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from collections.abc import Sequence from typing import Literal as L, TypeAlias from numpy import complex128, float64 from numpy._typing import ArrayLike, NDArray, _ArrayLikeNumber_co __all__ = [ "fft", "ifft", "rfft", "irfft", "hfft", "ihfft", "rfftn", "irfftn", "rfft2", "irfft2", "fft2", "ifft2", "fftn", "ifftn", ] _NormKind: TypeAlias = L[None, "backward", "ortho", "forward"] def fft( a: ArrayLike, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def ifft( a: ArrayLike, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def rfft( a: ArrayLike, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def irfft( a: ArrayLike, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[float64] = ..., ) -> NDArray[float64]: ... # Input array must be compatible with `np.conjugate` def hfft( a: _ArrayLikeNumber_co, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[float64] = ..., ) -> NDArray[float64]: ... def ihfft( a: ArrayLike, n: None | int = ..., axis: int = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def fftn( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def ifftn( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def rfftn( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def irfftn( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[float64] = ..., ) -> NDArray[float64]: ... def fft2( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def ifft2( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def rfft2( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[complex128] = ..., ) -> NDArray[complex128]: ... def irfft2( a: ArrayLike, s: None | Sequence[int] = ..., axes: None | Sequence[int] = ..., norm: _NormKind = ..., out: None | NDArray[float64] = ..., ) -> NDArray[float64]: ...