General Polynomial Stepper

exponax.stepper.GeneralPolynomialStepper

Bases: BaseStepper

Source code in exponax/stepper/_polynomial.py

class GeneralPolynomialStepper(BaseStepper):
    coefficients: tuple[float, ...]
    polynomial_scales: tuple[float, ...]
    dealiasing_fraction: float

    def __init__(
        self,
        num_spatial_dims: int,
        domain_extent: float,
        num_points: int,
        dt: float,
        *,
        coefficients: tuple[float, ...] = (10.0, 0.0, 0.01),
        polynomial_scales: tuple[float, ...] = (0.0, 0.0, 10.0),
        order=2,
        dealiasing_fraction: float = 2 / 3,
        num_circle_points: int = 16,
        circle_radius: float = 1.0,
    ):
        """
        By default: Fisher-KPP with a small diffusion and 10.0 reactivity

        Note that the first two entries in the polynomial_scales list are often zero.

        The effect of polynomial_scale[1] is similar to the effect of coefficients[0]
        """
        self.coefficients = coefficients
        self.polynomial_scales = polynomial_scales
        self.dealiasing_fraction = dealiasing_fraction

        super().__init__(
            num_spatial_dims=num_spatial_dims,
            domain_extent=domain_extent,
            num_points=num_points,
            dt=dt,
            num_channels=1,
            order=order,
            num_circle_points=num_circle_points,
            circle_radius=circle_radius,
        )

    def _build_linear_operator(
        self,
        derivative_operator: Complex[Array, "D ... (N//2)+1"],
    ) -> Complex[Array, "1 ... (N//2)+1"]:
        linear_operator = sum(
            jnp.sum(
                c * (derivative_operator) ** i,
                axis=0,
                keepdims=True,
            )
            for i, c in enumerate(self.coefficients)
        )
        return linear_operator

    def _build_nonlinear_fun(
        self,
        derivative_operator: Complex[Array, "D ... (N//2)+1"],
    ) -> PolynomialNonlinearFun:
        return PolynomialNonlinearFun(
            self.num_spatial_dims,
            self.num_points,
            dealiasing_fraction=self.dealiasing_fraction,
            coefficients=self.polynomial_scales,
        )

__init__

__init__(
    num_spatial_dims: int,
    domain_extent: float,
    num_points: int,
    dt: float,
    *,
    coefficients: tuple[float, ...] = (10.0, 0.0, 0.01),
    polynomial_scales: tuple[float, ...] = (0.0, 0.0, 10.0),
    order=2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0
)

By default: Fisher-KPP with a small diffusion and 10.0 reactivity

Note that the first two entries in the polynomial_scales list are often zero.

The effect of polynomial_scale[1] is similar to the effect of coefficients[0]

Source code in exponax/stepper/_polynomial.py

def __init__(
    self,
    num_spatial_dims: int,
    domain_extent: float,
    num_points: int,
    dt: float,
    *,
    coefficients: tuple[float, ...] = (10.0, 0.0, 0.01),
    polynomial_scales: tuple[float, ...] = (0.0, 0.0, 10.0),
    order=2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0,
):
    """
    By default: Fisher-KPP with a small diffusion and 10.0 reactivity

    Note that the first two entries in the polynomial_scales list are often zero.

    The effect of polynomial_scale[1] is similar to the effect of coefficients[0]
    """
    self.coefficients = coefficients
    self.polynomial_scales = polynomial_scales
    self.dealiasing_fraction = dealiasing_fraction

    super().__init__(
        num_spatial_dims=num_spatial_dims,
        domain_extent=domain_extent,
        num_points=num_points,
        dt=dt,
        num_channels=1,
        order=order,
        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

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)