def test_dmd_time_3(self):
dmd = DMD()
dmd.fit(X=sample_data)
dmd.dmd_time['t0'] = 8
dmd.dmd_time['tend'] = 11
expected_data = sample_data[:, 8:12]
np.testing.assert_allclose(dmd.reconstructed_data, expected_data)
def test_plot_eigs_3(self):
dmd = DMD()
dmd.fit(X=sample_data)
dmd.plot_eigs(show_axes=False,
show_unit_circle=True,
filename='eigs.png')
self.addCleanup(os.remove, 'eigs.png')
def test_Atilde_values(self):
dmd = DMD(svd_rank=2)
dmd.fit(X=sample_data)
exact_atilde = np.array(
[[-0.70558526 + 0.67815084j, 0.22914898 + 0.20020143j],
[0.10459069 + 0.09137814j, -0.57730040 + 0.79022994j]])
np.testing.assert_allclose(exact_atilde, dmd.atilde)
def test_eigs_3(self):
dmd = DMD(svd_rank=2)
dmd.fit(X=sample_data)
expected_eigs = np.array([
-8.09016994e-01 + 5.87785252e-01j, -4.73868662e-01 + 8.80595532e-01j
])
np.testing.assert_almost_equal(dmd.eigs, expected_eigs, decimal=6)
def test_advanced_snapshot_parameter(self):
dmd = DMD(svd_rank=0.99)
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=0.99, opt=-1)
dmd2.fit(sample_data)
np.testing.assert_almost_equal(dmd2.reconstructed_data.real,
dmd.reconstructed_data.real, decimal=6)
def test_dmd_time_4(self):
dmd = DMD(svd_rank=3)
dmd.fit(X=sample_data)
dmd.dmd_time['t0'] = 20
dmd.dmd_time['tend'] = 20
expected_data = np.array([[-7.29383297e+00 - 4.90248179e-14j],
[-5.69109796e+00 - 2.74068833e+00j],
[3.38410649e-83 + 3.75677740e-83j]])
np.testing.assert_almost_equal(dmd.dynamics, expected_data, decimal=6)
def test_rescale_mode_same_evolution(self):
dmd_no_rescale = DMD(svd_rank=5, opt=True, rescale_mode=None)
dmd_no_rescale.fit(X=sample_data)
dmd_no_rescale.dmd_time['tend'] *= 2
dmd_rescale = DMD(svd_rank=5, opt=True, rescale_mode=
np.linspace(5,10, 5))
dmd_rescale.fit(X=sample_data)
dmd_rescale.dmd_time['tend'] *= 2
np.testing.assert_almost_equal(dmd_rescale.reconstructed_data,
dmd_no_rescale.reconstructed_data, decimal=6)
def test_sorted_eigs_real_right_eigenvectors(self):
dmd = DMD(svd_rank=20, sorted_eigs='real')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
for idx, eig in enumerate(dmd2.eigs):
eigenvector = dmd2.operator.eigenvectors.T[idx]
for idx_new, eig_new in enumerate(dmd.eigs):
if eig_new == eig:
assert all(dmd.operator.eigenvectors.T[idx_new] == eigenvector)
break
def test_dynamics_opt_2(self):
dmd = DMD(svd_rank=1, opt=True)
dmd.fit(X=sample_data)
expected_dynamics = np.array([[
-4.56004133 - 6.48054238j, 7.61228319 + 1.4801793j,
-6.37489962 + 4.11788355j, 1.70548899 - 7.22866146j,
3.69875496 + 6.25701574j, -6.85298745 - 1.90654427j,
6.12829151 - 3.30212967j, -2.08469012 + 6.48584004j,
-2.92745126 - 5.99004747j, 6.12772217 + 2.24123565j,
-5.84352626 + 2.57413711j, 2.37745273 - 5.77906544j,
2.24158249 + 5.68989493j, -5.44023459 - 2.49457492j,
5.53024740 - 1.92916437j
]])
np.testing.assert_allclose(dmd.dynamics, expected_dynamics)
def test_rescale_mode_auto(self):
dmd_no_rescale = DMD(svd_rank=5, opt=True, rescale_mode=None)
dmd_no_rescale.fit(X=sample_data)
dmd_auto_rescale = DMD(svd_rank=5, opt=True, rescale_mode='auto')
dmd_auto_rescale.fit(X=sample_data)
dmd_auto_rescale_normalized_modes = np.apply_along_axis(
lambda vector: vector / np.linalg.norm(vector), 0,
dmd_auto_rescale._modes)
np.testing.assert_almost_equal(dmd_no_rescale._modes,
dmd_auto_rescale_normalized_modes,
decimal=6)
def test_predict(self):
def f1(x, t):
return 1. / np.cosh(x + 3) * np.exp(2.3j * t)
def f2(x, t):
return 2. / np.cosh(x) * np.tanh(x) * np.exp(2.8j * t)
x = np.linspace(-2, 2, 4)
t = np.linspace(0, 4 * np.pi, 10)
xgrid, tgrid = np.meshgrid(x, t)
X1 = f1(xgrid, tgrid)
X2 = f2(xgrid, tgrid)
X = X1 + X2
dmd = DMD()
dmd.fit(X.T)
expected = np.array(
[[
0.35407111 + 0.31966903j, 0.0581077 - 0.51616519j,
-0.4936891 + 0.36476117j, 0.70397844 + 0.05332291j,
-0.56648961 - 0.50687223j, 0.15372065 + 0.74444603j,
0.30751808 - 0.63550106j, -0.5633934 + 0.24365451j,
0.47550633 + 0.20903766j, -0.0985528 - 0.46673545j
],
[
0.52924739 + 0.47782492j, 0.08685642 - 0.77153733j,
-0.73794122 + 0.54522635j, 1.05227097 + 0.07970435j,
-0.8467597 - 0.7576467j, 0.22977376 + 1.11275987j,
0.4596623 - 0.94991449j, -0.84213164 + 0.3642023j,
0.71076254 + 0.3124588j, -0.14731169 - 0.69765229j
],
[
-0.49897731 - 0.45049592j, -0.0818887 + 0.72740958j,
0.69573498 - 0.51404236j, -0.99208678 - 0.0751457j,
0.79832963 + 0.71431342j, -0.21663195 - 1.04911604j,
-0.43337211 + 0.89558454j, 0.79396628 - 0.3433719j,
-0.67011078 - 0.29458785j, 0.13888626 + 0.65775036j
],
[
-0.2717424 - 0.2453395j, -0.04459648 + 0.39614632j,
0.37889637 - 0.2799468j, -0.54028918 - 0.04092425j,
0.43476929 + 0.38901417j, -0.11797748 - 0.57134724j,
-0.23601389 + 0.48773418j, 0.43239301 - 0.18699989j,
-0.36494147 - 0.16043216j, 0.07563728 + 0.35821j
]])
np.testing.assert_almost_equal(dmd.predict(X.T), expected, decimal=6)
def test_sorted_eigs_amplitudes(self):
dmd = DMD(svd_rank=20, sorted_eigs='abs')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
for idx, eig in enumerate(dmd2.eigs):
amp = dmd2.amplitudes[idx]
for idx_new, eig_new in enumerate(dmd.eigs):
if eig_new == eig:
np.testing.assert_almost_equal(dmd.amplitudes[idx_new],
amp, decimal=6)
break
def test_sorted_eigs_frequency(self):
dmd = DMD(svd_rank=20, sorted_eigs='abs')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
for idx, eig in enumerate(dmd2.eigs):
frq = dmd2.frequency[idx]
for idx_new, eig_new in enumerate(dmd.eigs):
if eig_new == eig:
np.testing.assert_almost_equal(dmd.frequency[idx_new],
frq, decimal=6)
break
def test_sorted_eigs_real_right_modes(self):
dmd = DMD(svd_rank=20, sorted_eigs='real')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
for idx, eig in enumerate(dmd2.eigs):
mode = dmd2.modes.T[idx]
for idx_new, eig_new in enumerate(dmd.eigs):
if eig_new == eig:
np.testing.assert_almost_equal(dmd.modes.T[idx_new], mode,
decimal=6)
break
def test_dynamics_2(self):
dmd = DMD(svd_rank=1)
dmd.fit(X=sample_data)
expected_dynamics = np.array([[
-2.20639502 - 9.10168802e-16j, 1.55679980 - 1.49626864e+00j,
-0.08375915 + 2.11149018e+00j, -1.37280962 - 1.54663768e+00j,
2.01748787 + 1.60312745e-01j, -1.53222592 + 1.25504678e+00j,
0.23000498 - 1.92462280e+00j, 1.14289644 + 1.51396355e+00j,
-1.83310653 - 2.93174173e-01j, 1.49222925 - 1.03626336e+00j,
-0.35015209 + 1.74312867e+00j, -0.93504202 - 1.46738182e+00j,
1.65485808 + 4.01263449e-01j, -1.43976061 + 8.39117825e-01j,
0.44682540 - 1.56844403e+00j
]])
np.testing.assert_allclose(dmd.dynamics, expected_dynamics)
def test_sorted_eigs_abs_right_eigs(self):
dmd = DMD(svd_rank=20, sorted_eigs='abs')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
assert len(dmd.eigs) == len(dmd2.eigs)
assert set(dmd.eigs) == set(dmd2.eigs)
previous = dmd.eigs[0]
for eig in dmd.eigs[1:]:
assert abs(previous) <= abs(eig)
previous = eig
def test_sorted_eigs_real_right_eigs(self):
dmd = DMD(svd_rank=20, sorted_eigs='real')
dmd.fit(sample_data)
dmd2 = DMD(svd_rank=20)
dmd2.fit(sample_data)
assert len(dmd.eigs) == len(dmd2.eigs)
assert set(dmd.eigs) == set(dmd2.eigs)
previous = complex(dmd.eigs[0])
for eig in dmd.eigs[1:]:
x = complex(eig)
assert x.real > previous.real or (x.real == previous.real and x.imag >= previous.imag)
previous = x
def test_rescale_mode_auto_same_modes(self):
dmd_no_rescale = DMD(svd_rank=2, opt=True, rescale_mode=None)
dmd_no_rescale.fit(X=sample_data)
dmd_auto_rescale = DMD(svd_rank=2, opt=True, rescale_mode='auto')
dmd_auto_rescale.fit(X=sample_data)
def normalize(vector):
return vector / np.linalg.norm(vector)
dmd_rescale_normalized_modes = np.apply_along_axis(normalize, 0,
dmd_auto_rescale.modes)
dmd_no_rescale_normalized_modes = np.apply_along_axis(normalize, 0,
dmd_no_rescale.modes)
np.testing.assert_almost_equal(dmd_no_rescale_normalized_modes,
dmd_rescale_normalized_modes, decimal=3)
def test_predict_nexact(self):
dmd = DMD(exact=False)
expected = np.load(
'tests/test_datasets/input_sample_predict_nexact.npy')
np.testing.assert_almost_equal(dmd.fit(sample_data).predict(
sample_data[:, 10:30]),
expected,
decimal=6)
def test_dynamics_1(self):
dmd = DMD(svd_rank=5)
dmd.fit(X=sample_data)
assert dmd.dynamics.shape == (5, sample_data.shape[1])
def test_eigs_2(self):
dmd = DMD(svd_rank=5)
dmd.fit(X=sample_data)
assert len(dmd.eigs) == 5
def test_fit_given_Y(self):
dmd = DMD(svd_rank=2)
X = np.copy(sample_data[:, :-1])
Y = np.copy(sample_data[:, 1:])
dmd.fit(X=X, Y=Y)
np.testing.assert_allclose(Y, dmd._Y)
def test_Atilde_shape(self):
dmd = DMD(svd_rank=3)
dmd.fit(X=sample_data)
assert dmd.atilde.shape == (dmd.svd_rank, dmd.svd_rank)
def test_truncation_shape(self):
dmd = DMD(svd_rank=3)
dmd.fit(X=sample_data)
assert dmd.modes.shape[1] == 3
def test_shape(self):
dmd = DMD(svd_rank=-1)
dmd.fit(X=sample_data)
assert dmd.modes.shape[1] == sample_data.shape[1] - 1
def test_tdmd_plot(self):
dmd = DMD(tlsq_rank=3)
dmd.fit(X=sample_data)
dmd.plot_eigs(show_axes=False, show_unit_circle=False)
plt.close()
def test_plot_snapshots_5(self):
dmd = DMD()
snapshots = [snap.reshape(20, 20) for snap in sample_data.T]
dmd.fit(X=snapshots)
dmd.plot_snapshots_2D(index_snap=2, filename='tmp.png')
self.addCleanup(os.remove, 'tmp.2.png')
def test_plot_snapshots_4(self):
dmd = DMD()
snapshots = [snap.reshape(20, 20) for snap in sample_data.T]
dmd.fit(X=snapshots)
dmd.plot_snapshots_2D(index_snap=2)
plt.close()
def test_plot_snapshots_2(self):
dmd = DMD(svd_rank=-1)
dmd.fit(X=sample_data)
dmd.plot_snapshots_2D((1, 2, 5), x=np.arange(20), y=np.arange(20))
plt.close()
def test_plot_snapshots_1(self):
dmd = DMD()
dmd.fit(X=sample_data)
with self.assertRaises(ValueError):
dmd.plot_snapshots_2D()