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hydrogym.firedrake.utils.linalg

LinearOperator Objects​

class LinearOperator(metaclass=abc.ABCMeta)

__matmul__​

@abc.abstractmethod
def __matmul__(v: fd.Function)

Return the matrix-vector product A @ v.

DirectOperator Objects​

class DirectOperator(LinearOperator)

T​

@property
def T() -> InverseOperator

Return the adjoint operator.

This will solve the matrix pencil A^T @ f = M^T @ v0 for f.

InverseOperator Objects​

@dataclasses.dataclass
class InverseOperator(LinearOperator)

A simple wrapper for the inverse of a matrix pencil.

Note that this object will own the output Function unless copy_output=True is set. This is memory-efficient, but could lead to confusion if the output reference is modified. The Arnoldi iteration algorithm is written so this isn't a problem.

T​

@property
def T() -> InverseOperator

Return the adjoint operator.

This will solve the matrix pencil A^T @ f = M^T @ v0 for f.

__matmul__​

def __matmul__(v0)

Solve the matrix pencil A @ f = M @ v0 for f.

This is equivalent to the "inverse iteration" f = (A^-1 @ M) @ v0