta_val : np.ndarray (nroots, ), the change in eigenvalue from the last iteration to this ones

    • collapse : bool, if a subspace collapse was performed

    • product_count : int, the running total of product evaluations that was performed

    • done : bool, if all roots were converged

Notes

The solution vector is normalized to 1/2

The solver will return even when maxiter iterations are performed without convergence. The caller must check stats[-1]['done'] for failure and handle each case accordingly.