dmdlab¶
Dynamic Mode Decomposition in Python¶
Dynamic Mode Decomposition (DMD) is an algorithm for determining an equation-free representation of a dynamical system based on dominant spatiotemporal coherent structures.
Installation:
pip install dmdlab
Usage:
from dmdlab import DMD, plot_eigs
import numpy as np
from scipy.linalg import logm
# Generate toy data
ts = np.linspace(0,6,50)
theta = 1/10
A_dst = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]])
A_cts = logm(A_dst)/(ts[1]-ts[0])
x0 = np.array([1,0])
X = np.vstack([expm(A_cts*ti)@x0 for ti in ts]).T
# Fit model
model = DMD.from_full(X, ts)
# Print the eigenvalue phases
print(np.angle(model.eigs))
>>> [0.1, -0.1]
For a technical reference, check out the DMD book.