def test_constructors():
""" Check that the constructor works
"""
dmdtools.DMD()
dmdtools.DMD(10)
dmdtools.DMD(10, True)
dmdtools.DMD(10, True, True)
# Check the arguments are copied properly
args = {"n_rank": 131, "exact": True, "total": False}
tmp = dmdtools.DMD(**args)
assert tmp.n_rank == args["n_rank"]
assert tmp.total == args["total"]
assert tmp.exact == args["exact"]
def check_dmd_computation_simple_timeseries(exact, total):
""" Check DMD computations on a problem where the
true solution is known. All variants of DMD
should give identical outputs.
"""
num_snapshots = 10
A = np.array([[0.9, 0.1], [0.0, 0.8]])
# Create a time series of data
data = np.zeros((2, num_snapshots + 1))
data[:, 0] = np.random.randn(2)
for ii in range(num_snapshots):
data[:, ii + 1] = A.dot(data[:, ii])
X = data[:, :-1]
Y = data[:, 1:]
ADMD = Y.dot(np.linalg.pinv(X))
vals, vecs = np.linalg.eig(ADMD)
inds = np.argsort(np.abs(vals))[::-1]
vals = vals[inds]
vecs = vecs[:, inds]
# DMD class with rank 2
DMD = dmdtools.DMD(2, exact, total)
DMD.fit(data)
dmd_vals, dmd_modes = dmdtools.sort_modes_evals(DMD)
for ii in range(len(vals)):
assert np.abs(dmd_vals[ii] - vals[ii]) < 1e-10
check_eigenvectors(vecs[:, ii], dmd_modes[:, ii])
def standard_dmd():
X = np.zeros((n_states, n_snaps - 1))
Y = np.zeros((n_states, n_snaps - 1))
snaps = snapshots(n_states, n_snaps, noise_cov)
x = snaps.next()
for k, y in enumerate(snaps):
X[:, k] = x
Y[:, k] = y
x = y
DMD = dmdtools.DMD()
DMD.fit(X, Y)
return DMD.modes, DMD.evals
Q = np.linalg.qr(np.random.randn(n, 2))[0]
data = Q.dot(data)
data = np.r_[data.real, data.imag] # Split and stack real and image parts
# Add noise to the data
noisy_data = data + std * np.random.randn(data.shape[0], data.shape[1])
# Create a new figure for output
fig = plt.figure(1)
th = np.linspace(0, 2 * np.pi, 101)
plt.plot(np.cos(th), np.sin(th), '-', color='0.75', lw=4)
plt.plot(np.diag(Alow).real, np.diag(Alow).imag, 'ko', ms=14)
# Note: n_rank is doubled because we only deal with real numbers
dmd = dmdtools.DMD(n_rank * 2, False, False) # "standard" DMD
dmd = dmd.fit(noisy_data)
dmd_vals, dmd_modes = dmd.get_mode_pairs(sortby="LM")
# Plot the DMD eigenvalues
plt.plot(dmd_vals.real, dmd_vals.imag, 'rv', ms=14)
# With TLS DMD
tlsdmd = dmdtools.DMD(n_rank * 2, False, True) # "standard" DMD
tlsdmd = tlsdmd.fit(noisy_data)
tlsdmd_vals, tlsdmd_modes = tlsdmd.get_mode_pairs(sortby="LM")
# Plot the DMD eigenvalues
plt.plot(tlsdmd_vals.real, tlsdmd_vals.imag, 'b^', ms=14)
plt.xlabel("$\Re(\mu)$")
plt.ylabel("$\Im(\mu)$")