def test_gauss_function(self):
f = tdt.GaussFunction(1, 0.5, 0.5)
x = np.random.random((3,))
grad = np.zeros((3,))
grad[1] = -np.exp(-(0.5 * (0.5 - x[1]) ** 2) / 0.5) * (-0.5 + x[1]) / 0.5
self.assertEqual(f(x), np.exp(-0.5 * (x[1] - 0.5) ** 2 / 0.5))
self.assertEqual(f.partial(x, 0), 0)
self.assertEqual(f.partial(x, 1), -np.exp(-(0.5 * (0.5 - x[1]) ** 2) / 0.5) * (-0.5 + x[1]) / 0.5)
self.assertTrue((f.gradient(x) - grad == 0).all())
with self.assertRaises(ValueError):
tdt.GaussFunction(1, 0.5, 0)
def plot_basis_functions(dimension, downsampling_rate, directory):
"""Plot basis functions
Parameters
----------
dimension: int
number of contact indices
downsampling_rate: int
downsampling rate for trajectory data
directory: string
directory data to load
"""
# load contact indices (sorted by relevance)
contact_indices = np.load(
directory + 'ntl9_contact_indices.npz')['indices'][:dimension]
# load trajectories
data, trajectory_lengths = load_data(directory, 1, contact_indices)
# plot basis functions
plt.figure(dpi=300)
plt.hist(data[:10].flatten(), 10000, histtype='bar')
x_values = np.arange(0, 1, 0.001)[:, None]
y_values = tdt.GaussFunction(0, 0.285, 0.001)(x_values.T)
plt.plot(x_values, 170000 * y_values, linewidth=2)
y_values = tdt.GaussFunction(0, 0.62, 0.01)(x_values.T)
plt.plot(x_values, 2500 * y_values, linewidth=2)
plt.xlim([0, 1])
plt.xlabel(r"$\Delta [\mathrm{nm}]$")
plt.savefig(directory + 'ntl9_basis_functions_1.pdf')
plt.show()
plt.figure(dpi=300)
x = np.arange(0, 1, 0.001)[:, None]
plt.plot(x, tdt.ConstantFunction(0)(x.T), linewidth=2)
plt.plot(x, tdt.GaussFunction(0, 0.285, 0.001)(x.T), linewidth=2)
plt.plot(x, tdt.GaussFunction(0, 0.62, 0.01)(x.T), linewidth=2)
plt.xlim([0, 1])
plt.ylim([0, 1.2])
plt.xlabel(r"$\Delta [\mathrm{nm}]$")
plt.savefig(directory + 'ntl9_basis_functions_2.pdf')
plt.show()
def test_periodicgauss_function(self):
f = tdt.PeriodicGaussFunction(1, 0.5, 0.5)
x = np.random.random((3,))
grad = np.zeros((3,))
grad[1] = (0.5 * np.exp(-(0.5 * np.sin(0.5 * 0.5 - 0.5 * x[1]) ** 2) / 0.5) *
np.cos(0.5 * 0.5 - 0.5 * x[1]) * np.sin(0.5 * 0.5 - 0.5 * x[1])) / 0.5
self.assertEqual(f(x), np.exp(-0.5 * np.sin(0.5 * (x[1] - 0.5)) ** 2 / 0.5))
self.assertEqual(f.partial(x, 0), 0)
self.assertEqual(f.partial(x, 1), (0.5 * np.exp(-(0.5 * np.sin(0.5 * 0.5 - 0.5 * x[1]) ** 2) / 0.5) *
np.cos(0.5 * 0.5 - 0.5 * x[1]) * np.sin(0.5 * 0.5 - 0.5 * x[1])) / 0.5)
self.assertTrue((f.gradient(x) - grad == 0).all())
with self.assertRaises(ValueError):
tdt.GaussFunction(1, 0.5, 0)
def tedmd_hocur(dimensions, downsampling_rate, integer_lag_times, max_rank,
directory):
"""tEDMD using AMUSEt with HOSVD
Parameters
----------
dimensions: list[int]
numbers of contact indices
downsampling_rate: int
downsampling rate for trajectory data
integer_lag_times: list[int]
integer lag times for application of tEDMD
max_rank: int
maximum rank for HOCUR
directory: string
directory data to load
"""
# progress
start_time = utl.progress('Apply AMUSEt (HOCUR)', 0)
for i in range(len(dimensions)):
# parameters
time_step = 2e-3
lag_times = time_step * downsampling_rate * integer_lag_times
# define basis list
basis_list = [[
tdt.ConstantFunction(),
tdt.GaussFunction(i, 0.285, 0.001),
tdt.GaussFunction(i, 0.62, 0.01)
] for i in range(dimensions[i])]
# progress
utl.progress('Apply AMUSEt (HOCUR, p=' + str(dimensions[i]) + ')',
100 * i / len(dimensions),
cpu_time=_time.time() - start_time)
# load contact indices (sorted by relevance)
contact_indices = np.load(
directory + 'ntl9_contact_indices.npz')['indices'][:dimensions[i]]
# load data
data, trajectory_lengths = load_data(directory,
downsampling_rate,
contact_indices,
progress=False)
# select snapshot indices for x and y data
x_indices = []
y_indices = []
for j in range(len(integer_lag_times)):
x_ind, y_ind = xy_indices(trajectory_lengths, integer_lag_times[j])
x_indices.append(x_ind)
y_indices.append(y_ind)
# apply AMUSEt
with utl.timer() as timer:
eigenvalues, _ = tedmd.amuset_hocur(data,
x_indices,
y_indices,
basis_list,
max_rank=max_rank)
cpu_time = timer.elapsed
for j in range(len(integer_lag_times)):
eigenvalues[j] = [eigenvalues[j][1]]
# Save results to file:
dic = {}
dic["lag_times"] = lag_times
dic["eigenvalues"] = eigenvalues
dic["cpu_time"] = cpu_time
np.savez_compressed(
directory + "Results_NTL9_HOCUR_d" + str(dimensions[i]) + ".npz",
**dic)
utl.progress('Apply AMUSEt (HOCUR)',
100 * (i + 1) / len(dimensions),
cpu_time=_time.time() - start_time)