Implement POD functionality

[dsj976]

Implement Proper Orthogonal Decomposition (POD) in the src/svdrom/pod.py module.

The POD should use the SVD class/function (see #2)

POD calculation using NumPy:

import numpy as np

n_snapshots = 200  # number of temporal snapshots
n_points = 10_000  # number of grid points

X = np.random.rand(n_snapshots, n_points)  # data matrix with dimensions (n_snapshots x n_points)

X_mean = np.mean(X, axis=0)  # time average
X_fluc = X - X_mean  # fluctuations about the time average

u, s, v = np.linalg.svd(X_fluc/np.sqrt(n_snapshots), full_matrices=False)

phi = v.T  # these are the POD modes (i.e. spatial modes)
coeffs = u @ np.diag(s)  # these are the temporal coefficients, should be equivalent to `X_fluc/np.sqrt(n_snapshots) @ phi`
energy = s**2  # energy associated with each POD mode

# Note the following:

C = X_fluc.T @ X_fluc / n_snapshots  # covariance matrix (a.k.a. Reynolds Stress Tensor)
total_energy = np.trace(C)  # should be equivalent to `np.sum(coeffs**2)` and to `np.sum(energy)`

References:

• A tutorial on the POD by Julien Weiss
• https://examples.dask.org/machine-learning/svd.html
• https://blog.dask.org/2020/05/13/large-svds