flowtorch.analysis

flowtorch.analysis.svd

Classes and functions wrapping around torch.linalg.svd.

class flowtorch.analysis.svd.SVD(data_matrix: torch.Tensor, rank: Optional[int] = None)

Bases: object

Compute and analyze the SVD of a data matrix.

Parameters

• U (pt.Tensor) – left singular vectors

• s (pt.Tensor) – singular values

• s_rel (pt.Tensor) – singular values normalized with their sum in percent

• s_cum (pt.Tensor) – cumulative normalized singular values in percent

• V (pt.Tensor) – right singular values

• rank (int) – rank used for truncation

• opt_rank (int) – optimal rank according to SVHT

• required_memory (int) – memory required to store the truncation U, s, and V

Examples

>>> from flowtorch import DATASETS
>>> from flowtorch.data import FOAMDataloader
>>> from flowtorch.analysis import SVD
>>> loader = FOAMDataloader(DATASETS["of_cavity_ascii"])
>>> data = loader.load_snapshot("p", loader.write_times[1:])
>>> svd = SVD(data, rank=100)
>>> print(svd)
SVD of a 400x5 data matrix
Selected/optimal rank: 5/2
data type: torch.float32 (4b)
truncated SVD size: 7.9297Kb
>>> svd.s_rel
tensor([9.9969e+01, 3.0860e-02, 3.0581e-04, 7.8097e-05, 3.2241e-05])
>>> svd.s_cum
tensor([ 99.9687,  99.9996,  99.9999, 100.0000, 100.0000])
>>> svd.U.shape
torch.Size([400, 5])

property U

property V

property opt_rank

property rank

reconstruct(rank: Optional[int] = None) → torch.Tensor

Reconstruct the data matrix for a given rank.

Parameters

rank (int, optional) – rank used to compute a truncated reconstruction

Returns

reconstruction of the input data matrix

Return type

pt.Tensor

property required_memory

Compute the memory size in bytes of the truncated SVD.

Returns

cumulative size of truncated U, s, and V tensors in bytes

Return type

int

property s

property s_cum

property s_rel

flowtorch.analysis.dmd

Classes and functions to compute the dynamic mode decomposition (DMD) of a data matrix.

class flowtorch.analysis.dmd.DMD(data_matrix: torch.Tensor, dt: float, rank: Optional[int] = None)

Bases: object

Class computing the exact DMD of a data matrix.

Currently, no advanced mode selection algorithms are implemented. The mode amplitudes are computed using the first snapshot.

Examples

>>> from flowtorch import DATASETS
>>> from flowtorch.data import FOAMDataloader
>>> from flowtorch.analysis import DMD
>>> path = DATASETS["of_cavity_binary"]
>>> loader = FOAMDataloader(path)
>>> data_matrix = loader.load_snapshot("p", loader.write_times)
>>> dmd = DMD(data_matrix, dt=0.1, rank=3)
>>> dmd.frequency
tensor([0., 5., 0.])
>>> dmd.growth_rate
tensor([-2.3842e-06, -4.2345e+01, -1.8552e+01])
>>> dmd.amplitude
tensor([10.5635+0.j, -0.0616+0.j, -0.0537+0.j])

property amplitude

property dynamics

property eigvals

property eigvecs

property frequency

property growth_rate

property modes

partial_reconstruction(mode_indices: Set[int]) → torch.Tensor

Reconstruct data matrix with limited number of modes.

Parameters

mode_indices (Set[int]) – mode indices to keep

Returns

reconstructed data matrix

Return type

pt.Tensor

property reconstruction

property required_memory

Compute the memory size in bytes of the DMD.

Returns

cumulative size of SVD, eigen values/vectors, and DMD modes in bytes

Return type

int

property svd

flowtorch.analysis.psp_explorer

Module with classes and functions to explore and analyse iPSP data.

class flowtorch.analysis.psp_explorer.PSPExplorer(file_path: str)

Bases: object

Explore iPSP data interactively.

interact(zone: str, field_name: str, times: list, mask: bool = True, width: int = 1024, every: int = 5, cmin: float = - 2, cmax: float = 0.5) → plotly.graph_objs._figure.Figure

property loader

mean(zone: str, field_name: str, times: list, mask: bool = True, width: int = 1024, every=5, cmin: float = - 2, cmax: float = 0.5) → plotly.graph_objs._figure.Figure

std(zone: str, field_name: str, times: list, mask: bool = True, width: int = 1024, every=5, cmin: float = 0, cmax: float = 0.5) → plotly.graph_objs._figure.Figure