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Sine Waves in 1D¤

exponax.ic.RandomSineWaves1d ¤

Bases: BaseRandomICGenerator

Source code in exponax/ic/_sine_waves_1d.py 
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class RandomSineWaves1d(BaseRandomICGenerator):
    num_spatial_dims: int
    domain_extent: float
    cutoff: int
    amplitude_range: tuple[float, float]
    phase_range: tuple[float, float]
    offset_range: tuple[float, float]

    std_one: bool
    max_one: bool

    def __init__(
        self,
        num_spatial_dims: int,
        *,
        domain_extent: float = 1.0,
        cutoff: int = 5,
        amplitude_range: tuple[float, float] = (-1.0, 1.0),
        phase_range: tuple[float, float] = (0.0, 2 * jnp.pi),
        offset_range: tuple[float, float] = (0.0, 0.0),
        std_one: bool = False,
        max_one: bool = False,
    ):
        """
        Random generator for initial states described by a collection of sine
        waves. Only works in 1d.

        This is a simplified version of the `RandomTruncatedFourierSeries`
        generator that works in arbitrary dimensions. However, only this
        generator can produce a functional representation of the initial
        condition.

        **Arguments**:

        - `num_spatial_dims`: The number of spatial dimensions.
        - `domain_extent`: The extent of the domain.
        - `cutoff`: The cutoff of the wavenumbers. This limits the
            "complexity" of the initial state. Note that some dynamics are very
            sensitive to high-frequency information.
        - `amplitude_range`: The range of the amplitudes. Defaults to
            `(-1.0, 1.0)`.
        - `phase_range`: The range of the phases. Defaults to `(0.0, 2π)`.
        - `offset_range`: The range of the offsets. Defaults to `(0.0,
            0.0)`, meaning **zero-mean** by default.
        - `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 num_spatial_dims != 1:
            raise ValueError("RandomSineWaves1d only works in 1d.")
        if offset_range != (0.0, 0.0) and std_one:
            raise ValueError("Cannot have non-zero offset 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.cutoff = cutoff
        self.amplitude_range = amplitude_range
        self.phase_range = phase_range
        self.offset_range = offset_range
        self.std_one = std_one
        self.max_one = max_one

    def gen_ic_fun(self, *, key: PRNGKeyArray) -> SineWaves1d:
        amplitude_key, phase_key, offset_key = jr.split(key, 3)

        amplitudes = jr.uniform(
            amplitude_key,
            shape=(self.cutoff,),
            minval=self.amplitude_range[0],
            maxval=self.amplitude_range[1],
        )
        phases = jr.uniform(
            phase_key,
            shape=(self.cutoff,),
            minval=self.phase_range[0],
            maxval=self.phase_range[1],
        )
        offset = jr.uniform(
            offset_key,
            shape=(),
            minval=self.offset_range[0],
            maxval=self.offset_range[1],
        )

        return SineWaves1d(
            domain_extent=self.domain_extent,
            amplitudes=amplitudes,
            wavenumbers=jnp.arange(1, self.cutoff + 1),
            phases=phases,
            offset=offset,
            std_one=self.std_one,
            max_one=self.max_one,
        )
__init__ ¤
__init__(
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    cutoff: int = 5,
    amplitude_range: tuple[float, float] = (-1.0, 1.0),
    phase_range: tuple[float, float] = (0.0, 2 * jnp.pi),
    offset_range: tuple[float, float] = (0.0, 0.0),
    std_one: bool = False,
    max_one: bool = False
)

Random generator for initial states described by a collection of sine waves. Only works in 1d.

This is a simplified version of the RandomTruncatedFourierSeries generator that works in arbitrary dimensions. However, only this generator can produce a functional representation of the initial condition.

Arguments:

  • num_spatial_dims: The number of spatial dimensions.
  • domain_extent: The extent of the domain.
  • cutoff: The cutoff of the wavenumbers. This limits the "complexity" of the initial state. Note that some dynamics are very sensitive to high-frequency information.
  • amplitude_range: The range of the amplitudes. Defaults to (-1.0, 1.0).
  • phase_range: The range of the phases. Defaults to (0.0, 2π).
  • offset_range: The range of the offsets. Defaults to (0.0, 0.0), meaning zero-mean by default.
  • 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/_sine_waves_1d.py 
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def __init__(
    self,
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    cutoff: int = 5,
    amplitude_range: tuple[float, float] = (-1.0, 1.0),
    phase_range: tuple[float, float] = (0.0, 2 * jnp.pi),
    offset_range: tuple[float, float] = (0.0, 0.0),
    std_one: bool = False,
    max_one: bool = False,
):
    """
    Random generator for initial states described by a collection of sine
    waves. Only works in 1d.

    This is a simplified version of the `RandomTruncatedFourierSeries`
    generator that works in arbitrary dimensions. However, only this
    generator can produce a functional representation of the initial
    condition.

    **Arguments**:

    - `num_spatial_dims`: The number of spatial dimensions.
    - `domain_extent`: The extent of the domain.
    - `cutoff`: The cutoff of the wavenumbers. This limits the
        "complexity" of the initial state. Note that some dynamics are very
        sensitive to high-frequency information.
    - `amplitude_range`: The range of the amplitudes. Defaults to
        `(-1.0, 1.0)`.
    - `phase_range`: The range of the phases. Defaults to `(0.0, 2π)`.
    - `offset_range`: The range of the offsets. Defaults to `(0.0,
        0.0)`, meaning **zero-mean** by default.
    - `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 num_spatial_dims != 1:
        raise ValueError("RandomSineWaves1d only works in 1d.")
    if offset_range != (0.0, 0.0) and std_one:
        raise ValueError("Cannot have non-zero offset 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.cutoff = cutoff
    self.amplitude_range = amplitude_range
    self.phase_range = phase_range
    self.offset_range = offset_range
    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.SineWaves1d ¤

Bases: BaseIC

Source code in exponax/ic/_sine_waves_1d.py 
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class SineWaves1d(BaseIC):
    domain_extent: float
    amplitudes: tuple[float, ...]
    wavenumbers: tuple[float, ...]
    phases: tuple[float, ...]
    offset: float

    std_one: bool
    max_one: bool

    def __init__(
        self,
        domain_extent: float,
        amplitudes: tuple[float, ...],
        wavenumbers: tuple[float, ...],
        phases: tuple[float, ...],
        offset: float = 0.0,
        std_one: bool = False,
        max_one: bool = False,
    ):
        """
        A state described by a collection of sine waves. Only works in 1d.

        **Arguments**:

        - `domain_extent`: The extent of the domain.
        - `amplitudes`: A tuple of amplitudes.
        - `wavenumbers`: A tuple of wavenumbers.
        - `phases`: A tuple of phases.
        - `offset`: A constant offset.
        - `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 offset != 0.0 and std_one:
            raise ValueError("Cannot have non-zero offset and `std_one=True`.")
        if std_one and max_one:
            raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

        if len(amplitudes) != len(wavenumbers) or len(wavenumbers) != len(phases):
            raise ValueError(
                "The number of amplitudes, wavenumbers, and phases must be the same."
            )

        self.domain_extent = domain_extent
        self.amplitudes = amplitudes
        self.wavenumbers = wavenumbers
        self.phases = phases
        self.offset = offset
        self.std_one = std_one
        self.max_one = max_one

    def __call__(self, x: Float[Array, "1 N"]) -> Float[Array, "1 N"]:
        if x.shape[0] != 1:
            raise ValueError("SineWaves1d only works in 1d.")
        result = jnp.zeros_like(x)
        for a, k, p in zip(self.amplitudes, self.wavenumbers, self.phases):
            result += a * jnp.sin(k * (2 * jnp.pi / self.domain_extent) * x + p)
        result += self.offset

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

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

        return result
__init__ ¤
__init__(
    domain_extent: float,
    amplitudes: tuple[float, ...],
    wavenumbers: tuple[float, ...],
    phases: tuple[float, ...],
    offset: float = 0.0,
    std_one: bool = False,
    max_one: bool = False,
)

A state described by a collection of sine waves. Only works in 1d.

Arguments:

  • domain_extent: The extent of the domain.
  • amplitudes: A tuple of amplitudes.
  • wavenumbers: A tuple of wavenumbers.
  • phases: A tuple of phases.
  • offset: A constant offset.
  • 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/_sine_waves_1d.py 
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def __init__(
    self,
    domain_extent: float,
    amplitudes: tuple[float, ...],
    wavenumbers: tuple[float, ...],
    phases: tuple[float, ...],
    offset: float = 0.0,
    std_one: bool = False,
    max_one: bool = False,
):
    """
    A state described by a collection of sine waves. Only works in 1d.

    **Arguments**:

    - `domain_extent`: The extent of the domain.
    - `amplitudes`: A tuple of amplitudes.
    - `wavenumbers`: A tuple of wavenumbers.
    - `phases`: A tuple of phases.
    - `offset`: A constant offset.
    - `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 offset != 0.0 and std_one:
        raise ValueError("Cannot have non-zero offset and `std_one=True`.")
    if std_one and max_one:
        raise ValueError("Cannot have `std_one=True` and `max_one=True`.")

    if len(amplitudes) != len(wavenumbers) or len(wavenumbers) != len(phases):
        raise ValueError(
            "The number of amplitudes, wavenumbers, and phases must be the same."
        )

    self.domain_extent = domain_extent
    self.amplitudes = amplitudes
    self.wavenumbers = wavenumbers
    self.phases = phases
    self.offset = offset
    self.std_one = std_one
    self.max_one = max_one
__call__ ¤
__call__(x: Float[Array, '1 N']) -> Float[Array, '1 N']
Source code in exponax/ic/_sine_waves_1d.py 
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def __call__(self, x: Float[Array, "1 N"]) -> Float[Array, "1 N"]:
    if x.shape[0] != 1:
        raise ValueError("SineWaves1d only works in 1d.")
    result = jnp.zeros_like(x)
    for a, k, p in zip(self.amplitudes, self.wavenumbers, self.phases):
        result += a * jnp.sin(k * (2 * jnp.pi / self.domain_extent) * x + p)
    result += self.offset

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

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

    return result