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cagpjax.policies.lanczos

Lanczos-based policies.

Classes:

  • LanczosPolicy –

    Lanczos-based policy for eigenvalue decomposition approximation.

LanczosPolicy

Bases: AbstractBatchLinearSolverPolicy

Lanczos-based policy for eigenvalue decomposition approximation.

This policy uses the Lanczos algorithm to compute the top n_actions eigenvectors of the linear operator \(A\).

Attributes:

  • n_actions (int) –

    Number of Lanczos vectors/actions to compute.

  • grad_rtol (float | None) –

    Specifies the cutoff for similar eigenvalues, used to improve gradient computation for (almost-)degenerate matrices. If not provided, the default is 0.0. If None or negative, all eigenvalues are treated as distinct. (see cagpjax.linalg.eigh for more details)

Methods:

to_actions 

to_actions(A: LinearOperator, *, key: PRNGKeyArray | None = None) -> LinearOperator

Compute action matrix.

Parameters:

  • A

    (LinearOperator) –

    Symmetric linear operator representing the linear system.

  • key

    (PRNGKeyArray | None, default: None ) –

    Random key used to initialize the Lanczos run.

Returns:

  • LinearOperator –

    Linear operator containing the Lanczos vectors as columns.

Source code in src/cagpjax/policies/lanczos.py 
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@override
def to_actions(
    self, A: LinearOperator, *, key: PRNGKeyArray | None = None
) -> LinearOperator:
    """Compute action matrix.

    Args:
        A: Symmetric linear operator representing the linear system.
        key: Random key used to initialize the Lanczos run.

    Returns:
        Linear operator containing the Lanczos vectors as columns.
    """
    vecs = eigh(
        A, alg=Lanczos(self.n_actions, key=key), grad_rtol=self.grad_rtol
    ).eigenvectors
    return vecs