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9. Base Classes for Operators

torchfsm.operator.LinearCoef ¤

Bases: ABC

Abstract class for linear coefficients.

Source code in torchfsm/operator/_base.py 
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class LinearCoef(ABC):

    r"""
    Abstract class for linear coefficients.
    """

    @abstractmethod
    def __call__(
        self, f_mesh: FourierMesh, n_channel: int
    ) -> FourierTensor["B C H ..."]:
        r"""
        Abstract method to be implemented by subclasses. It should define the linear coefficient tensor.

        Args:
            f_mesh (FourierMesh): Fourier mesh object.
            n_channel (int): Number of channels of the input tensor.

        Returns:
            FourierTensor: Linear coefficient tensor.
        """

        raise NotImplementedError

    def nonlinear_like(
        self,
        u_fft: FourierTensor["B C H ..."],
        f_mesh: FourierMesh,
        u: Optional[SpatialTensor["B C H ..."]]=None,
    ) -> FourierTensor["B C H ..."]:
        r"""
        Calculate the result out based on the linear coefficient. It is designed to have same pattern as the nonlinear function.

        Args:
            u_fft (FourierTensor): Fourier-transformed input tensor.
            f_mesh (FourierMesh): Fourier mesh object.
            u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

        Returns:
            FourierTensor: Nonlinear-like tensor.
        """
        return self(f_mesh, u_fft.shape[1]) * u_fft
__call__ abstractmethod ¤
__call__(
    f_mesh: FourierMesh, n_channel: int
) -> FourierTensor["B C H ..."]

Abstract method to be implemented by subclasses. It should define the linear coefficient tensor.

Parameters:

Name Type Description Default
f_mesh FourierMesh

Fourier mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required

Returns:

Name Type Description
FourierTensor FourierTensor['B C H ...']

Linear coefficient tensor.
Source code in torchfsm/operator/_base.py 
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@abstractmethod
def __call__(
    self, f_mesh: FourierMesh, n_channel: int
) -> FourierTensor["B C H ..."]:
    r"""
    Abstract method to be implemented by subclasses. It should define the linear coefficient tensor.

    Args:
        f_mesh (FourierMesh): Fourier mesh object.
        n_channel (int): Number of channels of the input tensor.

    Returns:
        FourierTensor: Linear coefficient tensor.
    """

    raise NotImplementedError
nonlinear_like ¤
nonlinear_like(
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]] = None,
) -> FourierTensor["B C H ..."]

Calculate the result out based on the linear coefficient. It is designed to have same pattern as the nonlinear function.

Parameters:

Name Type Description Default
u_fft FourierTensor

Fourier-transformed input tensor.

 required
f_mesh FourierMesh

Fourier mesh object.

 required
u Optional[SpatialTensor]

Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

 None

Returns:

Name Type Description
FourierTensor FourierTensor['B C H ...']

Nonlinear-like tensor.
Source code in torchfsm/operator/_base.py 
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def nonlinear_like(
    self,
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]]=None,
) -> FourierTensor["B C H ..."]:
    r"""
    Calculate the result out based on the linear coefficient. It is designed to have same pattern as the nonlinear function.

    Args:
        u_fft (FourierTensor): Fourier-transformed input tensor.
        f_mesh (FourierMesh): Fourier mesh object.
        u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

    Returns:
        FourierTensor: Nonlinear-like tensor.
    """
    return self(f_mesh, u_fft.shape[1]) * u_fft

torchfsm.operator.NonlinearFunc ¤

Bases: ABC

Abstract class for nonlinear functions.

Parameters:

Name Type Description Default
dealiasing_swtich bool

Whether to apply dealiasing. Default is True. If True, the dealiased version of u_fft will be input to the function in operator. If False, the original u_fft will be used.

 True
Source code in torchfsm/operator/_base.py 
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class NonlinearFunc(ABC):

    r"""
    Abstract class for nonlinear functions.

    Args:
        dealiasing_swtich (bool): Whether to apply dealiasing. Default is True.
            If True, the dealiased version of u_fft will be input to the function in operator.
            If False, the original u_fft will be used.
    """

    def __init__(self, dealiasing_swtich: bool = True) -> None:
        self._dealiasing_swtich = dealiasing_swtich

    @abstractmethod
    def __call__(
        self,
        u_fft: FourierTensor["B C H ..."],
        f_mesh: FourierMesh,
        u: Optional[SpatialTensor["B C H ..."]]=None,
    ) -> FourierTensor["B C H ..."]:
        r"""
        Abstract method to be implemented by subclasses. It should define the nonlinear function.

        Args:
            u_fft (FourierTensor): Fourier-transformed input tensor.
            f_mesh (FourierMesh): Fourier mesh object.
            u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

        Returns:
            FourierTensor: Result of the nonlinear function.
        """
        raise NotImplementedError

    def spatial_value(
        self,
        u_fft: FourierTensor["B C H ..."],
        f_mesh: FourierMesh,
        u: Optional[SpatialTensor["B C H ..."]]=None,
    ) -> SpatialTensor["B C H ..."]:
        r"""
        Return the result of the nonlinear function in spatial domain.

        Args:
            u_fft (FourierTensor): Fourier-transformed input tensor.
            f_mesh (FourierMesh): Fourier mesh object.
            u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

        Returns:
            SpatialTensor: Result of the nonlinear function in spatial domain.
        """

        return f_mesh.ifft(self(u_fft, f_mesh, u)).real
_dealiasing_swtich instance-attribute ¤
_dealiasing_swtich = dealiasing_swtich
__init__ ¤
__init__(dealiasing_swtich: bool = True) -> None
Source code in torchfsm/operator/_base.py 
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def __init__(self, dealiasing_swtich: bool = True) -> None:
    self._dealiasing_swtich = dealiasing_swtich
__call__ abstractmethod ¤
__call__(
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]] = None,
) -> FourierTensor["B C H ..."]

Abstract method to be implemented by subclasses. It should define the nonlinear function.

Parameters:

Name Type Description Default
u_fft FourierTensor

Fourier-transformed input tensor.

 required
f_mesh FourierMesh

Fourier mesh object.

 required
u Optional[SpatialTensor]

Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

 None

Returns:

Name Type Description
FourierTensor FourierTensor['B C H ...']

Result of the nonlinear function.
Source code in torchfsm/operator/_base.py 
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@abstractmethod
def __call__(
    self,
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]]=None,
) -> FourierTensor["B C H ..."]:
    r"""
    Abstract method to be implemented by subclasses. It should define the nonlinear function.

    Args:
        u_fft (FourierTensor): Fourier-transformed input tensor.
        f_mesh (FourierMesh): Fourier mesh object.
        u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

    Returns:
        FourierTensor: Result of the nonlinear function.
    """
    raise NotImplementedError
spatial_value ¤
spatial_value(
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]] = None,
) -> SpatialTensor["B C H ..."]

Return the result of the nonlinear function in spatial domain.

Parameters:

Name Type Description Default
u_fft FourierTensor

Fourier-transformed input tensor.

 required
f_mesh FourierMesh

Fourier mesh object.

 required
u Optional[SpatialTensor]

Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

 None

Returns:

Name Type Description
SpatialTensor SpatialTensor['B C H ...']

Result of the nonlinear function in spatial domain.
Source code in torchfsm/operator/_base.py 
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def spatial_value(
    self,
    u_fft: FourierTensor["B C H ..."],
    f_mesh: FourierMesh,
    u: Optional[SpatialTensor["B C H ..."]]=None,
) -> SpatialTensor["B C H ..."]:
    r"""
    Return the result of the nonlinear function in spatial domain.

    Args:
        u_fft (FourierTensor): Fourier-transformed input tensor.
        f_mesh (FourierMesh): Fourier mesh object.
        u (Optional[SpatialTensor]): Corresponding tensor of u_fft in spatial domain. This option aims to avoid repeating the inverse FFT operation in operators.

    Returns:
        SpatialTensor: Result of the nonlinear function in spatial domain.
    """

    return f_mesh.ifft(self(u_fft, f_mesh, u)).real

torchfsm.operator.CoreGenerator ¤

Bases: ABC

Abstract class for core generator. A core generator is a callable that generates a linear coefficient or a nonlinear function based on the Fourier mesh and channels of the tensor.

Source code in torchfsm/operator/_base.py 
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class CoreGenerator(ABC):

    r"""
    Abstract class for core generator. A core generator is a callable that generates a linear coefficient or a nonlinear function based on the Fourier mesh and channels of the tensor.
    """

    @abstractmethod
    def __call__(
        self, f_mesh: FourierMesh, n_channel: int
    ) -> Union[LinearCoef, NonlinearFunc]:
        r"""
        Abstract method to be implemented by subclasses. It should define the core generator.

        Args:
            f_mesh (FourierMesh): Fourier mesh object.
            n_channel (int): Number of channels of the input tensor.

        Returns:
            Union[LinearCoef, NonlinearFunc]: Linear coefficient or nonlinear function.
        """
        raise NotImplementedError
__call__ abstractmethod ¤
__call__(
    f_mesh: FourierMesh, n_channel: int
) -> Union[LinearCoef, NonlinearFunc]

Abstract method to be implemented by subclasses. It should define the core generator.

Parameters:

Name Type Description Default
f_mesh FourierMesh

Fourier mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required

Returns:

Type Description
Union[LinearCoef, NonlinearFunc]

Union[LinearCoef, NonlinearFunc]: Linear coefficient or nonlinear function.
Source code in torchfsm/operator/_base.py 
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@abstractmethod
def __call__(
    self, f_mesh: FourierMesh, n_channel: int
) -> Union[LinearCoef, NonlinearFunc]:
    r"""
    Abstract method to be implemented by subclasses. It should define the core generator.

    Args:
        f_mesh (FourierMesh): Fourier mesh object.
        n_channel (int): Number of channels of the input tensor.

    Returns:
        Union[LinearCoef, NonlinearFunc]: Linear coefficient or nonlinear function.
    """
    raise NotImplementedError

torchfsm.operator._base._MutableMixIn ¤

Mixin class for mutable operations. This class supports basic arithmetic operations for the operator.

Source code in torchfsm/operator/_base.py 
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class _MutableMixIn:

    r'''
    Mixin class for mutable operations. This class supports basic arithmetic operations for the operator.
    '''

    def __radd__(self, other):
        return self + other

    def __iadd__(self, other):
        return self + other

    def __sub__(self, other):
        try:
            return self + (-1 * other)
        except Exception:
            return NotImplemented

    def __rsub__(self, other):
        try:
            return other + (-1 * self)
        except Exception:
            return NotImplemented

    def __isub__(self, other):
        return self - other

    def __rmul__(self, other):
        return self * other

    def __imul__(self, other):
        return self * other

    def __truediv__(self, other):
        try:
            return self * (1 / other)
        except:
            return NotImplemented
__radd__ ¤
__radd__(other)
Source code in torchfsm/operator/_base.py 
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def __radd__(self, other):
    return self + other
__iadd__ ¤
__iadd__(other)
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def __iadd__(self, other):
    return self + other
__sub__ ¤
__sub__(other)
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def __sub__(self, other):
    try:
        return self + (-1 * other)
    except Exception:
        return NotImplemented
__rsub__ ¤
__rsub__(other)
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def __rsub__(self, other):
    try:
        return other + (-1 * self)
    except Exception:
        return NotImplemented
__isub__ ¤
__isub__(other)
Source code in torchfsm/operator/_base.py 
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def __isub__(self, other):
    return self - other
__rmul__ ¤
__rmul__(other)
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def __rmul__(self, other):
    return self * other
__imul__ ¤
__imul__(other)
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def __imul__(self, other):
    return self * other
__truediv__ ¤
__truediv__(other)
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def __truediv__(self, other):
    try:
        return self * (1 / other)
    except:
        return NotImplemented

torchfsm.operator._base._InverseSolveMixin ¤

Source code in torchfsm/operator/_base.py 
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class _InverseSolveMixin:
    _state_dict: Optional[dict]
    register_mesh: Callable

    r'''
    Mixin class for inverse solving operations. This class supports solving the linear operator equation.
    '''

    def solve(
        self,
        b: Optional[torch.Tensor] = None,
        b_fft: Optional[torch.Tensor] = None,
        mesh: Optional[
            Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
        ] = None,
        n_channel: Optional[int] = None,
        return_in_fourier=False,
    ) -> Union[SpatialTensor["B C H ..."], SpatialTensor["B C H ..."]]:

        r"""
        Solve the linear operator equation $Ax = b$, where $A$ is the linear operator and $b$ is the right-hand side.

        Args:
            b (Optional[torch.Tensor]): Right-hand side tensor in spatial domain. If None, b_fft should be provided.
            b_fft (Optional[torch.Tensor]): Right-hand side tensor in Fourier domain. If None, b should be provided.
            mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. If None, the mesh registered in the operator will be used.
            n_channel (Optional[int]): Number of channels of $x$. If None, the number of channels registered in the operator will be used.
            return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain.

        Returns:
            Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Solution tensor in spatial or Fourier domain.
        """
        if not (mesh is not None and n_channel is not None):
            assert (
                self._state_dict["f_mesh"] is not None
            ), "Mesh and n_channel should be given when calling solve"
        if not (mesh is None and n_channel is None):
            mesh = self._state_dict["f_mesh"] if mesh is None else mesh
            n_channel = (
                self._state_dict["n_channel"] if n_channel is None else n_channel
            )
            self.register_mesh(mesh, n_channel)
        if self._state_dict["invert_linear_coef"] is None:
            self._state_dict["invert_linear_coef"] = torch.where(
                self._state_dict["linear_coef"] == 0,
                1.0,
                1 / self._state_dict["linear_coef"],
            )
        if b_fft is None:
            b_fft = self._state_dict["f_mesh"].fft(b)
        value_fft = b_fft * self._state_dict["invert_linear_coef"]
        if return_in_fourier:
            return value_fft
        else:
            return self._state_dict["f_mesh"].ifft(value_fft).real
_state_dict instance-attribute ¤
_state_dict: Optional[dict]
register_mesh instance-attribute ¤
register_mesh: Callable

Mixin class for inverse solving operations. This class supports solving the linear operator equation.

solve ¤
solve(
    b: Optional[torch.Tensor] = None,
    b_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    n_channel: Optional[int] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], SpatialTensor["B C H ..."]
]

Solve the linear operator equation \(Ax = b\), where \(A\) is the linear operator and \(b\) is the right-hand side.

Parameters:

Name Type Description Default
b Optional[Tensor]

Right-hand side tensor in spatial domain. If None, b_fft should be provided.

 None
b_fft Optional[Tensor]

Right-hand side tensor in Fourier domain. If None, b should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. If None, the mesh registered in the operator will be used.

 None
n_channel Optional[int]

Number of channels of \(x\). If None, the number of channels registered in the operator will be used.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Solution tensor in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def solve(
    self,
    b: Optional[torch.Tensor] = None,
    b_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    n_channel: Optional[int] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], SpatialTensor["B C H ..."]]:

    r"""
    Solve the linear operator equation $Ax = b$, where $A$ is the linear operator and $b$ is the right-hand side.

    Args:
        b (Optional[torch.Tensor]): Right-hand side tensor in spatial domain. If None, b_fft should be provided.
        b_fft (Optional[torch.Tensor]): Right-hand side tensor in Fourier domain. If None, b should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. If None, the mesh registered in the operator will be used.
        n_channel (Optional[int]): Number of channels of $x$. If None, the number of channels registered in the operator will be used.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Solution tensor in spatial or Fourier domain.
    """
    if not (mesh is not None and n_channel is not None):
        assert (
            self._state_dict["f_mesh"] is not None
        ), "Mesh and n_channel should be given when calling solve"
    if not (mesh is None and n_channel is None):
        mesh = self._state_dict["f_mesh"] if mesh is None else mesh
        n_channel = (
            self._state_dict["n_channel"] if n_channel is None else n_channel
        )
        self.register_mesh(mesh, n_channel)
    if self._state_dict["invert_linear_coef"] is None:
        self._state_dict["invert_linear_coef"] = torch.where(
            self._state_dict["linear_coef"] == 0,
            1.0,
            1 / self._state_dict["linear_coef"],
        )
    if b_fft is None:
        b_fft = self._state_dict["f_mesh"].fft(b)
    value_fft = b_fft * self._state_dict["invert_linear_coef"]
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real

torchfsm.operator._base._DeAliasMixin ¤

Source code in torchfsm/operator/_base.py 
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class _DeAliasMixin:
    _de_aliasing_rate: float
    _state_dict: Optional[dict]

    r'''
    Mixin class for de-aliasing operations. This class supports setting the de-aliasing rate for the nonlinear operator.
    '''

    def set_de_aliasing_rate(self, de_aliasing_rate: float):
        r"""
        Set the de-aliasing rate for the nonlinear operator.
        Args:
            de_aliasing_rate (float): De-aliasing rate. Default is 2/3.
        """

        self._de_aliasing_rate = de_aliasing_rate
        self._state_dict = None
_de_aliasing_rate instance-attribute ¤
_de_aliasing_rate: float
_state_dict instance-attribute ¤
_state_dict: Optional[dict]

Mixin class for de-aliasing operations. This class supports setting the de-aliasing rate for the nonlinear operator.

set_de_aliasing_rate ¤
set_de_aliasing_rate(de_aliasing_rate: float)

Set the de-aliasing rate for the nonlinear operator. Args: de_aliasing_rate (float): De-aliasing rate. Default is ⅔.

Source code in torchfsm/operator/_base.py 
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def set_de_aliasing_rate(self, de_aliasing_rate: float):
    r"""
    Set the de-aliasing rate for the nonlinear operator.
    Args:
        de_aliasing_rate (float): De-aliasing rate. Default is 2/3.
    """

    self._de_aliasing_rate = de_aliasing_rate
    self._state_dict = None

torchfsm.operator.OperatorLike ¤

Bases: _MutableMixIn

Base class for All Operators.

Parameters:

Name Type Description Default
operator_generators Optional[ValueList[GeneratorLike]]

List of operator generators. Default is None. Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 None
coefs Optional[List]

List of coefficients for each operator generator. Default is None. If None, all coefficients are set to 1. The length of the list should match the number of operator generators.

 None
Source code in torchfsm/operator/_base.py 
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class OperatorLike(_MutableMixIn):

    r"""
    Base class for All Operators.

    Args:
        operator_generators (Optional[ValueList[GeneratorLike]]): List of operator generators. Default is None.
            Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coefs (Optional[List]): List of coefficients for each operator generator. Default is None.
            If None, all coefficients are set to 1.
            The length of the list should match the number of operator generators.

    """

    def __init__(
        self,
        operator_generators: Optional[ValueList[GeneratorLike]] = None,
        coefs: Optional[List] = None,
    ) -> None:
        super().__init__()
        self.operator_generators = default(operator_generators, [])
        if not isinstance(self.operator_generators, list):
            self.operator_generators = [self.operator_generators]
        self.coefs = default(coefs, [1] * len(self.operator_generators))
        self._state_dict = {
            "f_mesh": None,
            "n_channel": None,
            "linear_coef": None,
            "nonlinear_func": None,
            "operator": None,
            "integrator": None,
            "invert_linear_coef": None,
        }
        self._nonlinear_funcs = []
        self._de_aliasing_rate = 2 / 3
        self._value_mesh_check_func = lambda dim_value, dim_mesh: True
        self._integrator = "auto"
        self._integrator_config = {}
        self._is_etdrk_integrator = True

    @property
    def is_linear(self) -> bool:
        r"""
        Check if the operator is linear.

        Returns:
            bool: True if the operator is linear, False otherwise.
        """
        assert (
            self._state_dict["f_mesh"] is not None
        ), "Mesh should be registered before checking if the operator is linear"
        return (
            self._state_dict["nonlinear_func"] is None
            and self._state_dict["linear_coef"] is not None
        )

    def _build_linear_coefs(
        self, linear_coefs: Optional[Sequence[LinearCoef]]
    ):
        r"""
        Build the linear coefficients based on the provided linear coefficient generators.

        Args:
            linear_coefs (Optional[Sequence[LinearCoef]]): List of linear coefficient generators.

        """
        if len(linear_coefs) == 0:
            linear_coefs = None
        else:
            linear_coefs = sum(
                [
                    coef * op(self._state_dict["f_mesh"], self._state_dict["n_channel"])
                    for coef, op in linear_coefs
                ]
            )
        self._state_dict["linear_coef"] = linear_coefs

    def _build_nonlinear_funcs(
        self, nonlinear_funcs: Optional[Sequence[NonlinearFunc]]
    ):
        r"""
        Build the nonlinear functions based on the provided nonlinear function generators.

        Args:
            nonlinear_funcs (Optional[Sequence[NonlinearFunc]]): List of nonlinear function generators.
        """
        if len(nonlinear_funcs) == 0:
            nonlinear_funcs_all = None
        else:
            self._state_dict["f_mesh"].set_default_freq_threshold(
                self._de_aliasing_rate
            )

            def nonlinear_funcs_all(u_fft):
                result = 0.0
                dealiased_u_fft = None
                dealiased_u = None
                u = None
                for coef, fun in nonlinear_funcs:
                    if fun._dealiasing_swtich:
                        if dealiased_u_fft is None:
                            dealiased_u_fft = u_fft * self._state_dict[
                                "f_mesh"
                            ].low_pass_filter(self._de_aliasing_rate)
                            dealiased_u = (
                                self._state_dict["f_mesh"].ifft(dealiased_u_fft).real
                            )
                        result += coef * fun(
                            dealiased_u_fft,
                            self._state_dict["f_mesh"],
                            dealiased_u,
                        )
                    else:
                        if u is None:
                            u = self._state_dict["f_mesh"].ifft(u_fft).real
                        result += coef * fun(
                            u_fft,
                            self._state_dict["f_mesh"],
                            u,
                        )

                return result

        self._state_dict["nonlinear_func"] = nonlinear_funcs_all

    def _build_operator(self):
        r"""
        Build the operator based on the linear coefficient and nonlinear function.
        If both linear coefficient and nonlinear function are None, the operator is set to None.
        """
        if self._state_dict["nonlinear_func"] is None:
            def operator(u_fft):
                return self._state_dict["linear_coef"] * u_fft
        elif self._state_dict["linear_coef"] is None:
            def operator(u_fft):
                return self._state_dict["nonlinear_func"](u_fft)
        elif self._state_dict["nonlinear_func"] is not None and self._state_dict["linear_coef"] is not None:
            def operator(u_fft):
                return self._state_dict["linear_coef"] * u_fft + self._state_dict[
                    "nonlinear_func"
                ](u_fft)
        else:
            raise ValueError(
                "Both linear coefficient and nonlinear function are None. Cannot build operator."
            )

        self._state_dict["operator"] = operator

    def _build_integrator(
        self,
        dt: float,
    ):
        r"""
        Build the integrator based on the provided time step and integrator type.

        Args:
            dt (float): Time step for the integrator.
        """
        if self._integrator == "auto":
            if self.is_linear:
                solver = ETDRKIntegrator.ETDRK0
            else:
                solver = ETDRKIntegrator.ETDRK4
        else:
            solver = self._integrator
        self._is_etdrk_integrator = isinstance(solver, ETDRKIntegrator)
        if self._is_etdrk_integrator:
            if solver == ETDRKIntegrator.ETDRK0:
                assert self.is_linear, "The ETDRK0 integrator only supports linear term"
                self._state_dict["integrator"] = solver.value(
                    dt,
                    self._state_dict["linear_coef"],
                    **self._integrator_config,
                )
            else:
                if self._state_dict["linear_coef"] is None:
                    linear_coef = torch.tensor(
                        [0.0],
                        dtype=self._state_dict["f_mesh"].dtype,
                        device=self._state_dict["f_mesh"].device,
                    )
                else:
                    linear_coef = self._state_dict["linear_coef"]
                self._state_dict["integrator"] = solver.value(
                    dt,
                    linear_coef,
                    self._state_dict["nonlinear_func"],
                    **self._integrator_config,
                )
            setattr(
                self._state_dict["integrator"],
                "forward",
                lambda u_fft, dt: self._state_dict["integrator"].step(u_fft),
            )
        elif isinstance(solver, RKIntegrator):
            if self._state_dict["operator"] is None:
                self._build_operator()
            self._state_dict["integrator"] = solver.value(**self._integrator_config)
            setattr(
                self._state_dict["integrator"],
                "forward",
                lambda u_fft, dt: self._state_dict["integrator"].step(
                    self._state_dict["operator"], u_fft, dt
                ),
            )

    def _pre_check(
        self,
        u: Optional[SpatialTensor["B C H ..."]] = None,
        u_fft: Optional[FourierTensor["B C H ..."]] = None,
        mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh] = None,
    ) -> Tuple[FourierMesh, int]:
        r"""
        Pre-check the input tensor and mesh. If the mesh is not registered, register it.

        Args:
            u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
            u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
                At least one of u or u_fft should be provided.
            mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object. Default is None.
                If None, the mesh registered in the operator will be used.

        Returns:
            Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
        """

        if u_fft is None and u is None:
            raise ValueError("Either u or u_fft should be given")
        if u_fft is not None and u is not None:
            assert u.shape == u_fft.shape, "The shape of u and u_fft should be the same"
        assert mesh is not None, "Mesh should be given"
        value_device = u.device if u is not None else u_fft.device
        value_dtype = u.dtype if u is not None else u_fft.dtype
        if not isinstance(mesh, FourierMesh):
            if not isinstance(mesh, MeshGrid):
                mesh = FourierMesh(mesh, device=value_device, dtype=value_dtype)
            else:
                mesh = FourierMesh(mesh)
        n_channel = u.shape[1] if u is not None else u_fft.shape[1]
        value_shape = u.shape if u is not None else u_fft.shape
        assert (
            len(value_shape) == mesh.n_dim + 2
        ), f"the value shape {value_shape} is not compatible with mesh dim {mesh.n_dim}"
        for i in range(mesh.n_dim):
            assert (
                value_shape[i + 2] == mesh.mesh_info[i][2]
            ), f"Expect to have {mesh.mesh_info[i][2]} points in dim {i} but got {value_shape[i+2]}"
        assert (
            value_device == mesh.device
        ), "The device of mesh {} and the device of value {} are not the same".format(
            mesh.device, value_device
        )
        # assert value_dtype==mesh.dtype, "The dtype of mesh {} and the dtype of value {} are not the same".format(mesh.dtype,value_dtype)
        # value fft is a complex dtype
        assert self._value_mesh_check_func(
            len(value_shape) - 2, mesh.n_dim
        ), "Value and mesh do not match the requirement"
        return mesh, n_channel

    def register_mesh(
        self,
        mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh],
        n_channel: int,
        device=None,
        dtype=None,
    ):
        r"""
        Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

        Args:
            mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object.
            n_channel (int): Number of channels of the input tensor.
            device (Optional[torch.device]): Device to which the mesh should be moved. Default is None.
            dtype (Optional[torch.dtype]): Data type of the mesh. Default is None.
        """
        if isinstance(mesh, FourierMesh):
            f_mesh = mesh
            if device is not None or dtype is not None:
                f_mesh.to(device=device, dtype=dtype)
        else:
            f_mesh = FourierMesh(mesh, device=device, dtype=dtype)
        for key in self._state_dict:
            self._state_dict[key] = None
        self._state_dict.update(
            {
                "f_mesh": f_mesh,
                "n_channel": n_channel,
            }
        )
        linear_coefs = []
        nonlinear_funcs = []
        for coef, generator in zip(self.coefs, self.operator_generators):
            op = generator(f_mesh, n_channel)
            if isinstance(op, LinearCoef):
                linear_coefs.append((coef, op))
            elif isinstance(op, NonlinearFunc):
                nonlinear_funcs.append((coef, op))
            else:
                raise ValueError(f"Operator {op} is not supported")
        self._nonlinear_funcs = nonlinear_funcs
        self._build_linear_coefs(linear_coefs)
        self._build_nonlinear_funcs(self._nonlinear_funcs)

    def regisiter_additional_check(self, func: Callable[[int, int], bool]):
        r"""
        Register an additional check function for the value and mesh compatibility.

        Args:
            func (Callable[[int, int], bool]): Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.
        """
        self._value_mesh_check_func = func

    def add_generator(self, generator: GeneratorLike, coef=1):
        r"""
        Add a generator to the operator.

        Args:
            generator (GeneratorLike): Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
            coef (float): Coefficient for the generator. Default is 1.
        """
        self.operator_generators.append(generator)
        self.coefs.append(coef)

    def set_integrator(
        self,
        integrator: Union[Literal["auto"], ETDRKIntegrator, RKIntegrator],
        **integrator_config,
    ):
        r"""
        Set the integrator for the operator. The integrator is used for time integration of the operator.

        Args:
            integrator (Union[Literal["auto"], ETDRKIntegrator, RKIntegrator]): Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type.
                If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.
            **integrator_config: Additional configuration for the integrator.
        """

        if isinstance(integrator, str):
            assert (
                integrator == "auto"
            ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
        else:
            assert isinstance(integrator, ETDRKIntegrator) or isinstance(
                integrator, RKIntegrator
            ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
        self._integrator = integrator
        self._integrator_config = integrator_config
        self._state_dict["integrator"] = None

    def integrate(
        self,
        u_0: Optional[torch.Tensor] = None,
        u_0_fft: Optional[torch.Tensor] = None,
        dt: float = 1,
        step: int = 1,
        mesh: Optional[
            Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
        ] = None,
        progressive: bool = False,
        trajectory_recorder: Optional[_TrajRecorder] = None,
        return_in_fourier: bool = False,

    ) -> Union[
            SpatialTensor["B C H ..."],
            SpatialTensor["B T C H ..."],
            FourierTensor["B C H ..."],
            FourierTensor["B T C H ..."],
        ]:
        r"""
        Integrate the operator using the provided initial condition and time step.  

        Args:
            u_0 (Optional[torch.Tensor]): Initial condition in spatial domain. Default is None.
            u_0_fft (Optional[torch.Tensor]): Initial condition in Fourier domain. Default is None.
                At least one of u_0 or u_0_fft should be provided.
            dt (float): Time step for the integrator. Default is 1.
            step (int): Number of time steps to integrate. Default is 1.
            mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
                If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before integration.
            progressive (bool): If True, show a progress bar during integration. Default is False.
            trajectory_recorder (Optional[_TrajRecorder]): Trajectory recorder for recording the trajectory during integration. Default is None.
                If None, no trajectory will be recorded. The function will only return the final frame.
            return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

        Returns:
            Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain.
                If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...).
                If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.

        """
        if self._state_dict["f_mesh"] is None or mesh is not None:
            mesh, n_channel = self._pre_check(u=u_0, u_fft=u_0_fft, mesh=mesh)
            self.register_mesh(mesh, n_channel)
        else:
            self._pre_check(u=u_0, u_fft=u_0_fft, mesh=self._state_dict["f_mesh"])
        if self._state_dict["integrator"] is None:
            self._build_integrator(dt)
        elif self._is_etdrk_integrator:
            if self._state_dict["integrator"].dt != dt:
                self._build_integrator(dt)
        f_mesh = self._state_dict["f_mesh"]
        if u_0_fft is None:
            u_0_fft = f_mesh.fft(u_0)
        p_bar = tqdm(range(step), desc="Integrating", disable=not progressive)
        for i in p_bar:
            if trajectory_recorder is not None:
                trajectory_recorder.record(i, u_0_fft)
            u_0_fft = self._state_dict["integrator"].forward(u_0_fft, dt)
        if trajectory_recorder is not None:
            trajectory_recorder.record(i + 1, u_0_fft)
            trajectory_recorder.return_in_fourier = return_in_fourier
            return trajectory_recorder.trajectory
        else:
            if return_in_fourier:
                return u_0_fft
            else:
                return f_mesh.ifft(u_0_fft).real

    def __call__(
        self,
        u: Optional[SpatialTensor["B C H ..."]] = None,
        u_fft: Optional[FourierTensor["B C H ..."]] = None,
        mesh: Optional[
            Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
        ] = None,
        return_in_fourier=False,
    ) -> Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]:
        r"""
        Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

        Args:
            u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
            u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
                At least one of u or u_fft should be provided.
            mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
                If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before calling the operator.
            return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

        Returns:
            Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
        """    

        if self._state_dict["f_mesh"] is None or mesh is not None:
            mesh, n_channel = self._pre_check(u, u_fft, mesh)
            self.register_mesh(mesh, n_channel)
        else:
            self._pre_check(u=u, u_fft=u_fft, mesh=self._state_dict["f_mesh"])
        if self._state_dict["operator"] is None:
            self._build_operator()
        if u_fft is None:
            u_fft = self._state_dict["f_mesh"].fft(u)
        value_fft = self._state_dict["operator"](u_fft)
        if return_in_fourier:
            return value_fft
        else:
            return self._state_dict["f_mesh"].ifft(value_fft).real

    def to(self, device=None, dtype=None):
        r"""
        Move the operator to the specified device and change the data type.

        Args:
            device (Optional[torch.device]): Device to which the operator should be moved. Default is None.
            dtype (Optional[torch.dtype]): Data type of the operator. Default is None.
        """
        if self._state_dict is not None:
            self._state_dict["f_mesh"].to(device=device, dtype=dtype)
            self.register_mesh(self._state_dict["f_mesh"], self._state_dict["n_channel"])
operator_generators instance-attribute ¤
operator_generators = default(operator_generators, [])
coefs instance-attribute ¤
coefs = default(coefs, [1] * len(operator_generators))
_state_dict instance-attribute ¤
_state_dict = {
    "f_mesh": None,
    "n_channel": None,
    "linear_coef": None,
    "nonlinear_func": None,
    "operator": None,
    "integrator": None,
    "invert_linear_coef": None,
}
_nonlinear_funcs instance-attribute ¤
_nonlinear_funcs = []
_de_aliasing_rate instance-attribute ¤
_de_aliasing_rate = 2 / 3
_value_mesh_check_func instance-attribute ¤
_value_mesh_check_func = lambda dim_value, dim_mesh: True
_integrator instance-attribute ¤
_integrator = 'auto'
_integrator_config instance-attribute ¤
_integrator_config = {}
_is_etdrk_integrator instance-attribute ¤
_is_etdrk_integrator = True
is_linear property ¤
is_linear: bool

Check if the operator is linear.

Returns:

Name Type Description
bool bool

True if the operator is linear, False otherwise.
__radd__ ¤
__radd__(other)
Source code in torchfsm/operator/_base.py 
176
177
def __radd__(self, other):
    return self + other
__iadd__ ¤
__iadd__(other)
Source code in torchfsm/operator/_base.py 
179
180
def __iadd__(self, other):
    return self + other
__sub__ ¤
__sub__(other)
Source code in torchfsm/operator/_base.py 
182
183
184
185
186
def __sub__(self, other):
    try:
        return self + (-1 * other)
    except Exception:
        return NotImplemented
__rsub__ ¤
__rsub__(other)
Source code in torchfsm/operator/_base.py 
188
189
190
191
192
def __rsub__(self, other):
    try:
        return other + (-1 * self)
    except Exception:
        return NotImplemented
__isub__ ¤
__isub__(other)
Source code in torchfsm/operator/_base.py 
194
195
def __isub__(self, other):
    return self - other
__rmul__ ¤
__rmul__(other)
Source code in torchfsm/operator/_base.py 
197
198
def __rmul__(self, other):
    return self * other
__imul__ ¤
__imul__(other)
Source code in torchfsm/operator/_base.py 
200
201
def __imul__(self, other):
    return self * other
__truediv__ ¤
__truediv__(other)
Source code in torchfsm/operator/_base.py 
203
204
205
206
207
def __truediv__(self, other):
    try:
        return self * (1 / other)
    except:
        return NotImplemented
__init__ ¤
__init__(
    operator_generators: Optional[
        ValueList[GeneratorLike]
    ] = None,
    coefs: Optional[List] = None,
) -> None
Source code in torchfsm/operator/_base.py 
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def __init__(
    self,
    operator_generators: Optional[ValueList[GeneratorLike]] = None,
    coefs: Optional[List] = None,
) -> None:
    super().__init__()
    self.operator_generators = default(operator_generators, [])
    if not isinstance(self.operator_generators, list):
        self.operator_generators = [self.operator_generators]
    self.coefs = default(coefs, [1] * len(self.operator_generators))
    self._state_dict = {
        "f_mesh": None,
        "n_channel": None,
        "linear_coef": None,
        "nonlinear_func": None,
        "operator": None,
        "integrator": None,
        "invert_linear_coef": None,
    }
    self._nonlinear_funcs = []
    self._de_aliasing_rate = 2 / 3
    self._value_mesh_check_func = lambda dim_value, dim_mesh: True
    self._integrator = "auto"
    self._integrator_config = {}
    self._is_etdrk_integrator = True
_build_linear_coefs ¤
_build_linear_coefs(
    linear_coefs: Optional[Sequence[LinearCoef]],
)

Build the linear coefficients based on the provided linear coefficient generators.

Parameters:

Name Type Description Default
linear_coefs Optional[Sequence[LinearCoef]]

List of linear coefficient generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_linear_coefs(
    self, linear_coefs: Optional[Sequence[LinearCoef]]
):
    r"""
    Build the linear coefficients based on the provided linear coefficient generators.

    Args:
        linear_coefs (Optional[Sequence[LinearCoef]]): List of linear coefficient generators.

    """
    if len(linear_coefs) == 0:
        linear_coefs = None
    else:
        linear_coefs = sum(
            [
                coef * op(self._state_dict["f_mesh"], self._state_dict["n_channel"])
                for coef, op in linear_coefs
            ]
        )
    self._state_dict["linear_coef"] = linear_coefs
_build_nonlinear_funcs ¤
_build_nonlinear_funcs(
    nonlinear_funcs: Optional[Sequence[NonlinearFunc]],
)

Build the nonlinear functions based on the provided nonlinear function generators.

Parameters:

Name Type Description Default
nonlinear_funcs Optional[Sequence[NonlinearFunc]]

List of nonlinear function generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_nonlinear_funcs(
    self, nonlinear_funcs: Optional[Sequence[NonlinearFunc]]
):
    r"""
    Build the nonlinear functions based on the provided nonlinear function generators.

    Args:
        nonlinear_funcs (Optional[Sequence[NonlinearFunc]]): List of nonlinear function generators.
    """
    if len(nonlinear_funcs) == 0:
        nonlinear_funcs_all = None
    else:
        self._state_dict["f_mesh"].set_default_freq_threshold(
            self._de_aliasing_rate
        )

        def nonlinear_funcs_all(u_fft):
            result = 0.0
            dealiased_u_fft = None
            dealiased_u = None
            u = None
            for coef, fun in nonlinear_funcs:
                if fun._dealiasing_swtich:
                    if dealiased_u_fft is None:
                        dealiased_u_fft = u_fft * self._state_dict[
                            "f_mesh"
                        ].low_pass_filter(self._de_aliasing_rate)
                        dealiased_u = (
                            self._state_dict["f_mesh"].ifft(dealiased_u_fft).real
                        )
                    result += coef * fun(
                        dealiased_u_fft,
                        self._state_dict["f_mesh"],
                        dealiased_u,
                    )
                else:
                    if u is None:
                        u = self._state_dict["f_mesh"].ifft(u_fft).real
                    result += coef * fun(
                        u_fft,
                        self._state_dict["f_mesh"],
                        u,
                    )

            return result

    self._state_dict["nonlinear_func"] = nonlinear_funcs_all
_build_operator ¤
_build_operator()

Build the operator based on the linear coefficient and nonlinear function. If both linear coefficient and nonlinear function are None, the operator is set to None.

Source code in torchfsm/operator/_base.py 
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def _build_operator(self):
    r"""
    Build the operator based on the linear coefficient and nonlinear function.
    If both linear coefficient and nonlinear function are None, the operator is set to None.
    """
    if self._state_dict["nonlinear_func"] is None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft
    elif self._state_dict["linear_coef"] is None:
        def operator(u_fft):
            return self._state_dict["nonlinear_func"](u_fft)
    elif self._state_dict["nonlinear_func"] is not None and self._state_dict["linear_coef"] is not None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft + self._state_dict[
                "nonlinear_func"
            ](u_fft)
    else:
        raise ValueError(
            "Both linear coefficient and nonlinear function are None. Cannot build operator."
        )

    self._state_dict["operator"] = operator
_build_integrator ¤
_build_integrator(dt: float)

Build the integrator based on the provided time step and integrator type.

Parameters:

Name Type Description Default
dt float

Time step for the integrator.

 required
Source code in torchfsm/operator/_base.py 
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def _build_integrator(
    self,
    dt: float,
):
    r"""
    Build the integrator based on the provided time step and integrator type.

    Args:
        dt (float): Time step for the integrator.
    """
    if self._integrator == "auto":
        if self.is_linear:
            solver = ETDRKIntegrator.ETDRK0
        else:
            solver = ETDRKIntegrator.ETDRK4
    else:
        solver = self._integrator
    self._is_etdrk_integrator = isinstance(solver, ETDRKIntegrator)
    if self._is_etdrk_integrator:
        if solver == ETDRKIntegrator.ETDRK0:
            assert self.is_linear, "The ETDRK0 integrator only supports linear term"
            self._state_dict["integrator"] = solver.value(
                dt,
                self._state_dict["linear_coef"],
                **self._integrator_config,
            )
        else:
            if self._state_dict["linear_coef"] is None:
                linear_coef = torch.tensor(
                    [0.0],
                    dtype=self._state_dict["f_mesh"].dtype,
                    device=self._state_dict["f_mesh"].device,
                )
            else:
                linear_coef = self._state_dict["linear_coef"]
            self._state_dict["integrator"] = solver.value(
                dt,
                linear_coef,
                self._state_dict["nonlinear_func"],
                **self._integrator_config,
            )
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(u_fft),
        )
    elif isinstance(solver, RKIntegrator):
        if self._state_dict["operator"] is None:
            self._build_operator()
        self._state_dict["integrator"] = solver.value(**self._integrator_config)
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(
                self._state_dict["operator"], u_fft, dt
            ),
        )
_pre_check ¤
_pre_check(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ] = None,
) -> Tuple[FourierMesh, int]

Pre-check the input tensor and mesh. If the mesh is not registered, register it.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used.

 None

Returns:

Type Description
Tuple[FourierMesh, int]

Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
Source code in torchfsm/operator/_base.py 
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def _pre_check(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh] = None,
) -> Tuple[FourierMesh, int]:
    r"""
    Pre-check the input tensor and mesh. If the mesh is not registered, register it.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used.

    Returns:
        Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
    """

    if u_fft is None and u is None:
        raise ValueError("Either u or u_fft should be given")
    if u_fft is not None and u is not None:
        assert u.shape == u_fft.shape, "The shape of u and u_fft should be the same"
    assert mesh is not None, "Mesh should be given"
    value_device = u.device if u is not None else u_fft.device
    value_dtype = u.dtype if u is not None else u_fft.dtype
    if not isinstance(mesh, FourierMesh):
        if not isinstance(mesh, MeshGrid):
            mesh = FourierMesh(mesh, device=value_device, dtype=value_dtype)
        else:
            mesh = FourierMesh(mesh)
    n_channel = u.shape[1] if u is not None else u_fft.shape[1]
    value_shape = u.shape if u is not None else u_fft.shape
    assert (
        len(value_shape) == mesh.n_dim + 2
    ), f"the value shape {value_shape} is not compatible with mesh dim {mesh.n_dim}"
    for i in range(mesh.n_dim):
        assert (
            value_shape[i + 2] == mesh.mesh_info[i][2]
        ), f"Expect to have {mesh.mesh_info[i][2]} points in dim {i} but got {value_shape[i+2]}"
    assert (
        value_device == mesh.device
    ), "The device of mesh {} and the device of value {} are not the same".format(
        mesh.device, value_device
    )
    # assert value_dtype==mesh.dtype, "The dtype of mesh {} and the dtype of value {} are not the same".format(mesh.dtype,value_dtype)
    # value fft is a complex dtype
    assert self._value_mesh_check_func(
        len(value_shape) - 2, mesh.n_dim
    ), "Value and mesh do not match the requirement"
    return mesh, n_channel
register_mesh ¤
register_mesh(
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ],
    n_channel: int,
    device=None,
    dtype=None,
)

Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

Parameters:

Name Type Description Default
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required
device Optional[device]

Device to which the mesh should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the mesh. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def register_mesh(
    self,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh],
    n_channel: int,
    device=None,
    dtype=None,
):
    r"""
    Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

    Args:
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object.
        n_channel (int): Number of channels of the input tensor.
        device (Optional[torch.device]): Device to which the mesh should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the mesh. Default is None.
    """
    if isinstance(mesh, FourierMesh):
        f_mesh = mesh
        if device is not None or dtype is not None:
            f_mesh.to(device=device, dtype=dtype)
    else:
        f_mesh = FourierMesh(mesh, device=device, dtype=dtype)
    for key in self._state_dict:
        self._state_dict[key] = None
    self._state_dict.update(
        {
            "f_mesh": f_mesh,
            "n_channel": n_channel,
        }
    )
    linear_coefs = []
    nonlinear_funcs = []
    for coef, generator in zip(self.coefs, self.operator_generators):
        op = generator(f_mesh, n_channel)
        if isinstance(op, LinearCoef):
            linear_coefs.append((coef, op))
        elif isinstance(op, NonlinearFunc):
            nonlinear_funcs.append((coef, op))
        else:
            raise ValueError(f"Operator {op} is not supported")
    self._nonlinear_funcs = nonlinear_funcs
    self._build_linear_coefs(linear_coefs)
    self._build_nonlinear_funcs(self._nonlinear_funcs)
regisiter_additional_check ¤
regisiter_additional_check(
    func: Callable[[int, int], bool]
)

Register an additional check function for the value and mesh compatibility.

Parameters:

Name Type Description Default
func Callable[[int, int], bool]

Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.

 required
Source code in torchfsm/operator/_base.py 
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def regisiter_additional_check(self, func: Callable[[int, int], bool]):
    r"""
    Register an additional check function for the value and mesh compatibility.

    Args:
        func (Callable[[int, int], bool]): Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.
    """
    self._value_mesh_check_func = func
add_generator ¤
add_generator(generator: GeneratorLike, coef=1)

Add a generator to the operator.

Parameters:

Name Type Description Default
generator GeneratorLike

Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 required
coef float

Coefficient for the generator. Default is 1.

 1
Source code in torchfsm/operator/_base.py 
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def add_generator(self, generator: GeneratorLike, coef=1):
    r"""
    Add a generator to the operator.

    Args:
        generator (GeneratorLike): Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coef (float): Coefficient for the generator. Default is 1.
    """
    self.operator_generators.append(generator)
    self.coefs.append(coef)
set_integrator ¤
set_integrator(
    integrator: Union[
        Literal["auto"], ETDRKIntegrator, RKIntegrator
    ],
    **integrator_config
)

Set the integrator for the operator. The integrator is used for time integration of the operator.

Parameters:

Name Type Description Default
integrator Union[Literal['auto'], ETDRKIntegrator, RKIntegrator]

Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type. If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.

 required
**integrator_config

Additional configuration for the integrator.

 {}
Source code in torchfsm/operator/_base.py 
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def set_integrator(
    self,
    integrator: Union[Literal["auto"], ETDRKIntegrator, RKIntegrator],
    **integrator_config,
):
    r"""
    Set the integrator for the operator. The integrator is used for time integration of the operator.

    Args:
        integrator (Union[Literal["auto"], ETDRKIntegrator, RKIntegrator]): Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type.
            If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.
        **integrator_config: Additional configuration for the integrator.
    """

    if isinstance(integrator, str):
        assert (
            integrator == "auto"
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    else:
        assert isinstance(integrator, ETDRKIntegrator) or isinstance(
            integrator, RKIntegrator
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    self._integrator = integrator
    self._integrator_config = integrator_config
    self._state_dict["integrator"] = None
integrate ¤
integrate(
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,
) -> Union[
    SpatialTensor["B C H ..."],
    SpatialTensor["B T C H ..."],
    FourierTensor["B C H ..."],
    FourierTensor["B T C H ..."],
]

Integrate the operator using the provided initial condition and time step.

Parameters:

Name Type Description Default
u_0 Optional[Tensor]

Initial condition in spatial domain. Default is None.

 None
u_0_fft Optional[Tensor]

Initial condition in Fourier domain. Default is None. At least one of u_0 or u_0_fft should be provided.

 None
dt float

Time step for the integrator. Default is 1.

 1
step int

Number of time steps to integrate. Default is 1.

 1
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before integration.

 None
progressive bool

If True, show a progress bar during integration. Default is False.

 False
trajectory_recorder Optional[_TrajRecorder]

Trajectory recorder for recording the trajectory during integration. Default is None. If None, no trajectory will be recorded. The function will only return the final frame.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B T C H ...'], FourierTensor['B C H ...'], FourierTensor['B T C H ...']]

Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain. If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...). If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.
Source code in torchfsm/operator/_base.py 
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def integrate(
    self,
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,

) -> Union[
        SpatialTensor["B C H ..."],
        SpatialTensor["B T C H ..."],
        FourierTensor["B C H ..."],
        FourierTensor["B T C H ..."],
    ]:
    r"""
    Integrate the operator using the provided initial condition and time step.  

    Args:
        u_0 (Optional[torch.Tensor]): Initial condition in spatial domain. Default is None.
        u_0_fft (Optional[torch.Tensor]): Initial condition in Fourier domain. Default is None.
            At least one of u_0 or u_0_fft should be provided.
        dt (float): Time step for the integrator. Default is 1.
        step (int): Number of time steps to integrate. Default is 1.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before integration.
        progressive (bool): If True, show a progress bar during integration. Default is False.
        trajectory_recorder (Optional[_TrajRecorder]): Trajectory recorder for recording the trajectory during integration. Default is None.
            If None, no trajectory will be recorded. The function will only return the final frame.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain.
            If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...).
            If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.

    """
    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u=u_0, u_fft=u_0_fft, mesh=mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u_0, u_fft=u_0_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["integrator"] is None:
        self._build_integrator(dt)
    elif self._is_etdrk_integrator:
        if self._state_dict["integrator"].dt != dt:
            self._build_integrator(dt)
    f_mesh = self._state_dict["f_mesh"]
    if u_0_fft is None:
        u_0_fft = f_mesh.fft(u_0)
    p_bar = tqdm(range(step), desc="Integrating", disable=not progressive)
    for i in p_bar:
        if trajectory_recorder is not None:
            trajectory_recorder.record(i, u_0_fft)
        u_0_fft = self._state_dict["integrator"].forward(u_0_fft, dt)
    if trajectory_recorder is not None:
        trajectory_recorder.record(i + 1, u_0_fft)
        trajectory_recorder.return_in_fourier = return_in_fourier
        return trajectory_recorder.trajectory
    else:
        if return_in_fourier:
            return u_0_fft
        else:
            return f_mesh.ifft(u_0_fft).real
__call__ ¤
__call__(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], FourierTensor["B C H ..."]
]

Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before calling the operator.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], FourierTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def __call__(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]:
    r"""
    Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before calling the operator.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
    """    

    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u, u_fft, mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u, u_fft=u_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["operator"] is None:
        self._build_operator()
    if u_fft is None:
        u_fft = self._state_dict["f_mesh"].fft(u)
    value_fft = self._state_dict["operator"](u_fft)
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real
to ¤
to(device=None, dtype=None)

Move the operator to the specified device and change the data type.

Parameters:

Name Type Description Default
device Optional[device]

Device to which the operator should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the operator. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def to(self, device=None, dtype=None):
    r"""
    Move the operator to the specified device and change the data type.

    Args:
        device (Optional[torch.device]): Device to which the operator should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the operator. Default is None.
    """
    if self._state_dict is not None:
        self._state_dict["f_mesh"].to(device=device, dtype=dtype)
        self.register_mesh(self._state_dict["f_mesh"], self._state_dict["n_channel"])

torchfsm.operator.Operator ¤

Bases: OperatorLike, _DeAliasMixin

Operator class for linear and nonlinear operations.

Parameters:

Name Type Description Default
operator_generators Optional[ValueList[GeneratorLike]]

List of operator generators. Default is None. Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 None
coefs Optional[List]

List of coefficients for each operator generator. Default is None. If None, all coefficients are set to 1. The length of the list should match the number of operator generators.

 None
Source code in torchfsm/operator/_base.py 
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class Operator(OperatorLike, _DeAliasMixin):
    r"""
    Operator class for linear and nonlinear operations.

    Args:
        operator_generators (Optional[ValueList[GeneratorLike]]): List of operator generators. Default is None.
            Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coefs (Optional[List]): List of coefficients for each operator generator. Default is None.
            If None, all coefficients are set to 1.
            The length of the list should match the number of operator generators.
    """

    def __init__(
        self,
        operator_generators: Optional[ValueList[GeneratorLike]] = None,
        coefs: Optional[List] = None,
    ) -> None:
        super().__init__(operator_generators, coefs)

    def __add__(self, other):
        if isinstance(other, OperatorLike):
            return Operator(
                self.operator_generators + other.operator_generators,
                self.coefs + other.coefs,
            )
        elif isinstance(other, Tensor):
            return Operator(
                self.operator_generators
                + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
                self.coefs + [1],
            )
        else:
            return NotImplemented

    def __mul__(self, other):
        if isinstance(other, OperatorLike):
            return NotImplemented
        else:
            return Operator(
                self.operator_generators, [coef * other for coef in self.coefs]
            )

    def __neg__(self):
        return Operator(self.operator_generators, [-1 * coef for coef in self.coefs])
_de_aliasing_rate instance-attribute ¤
_de_aliasing_rate = 2 / 3
_state_dict instance-attribute ¤
_state_dict = {
    "f_mesh": None,
    "n_channel": None,
    "linear_coef": None,
    "nonlinear_func": None,
    "operator": None,
    "integrator": None,
    "invert_linear_coef": None,
}
operator_generators instance-attribute ¤
operator_generators = default(operator_generators, [])
coefs instance-attribute ¤
coefs = default(coefs, [1] * len(operator_generators))
_nonlinear_funcs instance-attribute ¤
_nonlinear_funcs = []
_value_mesh_check_func instance-attribute ¤
_value_mesh_check_func = lambda dim_value, dim_mesh: True
_integrator instance-attribute ¤
_integrator = 'auto'
_integrator_config instance-attribute ¤
_integrator_config = {}
_is_etdrk_integrator instance-attribute ¤
_is_etdrk_integrator = True
is_linear property ¤
is_linear: bool

Check if the operator is linear.

Returns:

Name Type Description
bool bool

True if the operator is linear, False otherwise.
set_de_aliasing_rate ¤
set_de_aliasing_rate(de_aliasing_rate: float)

Set the de-aliasing rate for the nonlinear operator. Args: de_aliasing_rate (float): De-aliasing rate. Default is ⅔.

Source code in torchfsm/operator/_base.py 
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def set_de_aliasing_rate(self, de_aliasing_rate: float):
    r"""
    Set the de-aliasing rate for the nonlinear operator.
    Args:
        de_aliasing_rate (float): De-aliasing rate. Default is 2/3.
    """

    self._de_aliasing_rate = de_aliasing_rate
    self._state_dict = None
__radd__ ¤
__radd__(other)
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def __radd__(self, other):
    return self + other
__iadd__ ¤
__iadd__(other)
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def __iadd__(self, other):
    return self + other
__sub__ ¤
__sub__(other)
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def __sub__(self, other):
    try:
        return self + (-1 * other)
    except Exception:
        return NotImplemented
__rsub__ ¤
__rsub__(other)
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def __rsub__(self, other):
    try:
        return other + (-1 * self)
    except Exception:
        return NotImplemented
__isub__ ¤
__isub__(other)
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def __isub__(self, other):
    return self - other
__rmul__ ¤
__rmul__(other)
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def __rmul__(self, other):
    return self * other
__imul__ ¤
__imul__(other)
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def __imul__(self, other):
    return self * other
__truediv__ ¤
__truediv__(other)
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def __truediv__(self, other):
    try:
        return self * (1 / other)
    except:
        return NotImplemented
_build_linear_coefs ¤
_build_linear_coefs(
    linear_coefs: Optional[Sequence[LinearCoef]],
)

Build the linear coefficients based on the provided linear coefficient generators.

Parameters:

Name Type Description Default
linear_coefs Optional[Sequence[LinearCoef]]

List of linear coefficient generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_linear_coefs(
    self, linear_coefs: Optional[Sequence[LinearCoef]]
):
    r"""
    Build the linear coefficients based on the provided linear coefficient generators.

    Args:
        linear_coefs (Optional[Sequence[LinearCoef]]): List of linear coefficient generators.

    """
    if len(linear_coefs) == 0:
        linear_coefs = None
    else:
        linear_coefs = sum(
            [
                coef * op(self._state_dict["f_mesh"], self._state_dict["n_channel"])
                for coef, op in linear_coefs
            ]
        )
    self._state_dict["linear_coef"] = linear_coefs
_build_nonlinear_funcs ¤
_build_nonlinear_funcs(
    nonlinear_funcs: Optional[Sequence[NonlinearFunc]],
)

Build the nonlinear functions based on the provided nonlinear function generators.

Parameters:

Name Type Description Default
nonlinear_funcs Optional[Sequence[NonlinearFunc]]

List of nonlinear function generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_nonlinear_funcs(
    self, nonlinear_funcs: Optional[Sequence[NonlinearFunc]]
):
    r"""
    Build the nonlinear functions based on the provided nonlinear function generators.

    Args:
        nonlinear_funcs (Optional[Sequence[NonlinearFunc]]): List of nonlinear function generators.
    """
    if len(nonlinear_funcs) == 0:
        nonlinear_funcs_all = None
    else:
        self._state_dict["f_mesh"].set_default_freq_threshold(
            self._de_aliasing_rate
        )

        def nonlinear_funcs_all(u_fft):
            result = 0.0
            dealiased_u_fft = None
            dealiased_u = None
            u = None
            for coef, fun in nonlinear_funcs:
                if fun._dealiasing_swtich:
                    if dealiased_u_fft is None:
                        dealiased_u_fft = u_fft * self._state_dict[
                            "f_mesh"
                        ].low_pass_filter(self._de_aliasing_rate)
                        dealiased_u = (
                            self._state_dict["f_mesh"].ifft(dealiased_u_fft).real
                        )
                    result += coef * fun(
                        dealiased_u_fft,
                        self._state_dict["f_mesh"],
                        dealiased_u,
                    )
                else:
                    if u is None:
                        u = self._state_dict["f_mesh"].ifft(u_fft).real
                    result += coef * fun(
                        u_fft,
                        self._state_dict["f_mesh"],
                        u,
                    )

            return result

    self._state_dict["nonlinear_func"] = nonlinear_funcs_all
_build_operator ¤
_build_operator()

Build the operator based on the linear coefficient and nonlinear function. If both linear coefficient and nonlinear function are None, the operator is set to None.

Source code in torchfsm/operator/_base.py 
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def _build_operator(self):
    r"""
    Build the operator based on the linear coefficient and nonlinear function.
    If both linear coefficient and nonlinear function are None, the operator is set to None.
    """
    if self._state_dict["nonlinear_func"] is None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft
    elif self._state_dict["linear_coef"] is None:
        def operator(u_fft):
            return self._state_dict["nonlinear_func"](u_fft)
    elif self._state_dict["nonlinear_func"] is not None and self._state_dict["linear_coef"] is not None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft + self._state_dict[
                "nonlinear_func"
            ](u_fft)
    else:
        raise ValueError(
            "Both linear coefficient and nonlinear function are None. Cannot build operator."
        )

    self._state_dict["operator"] = operator
_build_integrator ¤
_build_integrator(dt: float)

Build the integrator based on the provided time step and integrator type.

Parameters:

Name Type Description Default
dt float

Time step for the integrator.

 required
Source code in torchfsm/operator/_base.py 
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def _build_integrator(
    self,
    dt: float,
):
    r"""
    Build the integrator based on the provided time step and integrator type.

    Args:
        dt (float): Time step for the integrator.
    """
    if self._integrator == "auto":
        if self.is_linear:
            solver = ETDRKIntegrator.ETDRK0
        else:
            solver = ETDRKIntegrator.ETDRK4
    else:
        solver = self._integrator
    self._is_etdrk_integrator = isinstance(solver, ETDRKIntegrator)
    if self._is_etdrk_integrator:
        if solver == ETDRKIntegrator.ETDRK0:
            assert self.is_linear, "The ETDRK0 integrator only supports linear term"
            self._state_dict["integrator"] = solver.value(
                dt,
                self._state_dict["linear_coef"],
                **self._integrator_config,
            )
        else:
            if self._state_dict["linear_coef"] is None:
                linear_coef = torch.tensor(
                    [0.0],
                    dtype=self._state_dict["f_mesh"].dtype,
                    device=self._state_dict["f_mesh"].device,
                )
            else:
                linear_coef = self._state_dict["linear_coef"]
            self._state_dict["integrator"] = solver.value(
                dt,
                linear_coef,
                self._state_dict["nonlinear_func"],
                **self._integrator_config,
            )
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(u_fft),
        )
    elif isinstance(solver, RKIntegrator):
        if self._state_dict["operator"] is None:
            self._build_operator()
        self._state_dict["integrator"] = solver.value(**self._integrator_config)
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(
                self._state_dict["operator"], u_fft, dt
            ),
        )
_pre_check ¤
_pre_check(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ] = None,
) -> Tuple[FourierMesh, int]

Pre-check the input tensor and mesh. If the mesh is not registered, register it.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used.

 None

Returns:

Type Description
Tuple[FourierMesh, int]

Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
Source code in torchfsm/operator/_base.py 
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def _pre_check(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh] = None,
) -> Tuple[FourierMesh, int]:
    r"""
    Pre-check the input tensor and mesh. If the mesh is not registered, register it.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used.

    Returns:
        Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
    """

    if u_fft is None and u is None:
        raise ValueError("Either u or u_fft should be given")
    if u_fft is not None and u is not None:
        assert u.shape == u_fft.shape, "The shape of u and u_fft should be the same"
    assert mesh is not None, "Mesh should be given"
    value_device = u.device if u is not None else u_fft.device
    value_dtype = u.dtype if u is not None else u_fft.dtype
    if not isinstance(mesh, FourierMesh):
        if not isinstance(mesh, MeshGrid):
            mesh = FourierMesh(mesh, device=value_device, dtype=value_dtype)
        else:
            mesh = FourierMesh(mesh)
    n_channel = u.shape[1] if u is not None else u_fft.shape[1]
    value_shape = u.shape if u is not None else u_fft.shape
    assert (
        len(value_shape) == mesh.n_dim + 2
    ), f"the value shape {value_shape} is not compatible with mesh dim {mesh.n_dim}"
    for i in range(mesh.n_dim):
        assert (
            value_shape[i + 2] == mesh.mesh_info[i][2]
        ), f"Expect to have {mesh.mesh_info[i][2]} points in dim {i} but got {value_shape[i+2]}"
    assert (
        value_device == mesh.device
    ), "The device of mesh {} and the device of value {} are not the same".format(
        mesh.device, value_device
    )
    # assert value_dtype==mesh.dtype, "The dtype of mesh {} and the dtype of value {} are not the same".format(mesh.dtype,value_dtype)
    # value fft is a complex dtype
    assert self._value_mesh_check_func(
        len(value_shape) - 2, mesh.n_dim
    ), "Value and mesh do not match the requirement"
    return mesh, n_channel
register_mesh ¤
register_mesh(
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ],
    n_channel: int,
    device=None,
    dtype=None,
)

Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

Parameters:

Name Type Description Default
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required
device Optional[device]

Device to which the mesh should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the mesh. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def register_mesh(
    self,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh],
    n_channel: int,
    device=None,
    dtype=None,
):
    r"""
    Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

    Args:
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object.
        n_channel (int): Number of channels of the input tensor.
        device (Optional[torch.device]): Device to which the mesh should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the mesh. Default is None.
    """
    if isinstance(mesh, FourierMesh):
        f_mesh = mesh
        if device is not None or dtype is not None:
            f_mesh.to(device=device, dtype=dtype)
    else:
        f_mesh = FourierMesh(mesh, device=device, dtype=dtype)
    for key in self._state_dict:
        self._state_dict[key] = None
    self._state_dict.update(
        {
            "f_mesh": f_mesh,
            "n_channel": n_channel,
        }
    )
    linear_coefs = []
    nonlinear_funcs = []
    for coef, generator in zip(self.coefs, self.operator_generators):
        op = generator(f_mesh, n_channel)
        if isinstance(op, LinearCoef):
            linear_coefs.append((coef, op))
        elif isinstance(op, NonlinearFunc):
            nonlinear_funcs.append((coef, op))
        else:
            raise ValueError(f"Operator {op} is not supported")
    self._nonlinear_funcs = nonlinear_funcs
    self._build_linear_coefs(linear_coefs)
    self._build_nonlinear_funcs(self._nonlinear_funcs)
regisiter_additional_check ¤
regisiter_additional_check(
    func: Callable[[int, int], bool]
)

Register an additional check function for the value and mesh compatibility.

Parameters:

Name Type Description Default
func Callable[[int, int], bool]

Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.

 required
Source code in torchfsm/operator/_base.py 
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def regisiter_additional_check(self, func: Callable[[int, int], bool]):
    r"""
    Register an additional check function for the value and mesh compatibility.

    Args:
        func (Callable[[int, int], bool]): Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.
    """
    self._value_mesh_check_func = func
add_generator ¤
add_generator(generator: GeneratorLike, coef=1)

Add a generator to the operator.

Parameters:

Name Type Description Default
generator GeneratorLike

Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 required
coef float

Coefficient for the generator. Default is 1.

 1
Source code in torchfsm/operator/_base.py 
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def add_generator(self, generator: GeneratorLike, coef=1):
    r"""
    Add a generator to the operator.

    Args:
        generator (GeneratorLike): Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coef (float): Coefficient for the generator. Default is 1.
    """
    self.operator_generators.append(generator)
    self.coefs.append(coef)
set_integrator ¤
set_integrator(
    integrator: Union[
        Literal["auto"], ETDRKIntegrator, RKIntegrator
    ],
    **integrator_config
)

Set the integrator for the operator. The integrator is used for time integration of the operator.

Parameters:

Name Type Description Default
integrator Union[Literal['auto'], ETDRKIntegrator, RKIntegrator]

Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type. If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.

 required
**integrator_config

Additional configuration for the integrator.

 {}
Source code in torchfsm/operator/_base.py 
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def set_integrator(
    self,
    integrator: Union[Literal["auto"], ETDRKIntegrator, RKIntegrator],
    **integrator_config,
):
    r"""
    Set the integrator for the operator. The integrator is used for time integration of the operator.

    Args:
        integrator (Union[Literal["auto"], ETDRKIntegrator, RKIntegrator]): Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type.
            If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.
        **integrator_config: Additional configuration for the integrator.
    """

    if isinstance(integrator, str):
        assert (
            integrator == "auto"
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    else:
        assert isinstance(integrator, ETDRKIntegrator) or isinstance(
            integrator, RKIntegrator
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    self._integrator = integrator
    self._integrator_config = integrator_config
    self._state_dict["integrator"] = None
integrate ¤
integrate(
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,
) -> Union[
    SpatialTensor["B C H ..."],
    SpatialTensor["B T C H ..."],
    FourierTensor["B C H ..."],
    FourierTensor["B T C H ..."],
]

Integrate the operator using the provided initial condition and time step.

Parameters:

Name Type Description Default
u_0 Optional[Tensor]

Initial condition in spatial domain. Default is None.

 None
u_0_fft Optional[Tensor]

Initial condition in Fourier domain. Default is None. At least one of u_0 or u_0_fft should be provided.

 None
dt float

Time step for the integrator. Default is 1.

 1
step int

Number of time steps to integrate. Default is 1.

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mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before integration.

 None
progressive bool

If True, show a progress bar during integration. Default is False.

 False
trajectory_recorder Optional[_TrajRecorder]

Trajectory recorder for recording the trajectory during integration. Default is None. If None, no trajectory will be recorded. The function will only return the final frame.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B T C H ...'], FourierTensor['B C H ...'], FourierTensor['B T C H ...']]

Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain. If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...). If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.
Source code in torchfsm/operator/_base.py 
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def integrate(
    self,
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,

) -> Union[
        SpatialTensor["B C H ..."],
        SpatialTensor["B T C H ..."],
        FourierTensor["B C H ..."],
        FourierTensor["B T C H ..."],
    ]:
    r"""
    Integrate the operator using the provided initial condition and time step.  

    Args:
        u_0 (Optional[torch.Tensor]): Initial condition in spatial domain. Default is None.
        u_0_fft (Optional[torch.Tensor]): Initial condition in Fourier domain. Default is None.
            At least one of u_0 or u_0_fft should be provided.
        dt (float): Time step for the integrator. Default is 1.
        step (int): Number of time steps to integrate. Default is 1.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before integration.
        progressive (bool): If True, show a progress bar during integration. Default is False.
        trajectory_recorder (Optional[_TrajRecorder]): Trajectory recorder for recording the trajectory during integration. Default is None.
            If None, no trajectory will be recorded. The function will only return the final frame.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain.
            If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...).
            If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.

    """
    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u=u_0, u_fft=u_0_fft, mesh=mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u_0, u_fft=u_0_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["integrator"] is None:
        self._build_integrator(dt)
    elif self._is_etdrk_integrator:
        if self._state_dict["integrator"].dt != dt:
            self._build_integrator(dt)
    f_mesh = self._state_dict["f_mesh"]
    if u_0_fft is None:
        u_0_fft = f_mesh.fft(u_0)
    p_bar = tqdm(range(step), desc="Integrating", disable=not progressive)
    for i in p_bar:
        if trajectory_recorder is not None:
            trajectory_recorder.record(i, u_0_fft)
        u_0_fft = self._state_dict["integrator"].forward(u_0_fft, dt)
    if trajectory_recorder is not None:
        trajectory_recorder.record(i + 1, u_0_fft)
        trajectory_recorder.return_in_fourier = return_in_fourier
        return trajectory_recorder.trajectory
    else:
        if return_in_fourier:
            return u_0_fft
        else:
            return f_mesh.ifft(u_0_fft).real
__call__ ¤
__call__(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], FourierTensor["B C H ..."]
]

Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before calling the operator.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], FourierTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def __call__(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]:
    r"""
    Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before calling the operator.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
    """    

    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u, u_fft, mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u, u_fft=u_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["operator"] is None:
        self._build_operator()
    if u_fft is None:
        u_fft = self._state_dict["f_mesh"].fft(u)
    value_fft = self._state_dict["operator"](u_fft)
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real
to ¤
to(device=None, dtype=None)

Move the operator to the specified device and change the data type.

Parameters:

Name Type Description Default
device Optional[device]

Device to which the operator should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the operator. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def to(self, device=None, dtype=None):
    r"""
    Move the operator to the specified device and change the data type.

    Args:
        device (Optional[torch.device]): Device to which the operator should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the operator. Default is None.
    """
    if self._state_dict is not None:
        self._state_dict["f_mesh"].to(device=device, dtype=dtype)
        self.register_mesh(self._state_dict["f_mesh"], self._state_dict["n_channel"])
__init__ ¤
__init__(
    operator_generators: Optional[
        ValueList[GeneratorLike]
    ] = None,
    coefs: Optional[List] = None,
) -> None
Source code in torchfsm/operator/_base.py 
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def __init__(
    self,
    operator_generators: Optional[ValueList[GeneratorLike]] = None,
    coefs: Optional[List] = None,
) -> None:
    super().__init__(operator_generators, coefs)
__add__ ¤
__add__(other)
Source code in torchfsm/operator/_base.py 
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def __add__(self, other):
    if isinstance(other, OperatorLike):
        return Operator(
            self.operator_generators + other.operator_generators,
            self.coefs + other.coefs,
        )
    elif isinstance(other, Tensor):
        return Operator(
            self.operator_generators
            + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
            self.coefs + [1],
        )
    else:
        return NotImplemented
__mul__ ¤
__mul__(other)
Source code in torchfsm/operator/_base.py 
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def __mul__(self, other):
    if isinstance(other, OperatorLike):
        return NotImplemented
    else:
        return Operator(
            self.operator_generators, [coef * other for coef in self.coefs]
        )
__neg__ ¤
__neg__()
Source code in torchfsm/operator/_base.py 
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def __neg__(self):
    return Operator(self.operator_generators, [-1 * coef for coef in self.coefs])

torchfsm.operator.LinearOperator ¤

Bases: OperatorLike, _InverseSolveMixin

Operators that contain only linear operations.

Parameters:

Name Type Description Default
linear_coef ValueList[Union[LinearCoef, GeneratorLike]]

List of linear coefficient generators. Default is None. Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient.

 None
coefs Optional[List]

List of coefficients for each linear coefficient generator. Default is None. If None, all coefficients are set to 1. The length of the list should match the number of linear coefficient generators.

 None
Source code in torchfsm/operator/_base.py 
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class LinearOperator(OperatorLike, _InverseSolveMixin):

    r"""
    Operators that contain only linear operations.

    Args:
        linear_coef (ValueList[Union[LinearCoef, GeneratorLike]]): List of linear coefficient generators. Default is None.
            Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient.
        coefs (Optional[List]): List of coefficients for each linear coefficient generator. Default is None.
            If None, all coefficients are set to 1.
            The length of the list should match the number of linear coefficient generators.
    """


    def __init__(
        self,
        linear_coef: ValueList[Union[LinearCoef, GeneratorLike]] = None,
        coefs: Optional[List] = None,
    ) -> None:
        if not isinstance(linear_coef, list):
            linear_coef = [linear_coef]
        super().__init__(
            operator_generators=[
                (
                    linear_coef_i
                    if not isinstance(linear_coef_i, LinearCoef)
                    else lambda f_mesh, n_channel: linear_coef_i
                )
                for linear_coef_i in linear_coef
            ],
            coefs=coefs,
        )

    @property
    def is_linear(self):
        return True

    def __add__(self, other):
        if isinstance(other, LinearOperator):
            return LinearOperator(
                self.operator_generators + other.operator_generators,
                self.coefs + other.coefs,
            )
        elif isinstance(other, OperatorLike):
            return Operator(
                self.operator_generators + other.operator_generators,
                self.coefs + other.coefs,
            )
        elif isinstance(other, Tensor):
            return Operator(
                self.operator_generators
                + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
                self.coefs + [1],
            )
        else:
            return NotImplemented

    def __mul__(self, other):
        if isinstance(other, OperatorLike):
            return NotImplemented
        else:
            return LinearOperator(
                self.operator_generators, [coef * other for coef in self.coefs]
            )

    def __neg__(self):
        return LinearOperator(
            self.operator_generators, [-1 * coef for coef in self.coefs]
        )
_state_dict instance-attribute ¤
_state_dict = {
    "f_mesh": None,
    "n_channel": None,
    "linear_coef": None,
    "nonlinear_func": None,
    "operator": None,
    "integrator": None,
    "invert_linear_coef": None,
}
operator_generators instance-attribute ¤
operator_generators = default(operator_generators, [])
coefs instance-attribute ¤
coefs = default(coefs, [1] * len(operator_generators))
_nonlinear_funcs instance-attribute ¤
_nonlinear_funcs = []
_de_aliasing_rate instance-attribute ¤
_de_aliasing_rate = 2 / 3
_value_mesh_check_func instance-attribute ¤
_value_mesh_check_func = lambda dim_value, dim_mesh: True
_integrator instance-attribute ¤
_integrator = 'auto'
_integrator_config instance-attribute ¤
_integrator_config = {}
_is_etdrk_integrator instance-attribute ¤
_is_etdrk_integrator = True
is_linear property ¤
is_linear
register_mesh ¤
register_mesh(
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ],
    n_channel: int,
    device=None,
    dtype=None,
)

Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

Parameters:

Name Type Description Default
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required
device Optional[device]

Device to which the mesh should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the mesh. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def register_mesh(
    self,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh],
    n_channel: int,
    device=None,
    dtype=None,
):
    r"""
    Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

    Args:
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object.
        n_channel (int): Number of channels of the input tensor.
        device (Optional[torch.device]): Device to which the mesh should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the mesh. Default is None.
    """
    if isinstance(mesh, FourierMesh):
        f_mesh = mesh
        if device is not None or dtype is not None:
            f_mesh.to(device=device, dtype=dtype)
    else:
        f_mesh = FourierMesh(mesh, device=device, dtype=dtype)
    for key in self._state_dict:
        self._state_dict[key] = None
    self._state_dict.update(
        {
            "f_mesh": f_mesh,
            "n_channel": n_channel,
        }
    )
    linear_coefs = []
    nonlinear_funcs = []
    for coef, generator in zip(self.coefs, self.operator_generators):
        op = generator(f_mesh, n_channel)
        if isinstance(op, LinearCoef):
            linear_coefs.append((coef, op))
        elif isinstance(op, NonlinearFunc):
            nonlinear_funcs.append((coef, op))
        else:
            raise ValueError(f"Operator {op} is not supported")
    self._nonlinear_funcs = nonlinear_funcs
    self._build_linear_coefs(linear_coefs)
    self._build_nonlinear_funcs(self._nonlinear_funcs)
solve ¤
solve(
    b: Optional[torch.Tensor] = None,
    b_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    n_channel: Optional[int] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], SpatialTensor["B C H ..."]
]

Solve the linear operator equation \(Ax = b\), where \(A\) is the linear operator and \(b\) is the right-hand side.

Parameters:

Name Type Description Default
b Optional[Tensor]

Right-hand side tensor in spatial domain. If None, b_fft should be provided.

 None
b_fft Optional[Tensor]

Right-hand side tensor in Fourier domain. If None, b should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. If None, the mesh registered in the operator will be used.

 None
n_channel Optional[int]

Number of channels of \(x\). If None, the number of channels registered in the operator will be used.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Solution tensor in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def solve(
    self,
    b: Optional[torch.Tensor] = None,
    b_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    n_channel: Optional[int] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], SpatialTensor["B C H ..."]]:

    r"""
    Solve the linear operator equation $Ax = b$, where $A$ is the linear operator and $b$ is the right-hand side.

    Args:
        b (Optional[torch.Tensor]): Right-hand side tensor in spatial domain. If None, b_fft should be provided.
        b_fft (Optional[torch.Tensor]): Right-hand side tensor in Fourier domain. If None, b should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. If None, the mesh registered in the operator will be used.
        n_channel (Optional[int]): Number of channels of $x$. If None, the number of channels registered in the operator will be used.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Solution tensor in spatial or Fourier domain.
    """
    if not (mesh is not None and n_channel is not None):
        assert (
            self._state_dict["f_mesh"] is not None
        ), "Mesh and n_channel should be given when calling solve"
    if not (mesh is None and n_channel is None):
        mesh = self._state_dict["f_mesh"] if mesh is None else mesh
        n_channel = (
            self._state_dict["n_channel"] if n_channel is None else n_channel
        )
        self.register_mesh(mesh, n_channel)
    if self._state_dict["invert_linear_coef"] is None:
        self._state_dict["invert_linear_coef"] = torch.where(
            self._state_dict["linear_coef"] == 0,
            1.0,
            1 / self._state_dict["linear_coef"],
        )
    if b_fft is None:
        b_fft = self._state_dict["f_mesh"].fft(b)
    value_fft = b_fft * self._state_dict["invert_linear_coef"]
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real
__radd__ ¤
__radd__(other)
Source code in torchfsm/operator/_base.py 
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def __radd__(self, other):
    return self + other
__iadd__ ¤
__iadd__(other)
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def __iadd__(self, other):
    return self + other
__sub__ ¤
__sub__(other)
Source code in torchfsm/operator/_base.py 
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def __sub__(self, other):
    try:
        return self + (-1 * other)
    except Exception:
        return NotImplemented
__rsub__ ¤
__rsub__(other)
Source code in torchfsm/operator/_base.py 
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def __rsub__(self, other):
    try:
        return other + (-1 * self)
    except Exception:
        return NotImplemented
__isub__ ¤
__isub__(other)
Source code in torchfsm/operator/_base.py 
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def __isub__(self, other):
    return self - other
__rmul__ ¤
__rmul__(other)
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def __rmul__(self, other):
    return self * other
__imul__ ¤
__imul__(other)
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def __imul__(self, other):
    return self * other
__truediv__ ¤
__truediv__(other)
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def __truediv__(self, other):
    try:
        return self * (1 / other)
    except:
        return NotImplemented
_build_linear_coefs ¤
_build_linear_coefs(
    linear_coefs: Optional[Sequence[LinearCoef]],
)

Build the linear coefficients based on the provided linear coefficient generators.

Parameters:

Name Type Description Default
linear_coefs Optional[Sequence[LinearCoef]]

List of linear coefficient generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_linear_coefs(
    self, linear_coefs: Optional[Sequence[LinearCoef]]
):
    r"""
    Build the linear coefficients based on the provided linear coefficient generators.

    Args:
        linear_coefs (Optional[Sequence[LinearCoef]]): List of linear coefficient generators.

    """
    if len(linear_coefs) == 0:
        linear_coefs = None
    else:
        linear_coefs = sum(
            [
                coef * op(self._state_dict["f_mesh"], self._state_dict["n_channel"])
                for coef, op in linear_coefs
            ]
        )
    self._state_dict["linear_coef"] = linear_coefs
_build_nonlinear_funcs ¤
_build_nonlinear_funcs(
    nonlinear_funcs: Optional[Sequence[NonlinearFunc]],
)

Build the nonlinear functions based on the provided nonlinear function generators.

Parameters:

Name Type Description Default
nonlinear_funcs Optional[Sequence[NonlinearFunc]]

List of nonlinear function generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_nonlinear_funcs(
    self, nonlinear_funcs: Optional[Sequence[NonlinearFunc]]
):
    r"""
    Build the nonlinear functions based on the provided nonlinear function generators.

    Args:
        nonlinear_funcs (Optional[Sequence[NonlinearFunc]]): List of nonlinear function generators.
    """
    if len(nonlinear_funcs) == 0:
        nonlinear_funcs_all = None
    else:
        self._state_dict["f_mesh"].set_default_freq_threshold(
            self._de_aliasing_rate
        )

        def nonlinear_funcs_all(u_fft):
            result = 0.0
            dealiased_u_fft = None
            dealiased_u = None
            u = None
            for coef, fun in nonlinear_funcs:
                if fun._dealiasing_swtich:
                    if dealiased_u_fft is None:
                        dealiased_u_fft = u_fft * self._state_dict[
                            "f_mesh"
                        ].low_pass_filter(self._de_aliasing_rate)
                        dealiased_u = (
                            self._state_dict["f_mesh"].ifft(dealiased_u_fft).real
                        )
                    result += coef * fun(
                        dealiased_u_fft,
                        self._state_dict["f_mesh"],
                        dealiased_u,
                    )
                else:
                    if u is None:
                        u = self._state_dict["f_mesh"].ifft(u_fft).real
                    result += coef * fun(
                        u_fft,
                        self._state_dict["f_mesh"],
                        u,
                    )

            return result

    self._state_dict["nonlinear_func"] = nonlinear_funcs_all
_build_operator ¤
_build_operator()

Build the operator based on the linear coefficient and nonlinear function. If both linear coefficient and nonlinear function are None, the operator is set to None.

Source code in torchfsm/operator/_base.py 
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def _build_operator(self):
    r"""
    Build the operator based on the linear coefficient and nonlinear function.
    If both linear coefficient and nonlinear function are None, the operator is set to None.
    """
    if self._state_dict["nonlinear_func"] is None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft
    elif self._state_dict["linear_coef"] is None:
        def operator(u_fft):
            return self._state_dict["nonlinear_func"](u_fft)
    elif self._state_dict["nonlinear_func"] is not None and self._state_dict["linear_coef"] is not None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft + self._state_dict[
                "nonlinear_func"
            ](u_fft)
    else:
        raise ValueError(
            "Both linear coefficient and nonlinear function are None. Cannot build operator."
        )

    self._state_dict["operator"] = operator
_build_integrator ¤
_build_integrator(dt: float)

Build the integrator based on the provided time step and integrator type.

Parameters:

Name Type Description Default
dt float

Time step for the integrator.

 required
Source code in torchfsm/operator/_base.py 
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def _build_integrator(
    self,
    dt: float,
):
    r"""
    Build the integrator based on the provided time step and integrator type.

    Args:
        dt (float): Time step for the integrator.
    """
    if self._integrator == "auto":
        if self.is_linear:
            solver = ETDRKIntegrator.ETDRK0
        else:
            solver = ETDRKIntegrator.ETDRK4
    else:
        solver = self._integrator
    self._is_etdrk_integrator = isinstance(solver, ETDRKIntegrator)
    if self._is_etdrk_integrator:
        if solver == ETDRKIntegrator.ETDRK0:
            assert self.is_linear, "The ETDRK0 integrator only supports linear term"
            self._state_dict["integrator"] = solver.value(
                dt,
                self._state_dict["linear_coef"],
                **self._integrator_config,
            )
        else:
            if self._state_dict["linear_coef"] is None:
                linear_coef = torch.tensor(
                    [0.0],
                    dtype=self._state_dict["f_mesh"].dtype,
                    device=self._state_dict["f_mesh"].device,
                )
            else:
                linear_coef = self._state_dict["linear_coef"]
            self._state_dict["integrator"] = solver.value(
                dt,
                linear_coef,
                self._state_dict["nonlinear_func"],
                **self._integrator_config,
            )
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(u_fft),
        )
    elif isinstance(solver, RKIntegrator):
        if self._state_dict["operator"] is None:
            self._build_operator()
        self._state_dict["integrator"] = solver.value(**self._integrator_config)
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(
                self._state_dict["operator"], u_fft, dt
            ),
        )
_pre_check ¤
_pre_check(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ] = None,
) -> Tuple[FourierMesh, int]

Pre-check the input tensor and mesh. If the mesh is not registered, register it.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used.

 None

Returns:

Type Description
Tuple[FourierMesh, int]

Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
Source code in torchfsm/operator/_base.py 
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def _pre_check(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh] = None,
) -> Tuple[FourierMesh, int]:
    r"""
    Pre-check the input tensor and mesh. If the mesh is not registered, register it.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used.

    Returns:
        Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
    """

    if u_fft is None and u is None:
        raise ValueError("Either u or u_fft should be given")
    if u_fft is not None and u is not None:
        assert u.shape == u_fft.shape, "The shape of u and u_fft should be the same"
    assert mesh is not None, "Mesh should be given"
    value_device = u.device if u is not None else u_fft.device
    value_dtype = u.dtype if u is not None else u_fft.dtype
    if not isinstance(mesh, FourierMesh):
        if not isinstance(mesh, MeshGrid):
            mesh = FourierMesh(mesh, device=value_device, dtype=value_dtype)
        else:
            mesh = FourierMesh(mesh)
    n_channel = u.shape[1] if u is not None else u_fft.shape[1]
    value_shape = u.shape if u is not None else u_fft.shape
    assert (
        len(value_shape) == mesh.n_dim + 2
    ), f"the value shape {value_shape} is not compatible with mesh dim {mesh.n_dim}"
    for i in range(mesh.n_dim):
        assert (
            value_shape[i + 2] == mesh.mesh_info[i][2]
        ), f"Expect to have {mesh.mesh_info[i][2]} points in dim {i} but got {value_shape[i+2]}"
    assert (
        value_device == mesh.device
    ), "The device of mesh {} and the device of value {} are not the same".format(
        mesh.device, value_device
    )
    # assert value_dtype==mesh.dtype, "The dtype of mesh {} and the dtype of value {} are not the same".format(mesh.dtype,value_dtype)
    # value fft is a complex dtype
    assert self._value_mesh_check_func(
        len(value_shape) - 2, mesh.n_dim
    ), "Value and mesh do not match the requirement"
    return mesh, n_channel
regisiter_additional_check ¤
regisiter_additional_check(
    func: Callable[[int, int], bool]
)

Register an additional check function for the value and mesh compatibility.

Parameters:

Name Type Description Default
func Callable[[int, int], bool]

Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.

 required
Source code in torchfsm/operator/_base.py 
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def regisiter_additional_check(self, func: Callable[[int, int], bool]):
    r"""
    Register an additional check function for the value and mesh compatibility.

    Args:
        func (Callable[[int, int], bool]): Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.
    """
    self._value_mesh_check_func = func
add_generator ¤
add_generator(generator: GeneratorLike, coef=1)

Add a generator to the operator.

Parameters:

Name Type Description Default
generator GeneratorLike

Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 required
coef float

Coefficient for the generator. Default is 1.

 1
Source code in torchfsm/operator/_base.py 
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def add_generator(self, generator: GeneratorLike, coef=1):
    r"""
    Add a generator to the operator.

    Args:
        generator (GeneratorLike): Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coef (float): Coefficient for the generator. Default is 1.
    """
    self.operator_generators.append(generator)
    self.coefs.append(coef)
set_integrator ¤
set_integrator(
    integrator: Union[
        Literal["auto"], ETDRKIntegrator, RKIntegrator
    ],
    **integrator_config
)

Set the integrator for the operator. The integrator is used for time integration of the operator.

Parameters:

Name Type Description Default
integrator Union[Literal['auto'], ETDRKIntegrator, RKIntegrator]

Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type. If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.

 required
**integrator_config

Additional configuration for the integrator.

 {}
Source code in torchfsm/operator/_base.py 
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def set_integrator(
    self,
    integrator: Union[Literal["auto"], ETDRKIntegrator, RKIntegrator],
    **integrator_config,
):
    r"""
    Set the integrator for the operator. The integrator is used for time integration of the operator.

    Args:
        integrator (Union[Literal["auto"], ETDRKIntegrator, RKIntegrator]): Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type.
            If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.
        **integrator_config: Additional configuration for the integrator.
    """

    if isinstance(integrator, str):
        assert (
            integrator == "auto"
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    else:
        assert isinstance(integrator, ETDRKIntegrator) or isinstance(
            integrator, RKIntegrator
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    self._integrator = integrator
    self._integrator_config = integrator_config
    self._state_dict["integrator"] = None
integrate ¤
integrate(
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,
) -> Union[
    SpatialTensor["B C H ..."],
    SpatialTensor["B T C H ..."],
    FourierTensor["B C H ..."],
    FourierTensor["B T C H ..."],
]

Integrate the operator using the provided initial condition and time step.

Parameters:

Name Type Description Default
u_0 Optional[Tensor]

Initial condition in spatial domain. Default is None.

 None
u_0_fft Optional[Tensor]

Initial condition in Fourier domain. Default is None. At least one of u_0 or u_0_fft should be provided.

 None
dt float

Time step for the integrator. Default is 1.

 1
step int

Number of time steps to integrate. Default is 1.

 1
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before integration.

 None
progressive bool

If True, show a progress bar during integration. Default is False.

 False
trajectory_recorder Optional[_TrajRecorder]

Trajectory recorder for recording the trajectory during integration. Default is None. If None, no trajectory will be recorded. The function will only return the final frame.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B T C H ...'], FourierTensor['B C H ...'], FourierTensor['B T C H ...']]

Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain. If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...). If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.
Source code in torchfsm/operator/_base.py 
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def integrate(
    self,
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,

) -> Union[
        SpatialTensor["B C H ..."],
        SpatialTensor["B T C H ..."],
        FourierTensor["B C H ..."],
        FourierTensor["B T C H ..."],
    ]:
    r"""
    Integrate the operator using the provided initial condition and time step.  

    Args:
        u_0 (Optional[torch.Tensor]): Initial condition in spatial domain. Default is None.
        u_0_fft (Optional[torch.Tensor]): Initial condition in Fourier domain. Default is None.
            At least one of u_0 or u_0_fft should be provided.
        dt (float): Time step for the integrator. Default is 1.
        step (int): Number of time steps to integrate. Default is 1.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before integration.
        progressive (bool): If True, show a progress bar during integration. Default is False.
        trajectory_recorder (Optional[_TrajRecorder]): Trajectory recorder for recording the trajectory during integration. Default is None.
            If None, no trajectory will be recorded. The function will only return the final frame.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain.
            If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...).
            If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.

    """
    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u=u_0, u_fft=u_0_fft, mesh=mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u_0, u_fft=u_0_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["integrator"] is None:
        self._build_integrator(dt)
    elif self._is_etdrk_integrator:
        if self._state_dict["integrator"].dt != dt:
            self._build_integrator(dt)
    f_mesh = self._state_dict["f_mesh"]
    if u_0_fft is None:
        u_0_fft = f_mesh.fft(u_0)
    p_bar = tqdm(range(step), desc="Integrating", disable=not progressive)
    for i in p_bar:
        if trajectory_recorder is not None:
            trajectory_recorder.record(i, u_0_fft)
        u_0_fft = self._state_dict["integrator"].forward(u_0_fft, dt)
    if trajectory_recorder is not None:
        trajectory_recorder.record(i + 1, u_0_fft)
        trajectory_recorder.return_in_fourier = return_in_fourier
        return trajectory_recorder.trajectory
    else:
        if return_in_fourier:
            return u_0_fft
        else:
            return f_mesh.ifft(u_0_fft).real
__call__ ¤
__call__(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], FourierTensor["B C H ..."]
]

Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before calling the operator.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], FourierTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def __call__(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]:
    r"""
    Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before calling the operator.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
    """    

    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u, u_fft, mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u, u_fft=u_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["operator"] is None:
        self._build_operator()
    if u_fft is None:
        u_fft = self._state_dict["f_mesh"].fft(u)
    value_fft = self._state_dict["operator"](u_fft)
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real
to ¤
to(device=None, dtype=None)

Move the operator to the specified device and change the data type.

Parameters:

Name Type Description Default
device Optional[device]

Device to which the operator should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the operator. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def to(self, device=None, dtype=None):
    r"""
    Move the operator to the specified device and change the data type.

    Args:
        device (Optional[torch.device]): Device to which the operator should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the operator. Default is None.
    """
    if self._state_dict is not None:
        self._state_dict["f_mesh"].to(device=device, dtype=dtype)
        self.register_mesh(self._state_dict["f_mesh"], self._state_dict["n_channel"])
__init__ ¤
__init__(
    linear_coef: ValueList[
        Union[LinearCoef, GeneratorLike]
    ] = None,
    coefs: Optional[List] = None,
) -> None
Source code in torchfsm/operator/_base.py 
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def __init__(
    self,
    linear_coef: ValueList[Union[LinearCoef, GeneratorLike]] = None,
    coefs: Optional[List] = None,
) -> None:
    if not isinstance(linear_coef, list):
        linear_coef = [linear_coef]
    super().__init__(
        operator_generators=[
            (
                linear_coef_i
                if not isinstance(linear_coef_i, LinearCoef)
                else lambda f_mesh, n_channel: linear_coef_i
            )
            for linear_coef_i in linear_coef
        ],
        coefs=coefs,
    )
__add__ ¤
__add__(other)
Source code in torchfsm/operator/_base.py 
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def __add__(self, other):
    if isinstance(other, LinearOperator):
        return LinearOperator(
            self.operator_generators + other.operator_generators,
            self.coefs + other.coefs,
        )
    elif isinstance(other, OperatorLike):
        return Operator(
            self.operator_generators + other.operator_generators,
            self.coefs + other.coefs,
        )
    elif isinstance(other, Tensor):
        return Operator(
            self.operator_generators
            + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
            self.coefs + [1],
        )
    else:
        return NotImplemented
__mul__ ¤
__mul__(other)
Source code in torchfsm/operator/_base.py 
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def __mul__(self, other):
    if isinstance(other, OperatorLike):
        return NotImplemented
    else:
        return LinearOperator(
            self.operator_generators, [coef * other for coef in self.coefs]
        )
__neg__ ¤
__neg__()
Source code in torchfsm/operator/_base.py 
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def __neg__(self):
    return LinearOperator(
        self.operator_generators, [-1 * coef for coef in self.coefs]
    )

torchfsm.operator.NonlinearOperator ¤

Bases: OperatorLike, _DeAliasMixin

Operators that contain only nonlinear operations.

Parameters:

Name Type Description Default
nonlinear_func ValueList[Union[NonlinearFunc, GeneratorLike]]

List of nonlinear function generators. Default is None. Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a nonlinear function.

 None
coefs Optional[List]

List of coefficients for each nonlinear function generator. Default is None. If None, all coefficients are set to 1. The length of the list should match the number of nonlinear function generators.

 None
Source code in torchfsm/operator/_base.py 
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class NonlinearOperator(OperatorLike, _DeAliasMixin):

    r"""
    Operators that contain only nonlinear operations.

    Args:
        nonlinear_func (ValueList[Union[NonlinearFunc, GeneratorLike]]): List of nonlinear function generators. Default is None.
            Each generator should be a callable that takes a Fourier mesh and number of channels as input and returns a nonlinear function.
        coefs (Optional[List]): List of coefficients for each nonlinear function generator. Default is None.
            If None, all coefficients are set to 1.
            The length of the list should match the number of nonlinear function generators.
    """

    def __init__(
        self,
        nonlinear_func: ValueList[Union[NonlinearFunc, GeneratorLike]] = None,
        coefs: Optional[List] = None,
    ) -> None:
        if not isinstance(nonlinear_func, list):
            nonlinear_func = [nonlinear_func]
        super().__init__(
            operator_generators=[
                (
                    nonlinear_func_i
                    if not isinstance(nonlinear_func_i, NonlinearFunc)
                    else lambda f_mesh, n_channel: nonlinear_func_i
                )
                for nonlinear_func_i in nonlinear_func
            ],
            coefs=coefs,
        )

    @property
    def is_linear(self):
        return False

    def __add__(self, other):
        if isinstance(other, NonlinearOperator):
            return NonlinearOperator(
                self.operator_generators + other.operator_generators,
                self.coefs + other.coefs,
            )
        elif isinstance(other, OperatorLike):
            return Operator(
                self.operator_generators + other.operator_generators,
                self.coefs + other.coefs,
            )
        elif isinstance(other, Tensor):
            return Operator(
                self.operator_generators
                + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
                self.coefs + [1],
            )
        else:
            return NotImplemented

    def __mul__(self, other):
        if isinstance(other, OperatorLike):
            return NotImplemented
        else:
            return NonlinearOperator(
                self.operator_generators, [coef * other for coef in self.coefs]
            )

    def __neg__(self):
        return NonlinearOperator(
            self.operator_generators, [-1 * coef for coef in self.coefs]
        )
_de_aliasing_rate instance-attribute ¤
_de_aliasing_rate = 2 / 3
_state_dict instance-attribute ¤
_state_dict = {
    "f_mesh": None,
    "n_channel": None,
    "linear_coef": None,
    "nonlinear_func": None,
    "operator": None,
    "integrator": None,
    "invert_linear_coef": None,
}
operator_generators instance-attribute ¤
operator_generators = default(operator_generators, [])
coefs instance-attribute ¤
coefs = default(coefs, [1] * len(operator_generators))
_nonlinear_funcs instance-attribute ¤
_nonlinear_funcs = []
_value_mesh_check_func instance-attribute ¤
_value_mesh_check_func = lambda dim_value, dim_mesh: True
_integrator instance-attribute ¤
_integrator = 'auto'
_integrator_config instance-attribute ¤
_integrator_config = {}
_is_etdrk_integrator instance-attribute ¤
_is_etdrk_integrator = True
is_linear property ¤
is_linear
set_de_aliasing_rate ¤
set_de_aliasing_rate(de_aliasing_rate: float)

Set the de-aliasing rate for the nonlinear operator. Args: de_aliasing_rate (float): De-aliasing rate. Default is ⅔.

Source code in torchfsm/operator/_base.py 
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def set_de_aliasing_rate(self, de_aliasing_rate: float):
    r"""
    Set the de-aliasing rate for the nonlinear operator.
    Args:
        de_aliasing_rate (float): De-aliasing rate. Default is 2/3.
    """

    self._de_aliasing_rate = de_aliasing_rate
    self._state_dict = None
__radd__ ¤
__radd__(other)
Source code in torchfsm/operator/_base.py 
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def __radd__(self, other):
    return self + other
__iadd__ ¤
__iadd__(other)
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def __iadd__(self, other):
    return self + other
__sub__ ¤
__sub__(other)
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def __sub__(self, other):
    try:
        return self + (-1 * other)
    except Exception:
        return NotImplemented
__rsub__ ¤
__rsub__(other)
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def __rsub__(self, other):
    try:
        return other + (-1 * self)
    except Exception:
        return NotImplemented
__isub__ ¤
__isub__(other)
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def __isub__(self, other):
    return self - other
__rmul__ ¤
__rmul__(other)
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def __rmul__(self, other):
    return self * other
__imul__ ¤
__imul__(other)
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def __imul__(self, other):
    return self * other
__truediv__ ¤
__truediv__(other)
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def __truediv__(self, other):
    try:
        return self * (1 / other)
    except:
        return NotImplemented
_build_linear_coefs ¤
_build_linear_coefs(
    linear_coefs: Optional[Sequence[LinearCoef]],
)

Build the linear coefficients based on the provided linear coefficient generators.

Parameters:

Name Type Description Default
linear_coefs Optional[Sequence[LinearCoef]]

List of linear coefficient generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_linear_coefs(
    self, linear_coefs: Optional[Sequence[LinearCoef]]
):
    r"""
    Build the linear coefficients based on the provided linear coefficient generators.

    Args:
        linear_coefs (Optional[Sequence[LinearCoef]]): List of linear coefficient generators.

    """
    if len(linear_coefs) == 0:
        linear_coefs = None
    else:
        linear_coefs = sum(
            [
                coef * op(self._state_dict["f_mesh"], self._state_dict["n_channel"])
                for coef, op in linear_coefs
            ]
        )
    self._state_dict["linear_coef"] = linear_coefs
_build_nonlinear_funcs ¤
_build_nonlinear_funcs(
    nonlinear_funcs: Optional[Sequence[NonlinearFunc]],
)

Build the nonlinear functions based on the provided nonlinear function generators.

Parameters:

Name Type Description Default
nonlinear_funcs Optional[Sequence[NonlinearFunc]]

List of nonlinear function generators.

 required
Source code in torchfsm/operator/_base.py 
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def _build_nonlinear_funcs(
    self, nonlinear_funcs: Optional[Sequence[NonlinearFunc]]
):
    r"""
    Build the nonlinear functions based on the provided nonlinear function generators.

    Args:
        nonlinear_funcs (Optional[Sequence[NonlinearFunc]]): List of nonlinear function generators.
    """
    if len(nonlinear_funcs) == 0:
        nonlinear_funcs_all = None
    else:
        self._state_dict["f_mesh"].set_default_freq_threshold(
            self._de_aliasing_rate
        )

        def nonlinear_funcs_all(u_fft):
            result = 0.0
            dealiased_u_fft = None
            dealiased_u = None
            u = None
            for coef, fun in nonlinear_funcs:
                if fun._dealiasing_swtich:
                    if dealiased_u_fft is None:
                        dealiased_u_fft = u_fft * self._state_dict[
                            "f_mesh"
                        ].low_pass_filter(self._de_aliasing_rate)
                        dealiased_u = (
                            self._state_dict["f_mesh"].ifft(dealiased_u_fft).real
                        )
                    result += coef * fun(
                        dealiased_u_fft,
                        self._state_dict["f_mesh"],
                        dealiased_u,
                    )
                else:
                    if u is None:
                        u = self._state_dict["f_mesh"].ifft(u_fft).real
                    result += coef * fun(
                        u_fft,
                        self._state_dict["f_mesh"],
                        u,
                    )

            return result

    self._state_dict["nonlinear_func"] = nonlinear_funcs_all
_build_operator ¤
_build_operator()

Build the operator based on the linear coefficient and nonlinear function. If both linear coefficient and nonlinear function are None, the operator is set to None.

Source code in torchfsm/operator/_base.py 
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def _build_operator(self):
    r"""
    Build the operator based on the linear coefficient and nonlinear function.
    If both linear coefficient and nonlinear function are None, the operator is set to None.
    """
    if self._state_dict["nonlinear_func"] is None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft
    elif self._state_dict["linear_coef"] is None:
        def operator(u_fft):
            return self._state_dict["nonlinear_func"](u_fft)
    elif self._state_dict["nonlinear_func"] is not None and self._state_dict["linear_coef"] is not None:
        def operator(u_fft):
            return self._state_dict["linear_coef"] * u_fft + self._state_dict[
                "nonlinear_func"
            ](u_fft)
    else:
        raise ValueError(
            "Both linear coefficient and nonlinear function are None. Cannot build operator."
        )

    self._state_dict["operator"] = operator
_build_integrator ¤
_build_integrator(dt: float)

Build the integrator based on the provided time step and integrator type.

Parameters:

Name Type Description Default
dt float

Time step for the integrator.

 required
Source code in torchfsm/operator/_base.py 
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def _build_integrator(
    self,
    dt: float,
):
    r"""
    Build the integrator based on the provided time step and integrator type.

    Args:
        dt (float): Time step for the integrator.
    """
    if self._integrator == "auto":
        if self.is_linear:
            solver = ETDRKIntegrator.ETDRK0
        else:
            solver = ETDRKIntegrator.ETDRK4
    else:
        solver = self._integrator
    self._is_etdrk_integrator = isinstance(solver, ETDRKIntegrator)
    if self._is_etdrk_integrator:
        if solver == ETDRKIntegrator.ETDRK0:
            assert self.is_linear, "The ETDRK0 integrator only supports linear term"
            self._state_dict["integrator"] = solver.value(
                dt,
                self._state_dict["linear_coef"],
                **self._integrator_config,
            )
        else:
            if self._state_dict["linear_coef"] is None:
                linear_coef = torch.tensor(
                    [0.0],
                    dtype=self._state_dict["f_mesh"].dtype,
                    device=self._state_dict["f_mesh"].device,
                )
            else:
                linear_coef = self._state_dict["linear_coef"]
            self._state_dict["integrator"] = solver.value(
                dt,
                linear_coef,
                self._state_dict["nonlinear_func"],
                **self._integrator_config,
            )
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(u_fft),
        )
    elif isinstance(solver, RKIntegrator):
        if self._state_dict["operator"] is None:
            self._build_operator()
        self._state_dict["integrator"] = solver.value(**self._integrator_config)
        setattr(
            self._state_dict["integrator"],
            "forward",
            lambda u_fft, dt: self._state_dict["integrator"].step(
                self._state_dict["operator"], u_fft, dt
            ),
        )
_pre_check ¤
_pre_check(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ] = None,
) -> Tuple[FourierMesh, int]

Pre-check the input tensor and mesh. If the mesh is not registered, register it.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used.

 None

Returns:

Type Description
Tuple[FourierMesh, int]

Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
Source code in torchfsm/operator/_base.py 
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def _pre_check(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh] = None,
) -> Tuple[FourierMesh, int]:
    r"""
    Pre-check the input tensor and mesh. If the mesh is not registered, register it.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used.

    Returns:
        Tuple[FourierMesh, int]: Tuple of Fourier mesh and number of channels.
    """

    if u_fft is None and u is None:
        raise ValueError("Either u or u_fft should be given")
    if u_fft is not None and u is not None:
        assert u.shape == u_fft.shape, "The shape of u and u_fft should be the same"
    assert mesh is not None, "Mesh should be given"
    value_device = u.device if u is not None else u_fft.device
    value_dtype = u.dtype if u is not None else u_fft.dtype
    if not isinstance(mesh, FourierMesh):
        if not isinstance(mesh, MeshGrid):
            mesh = FourierMesh(mesh, device=value_device, dtype=value_dtype)
        else:
            mesh = FourierMesh(mesh)
    n_channel = u.shape[1] if u is not None else u_fft.shape[1]
    value_shape = u.shape if u is not None else u_fft.shape
    assert (
        len(value_shape) == mesh.n_dim + 2
    ), f"the value shape {value_shape} is not compatible with mesh dim {mesh.n_dim}"
    for i in range(mesh.n_dim):
        assert (
            value_shape[i + 2] == mesh.mesh_info[i][2]
        ), f"Expect to have {mesh.mesh_info[i][2]} points in dim {i} but got {value_shape[i+2]}"
    assert (
        value_device == mesh.device
    ), "The device of mesh {} and the device of value {} are not the same".format(
        mesh.device, value_device
    )
    # assert value_dtype==mesh.dtype, "The dtype of mesh {} and the dtype of value {} are not the same".format(mesh.dtype,value_dtype)
    # value fft is a complex dtype
    assert self._value_mesh_check_func(
        len(value_shape) - 2, mesh.n_dim
    ), "Value and mesh do not match the requirement"
    return mesh, n_channel
register_mesh ¤
register_mesh(
    mesh: Union[
        Sequence[tuple[float, float, int]],
        MeshGrid,
        FourierMesh,
    ],
    n_channel: int,
    device=None,
    dtype=None,
)

Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

Parameters:

Name Type Description Default
mesh Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]

Mesh information or mesh object.

 required
n_channel int

Number of channels of the input tensor.

 required
device Optional[device]

Device to which the mesh should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the mesh. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def register_mesh(
    self,
    mesh: Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh],
    n_channel: int,
    device=None,
    dtype=None,
):
    r"""
    Register the mesh and number of channels for the operator. Once a mesh is registered, mesh information is not required for integration and operator call.

    Args:
        mesh (Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]): Mesh information or mesh object.
        n_channel (int): Number of channels of the input tensor.
        device (Optional[torch.device]): Device to which the mesh should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the mesh. Default is None.
    """
    if isinstance(mesh, FourierMesh):
        f_mesh = mesh
        if device is not None or dtype is not None:
            f_mesh.to(device=device, dtype=dtype)
    else:
        f_mesh = FourierMesh(mesh, device=device, dtype=dtype)
    for key in self._state_dict:
        self._state_dict[key] = None
    self._state_dict.update(
        {
            "f_mesh": f_mesh,
            "n_channel": n_channel,
        }
    )
    linear_coefs = []
    nonlinear_funcs = []
    for coef, generator in zip(self.coefs, self.operator_generators):
        op = generator(f_mesh, n_channel)
        if isinstance(op, LinearCoef):
            linear_coefs.append((coef, op))
        elif isinstance(op, NonlinearFunc):
            nonlinear_funcs.append((coef, op))
        else:
            raise ValueError(f"Operator {op} is not supported")
    self._nonlinear_funcs = nonlinear_funcs
    self._build_linear_coefs(linear_coefs)
    self._build_nonlinear_funcs(self._nonlinear_funcs)
regisiter_additional_check ¤
regisiter_additional_check(
    func: Callable[[int, int], bool]
)

Register an additional check function for the value and mesh compatibility.

Parameters:

Name Type Description Default
func Callable[[int, int], bool]

Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.

 required
Source code in torchfsm/operator/_base.py 
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def regisiter_additional_check(self, func: Callable[[int, int], bool]):
    r"""
    Register an additional check function for the value and mesh compatibility.

    Args:
        func (Callable[[int, int], bool]): Function that takes the dimension of the value and mesh as input and returns a boolean indicating whether they are compatible.
    """
    self._value_mesh_check_func = func
add_generator ¤
add_generator(generator: GeneratorLike, coef=1)

Add a generator to the operator.

Parameters:

Name Type Description Default
generator GeneratorLike

Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.

 required
coef float

Coefficient for the generator. Default is 1.

 1
Source code in torchfsm/operator/_base.py 
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def add_generator(self, generator: GeneratorLike, coef=1):
    r"""
    Add a generator to the operator.

    Args:
        generator (GeneratorLike): Generator to be added. It should be a callable that takes a Fourier mesh and number of channels as input and returns a linear coefficient or nonlinear function.
        coef (float): Coefficient for the generator. Default is 1.
    """
    self.operator_generators.append(generator)
    self.coefs.append(coef)
set_integrator ¤
set_integrator(
    integrator: Union[
        Literal["auto"], ETDRKIntegrator, RKIntegrator
    ],
    **integrator_config
)

Set the integrator for the operator. The integrator is used for time integration of the operator.

Parameters:

Name Type Description Default
integrator Union[Literal['auto'], ETDRKIntegrator, RKIntegrator]

Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type. If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.

 required
**integrator_config

Additional configuration for the integrator.

 {}
Source code in torchfsm/operator/_base.py 
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def set_integrator(
    self,
    integrator: Union[Literal["auto"], ETDRKIntegrator, RKIntegrator],
    **integrator_config,
):
    r"""
    Set the integrator for the operator. The integrator is used for time integration of the operator.

    Args:
        integrator (Union[Literal["auto"], ETDRKIntegrator, RKIntegrator]): Integrator to be used. If "auto", the integrator will be chosen automatically based on the operator type.
            If "auto", the integrator will be set as ETDRKIntegrator.ETDRK0 for linear operators and ETDRKIntegrator.ETDRK4 for nonlinear operators.
        **integrator_config: Additional configuration for the integrator.
    """

    if isinstance(integrator, str):
        assert (
            integrator == "auto"
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    else:
        assert isinstance(integrator, ETDRKIntegrator) or isinstance(
            integrator, RKIntegrator
        ), "The integrator should be 'auto' or an instance of ETDRKIntegrator or RKIntegrator"
    self._integrator = integrator
    self._integrator_config = integrator_config
    self._state_dict["integrator"] = None
integrate ¤
integrate(
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,
) -> Union[
    SpatialTensor["B C H ..."],
    SpatialTensor["B T C H ..."],
    FourierTensor["B C H ..."],
    FourierTensor["B T C H ..."],
]

Integrate the operator using the provided initial condition and time step.

Parameters:

Name Type Description Default
u_0 Optional[Tensor]

Initial condition in spatial domain. Default is None.

 None
u_0_fft Optional[Tensor]

Initial condition in Fourier domain. Default is None. At least one of u_0 or u_0_fft should be provided.

 None
dt float

Time step for the integrator. Default is 1.

 1
step int

Number of time steps to integrate. Default is 1.

 1
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before integration.

 None
progressive bool

If True, show a progress bar during integration. Default is False.

 False
trajectory_recorder Optional[_TrajRecorder]

Trajectory recorder for recording the trajectory during integration. Default is None. If None, no trajectory will be recorded. The function will only return the final frame.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], SpatialTensor['B T C H ...'], FourierTensor['B C H ...'], FourierTensor['B T C H ...']]

Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain. If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...). If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.
Source code in torchfsm/operator/_base.py 
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def integrate(
    self,
    u_0: Optional[torch.Tensor] = None,
    u_0_fft: Optional[torch.Tensor] = None,
    dt: float = 1,
    step: int = 1,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    progressive: bool = False,
    trajectory_recorder: Optional[_TrajRecorder] = None,
    return_in_fourier: bool = False,

) -> Union[
        SpatialTensor["B C H ..."],
        SpatialTensor["B T C H ..."],
        FourierTensor["B C H ..."],
        FourierTensor["B T C H ..."],
    ]:
    r"""
    Integrate the operator using the provided initial condition and time step.  

    Args:
        u_0 (Optional[torch.Tensor]): Initial condition in spatial domain. Default is None.
        u_0_fft (Optional[torch.Tensor]): Initial condition in Fourier domain. Default is None.
            At least one of u_0 or u_0_fft should be provided.
        dt (float): Time step for the integrator. Default is 1.
        step (int): Number of time steps to integrate. Default is 1.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before integration.
        progressive (bool): If True, show a progress bar during integration. Default is False.
        trajectory_recorder (Optional[_TrajRecorder]): Trajectory recorder for recording the trajectory during integration. Default is None.
            If None, no trajectory will be recorded. The function will only return the final frame.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], SpatialTensor["B T C H ..."], FourierTensor["B C H ..."], FourierTensor["B T C H ..."]]: Integrated result in spatial or Fourier domain.
            If trajectory_recorder is provided, the result will be a trajectory tensor of shape (B, T, C, H, ...). Otherwise, the result will be a tensor of shape (B, C, H, ...).
            If return_in_fourier is True, the result will be in Fourier domain. Otherwise, it will be in spatial domain.

    """
    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u=u_0, u_fft=u_0_fft, mesh=mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u_0, u_fft=u_0_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["integrator"] is None:
        self._build_integrator(dt)
    elif self._is_etdrk_integrator:
        if self._state_dict["integrator"].dt != dt:
            self._build_integrator(dt)
    f_mesh = self._state_dict["f_mesh"]
    if u_0_fft is None:
        u_0_fft = f_mesh.fft(u_0)
    p_bar = tqdm(range(step), desc="Integrating", disable=not progressive)
    for i in p_bar:
        if trajectory_recorder is not None:
            trajectory_recorder.record(i, u_0_fft)
        u_0_fft = self._state_dict["integrator"].forward(u_0_fft, dt)
    if trajectory_recorder is not None:
        trajectory_recorder.record(i + 1, u_0_fft)
        trajectory_recorder.return_in_fourier = return_in_fourier
        return trajectory_recorder.trajectory
    else:
        if return_in_fourier:
            return u_0_fft
        else:
            return f_mesh.ifft(u_0_fft).real
__call__ ¤
__call__(
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    return_in_fourier=False,
) -> Union[
    SpatialTensor["B C H ..."], FourierTensor["B C H ..."]
]

Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

Parameters:

Name Type Description Default
u Optional[SpatialTensor]

Input tensor in spatial domain. Default is None.

 None
u_fft Optional[FourierTensor]

Input tensor in Fourier domain. Default is None. At least one of u or u_fft should be provided.

 None
mesh Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]

Mesh information or mesh object. Default is None. If None, the mesh registered in the operator will be used. You can use register_mesh to register a mesh before calling the operator.

 None
return_in_fourier bool

If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

 False

Returns:

Type Description
Union[SpatialTensor['B C H ...'], FourierTensor['B C H ...']]

Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
Source code in torchfsm/operator/_base.py 
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def __call__(
    self,
    u: Optional[SpatialTensor["B C H ..."]] = None,
    u_fft: Optional[FourierTensor["B C H ..."]] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    return_in_fourier=False,
) -> Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]:
    r"""
    Call the operator with the provided input tensor. The operator will apply the linear coefficient and nonlinear function to the input tensor.

    Args:
        u (Optional[SpatialTensor]): Input tensor in spatial domain. Default is None.
        u_fft (Optional[FourierTensor]): Input tensor in Fourier domain. Default is None.
            At least one of u or u_fft should be provided.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): Mesh information or mesh object. Default is None.
            If None, the mesh registered in the operator will be used. You can use `register_mesh` to register a mesh before calling the operator.
        return_in_fourier (bool): If True, return the result in Fourier domain. If False, return the result in spatial domain. Default is False.

    Returns:
        Union[SpatialTensor["B C H ..."], FourierTensor["B C H ..."]]: Result of the operator in spatial or Fourier domain.
    """    

    if self._state_dict["f_mesh"] is None or mesh is not None:
        mesh, n_channel = self._pre_check(u, u_fft, mesh)
        self.register_mesh(mesh, n_channel)
    else:
        self._pre_check(u=u, u_fft=u_fft, mesh=self._state_dict["f_mesh"])
    if self._state_dict["operator"] is None:
        self._build_operator()
    if u_fft is None:
        u_fft = self._state_dict["f_mesh"].fft(u)
    value_fft = self._state_dict["operator"](u_fft)
    if return_in_fourier:
        return value_fft
    else:
        return self._state_dict["f_mesh"].ifft(value_fft).real
to ¤
to(device=None, dtype=None)

Move the operator to the specified device and change the data type.

Parameters:

Name Type Description Default
device Optional[device]

Device to which the operator should be moved. Default is None.

 None
dtype Optional[dtype]

Data type of the operator. Default is None.

 None
Source code in torchfsm/operator/_base.py 
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def to(self, device=None, dtype=None):
    r"""
    Move the operator to the specified device and change the data type.

    Args:
        device (Optional[torch.device]): Device to which the operator should be moved. Default is None.
        dtype (Optional[torch.dtype]): Data type of the operator. Default is None.
    """
    if self._state_dict is not None:
        self._state_dict["f_mesh"].to(device=device, dtype=dtype)
        self.register_mesh(self._state_dict["f_mesh"], self._state_dict["n_channel"])
__init__ ¤
__init__(
    nonlinear_func: ValueList[
        Union[NonlinearFunc, GeneratorLike]
    ] = None,
    coefs: Optional[List] = None,
) -> None
Source code in torchfsm/operator/_base.py 
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def __init__(
    self,
    nonlinear_func: ValueList[Union[NonlinearFunc, GeneratorLike]] = None,
    coefs: Optional[List] = None,
) -> None:
    if not isinstance(nonlinear_func, list):
        nonlinear_func = [nonlinear_func]
    super().__init__(
        operator_generators=[
            (
                nonlinear_func_i
                if not isinstance(nonlinear_func_i, NonlinearFunc)
                else lambda f_mesh, n_channel: nonlinear_func_i
            )
            for nonlinear_func_i in nonlinear_func
        ],
        coefs=coefs,
    )
__add__ ¤
__add__(other)
Source code in torchfsm/operator/_base.py 
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def __add__(self, other):
    if isinstance(other, NonlinearOperator):
        return NonlinearOperator(
            self.operator_generators + other.operator_generators,
            self.coefs + other.coefs,
        )
    elif isinstance(other, OperatorLike):
        return Operator(
            self.operator_generators + other.operator_generators,
            self.coefs + other.coefs,
        )
    elif isinstance(other, Tensor):
        return Operator(
            self.operator_generators
            + [lambda f_mesh, n_channel: _ExplicitSourceCore(other)],
            self.coefs + [1],
        )
    else:
        return NotImplemented
__mul__ ¤
__mul__(other)
Source code in torchfsm/operator/_base.py 
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def __mul__(self, other):
    if isinstance(other, OperatorLike):
        return NotImplemented
    else:
        return NonlinearOperator(
            self.operator_generators, [coef * other for coef in self.coefs]
        )
__neg__ ¤
__neg__()
Source code in torchfsm/operator/_base.py 
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def __neg__(self):
    return NonlinearOperator(
        self.operator_generators, [-1 * coef for coef in self.coefs]
    )