Playing with Proper Orthogonal Decomposition in python using numpy

pod.py

"""Proper Orthogonal Decomposition.

Demonstrate how to use it.

---------------------------

MIT License

Copyright (c) 2018 Pamphile Tupui ROY

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SOFTWARE.
"""
import numpy as np

init_snapshots = np.array([[37., 40., 41., 49., 42., 46., 45., 48.], [40., 43., 47., 46., 41., 46., 45., 48.], [40., 41., 42., 45., 44., 46., 45., 47.]]).T
init_snapshots = np.array([[37., 40., 41., 49., 42., 46., 45., 48.], [40., 43., 47., 46., 41., 46., 45., 48.], [40., 41., 42., 45., 44., 46., 45., 47.]])


print("Initial snapshots:\n{}".format(init_snapshots))

m = init_snapshots.shape[0]  # Size of each snapshot
n = init_snapshots.shape[1]  # Number of snapshots
print("Size: ({}x{})".format(m, n))

mean_snapshot = np.average(init_snapshots, 1).reshape(m, -1)
print("Mean snapshot:\n{}".format(mean_snapshot))
snapshots = np.subtract(init_snapshots, mean_snapshot)

U, s, V = np.linalg.svd(snapshots, full_matrices=False)

print("\nU:\n{}\nS:\n{}\nV:\n{}\n".format(U, s, V))

rank = 3#8
dim = m - rank

S = np.diag(s)

if rank == m:
    fluctuation = np.dot(U, np.dot(S, V))
else:
    fluctuation = np.dot(U[:, :-dim], np.dot(S[:-dim, :-dim], V[:-dim, :]))

#print("Fluctuation:\n{}".format(fluctuation))

snap = 1
matrix_snap = mean_snapshot.flatten() + np.dot(U, np.dot(S, V)[:, snap])
print("Snapshot {}:\n{}".format(snap + 1, matrix_snap))
V = V.T
S = S.diagonal()
matrix_snap = mean_snapshot.flatten() + np.dot(U, V[snap]*S)
print("Snapshot {}:\n{}".format(snap + 1, matrix_snap))

reconstruction = mean_snapshot + fluctuation

print("\nReconstruction:\n{}".format(reconstruction))
equal = np.allclose(init_snapshots, reconstruction)
print("\nSame matrices: {}\n".format(equal))
if not equal:
    print("Difference:\n{}".format(reconstruction-init_snapshots))