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Nonlinear¤

exponax.normalized.DifficultyGeneralNonlinearStepper ¤

Bases: NormalizedGeneralNonlinearStepper

Source code in exponax/normalized/_general_nonlinear.py 
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class DifficultyGeneralNonlinearStepper(NormalizedGeneralNonlinearStepper):
    linear_difficulties: tuple[float, ...]
    nonlinear_difficulties: tuple[float, ...]

    def __init__(
        self,
        num_spatial_dims: int = 1,
        num_points: int = 48,
        *,
        linear_difficulties: tuple[float, ...] = (
            0.0,
            0.0,
            0.1 * 0.1 / 1.0 * 48**2 * 2,
        ),
        nonlinear_difficulties: tuple[float, ...] = (
            0.0,
            -1.0 * 0.1 / 1.0 * 48,
            0.0,
        ),
        maximum_absolute: float = 1.0,
        order: int = 2,
        dealiasing_fraction: float = 2 / 3,
        num_circle_points: int = 16,
        circle_radius: float = 1.0,
    ):
        """
        By default Burgers.
        """
        self.linear_difficulties = linear_difficulties
        self.nonlinear_difficulties = nonlinear_difficulties

        normalized_coefficients_linear = (
            extract_normalized_coefficients_from_difficulty(
                linear_difficulties,
                num_spatial_dims=num_spatial_dims,
                num_points=num_points,
            )
        )
        normalized_coefficients_nonlinear = (
            extract_normalized_nonlinear_scales_from_difficulty(
                nonlinear_difficulties,
                num_spatial_dims=num_spatial_dims,
                num_points=num_points,
                maximum_absolute=maximum_absolute,
            )
        )

        super().__init__(
            num_spatial_dims=num_spatial_dims,
            num_points=num_points,
            normalized_coefficients_linear=normalized_coefficients_linear,
            normalized_coefficients_nonlinear=normalized_coefficients_nonlinear,
            order=order,
            dealiasing_fraction=dealiasing_fraction,
            num_circle_points=num_circle_points,
            circle_radius=circle_radius,
        )
__init__ ¤
__init__(
    num_spatial_dims: int = 1,
    num_points: int = 48,
    *,
    linear_difficulties: tuple[float, ...] = (
        0.0,
        0.0,
        0.1 * 0.1 / 1.0 * 48**2 * 2,
    ),
    nonlinear_difficulties: tuple[float, ...] = (
        0.0,
        -1.0 * 0.1 / 1.0 * 48,
        0.0,
    ),
    maximum_absolute: float = 1.0,
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0
)

By default Burgers.

Source code in exponax/normalized/_general_nonlinear.py 
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def __init__(
    self,
    num_spatial_dims: int = 1,
    num_points: int = 48,
    *,
    linear_difficulties: tuple[float, ...] = (
        0.0,
        0.0,
        0.1 * 0.1 / 1.0 * 48**2 * 2,
    ),
    nonlinear_difficulties: tuple[float, ...] = (
        0.0,
        -1.0 * 0.1 / 1.0 * 48,
        0.0,
    ),
    maximum_absolute: float = 1.0,
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0,
):
    """
    By default Burgers.
    """
    self.linear_difficulties = linear_difficulties
    self.nonlinear_difficulties = nonlinear_difficulties

    normalized_coefficients_linear = (
        extract_normalized_coefficients_from_difficulty(
            linear_difficulties,
            num_spatial_dims=num_spatial_dims,
            num_points=num_points,
        )
    )
    normalized_coefficients_nonlinear = (
        extract_normalized_nonlinear_scales_from_difficulty(
            nonlinear_difficulties,
            num_spatial_dims=num_spatial_dims,
            num_points=num_points,
            maximum_absolute=maximum_absolute,
        )
    )

    super().__init__(
        num_spatial_dims=num_spatial_dims,
        num_points=num_points,
        normalized_coefficients_linear=normalized_coefficients_linear,
        normalized_coefficients_nonlinear=normalized_coefficients_nonlinear,
        order=order,
        dealiasing_fraction=dealiasing_fraction,
        num_circle_points=num_circle_points,
        circle_radius=circle_radius,
    )
__call__ ¤
__call__(
    u: Float[Array, "C ... N"]
) -> Float[Array, "C ... N"]

Performs a check

Source code in exponax/_base_stepper.py 
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def __call__(
    self,
    u: Float[Array, "C ... N"],
) -> Float[Array, "C ... N"]:
    """
    Performs a check
    """
    expected_shape = (self.num_channels,) + spatial_shape(
        self.num_spatial_dims, self.num_points
    )
    if u.shape != expected_shape:
        raise ValueError(
            f"Expected shape {expected_shape}, got {u.shape}. For batched operation use `jax.vmap` on this function."
        )
    return self.step(u)