def test_hawkes_set_timestamps(self):
"""...Test simulation after some timestamps have been set manually
"""
decay = 0.5
baseline = [0.2, 0.4]
adjacency = [[0.2, 0.1], [0, 0.3]]
hawkes = SimuHawkesExpKernels(
baseline=baseline, decays=decay, adjacency=adjacency,
verbose=False, seed=1393)
# timestamps generated by a hawkes process with the same
# characteristics simulated up to time 10
original_timestamps = [
np.array([7.096244, 9.389927]),
np.array([0.436199, 0.659153, 2.622352, 3.095093,
7.189881, 8.068153, 9.240032]),
]
hawkes.track_intensity(1)
hawkes.set_timestamps(original_timestamps, 10)
hawkes.end_time = 100
hawkes.simulate()
# Intensity up to time 10 is known
first_intensities = hawkes.tracked_intensity[0][:10]
np.testing.assert_array_almost_equal(
first_intensities,
[0.2, 0.2447256, 0.27988282, 0.24845138, 0.23549475,
0.27078386, 0.26749709, 0.27473586, 0.24532959, 0.22749379]
)
# Ensure other jumps have occured afterwards
self.assertGreater(hawkes.n_total_jumps,
sum(map(len, original_timestamps)))
def simulate(self):
n_nodes = 1
baseline = [0.1]
adjacency = [[0.1]]
end_time = 10000
# max_jumps=1000;
a_sim = SimuHawkesExpKernels(adjacency,
decays,
baseline=baseline,
end_time=end_time,
verbose=True)
a_sim.track_intensity(0.01)
a_sim.simulate()
# print(a_sim.timestamps)
# print('Tracked intensity: ', a_sim.tracked_intensity)
with open('sample_timestamps.txt', 'w') as f:
f.write(str(list(a_sim.timestamps[0])))
period_length = 100
t_values = np.linspace(0, period_length)
y_values = 0.2 * np.maximum(np.sin(t_values *
(2 * np.pi) / period_length), 0.2)
baselines = np.array(
[TimeFunction((t_values, y_values), border_type=TimeFunction.Cyclic)])
decay = 0.1
adjacency = np.array([[0.5]])
hawkes = SimuHawkesExpKernels(adjacency,
decay,
baseline=baselines,
seed=2093,
verbose=False)
hawkes.track_intensity(0.1)
hawkes.end_time = 6 * period_length
hawkes.simulate()
fig, ax = plt.subplots(1, 1, figsize=(10, 4))
plot_point_process(hawkes, ax=ax)
t_values = np.linspace(0, hawkes.end_time, 1000)
ax.plot(t_values,
hawkes.get_baseline_values(0, t_values),
label='baseline',
ls='--',
lw=1)
ax.set_ylabel("$\lambda(t)$", fontsize=18)
ax.legend()
class Test(unittest.TestCase):
def setUp(self):
np.random.seed(23982)
self.n_nodes = 3
self.baseline = np.random.rand(self.n_nodes)
self.adjacency = np.random.rand(self.n_nodes, self.n_nodes) / 2
self.decays = np.random.rand(self.n_nodes, self.n_nodes)
self.adjacency[0, 0] = 0
self.adjacency[-1, -1] = 0
self.hawkes = SimuHawkesExpKernels(self.adjacency,
self.decays,
baseline=self.baseline,
seed=203,
verbose=False)
def test_hawkes_exponential_kernels(self):
"""...Test creation of a Hawkes Process with exponential kernels
"""
kernel_0 = None
for i, j in product(range(self.n_nodes), range(self.n_nodes)):
kernel_ij = self.hawkes.kernels[i, j]
if self.adjacency[i, j] == 0:
self.assertEqual(kernel_ij.__class__, HawkesKernel0)
# We check that all 0 adjacency share the same kernel 0
# This might save lots of memory with very large,
# very sparse adjacency matrices
if kernel_0 is None:
kernel_0 = kernel_ij
else:
self.assertEqual(kernel_0, kernel_ij)
else:
self.assertEqual(kernel_ij.__class__, HawkesKernelExp)
self.assertEqual(kernel_ij.decay, self.decays[i, j])
self.assertEqual(kernel_ij.intensity, self.adjacency[i, j])
np.testing.assert_array_equal(self.baseline, self.hawkes.baseline)
def test_hawkes_spectral_radius_exp_kernel(self):
"""...Hawkes Process spectral radius and adjust spectral radius
methods
"""
self.assertAlmostEqual(self.hawkes.spectral_radius(),
0.6645446549735008)
self.hawkes.adjust_spectral_radius(0.6)
self.assertAlmostEqual(self.hawkes.spectral_radius(), 0.6)
def test_hawkes_mean_intensity(self):
"""...Test that Hawkes obtained mean intensity is consistent
"""
self.assertLess(self.hawkes.spectral_radius(), 1)
self.hawkes.end_time = 1000
self.hawkes.track_intensity(0.01)
self.hawkes.simulate()
mean_intensity = self.hawkes.mean_intensity()
for i in range(self.hawkes.n_nodes):
self.assertAlmostEqual(np.mean(self.hawkes.tracked_intensity[i]),
mean_intensity[i],
delta=0.1)