pyLOM.POD#
Module contents#
- pyLOM.POD.run(X: ndarray, remove_mean: bool = True, randomized: bool = False, r: int = 1, q: int = 3, seed: int = -1)[source]#
Run POD analysis of a matrix.
- Parameters:
X (np.ndarray) – data matrix of size [ndims*nmesh,n_temp_snapshots].
remove_mean (bool, optional) – whether or not to remove the mean flow (default:
True).randomized (bool, optional) – whether to perform randomized POD or not (default:
False).r (int, optional) – in case of performing randomized POD, how many modes do we want to recover. This option has no effect when randomized=False (default:
1).q (int, optional) – in case of performing randomized POD, how many power iterations are performed. This option has no effect when randomized=False (default:
3).seed (int, optional) – seed for reproducibility of randomized operations. This option has no effect when randomized=False (default:
-1).
- Returns:
POD spatial modes (left singular vectors), singular values and temporal coefficients (right singular vectors).
- Return type:
[(np.ndarray), (np.ndarray), (np.ndarray)]
- pyLOM.POD.truncate(U: ndarray, S: ndarray, V: ndarray, r: float = 1e-8)[source]#
Truncate POD matrices (U, S, V) given a residual, number of modes or cumulative energy r.
- Parameters:
U (np.ndarray) – of size (m,n), are the POD modes.
S (np.ndarray) – of size (n), are the singular values.
V (np.ndarray) – of size (n,n), are the right singular vectors.
r (float, optional) –
1e-8). * If r >= 1, it is treated as the number of modes. * If r < 1 and r > 0 it is treated as the residual target. * If r < 1 and r < 0 it is treated as the fraction of cumulative energy to retain. Note: must be in (0,-1] and r = -1 is valid
- Returns:
Truncated POD spatial modes (left singular vectors), singular values and temporal coefficients (right singular vectors).
- Return type:
[(np.array), (np.array), (np.array)]
- pyLOM.POD.reconstruct(U: ndarray, S: ndarray, V: ndarray)[source]#
Reconstruct the flow given the POD decomposition matrices that can be possibly truncated. N is the truncated size n is the number of snapshots
- Parameters:
U (np.ndarray) – of size (m,n), are the POD modes.
S (np.ndarray) – of size (n), are the singular values.
V (np.ndarray) – of size (n,n), are the right singular vectors.
- Returns:
Reconstructed flow.
- Return type:
(np.array)
- pyLOM.POD.extract_modes(U: ndarray, ivar: int, npoints: int, modes: list = [], reshape: bool = True)[source]#
When performing POD of several variables simultaneously, this function separates the spatial modes from each of the variables.
- Parameters:
U (np.ndarray) – POD spatial modes
ivar (int) – ID of the variable (i. e.) position in which it was concatenated to the rest of data (min=1, max=number of concatenated variables)
npoints (int) – number of points in the domain per variable
modes (list, optional) – list containing the id of the modes to separate (default
[]).reshape (bool, optional) – if true the output will be given as (len(modes)*npoints,) if not it the result will be (npoints, len(modes)) (default `` True ``)
- Returns:
modes of the variable ivar
- Return type:
np.ndarray
- pyLOM.POD.save(fname: str, U: ndarray, S: ndarray, V: ndarray, ptable: PartitionTable, nvars: int = 1, pointData: bool = True, mode: str = 'w')[source]#
Store POD results in serial or parallel according to the partition used to compute the POD. It will be saved on a h5 file.
- Parameters:
fname (str) – path to the .h5 file in which the POD will be saved
U (np.ndarray) – spatial modes to save. To avoid saving the spatial modes, just give None as input
S (np.ndarray) – singular values to save. To avoid saving the singular values, just give None as input
V (np.ndarray) – temporal coefficients to save. To avoid saving the temporal coefficients, just give None as input
ptable (PartitionTable) – partition table used to compute the POD
nvars (int, optional) – number of concatenated variables when computing the POD (default
1)pointData (bool, optional) – bool to specify if the POD was performed either on point data or cell data (default
True)mode (str, optional) – mode in which the HDF5 file is opened, ‘w’ stands for write mode and ‘a’ stands for append mode. Write mode will overwrite the file and append mode will add the informaiton at the end of the current file, choose with great care what to do in your case (default
w).
- pyLOM.POD.load(fname: str, vars: list = ['U', 'S', 'V'], nmod: int = -1, ptable: PartitionTable = None)[source]#
Load POD results from a .h5 file in serial or parallel according to the partition used to compute the POD.
- Parameters:
fname (str) – path to the .h5 file in which the POD was saved
vars (list) – list of variables to load. The following notation, consistent with the save function, is used, ‘U’: spatial modes ‘S’: singular values ‘V’: temporal coefficients
all (the default option is to load them)
script. (but it is not recommended to load the spatial modes if they are not going to be used during the rest of the)
nmod (int, optional) – number of modes to load. By default it will load all the saved modes (default,
-1)ptable (PartitionTable, optional) – partition table to use when loading the data (default
None).
- pyLOM.POD.plotMode(V: ndarray, t: ndarray, modes: ndarray = np.array([1], np.int32), fftfun: object = fft, scale_freq: float64 = 1., fig: figure = [], ax: axes = [])[source]#
Plot the temporal coefficient and its frequency spectrom of a set of modes
- Parameters:
V (np.ndarray) – array containing the temporal coefficients from the POD modes
t (np.ndarray) – array containing the time values
modes (np.ndarray) – array with the modes to plot
fftfun (object, optional) – function to use to compute the frequency spectra (default:
fft)scale_freq (double, optional) – value used to non-dimensionalize the frequencies (default:
1)fig (plt.figure, optional) – figure object in which the plot will be done (default:
[])axs (plt.axes, optional) – axes object in which the plot will be done (default:
[])
- Returns:
figure and axes objects of the plot
- Return type:
[plt.figure, plt.axes]