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Gaussian Blob¤

exponax.ic.RandomGaussianBlobs ¤

Bases: BaseRandomICGenerator

Source code in exponax/ic/_gaussian_blob.py 
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class RandomGaussianBlobs(BaseRandomICGenerator):
    num_spatial_dims: int
    domain_extent: float
    num_blobs: int

    position_range: tuple[float, float]
    variance_range: tuple[float, float]

    one_complement: bool

    def __init__(
        self,
        num_spatial_dims: int,
        *,
        domain_extent: float = 1.0,
        num_blobs: int = 1,
        position_range: tuple[float, float] = (0.4, 0.6),
        variance_range: tuple[float, float] = (0.005, 0.01),
        one_complement: bool = False,
    ):
        """
        A random Gaussian blob initial condition generator.

        **Arguments**:

        - `num_spatial_dims`: The number of spatial dimensions.
        - `domain_extent`: The extent of the domain.
        - `num_blobs`: The number of blobs.
        - `position_range`: The range of the position of the blobs. This
            will be scaled by the domain extent. Hence, this acts as if the
            domain_extent was 1
        - `variance_range`: The range of the variance of the blobs. This will
            be scaled by the domain extent. Hence, this acts as if the
            domain_extent was 1
        - `one_complement`: Whether to return one minus the Gaussian blob.
        """
        self.num_spatial_dims = num_spatial_dims
        self.domain_extent = domain_extent
        self.num_blobs = num_blobs
        self.position_range = position_range
        self.variance_range = variance_range
        self.one_complement = one_complement

    def gen_blob(self, *, key) -> GaussianBlob:
        """
        Generates a single Gaussian blob.
        """
        position_key, variance_key = jr.split(key)

        position = jr.uniform(
            position_key,
            shape=(self.num_spatial_dims,),
            minval=self.position_range[0] * self.domain_extent,
            maxval=self.position_range[1] * self.domain_extent,
        )
        variances = jr.uniform(
            variance_key,
            shape=(self.num_spatial_dims,),
            minval=self.variance_range[0] * self.domain_extent,
            maxval=self.variance_range[1] * self.domain_extent,
        )
        covariance = jnp.diag(variances)

        return GaussianBlob(position, covariance, one_complement=self.one_complement)

    def gen_ic_fun(self, *, key: PRNGKeyArray) -> GaussianBlobs:
        blob_list = []
        for _ in range(self.num_blobs):
            key, subkey = jr.split(key)
            blob_list.append(self.gen_blob(key=subkey))
        return GaussianBlobs(tuple(blob_list))
__init__ ¤
__init__(
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    num_blobs: int = 1,
    position_range: tuple[float, float] = (0.4, 0.6),
    variance_range: tuple[float, float] = (0.005, 0.01),
    one_complement: bool = False
)

A random Gaussian blob initial condition generator.

Arguments:

  • num_spatial_dims: The number of spatial dimensions.
  • domain_extent: The extent of the domain.
  • num_blobs: The number of blobs.
  • position_range: The range of the position of the blobs. This will be scaled by the domain extent. Hence, this acts as if the domain_extent was 1
  • variance_range: The range of the variance of the blobs. This will be scaled by the domain extent. Hence, this acts as if the domain_extent was 1
  • one_complement: Whether to return one minus the Gaussian blob.
Source code in exponax/ic/_gaussian_blob.py 
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def __init__(
    self,
    num_spatial_dims: int,
    *,
    domain_extent: float = 1.0,
    num_blobs: int = 1,
    position_range: tuple[float, float] = (0.4, 0.6),
    variance_range: tuple[float, float] = (0.005, 0.01),
    one_complement: bool = False,
):
    """
    A random Gaussian blob initial condition generator.

    **Arguments**:

    - `num_spatial_dims`: The number of spatial dimensions.
    - `domain_extent`: The extent of the domain.
    - `num_blobs`: The number of blobs.
    - `position_range`: The range of the position of the blobs. This
        will be scaled by the domain extent. Hence, this acts as if the
        domain_extent was 1
    - `variance_range`: The range of the variance of the blobs. This will
        be scaled by the domain extent. Hence, this acts as if the
        domain_extent was 1
    - `one_complement`: Whether to return one minus the Gaussian blob.
    """
    self.num_spatial_dims = num_spatial_dims
    self.domain_extent = domain_extent
    self.num_blobs = num_blobs
    self.position_range = position_range
    self.variance_range = variance_range
    self.one_complement = one_complement
__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.GaussianBlobs ¤

Bases: BaseIC

Source code in exponax/ic/_gaussian_blob.py 
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class GaussianBlobs(BaseIC):
    blob_list: tuple[GaussianBlob, ...]

    def __init__(
        self,
        blob_list: tuple[GaussianBlob, ...],
    ):
        """
        A state described by a collection of Gaussian blobs.

        **Arguments**:

        - `blob_list`: A tuple of Gaussian blobs.
        """
        self.blob_list = blob_list

    def __call__(self, x: Array) -> Array:
        summation = sum(blob(x) for blob in self.blob_list)
        return summation / len(self.blob_list)
blob_list instance-attribute ¤
blob_list: tuple[GaussianBlob, ...] = blob_list
__init__ ¤
__init__(blob_list: tuple[GaussianBlob, ...])

A state described by a collection of Gaussian blobs.

Arguments:

  • blob_list: A tuple of Gaussian blobs.
Source code in exponax/ic/_gaussian_blob.py 
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def __init__(
    self,
    blob_list: tuple[GaussianBlob, ...],
):
    """
    A state described by a collection of Gaussian blobs.

    **Arguments**:

    - `blob_list`: A tuple of Gaussian blobs.
    """
    self.blob_list = blob_list
__call__ ¤
__call__(x: Array) -> Array
Source code in exponax/ic/_gaussian_blob.py 
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def __call__(self, x: Array) -> Array:
    summation = sum(blob(x) for blob in self.blob_list)
    return summation / len(self.blob_list)