fhelium.experimental.bootstrap.linear.transform

Cyclic-diagonal representations of packed-slot linear maps.

ArrayLike

data View source

ArrayLike: TypeAlias = Sequence[complex] | np.ndarray | torch.Tensor

DiagonalLinearTransform

class View source

DiagonalLinearTransform(diagonals: Mapping[int, ArrayLike], slots: int, name: str = 'diagonal_linear_transform')

An immutable cyclic-diagonal linear map over packed CKKS slots.

The map is

$$y=\sum _k{d}_k\odot {\mathrm{Rot}}_k(x).$$

Each stored diagonal is a CPU complex128 NumPy vector with shape [slot]; reference accepts and returns the same one-dimensional shape. This object contains no choice of execution algorithm. The matching evaluator independently decides whether to use direct diagonals, BSGS, hoisting, distribution, or a user implementation. Offsets are cyclic modulo $S$; duplicate representatives such as -1 and slots - 1 are combined by normalized_diagonals.

Attributes

Name	Type	Default/value
diagonals	Mapping[int, ArrayLike]
slots	int
name	str	'diagonal_linear_transform'

normalized_diagonals

method

def normalized_diagonals() -> dict[int, np.ndarray]: ...

Map every offset to $kmodS$ and combine equal rotations.

The stored arrays remain immutable. A new mapping is returned because two input offsets can normalize to the same cyclic key and must then be added elementwise. Returned vectors retain shape [slot].

reference

method

def reference(values: ArrayLike) -> np.ndarray: ...

Apply $L(x)=\sum _k{d}_k\odot {\mathrm{Rot}}_k(x)$ in NumPy.

values must have shape [slot]. The returned CPU complex128 array has shape [slot]. This plaintext oracle does not encode, rescale, consume depths, or model CKKS error.