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3. functional

torchfsm.functional.biharmonic ¤

biharmonic(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the biharmonic operator. For details, see torchfsm.operator.Biharmonic.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the biharmonic operator to the input field.
Source code in torchfsm/functional.py 
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def biharmonic(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the biharmonic operator.
        For details, see `torchfsm.operator.Biharmonic`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the biharmonic operator to the input field.   
    """
    return Biharmonic()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.conservative_convection ¤

conservative_convection(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the conservative convection operator. For details, see torchfsm.operator.ConservativeConvection.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the conservative convection operator to the input field.
Source code in torchfsm/functional.py 
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def conservative_convection(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the conservative convection operator.
        For details, see `torchfsm.operator.ConservativeConvection`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the conservative convection operator to the input field.
    """
    return ConservativeConvection()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.convection ¤

convection(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the convection operator. For details, see torchfsm.operator.Convection.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the convection operator to the input field.
Source code in torchfsm/functional.py 
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def convection(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the convection operator.
        For details, see `torchfsm.operator.Convection`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the convection operator to the input field.
    """

    return Convection()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.curl ¤

curl(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the curl operator. For details, see torchfsm.operator.Curl.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the curl operator to the input field.
Source code in torchfsm/functional.py 
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def curl(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the curl operator.
        For details, see `torchfsm.operator.Curl`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the curl operator to the input field.
    """

    return Curl()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.div ¤

div(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the divergence operator. For details, see torchfsm.operator.Div.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the divergence operator to the input field.
Source code in torchfsm/functional.py 
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def div(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the divergence operator.
        For details, see `torchfsm.operator.Div`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the divergence operator to the input field.
    """

    return Div()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.dispersion ¤

dispersion(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the dispersion operator. For details, see torchfsm.operator.Dispersion.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the dispersion operator to the input field.
Source code in torchfsm/functional.py 
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def dispersion(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the dispersion operator.
        For details, see `torchfsm.operator.Dispersion`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the dispersion operator to the input field.
    """
    return Dispersion()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.grad ¤

grad(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the gradient operator. For details, see torchfsm.operator.Grad.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the gradient operator to the input field.
Source code in torchfsm/functional.py 
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def grad(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the gradient operator.
        For details, see `torchfsm.operator.Grad`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the gradient operator to the input field.
    """

    return Grad()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.hyper_diffusion ¤

hyper_diffusion(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the hyper diffusion operator. For details, see torchfsm.operator.HyperDiffusion.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the hyper diffusion operator to the input field.
Source code in torchfsm/functional.py 
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def hyper_diffusion(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the hyper diffusion operator.
        For details, see `torchfsm.operator.HyperDiffusion`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the hyper diffusion operator to the input field.
    """
    return HyperDiffusion()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.laplacian ¤

laplacian(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the Laplacian operator. For details, see torchfsm.operator.Laplacian.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the Laplacian operator to the input field.
Source code in torchfsm/functional.py 
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def laplacian(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the Laplacian operator.
        For details, see `torchfsm.operator.Laplacian`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the Laplacian operator to the input field.
    """
    return Laplacian()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.spatial_derivative ¤

spatial_derivative(
    dim_index: int,
    order: int,
    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,
) -> SpatialTensor["B C H ..."]

Function form for the spatial derivative operator. For details, see torchfsm.operator.SpatialDerivative.

Parameters:

Name Type Description Default
dim_index int

The index of the dimension to take the derivative along.

 required
order int

The order of the derivative.

 required
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the spatial derivative operator to the input field.
Source code in torchfsm/functional.py 
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def spatial_derivative(
    dim_index: int,
    order: int,
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the spatial derivative operator.
        For details, see `torchfsm.operator.SpatialDerivative`.

    Args:
        dim_index (int): The index of the dimension to take the derivative along.
        order (int): The order of the derivative.
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the spatial derivative operator to the input field.
    """
    return SpatialDerivative(dim_index, order)(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.ks_convection ¤

ks_convection(
    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,
    remove_mean: bool = True,
) -> SpatialTensor["B C H ..."]

Function form for the Kuramoto-Sivashinsky convection operator. For details, see torchfsm.operator.KSConvection.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None
remove_mean bool

If True, the mean of the input field will be removed before applying the operator.

 True

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the Kuramoto-Sivashinsky convection operator to the input field.
Source code in torchfsm/functional.py 
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def ks_convection(
    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,
    remove_mean: bool = True,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the Kuramoto-Sivashinsky convection operator.
        For details, see `torchfsm.operator.KSConvection`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.
        remove_mean (bool): If True, the mean of the input field will be removed before applying the operator.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the Kuramoto-Sivashinsky convection operator to the input field.
    """
    return KSConvection(remove_mean)(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.vorticity_convection ¤

vorticity_convection(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the vorticity convection operator. For details, see torchfsm.operator.VorticityConvection.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the vorticity convection operator to the input field.
Source code in torchfsm/functional.py 
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def vorticity_convection(
    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,
) -> SpatialTensor["B C H ..."]:

    r"""
    Function form for the vorticity convection operator.
        For details, see `torchfsm.operator.VorticityConvection`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the vorticity convection operator to the input field.
    """
    return VorticityConvection()(u=u, u_fft=u_fft, mesh=mesh)

torchfsm.functional.vorticity2velocity ¤

vorticity2velocity(
    vorticity: Optional[Tensor] = None,
    vorticity_fft: Optional[Tensor] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
) -> SpatialTensor["B C H ..."]

Function form for the vorticity to velocity operator. For details, see torchfsm.operator.Vorticity2Velocity.

Parameters:

Name Type Description Default
vorticity Optional[Tensor]

The input vorticity field.

 None
vorticity_fft Optional[Tensor]

The Fourier-transformed vorticity field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the vorticity to velocity operator to the input field.
Source code in torchfsm/functional.py 
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def vorticity2velocity(
    vorticity: Optional[torch.Tensor] = None,
    vorticity_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the vorticity to velocity operator.
        For details, see `torchfsm.operator.Vorticity2Velocity`.

    Args:
        vorticity (Optional[torch.Tensor]): The input vorticity field.
        vorticity_fft (Optional[torch.Tensor]): The Fourier-transformed vorticity field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the vorticity to velocity operator to the input field.
    """

    return Vorticity2Velocity()(u=vorticity, u_fft=vorticity_fft, mesh=mesh)

torchfsm.functional.vorticity2pressure ¤

vorticity2pressure(
    vorticity: Optional[Tensor] = None,
    vorticity_fft: Optional[Tensor] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    external_force: Optional[OperatorLike] = None,
) -> SpatialTensor["B C H ..."]

Function form for the vorticity to pressure operator. For details, see torchfsm.operator.Vorticity2Pressure.

Parameters:

Name Type Description Default
vorticity Optional[Tensor]

The input vorticity field.

 None
vorticity_fft Optional[Tensor]

The Fourier-transformed vorticity field.

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

The mesh for the field.

 None
external_force Optional[OperatorLike]

An optional external force to be applied.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the vorticity to pressure operator to the input field.
Source code in torchfsm/functional.py 
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def vorticity2pressure(
    vorticity: Optional[torch.Tensor] = None,
    vorticity_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    external_force: Optional[OperatorLike] = None,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the vorticity to pressure operator.
        For details, see `torchfsm.operator.Vorticity2Pressure`.

    Args:
        vorticity (Optional[torch.Tensor]): The input vorticity field.
        vorticity_fft (Optional[torch.Tensor]): The Fourier-transformed vorticity field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.
        external_force (Optional[OperatorLike]): An optional external force to be applied.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the vorticity to pressure operator to the input field.
    """

    vorticity_fft, f_mesh = _get_fft_with_mesh(
        value=vorticity, value_fft=vorticity_fft, mesh=mesh
    )
    velocity_fft = Vorticity2Velocity()(
        u_fft=vorticity_fft, mesh=f_mesh, return_in_fourier=True
    )
    convection = Convection()(u_fft=velocity_fft, mesh=f_mesh, return_in_fourier=True)
    if external_force is not None:
        convection -= external_force(
            u_fft=vorticity_fft, mesh=f_mesh, return_in_fourier=True
        )
    convection = Div()(u_fft=convection, mesh=f_mesh, return_in_fourier=True)
    return Laplacian().solve(b_fft=-1 * convection, mesh=f_mesh, n_channel=1)

torchfsm.functional.velocity2pressure ¤

velocity2pressure(
    velocity: Optional[Tensor] = None,
    velocity_fft: Optional[Tensor] = None,
    mesh: Optional[
        Union[
            Sequence[tuple[float, float, int]],
            MeshGrid,
            FourierMesh,
        ]
    ] = None,
    external_force: Optional[OperatorLike] = None,
) -> SpatialTensor["B C H ..."]

Function form for the velocity to pressure operator. For details, see torchfsm.operator.Velocity2Pressure.

Parameters:

Name Type Description Default
velocity Optional[Tensor]

The input velocity field.

 None
velocity_fft Optional[Tensor]

The Fourier-transformed velocity field.

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

The mesh for the field.

 None
external_force Optional[OperatorLike]

An optional external force to be applied.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the velocity to pressure operator to the input field.
Source code in torchfsm/functional.py 
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def velocity2pressure(
    velocity: Optional[torch.Tensor] = None,
    velocity_fft: Optional[torch.Tensor] = None,
    mesh: Optional[
        Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]
    ] = None,
    external_force: Optional[OperatorLike] = None,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the velocity to pressure operator.
        For details, see `torchfsm.operator.Velocity2Pressure`.

    Args:
        velocity (Optional[torch.Tensor]): The input velocity field.
        velocity_fft (Optional[torch.Tensor]): The Fourier-transformed velocity field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.
        external_force (Optional[OperatorLike]): An optional external force to be applied.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the velocity to pressure operator to the input field.
    """

    velocity_fft, f_mesh = _get_fft_with_mesh(
        value=velocity, value_fft=velocity_fft, mesh=mesh
    )
    convection = Convection()(u_fft=velocity_fft, mesh=f_mesh, return_in_fourier=True)
    if external_force is not None:
        convection -= external_force(
            u_fft=velocity_fft, mesh=f_mesh, return_in_fourier=True
        )
    convection = Div()(u_fft=convection, mesh=f_mesh, return_in_fourier=True)
    return Laplacian().solve(b_fft=-1 * convection, mesh=f_mesh, n_channel=1)

torchfsm.functional.leray ¤

leray(
    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,
) -> SpatialTensor["B C H ..."]

Function form for the Leray operator. For details, see torchfsm.operator.Leray.

Parameters:

Name Type Description Default
u Optional[SpatialTensor['B C H ...']]

The input field.

 None
u_fft Optional[FourierTensor['B C H ...']]

The Fourier-transformed input field.

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

The mesh for the field.

 None

Returns:

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

SpatialTensor["B C H ..."]: The result of applying the Leray operator to the input field.
Source code in torchfsm/functional.py 
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def leray(
    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,
) -> SpatialTensor["B C H ..."]:
    r"""
    Function form for the Leray operator.
        For details, see `torchfsm.operator.Leray`.

    Args:
        u (Optional[SpatialTensor["B C H ..."]]): The input field.
        u_fft (Optional[FourierTensor["B C H ..."]]): The Fourier-transformed input field.
        mesh (Optional[Union[Sequence[tuple[float, float, int]], MeshGrid, FourierMesh]]): The mesh for the field.

    Returns:
        SpatialTensor["B C H ..."]: The result of applying the Leray operator to the input field.
    """
    return Leray()(u=u, u_fft=u_fft, mesh=mesh)