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Discontinuities¤

exponax.ic.RandomDiscontinuities ¤

Bases: BaseRandomICGenerator

Source code in exponax/ic/_discontinuities.py 
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class RandomDiscontinuities(BaseRandomICGenerator):
    num_spatial_dims: int
    domain_extent: float
    num_discontinuities: int
    value_range: tuple[float, float]

    zero_mean: bool
    std_one: bool
    max_one: bool

    def __init__(
        self,
        num_spatial_dims: int,
        *,
        domain_extent: float = 1.0,
        num_discontinuities: int = 3,
        value_range: tuple[float, float] = (-1.0, 1.0),
        zero_mean: bool = False,
        std_one: bool = False,
        max_one: bool = False,
    ):
        """
        Random generator for initial states described by a collection of
        discontinuities.

        **Arguments**:

        - `num_spatial_dims`: The number of spatial dimensions.
        - `domain_extent`: The extent of the domain in each spatial direction.
        - `num_discontinuities`: The number of discontinuities.
        - `value_range`: The range of values for the discontinuities.
        - `zero_mean`: Whether the state should have zero mean.
        - `std_one`: Whether to normalize the state to have a standard
            deviation of one. Defaults to `False`. Only works if the offset is
            zero.
        - `max_one`: Whether to normalize the state to have the maximum
            absolute value of one. Defaults to `False`. Only one of `std_one`
            and `max_one` can be `True`.
        """
        if not zero_mean and std_one:
            raise ValueError("Cannot have `zero_mean=False` and `std_one=True`.")
        if std_one and max_one:
            raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

        self.num_spatial_dims = num_spatial_dims
        self.domain_extent = domain_extent
        self.num_discontinuities = num_discontinuities
        self.value_range = value_range

        self.zero_mean = zero_mean
        self.std_one = std_one
        self.max_one = max_one

    def gen_one_ic_fn(self, *, key: PRNGKeyArray) -> Discontinuity:
        """
        Generates a single discontinuity.
        """
        lower_limits = []
        upper_limits = []
        for i in range(self.num_spatial_dims):
            key_1, key_2, key = jr.split(key, 3)
            lim_1 = jr.uniform(key_1, (), minval=0.0, maxval=self.domain_extent)
            lim_2 = jr.uniform(key_2, (), minval=0.0, maxval=self.domain_extent)
            lower_limits.append(jnp.minimum(lim_1, lim_2))
            upper_limits.append(jnp.maximum(lim_1, lim_2))

        lower_limits = tuple(lower_limits)
        upper_limits = tuple(upper_limits)

        value = jr.uniform(
            key, (), minval=self.value_range[0], maxval=self.value_range[1]
        )

        return Discontinuity(
            lower_limits=lower_limits, upper_limits=upper_limits, value=value
        )

    def gen_ic_fun(self, *, key: PRNGKeyArray) -> BaseIC:
        disc_list = [
            self.gen_one_ic_fn(key=k) for k in jr.split(key, self.num_discontinuities)
        ]
        return Discontinuities(
            discontinuity_list=disc_list,
            zero_mean=self.zero_mean,
            std_one=self.std_one,
            max_one=self.max_one,
        )
__init__ ¤
__init__(
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    num_discontinuities: int = 3,
    value_range: tuple[float, float] = (-1.0, 1.0),
    zero_mean: bool = False,
    std_one: bool = False,
    max_one: bool = False
)

Random generator for initial states described by a collection of discontinuities.

Arguments:

  • num_spatial_dims: The number of spatial dimensions.
  • domain_extent: The extent of the domain in each spatial direction.
  • num_discontinuities: The number of discontinuities.
  • value_range: The range of values for the discontinuities.
  • zero_mean: Whether the state should have zero mean.
  • std_one: Whether to normalize the state to have a standard deviation of one. Defaults to False. Only works if the offset is zero.
  • max_one: Whether to normalize the state to have the maximum absolute value of one. Defaults to False. Only one of std_one and max_one can be True.
Source code in exponax/ic/_discontinuities.py 
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def __init__(
    self,
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    num_discontinuities: int = 3,
    value_range: tuple[float, float] = (-1.0, 1.0),
    zero_mean: bool = False,
    std_one: bool = False,
    max_one: bool = False,
):
    """
    Random generator for initial states described by a collection of
    discontinuities.

    **Arguments**:

    - `num_spatial_dims`: The number of spatial dimensions.
    - `domain_extent`: The extent of the domain in each spatial direction.
    - `num_discontinuities`: The number of discontinuities.
    - `value_range`: The range of values for the discontinuities.
    - `zero_mean`: Whether the state should have zero mean.
    - `std_one`: Whether to normalize the state to have a standard
        deviation of one. Defaults to `False`. Only works if the offset is
        zero.
    - `max_one`: Whether to normalize the state to have the maximum
        absolute value of one. Defaults to `False`. Only one of `std_one`
        and `max_one` can be `True`.
    """
    if not zero_mean and std_one:
        raise ValueError("Cannot have `zero_mean=False` and `std_one=True`.")
    if std_one and max_one:
        raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

    self.num_spatial_dims = num_spatial_dims
    self.domain_extent = domain_extent
    self.num_discontinuities = num_discontinuities
    self.value_range = value_range

    self.zero_mean = zero_mean
    self.std_one = std_one
    self.max_one = max_one
__call__ ¤
__call__(
    num_points: int, *, key: PRNGKeyArray
) -> Float[Array, "1 ... N"]

Generate a random initial condition on a grid with num_points points.

Arguments:

  • num_points: The number of grid points in each dimension.
  • key: A jax random key.

Returns:

  • u: The initial condition evaluated at the grid points.
Source code in exponax/ic/_base_ic.py 
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def __call__(
    self,
    num_points: int,
    *,
    key: PRNGKeyArray,
) -> Float[Array, "1 ... N"]:
    """
    Generate a random initial condition on a grid with `num_points` points.

    **Arguments**:

    - `num_points`: The number of grid points in each dimension.
    - `key`: A jax random key.

    **Returns**:

    - `u`: The initial condition evaluated at the grid points.
    """
    ic_fun = self.gen_ic_fun(key=key)
    grid = make_grid(
        self.num_spatial_dims,
        self.domain_extent,
        num_points,
        indexing=self.indexing,
    )
    return ic_fun(grid)

exponax.ic.Discontinuities ¤

Bases: BaseIC

Source code in exponax/ic/_discontinuities.py 
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class Discontinuities(BaseIC):
    discontinuity_list: tuple[Discontinuity, ...]
    zero_mean: bool
    std_one: bool
    max_one: bool

    def __init__(
        self,
        discontinuity_list: tuple[Discontinuity, ...],
        *,
        zero_mean: bool = True,
        std_one: bool = False,
        max_one: bool = False,
    ):
        """
        A state described by a collection of discontinuities.

        **Arguments**:

        - `discontinuity_list`: A tuple of discontinuities.
        - `zero_mean`: Whether the state should have zero mean.
        - `std_one`: Whether to normalize the state to have a standard
            deviation of one. Defaults to `False`. Only works if the offset is
            zero.
        - `max_one`: Whether to normalize the state to have the maximum
            absolute value of one. Defaults to `False`. Only one of `std_one`
            and `max_one` can be `True`.
        """
        if not zero_mean and std_one:
            raise ValueError("Cannot have `zero_mean=False` and `std_one=True`.")
        if std_one and max_one:
            raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

        self.discontinuity_list = discontinuity_list
        self.zero_mean = zero_mean
        self.std_one = std_one
        self.max_one = max_one

    def __call__(self, x: Array) -> Array:
        ic = sum(disc(x) for disc in self.discontinuity_list)

        if self.zero_mean:
            ic = ic - jnp.mean(ic)

        if self.std_one:
            ic = ic / jnp.std(ic)

        if self.max_one:
            ic = ic / jnp.max(jnp.abs(ic))

        return ic
__init__ ¤
__init__(
    discontinuity_list: tuple[Discontinuity, ...],
    *,
    zero_mean: bool = True,
    std_one: bool = False,
    max_one: bool = False
)

A state described by a collection of discontinuities.

Arguments:

  • discontinuity_list: A tuple of discontinuities.
  • zero_mean: Whether the state should have zero mean.
  • std_one: Whether to normalize the state to have a standard deviation of one. Defaults to False. Only works if the offset is zero.
  • max_one: Whether to normalize the state to have the maximum absolute value of one. Defaults to False. Only one of std_one and max_one can be True.
Source code in exponax/ic/_discontinuities.py 
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def __init__(
    self,
    discontinuity_list: tuple[Discontinuity, ...],
    *,
    zero_mean: bool = True,
    std_one: bool = False,
    max_one: bool = False,
):
    """
    A state described by a collection of discontinuities.

    **Arguments**:

    - `discontinuity_list`: A tuple of discontinuities.
    - `zero_mean`: Whether the state should have zero mean.
    - `std_one`: Whether to normalize the state to have a standard
        deviation of one. Defaults to `False`. Only works if the offset is
        zero.
    - `max_one`: Whether to normalize the state to have the maximum
        absolute value of one. Defaults to `False`. Only one of `std_one`
        and `max_one` can be `True`.
    """
    if not zero_mean and std_one:
        raise ValueError("Cannot have `zero_mean=False` and `std_one=True`.")
    if std_one and max_one:
        raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

    self.discontinuity_list = discontinuity_list
    self.zero_mean = zero_mean
    self.std_one = std_one
    self.max_one = max_one
__call__ ¤
__call__(x: Array) -> Array
Source code in exponax/ic/_discontinuities.py 
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def __call__(self, x: Array) -> Array:
    ic = sum(disc(x) for disc in self.discontinuity_list)

    if self.zero_mean:
        ic = ic - jnp.mean(ic)

    if self.std_one:
        ic = ic / jnp.std(ic)

    if self.max_one:
        ic = ic / jnp.max(jnp.abs(ic))

    return ic