cagpjax.linalg

Linear algebra functions.

Modules:

• congruence –

  Congruence transformations for linear operators.

• eigh –

  Hermitian eigenvalue decomposition.

• lower_cholesky –

  Lower Cholesky decomposition of positive semidefinite operators.

• orthogonalize –

  Orthogonalization methods.

• utils –

  Linear algebra utilities.

Classes:

• Eigh –

  Eigh algorithm for eigenvalue decomposition.

• Lanczos –

  Lanczos algorithm for approximate partial eigenvalue decomposition.

• OrthogonalizationMethod –

  Methods for orthogonalizing a matrix.

Functions:

• congruence_transform –

  Congruence transformation A.T @ B @ A.

Eigh

Bases: Algorithm

Eigh algorithm for eigenvalue decomposition.

Lanczos

Lanczos(max_iters: int | None = None, /, *, v0: Float[Array, N] | None = None, key: PRNGKeyArray | None = None)

Bases: Algorithm

Lanczos algorithm for approximate partial eigenvalue decomposition.

Parameters:

• max_iters

  (int | None, default: None ) –

  Maximum number of iterations (number of eigenvalues/vectors to compute). If None, all eigenvalues/eigenvectors are computed.

• v0

  (Float[Array, N] | None, default: None ) –

  Initial vector. If None, a random vector is generated using key.

• key

  (PRNGKeyArray | None, default: None ) –

  Random key for generating a random initial vector if v0 is not provided.

Source code in src/cagpjax/linalg/eigh.py

def __init__(
    self,
    max_iters: int | None = None,
    /,
    *,
    v0: Float[Array, "N"] | None = None,
    key: PRNGKeyArray | None = None,
):
    self.max_iters = max_iters
    self.v0 = v0
    self.key = key

OrthogonalizationMethod

Bases: Enum

Methods for orthogonalizing a matrix.

Attributes:

• CGS –

  Classical Gram–Schmidt orthogonalization

• MGS –

  Modified Gram–Schmidt orthogonalization

• QR –

  Householder QR decomposition

CGS class-attribute instance-attribute

CGS = 'cgs'

Classical Gram–Schmidt orthogonalization

MGS class-attribute instance-attribute

MGS = 'mgs'

Modified Gram–Schmidt orthogonalization

QR class-attribute instance-attribute

QR = 'qr'

Householder QR decomposition

congruence_transform

congruence_transform(A: Any, B: Any) -> Any

congruence_transform(A: Diagonal, B: Diagonal) -> Diagonal

congruence_transform(A: BlockDiagonalSparse, B: Diagonal | ScalarMul) -> Diagonal

congruence_transform(A: Any, B: Any) -> Any

Congruence transformation A.T @ B @ A.

Parameters:

• A

  (Any) –

  Linear operator or array to be applied.

• B

  (Any) –

  Square linear operator or array to be transformed.

Source code in src/cagpjax/linalg/congruence.py

@cola.dispatch
def congruence_transform(A: Any, B: Any) -> Any:
    """Congruence transformation ``A.T @ B @ A``.

    Args:
        A: Linear operator or array to be applied.
        B: Square linear operator or array to be transformed.
    """
    pass