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Polynomial¤

exponax.normalized.DifficultyPolynomialStepper ¤

Bases: NormalizedPolynomialStepper

Source code in exponax/normalized/_polynomial.py 
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class DifficultyPolynomialStepper(NormalizedPolynomialStepper):
    linear_difficulties: tuple[float, ...]
    polynomial_difficulties: tuple[float, ...]

    def __init__(
        self,
        num_spatial_dims: int = 1,
        num_points: int = 48,
        *,
        linear_difficulties: tuple[float, ...] = (
            10.0 * 0.001 / (10.0**0) * 48**0,
            0.0,
            1.0 * 0.001 / (10.0**2) * 48**2 * 2**1,
        ),
        polynomial_difficulties: tuple[float, ...] = (
            0.0,
            0.0,
            -10.0 * 0.001,
        ),
        order: int = 2,
        dealiasing_fraction: float = 2 / 3,
        num_circle_points: int = 16,
        circle_radius: float = 1.0,
    ):
        """
        By default: Fisher-KPP
        """
        self.linear_difficulties = linear_difficulties
        self.polynomial_difficulties = polynomial_difficulties

        normalized_coefficients = extract_normalized_coefficients_from_difficulty(
            linear_difficulties,
            num_spatial_dims=num_spatial_dims,
            num_points=num_points,
        )
        # For polynomial nonlinearities, we have difficulties == normalized scales
        normalized_polynomial_scales = polynomial_difficulties

        super().__init__(
            num_spatial_dims=num_spatial_dims,
            num_points=num_points,
            normalized_coefficients=normalized_coefficients,
            normalized_polynomial_scales=normalized_polynomial_scales,
            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, ...] = (
        10.0 * 0.001 / 10.0**0 * 48**0,
        0.0,
        1.0 * 0.001 / 10.0**2 * 48**2 * 2**1,
    ),
    polynomial_difficulties: tuple[float, ...] = (
        0.0,
        0.0,
        -10.0 * 0.001,
    ),
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0
)

By default: Fisher-KPP

Source code in exponax/normalized/_polynomial.py 
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def __init__(
    self,
    num_spatial_dims: int = 1,
    num_points: int = 48,
    *,
    linear_difficulties: tuple[float, ...] = (
        10.0 * 0.001 / (10.0**0) * 48**0,
        0.0,
        1.0 * 0.001 / (10.0**2) * 48**2 * 2**1,
    ),
    polynomial_difficulties: tuple[float, ...] = (
        0.0,
        0.0,
        -10.0 * 0.001,
    ),
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0,
):
    """
    By default: Fisher-KPP
    """
    self.linear_difficulties = linear_difficulties
    self.polynomial_difficulties = polynomial_difficulties

    normalized_coefficients = extract_normalized_coefficients_from_difficulty(
        linear_difficulties,
        num_spatial_dims=num_spatial_dims,
        num_points=num_points,
    )
    # For polynomial nonlinearities, we have difficulties == normalized scales
    normalized_polynomial_scales = polynomial_difficulties

    super().__init__(
        num_spatial_dims=num_spatial_dims,
        num_points=num_points,
        normalized_coefficients=normalized_coefficients,
        normalized_polynomial_scales=normalized_polynomial_scales,
        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)