FaDIn on simulated univariate Hawkes processes

This example demonstrates inference performed by FaDIn on univariate Hawkes processes simulated with specific kernels.

# Authors: Guillaume Staerman <guillaume.staerman@inria.fr>
#          Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Thomas Moreau <thomas.moreau@inria.fr>
#
# License: MIT

Let us first define the parameters of our model.

import numpy as np
import torch
import matplotlib.pyplot as plt

from fadin.utils.utils_simu import simu_hawkes_cluster
from fadin.solver import FaDIn
from fadin.kernels import DiscreteKernelFiniteSupport

n_dim = 1
dt = 0.01
T = 10_000
kernel_length = 5
L = int(1 / dt)
size_grid = int(T / dt) + 1
discretization = torch.linspace(0, kernel_length, L)

Here, we set the parameters of a Hawkes process with an Exponential(1) distribution.

baseline = np.array([.4])
alpha = np.array([[0.9]])
beta = 0.8

Here, we simulate the data.

# standard parameter is beta, the parameter of the exponential distribution,
# equal to one.
kernel = 'expon'
events = simu_hawkes_cluster(T, baseline, alpha, kernel,
                             params_kernel={'scale': 1 / beta})

Simulate generation 0
Simulate generation 1
Simulate generation 2
Simulate generation 3
Simulate generation 4
Simulate generation 5
Simulate generation 6
Simulate generation 7
Simulate generation 8
Simulate generation 9
Simulate generation 10
Simulate generation 11
Simulate generation 12
Simulate generation 13
Simulate generation 14
Simulate generation 15
Simulate generation 16
Simulate generation 17
Simulate generation 18
Simulate generation 19
Simulate generation 20
Simulate generation 21
Simulate generation 22
Simulate generation 23
Simulate generation 24
Simulate generation 25
Simulate generation 26
Simulate generation 27
Simulate generation 28
Simulate generation 29
Simulate generation 30
Simulate generation 31
Simulate generation 32
Simulate generation 33
Simulate generation 34
Simulate generation 35
Simulate generation 36
Simulate generation 37
Simulate generation 38
Simulate generation 39
Simulate generation 40
Simulate generation 41
Simulate generation 42
Simulate generation 43
Simulate generation 44
Simulate generation 45
Simulate generation 46
Simulate generation 47
Simulate generation 48
Simulate generation 49
Simulate generation 50
Simulate generation 51
Simulate generation 52
Simulate generation 53
Simulate generation 54
Simulate generation 55
Simulate generation 56
Simulate generation 57
Simulate generation 58
Simulate generation 59
Simulate generation 60
Simulate generation 61
Simulate generation 62
Simulate generation 63
Simulate generation 64
Simulate generation 65
Simulate generation 66
Simulate generation 67
Simulate generation 68
Simulate generation 69
Simulate generation 70
Simulate generation 71
Simulate generation 72
Simulate generation 73
Simulate generation 74
Simulate generation 75
Simulate generation 76
Simulate generation 77

Let’s take a closer look at the events

print('Type of events object', type(events))
# events is a list of numpy arrays, one for each dimension
print('Number of events', len(events[0]))
print('First 10 events timestamps', events[0][:10])
# For each event, its occurence time (timestamp) is stored in the numpy array.

# `events`` is a list. Its elements are numpy arrays containing the timestamps
# of the events. This is the expected data format for FaDIn.

Type of events object <class 'list'>
Number of events 41811
First 10 events timestamps [1.68108227 1.98098625 2.48291917 2.82973634 3.00234991 3.0273425
 3.34320519 3.5806931  3.61143936 3.61922749]

Here, we apply FaDIn.

solver = FaDIn(n_dim=1,
               kernel="truncated_exponential",
               kernel_length=kernel_length,
               delta=dt, optim="RMSprop",
               params_optim={'lr': 1e-3},
               max_iter=2000
               )
solver.fit(events, T)

number of events is: [41811]
precomput: 0.12331366539001465
Fitting model...   0.0%
Fitting model...   0.1%
Fitting model...   0.1%
Fitting model...   0.1%
Fitting model...   0.2%
Fitting model...   0.2%
Fitting model...   0.3%
Fitting model...   0.4%
Fitting model...   0.4%
Fitting model...   0.4%
Fitting model...   0.5%
Fitting model...   0.5%
Fitting model...   0.6%
Fitting model...   0.7%
Fitting model...   0.7%
Fitting model...   0.8%
Fitting model...   0.8%
Fitting model...   0.9%
Fitting model...   0.9%
Fitting model...   0.9%
Fitting model...   1.0%
Fitting model...   1.1%
Fitting model...   1.1%
Fitting model...   1.1%
Fitting model...   1.2%
Fitting model...   1.2%
Fitting model...   1.3%
Fitting model...   1.4%
Fitting model...   1.4%
Fitting model...   1.5%
Fitting model...   1.5%
Fitting model...   1.6%
Fitting model...   1.6%
Fitting model...   1.7%
Fitting model...   1.7%
Fitting model...   1.8%
Fitting model...   1.8%
Fitting model...   1.8%
Fitting model...   1.9%
Fitting model...   1.9%
Fitting model...   2.0%
Fitting model...   2.1%
Fitting model...   2.1%
Fitting model...   2.1%
Fitting model...   2.2%
Fitting model...   2.2%
Fitting model...   2.3%
Fitting model...   2.4%
Fitting model...   2.4%
Fitting model...   2.5%
Fitting model...   2.5%
Fitting model...   2.5%
Fitting model...   2.6%
Fitting model...   2.6%
Fitting model...   2.7%
Fitting model...   2.8%
Fitting model...   2.8%
Fitting model...   2.9%
Fitting model...   2.9%
Fitting model...   2.9%
Fitting model...   3.0%
Fitting model...   3.0%
Fitting model...   3.1%
Fitting model...   3.1%
Fitting model...   3.2%
Fitting model...   3.2%
Fitting model...   3.3%
Fitting model...   3.4%
Fitting model...   3.4%
Fitting model...   3.5%
Fitting model...   3.5%
Fitting model...   3.5%
Fitting model...   3.6%
Fitting model...   3.6%
Fitting model...   3.7%
Fitting model...   3.8%
Fitting model...   3.8%
Fitting model...   3.9%
Fitting model...   3.9%
Fitting model...   4.0%
Fitting model...   4.0%
Fitting model...   4.0%
Fitting model...   4.1%
Fitting model...   4.2%
Fitting model...   4.2%
Fitting model...   4.2%
Fitting model...   4.3%
Fitting model...   4.3%
Fitting model...   4.4%
Fitting model...   4.5%
Fitting model...   4.5%
Fitting model...   4.5%
Fitting model...   4.6%
Fitting model...   4.7%
Fitting model...   4.7%
Fitting model...   4.8%
Fitting model...   4.8%
Fitting model...   4.9%
Fitting model...   4.9%
Fitting model...   5.0%
Fitting model...   5.0%
Fitting model...   5.1%
Fitting model...   5.1%
Fitting model...   5.1%
Fitting model...   5.2%
Fitting model...   5.2%
Fitting model...   5.3%
Fitting model...   5.3%
Fitting model...   5.4%
Fitting model...   5.5%
Fitting model...   5.5%
Fitting model...   5.5%
Fitting model...   5.6%
Fitting model...   5.7%
Fitting model...   5.7%
Fitting model...   5.8%
Fitting model...   5.8%
Fitting model...   5.9%
Fitting model...   5.9%
Fitting model...   5.9%
Fitting model...   6.0%
Fitting model...   6.0%
Fitting model...   6.1%
Fitting model...   6.2%
Fitting model...   6.2%
Fitting model...   6.2%
Fitting model...   6.3%
Fitting model...   6.3%
Fitting model...   6.4%
Fitting model...   6.5%
Fitting model...   6.5%
Fitting model...   6.6%
Fitting model...   6.6%
Fitting model...   6.7%
Fitting model...   6.7%
Fitting model...   6.8%
Fitting model...   6.8%
Fitting model...   6.9%
Fitting model...   6.9%
Fitting model...   7.0%
Fitting model...   7.0%
Fitting model...   7.0%
Fitting model...   7.1%
Fitting model...   7.1%
Fitting model...   7.2%
Fitting model...   7.2%
Fitting model...   7.3%
Fitting model...   7.3%
Fitting model...   7.4%
Fitting model...   7.4%
Fitting model...   7.5%
Fitting model...   7.5%
Fitting model...   7.6%
Fitting model...   7.6%
Fitting model...   7.7%
Fitting model...   7.8%
Fitting model...   7.8%
Fitting model...   7.8%
Fitting model...   7.9%
Fitting model...   8.0%
Fitting model...   8.0%
Fitting model...   8.1%
Fitting model...   8.1%
Fitting model...   8.2%
Fitting model...   8.2%
Fitting model...   8.2%
Fitting model...   8.3%
Fitting model...   8.3%
Fitting model...   8.4%
Fitting model...   8.5%
Fitting model...   8.5%
Fitting model...   8.6%
Fitting model...   8.6%
Fitting model...   8.6%
Fitting model...   8.7%
Fitting model...   8.8%
Fitting model...   8.8%
Fitting model...   8.8%
Fitting model...   8.9%
Fitting model...   8.9%
Fitting model...   9.0%
Fitting model...   9.0%
Fitting model...   9.1%
Fitting model...   9.2%
Fitting model...   9.2%
Fitting model...   9.2%
Fitting model...   9.3%
Fitting model...   9.3%
Fitting model...   9.4%
Fitting model...   9.4%
Fitting model...   9.5%
Fitting model...   9.6%
Fitting model...   9.6%
Fitting model...   9.7%
Fitting model...   9.7%
Fitting model...   9.8%
Fitting model...   9.8%
Fitting model...   9.8%
Fitting model...   9.9%
Fitting model...  10.0%
Fitting model...  10.0%
Fitting model...  10.1%
Fitting model...  10.1%
Fitting model...  10.2%
Fitting model...  10.2%
Fitting model...  10.2%
Fitting model...  10.3%
Fitting model...  10.3%
Fitting model...  10.4%
Fitting model...  10.4%
Fitting model...  10.5%
Fitting model...  10.5%
Fitting model...  10.6%
Fitting model...  10.7%
Fitting model...  10.7%
Fitting model...  10.8%
Fitting model...  10.8%
Fitting model...  10.8%
Fitting model...  10.9%
Fitting model...  10.9%
Fitting model...  11.0%
Fitting model...  11.1%
Fitting model...  11.1%
Fitting model...  11.2%
Fitting model...  11.2%
Fitting model...  11.2%
Fitting model...  11.3%
Fitting model...  11.3%
Fitting model...  11.4%
Fitting model...  11.5%
Fitting model...  11.5%
Fitting model...  11.6%
Fitting model...  11.6%
Fitting model...  11.7%
Fitting model...  11.7%
Fitting model...  11.8%
Fitting model...  11.8%
Fitting model...  11.8%
Fitting model...  11.9%
Fitting model...  11.9%
Fitting model...  12.0%
Fitting model...  12.0%
Fitting model...  12.1%
Fitting model...  12.2%
Fitting model...  12.2%
Fitting model...  12.2%
Fitting model...  12.3%
Fitting model...  12.3%
Fitting model...  12.4%
Fitting model...  12.4%
Fitting model...  12.5%
Fitting model...  12.6%
Fitting model...  12.6%
Fitting model...  12.7%
Fitting model...  12.7%
Fitting model...  12.8%
Fitting model...  12.8%
Fitting model...  12.8%
Fitting model...  12.9%
Fitting model...  13.0%
Fitting model...  13.0%
Fitting model...  13.1%
Fitting model...  13.1%
Fitting model...  13.2%
Fitting model...  13.2%
Fitting model...  13.2%
Fitting model...  13.3%
Fitting model...  13.4%
Fitting model...  13.4%
Fitting model...  13.5%
Fitting model...  13.5%
Fitting model...  13.6%
Fitting model...  13.6%
Fitting model...  13.7%
Fitting model...  13.7%
Fitting model...  13.8%
Fitting model...  13.8%
Fitting model...  13.9%
Fitting model...  13.9%
Fitting model...  14.0%
Fitting model...  14.0%
Fitting model...  14.1%
Fitting model...  14.1%
Fitting model...  14.1%
Fitting model...  14.2%
Fitting model...  14.2%
Fitting model...  14.3%
Fitting model...  14.3%
Fitting model...  14.4%
Fitting model...  14.4%
Fitting model...  14.5%
Fitting model...  14.5%
Fitting model...  14.6%
Fitting model...  14.6%
Fitting model...  14.7%
Fitting model...  14.8%
Fitting model...  14.8%
Fitting model...  14.8%
Fitting model...  14.9%
Fitting model...  14.9%
Fitting model...  15.0%
Fitting model...  15.0%
Fitting model...  15.1%
Fitting model...  15.2%
Fitting model...  15.2%
Fitting model...  15.2%
Fitting model...  15.3%
Fitting model...  15.3%
Fitting model...  15.4%
Fitting model...  15.4%
Fitting model...  15.5%
Fitting model...  15.6%
Fitting model...  15.6%
Fitting model...  15.7%
Fitting model...  15.7%
Fitting model...  15.8%
Fitting model...  15.8%
Fitting model...  15.8%
Fitting model...  15.9%
Fitting model...  16.0%
Fitting model...  16.0%
Fitting model...  16.1%
Fitting model...  16.1%
Fitting model...  16.2%
Fitting model...  16.2%
Fitting model...  16.2%
Fitting model...  16.3%
Fitting model...  16.4%
Fitting model...  16.4%
Fitting model...  16.4%
Fitting model...  16.5%
Fitting model...  16.6%
Fitting model...  16.6%
Fitting model...  16.7%
Fitting model...  16.7%
Fitting model...  16.8%
Fitting model...  16.8%
Fitting model...  16.9%
Fitting model...  16.9%
Fitting model...  17.0%
Fitting model...  17.0%
Fitting model...  17.1%
Fitting model...  17.1%
Fitting model...  17.2%
Fitting model...  17.2%
Fitting model...  17.2%
Fitting model...  17.3%
Fitting model...  17.3%
Fitting model...  17.4%
Fitting model...  17.4%
Fitting model...  17.5%
Fitting model...  17.5%
Fitting model...  17.6%
Fitting model...  17.6%
Fitting model...  17.7%
Fitting model...  17.8%
Fitting model...  17.8%
Fitting model...  17.8%
Fitting model...  17.9%
Fitting model...  17.9%
Fitting model...  18.0%
Fitting model...  18.1%
Fitting model...  18.1%
Fitting model...  18.1%
Fitting model...  18.2%
Fitting model...  18.2%
Fitting model...  18.3%
Fitting model...  18.4%
Fitting model...  18.4%
Fitting model...  18.4%
Fitting model...  18.5%
Fitting model...  18.6%
Fitting model...  18.6%
Fitting model...  18.6%
Fitting model...  18.7%
Fitting model...  18.8%
Fitting model...  18.8%
Fitting model...  18.9%
Fitting model...  18.9%
Fitting model...  18.9%
Fitting model...  19.0%
Fitting model...  19.1%
Fitting model...  19.1%
Fitting model...  19.1%
Fitting model...  19.2%
Fitting model...  19.2%
Fitting model...  19.3%
Fitting model...  19.4%
Fitting model...  19.4%
Fitting model...  19.4%
Fitting model...  19.5%
Fitting model...  19.6%
Fitting model...  19.6%
Fitting model...  19.7%
Fitting model...  19.7%
Fitting model...  19.8%
Fitting model...  19.8%
Fitting model...  19.9%
Fitting model...  19.9%
Fitting model...  20.0%
Fitting model...  20.0%
Fitting model...  20.1%
Fitting model...  20.1%
Fitting model...  20.2%
Fitting model...  20.2%
Fitting model...  20.2%
Fitting model...  20.3%
Fitting model...  20.3%
Fitting model...  20.4%
Fitting model...  20.4%
Fitting model...  20.5%
Fitting model...  20.5%
Fitting model...  20.6%
Fitting model...  20.6%
Fitting model...  20.7%
Fitting model...  20.8%
Fitting model...  20.8%
Fitting model...  20.8%
Fitting model...  20.9%
Fitting model...  20.9%
Fitting model...  21.0%
Fitting model...  21.1%
Fitting model...  21.1%
Fitting model...  21.1%
Fitting model...  21.2%
Fitting model...  21.2%
Fitting model...  21.3%
Fitting model...  21.3%
Fitting model...  21.4%
Fitting model...  21.4%
Fitting model...  21.5%
Fitting model...  21.6%
Fitting model...  21.6%
Fitting model...  21.6%
Fitting model...  21.7%
Fitting model...  21.8%
Fitting model...  21.8%
Fitting model...  21.9%
Fitting model...  21.9%
Fitting model...  21.9%
Fitting model...  22.0%
Fitting model...  22.1%
Fitting model...  22.1%
Fitting model...  22.1%
Fitting model...  22.2%
Fitting model...  22.2%
Fitting model...  22.3%
Fitting model...  22.4%
Fitting model...  22.4%
Fitting model...  22.4%
Fitting model...  22.5%
Fitting model...  22.6%
Fitting model...  22.6%
Fitting model...  22.7%
Fitting model...  22.7%
Fitting model...  22.8%
Fitting model...  22.8%
Fitting model...  22.9%
Fitting model...  22.9%
Fitting model...  22.9%
Fitting model...  23.0%
Fitting model...  23.1%
Fitting model...  23.1%
Fitting model...  23.2%
Fitting model...  23.2%
Fitting model...  23.2%
Fitting model...  23.3%
Fitting model...  23.4%
Fitting model...  23.4%
Fitting model...  23.4%
Fitting model...  23.5%
Fitting model...  23.5%
Fitting model...  23.6%
Fitting model...  23.6%
Fitting model...  23.7%
Fitting model...  23.8%
Fitting model...  23.8%
Fitting model...  23.8%
Fitting model...  23.9%
Fitting model...  23.9%
Fitting model...  24.0%
Fitting model...  24.1%
Fitting model...  24.1%
Fitting model...  24.1%
Fitting model...  24.2%
Fitting model...  24.2%
Fitting model...  24.3%
Fitting model...  24.3%
Fitting model...  24.4%
Fitting model...  24.4%
Fitting model...  24.5%
Fitting model...  24.6%
Fitting model...  24.6%
Fitting model...  24.6%
Fitting model...  24.7%
Fitting model...  24.8%
Fitting model...  24.8%
Fitting model...  24.9%
Fitting model...  24.9%
Fitting model...  24.9%
Fitting model...  25.0%
Fitting model...  25.1%
Fitting model...  25.1%
Fitting model...  25.1%
Fitting model...  25.2%
Fitting model...  25.2%
Fitting model...  25.3%
Fitting model...  25.4%
Fitting model...  25.4%
Fitting model...  25.4%
Fitting model...  25.5%
Fitting model...  25.6%
Fitting model...  25.6%
Fitting model...  25.7%
Fitting model...  25.7%
Fitting model...  25.8%
Fitting model...  25.8%
Fitting model...  25.9%
Fitting model...  25.9%
Fitting model...  25.9%
Fitting model...  26.0%
Fitting model...  26.1%
Fitting model...  26.1%
Fitting model...  26.2%
Fitting model...  26.2%
Fitting model...  26.2%
Fitting model...  26.3%
Fitting model...  26.4%
Fitting model...  26.4%
Fitting model...  26.5%
Fitting model...  26.5%
Fitting model...  26.6%
Fitting model...  26.6%
Fitting model...  26.7%
Fitting model...  26.7%
Fitting model...  26.8%
Fitting model...  26.8%
Fitting model...  26.9%
Fitting model...  26.9%
Fitting model...  27.0%
Fitting model...  27.0%
Fitting model...  27.1%
Fitting model...  27.1%
Fitting model...  27.2%
Fitting model...  27.2%
Fitting model...  27.3%
Fitting model...  27.3%
Fitting model...  27.4%
Fitting model...  27.4%
Fitting model...  27.5%
Fitting model...  27.5%
Fitting model...  27.6%
Fitting model...  27.6%
Fitting model...  27.7%
Fitting model...  27.7%
Fitting model...  27.8%
Fitting model...  27.8%
Fitting model...  27.9%
Fitting model...  27.9%
Fitting model...  28.0%
Fitting model...  28.0%
Fitting model...  28.1%
Fitting model...  28.1%
Fitting model...  28.1%
Fitting model...  28.2%
Fitting model...  28.2%
Fitting model...  28.3%
Fitting model...  28.3%
Fitting model...  28.4%
Fitting model...  28.4%
Fitting model...  28.5%
Fitting model...  28.5%
Fitting model...  28.6%
Fitting model...  28.6%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.2%
Fitting model...  29.2%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.4%
Fitting model...  29.4%
Fitting model...  29.5%
Fitting model...  29.5%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.7%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.5%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.7%
Fitting model...  30.8%
Fitting model...  30.8%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  31.0%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.3%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.5%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.7%
Fitting model...  31.8%
Fitting model...  31.8%
Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  32.0%
Fitting model...  32.0%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.3%
Fitting model...  32.4%
Fitting model...  32.4%
Fitting model...  32.5%
Fitting model...  32.5%
Fitting model...  32.6%
Fitting model...  32.6%
Fitting model...  32.6%
Fitting model...  32.7%
Fitting model...  32.8%
Fitting model...  32.8%
Fitting model...  32.9%
Fitting model...  32.9%
Fitting model...  33.0%
Fitting model...  33.0%
Fitting model...  33.1%
Fitting model...  33.1%
Fitting model...  33.1%
Fitting model...  33.2%
Fitting model...  33.2%
Fitting model...  33.3%
Fitting model...  33.4%
Fitting model...  33.4%
Fitting model...  33.5%
Fitting model...  33.5%
Fitting model...  33.6%
Fitting model...  33.6%
Fitting model...  33.7%
Fitting model...  33.7%
Fitting model...  33.8%
Fitting model...  33.8%
Fitting model...  33.9%
Fitting model...  33.9%
Fitting model...  34.0%
Fitting model...  34.0%
Fitting model...  34.1%
Fitting model...  34.1%
Fitting model...  34.2%
Fitting model...  34.2%
Fitting model...  34.2%
Fitting model...  34.3%
Fitting model...  34.4%
Fitting model...  34.4%
Fitting model...  34.4%
Fitting model...  34.5%
Fitting model...  34.5%
Fitting model...  34.6%
Fitting model...  34.6%
Fitting model...  34.7%
Fitting model...  34.8%
Fitting model...  34.8%
Fitting model...  34.8%
Fitting model...  34.9%
Fitting model...  34.9%
Fitting model...  35.0%
Fitting model...  35.0%
Fitting model...  35.1%
Fitting model...  35.1%
Fitting model...  35.2%
Fitting model...  35.2%
Fitting model...  35.3%
Fitting model...  35.4%
Fitting model...  35.4%
Fitting model...  35.4%
Fitting model...  35.5%
Fitting model...  35.5%
Fitting model...  35.6%
Fitting model...  35.6%
Fitting model...  35.7%
Fitting model...  35.8%
Fitting model...  35.8%
Fitting model...  35.9%
Fitting model...  35.9%
Fitting model...  35.9%
Fitting model...  36.0%
Fitting model...  36.0%
Fitting model...  36.1%
Fitting model...  36.1%
Fitting model...  36.2%
Fitting model...  36.2%
Fitting model...  36.3%
Fitting model...  36.4%
Fitting model...  36.4%
Fitting model...  36.4%
Fitting model...  36.5%
Fitting model...  36.5%
Fitting model...  36.6%
Fitting model...  36.6%
Fitting model...  36.7%
Fitting model...  36.8%
Fitting model...  36.8%
Fitting model...  36.9%
Fitting model...  36.9%
Fitting model...  37.0%
Fitting model...  37.0%
Fitting model...  37.0%
Fitting model...  37.1%
Fitting model...  37.1%
Fitting model...  37.2%
Fitting model...  37.2%
Fitting model...  37.3%
Fitting model...  37.4%
Fitting model...  37.4%
Fitting model...  37.5%
Fitting model...  37.5%
Fitting model...  37.5%
Fitting model...  37.6%
Fitting model...  37.6%
Fitting model...  37.7%
Fitting model...  37.8%
Fitting model...  37.8%
Fitting model...  37.9%
Fitting model...  37.9%
Fitting model...  38.0%
Fitting model...  38.0%
Fitting model...  38.0%
Fitting model...  38.1%
Fitting model...  38.1%
Fitting model...  38.2%
Fitting model...  38.2%
Fitting model...  38.3%
Fitting model...  38.4%
Fitting model...  38.4%
Fitting model...  38.5%
Fitting model...  38.5%
Fitting model...  38.6%
Fitting model...  38.6%
Fitting model...  38.6%
Fitting model...  38.7%
Fitting model...  38.8%
Fitting model...  38.8%
Fitting model...  38.9%
Fitting model...  38.9%
Fitting model...  39.0%
Fitting model...  39.0%
Fitting model...  39.1%
Fitting model...  39.1%
Fitting model...  39.1%
Fitting model...  39.2%
Fitting model...  39.2%
Fitting model...  39.3%
Fitting model...  39.4%
Fitting model...  39.4%
Fitting model...  39.5%
Fitting model...  39.5%
Fitting model...  39.6%
Fitting model...  39.6%
Fitting model...  39.6%
Fitting model...  39.7%
Fitting model...  39.8%
Fitting model...  39.8%
Fitting model...  39.9%
Fitting model...  39.9%
Fitting model...  40.0%
Fitting model...  40.0%
Fitting model...  40.1%
Fitting model...  40.1%
Fitting model...  40.2%
Fitting model...  40.2%
Fitting model...  40.2%
Fitting model...  40.3%
Fitting model...  40.4%
Fitting model...  40.4%
Fitting model...  40.5%
Fitting model...  40.5%
Fitting model...  40.6%
Fitting model...  40.6%
Fitting model...  40.6%
Fitting model...  40.7%
Fitting model...  40.8%
Fitting model...  40.8%
Fitting model...  40.8%
Fitting model...  40.9%
Fitting model...  40.9%
Fitting model...  41.0%
Fitting model...  41.0%
Fitting model...  41.1%
Fitting model...  41.1%
Fitting model...  41.2%
Fitting model...  41.2%
Fitting model...  41.3%
Fitting model...  41.3%
Fitting model...  41.4%
Fitting model...  41.4%
Fitting model...  41.5%
Fitting model...  41.5%
Fitting model...  41.6%
Fitting model...  41.6%
Fitting model...  41.7%
Fitting model...  41.8%
Fitting model...  41.8%
Fitting model...  41.9%
Fitting model...  41.9%
Fitting model...  41.9%
Fitting model...  42.0%
Fitting model...  42.0%
Fitting model...  42.1%
Fitting model...  42.1%
Fitting model...  42.2%
Fitting model...  42.2%
Fitting model...  42.3%
Fitting model...  42.4%
Fitting model...  42.4%
Fitting model...  42.4%
Fitting model...  42.5%
Fitting model...  42.5%
Fitting model...  42.6%
Fitting model...  42.6%
Fitting model...  42.7%
Fitting model...  42.8%
Fitting model...  42.8%
Fitting model...  42.9%
Fitting model...  42.9%
Fitting model...  43.0%
Fitting model...  43.0%
Fitting model...  43.0%
Fitting model...  43.1%
Fitting model...  43.1%
Fitting model...  43.2%
Fitting model...  43.2%
Fitting model...  43.3%
Fitting model...  43.4%
Fitting model...  43.4%
Fitting model...  43.5%
Fitting model...  43.5%
Fitting model...  43.5%
Fitting model...  43.6%
Fitting model...  43.6%
Fitting model...  43.7%
Fitting model...  43.8%
Fitting model...  43.8%
Fitting model...  43.9%
Fitting model...  43.9%
Fitting model...  44.0%
Fitting model...  44.0%
Fitting model...  44.0%
Fitting model...  44.1%
Fitting model...  44.1%
Fitting model...  44.2%
Fitting model...  44.2%
Fitting model...  44.3%
Fitting model...  44.4%
Fitting model...  44.4%
Fitting model...  44.5%
Fitting model...  44.5%
Fitting model...  44.5%
Fitting model...  44.6%
Fitting model...  44.6%
Fitting model...  44.7%
Fitting model...  44.8%
Fitting model...  44.8%
Fitting model...  44.9%
Fitting model...  44.9%
Fitting model...  45.0%
Fitting model...  45.0%
Fitting model...  45.1%
Fitting model...  45.1%
Fitting model...  45.1%
Fitting model...  45.2%
Fitting model...  45.2%
Fitting model...  45.3%
Fitting model...  45.4%
Fitting model...  45.4%
Fitting model...  45.5%
Fitting model...  45.5%
Fitting model...  45.6%
Fitting model...  45.6%
Fitting model...  45.6%
Fitting model...  45.7%
Fitting model...  45.8%
Fitting model...  45.8%
Fitting model...  45.9%
Fitting model...  45.9%
Fitting model...  46.0%
Fitting model...  46.0%
Fitting model...  46.1%
Fitting model...  46.1%
Fitting model...  46.2%
Fitting model...  46.2%
Fitting model...  46.2%
Fitting model...  46.3%
Fitting model...  46.4%
Fitting model...  46.4%
Fitting model...  46.5%
Fitting model...  46.5%
Fitting model...  46.6%
Fitting model...  46.6%
Fitting model...  46.7%
Fitting model...  46.7%
Fitting model...  46.8%
Fitting model...  46.8%
Fitting model...  46.9%
Fitting model...  46.9%
Fitting model...  46.9%
Fitting model...  47.0%
Fitting model...  47.0%
Fitting model...  47.1%
Fitting model...  47.1%
Fitting model...  47.2%
Fitting model...  47.2%
Fitting model...  47.3%
Fitting model...  47.3%
Fitting model...  47.4%
Fitting model...  47.4%
Fitting model...  47.5%
Fitting model...  47.5%
Fitting model...  47.6%
Fitting model...  47.6%
Fitting model...  47.7%
Fitting model...  47.8%
Fitting model...  47.8%
Fitting model...  47.9%
Fitting model...  47.9%
Fitting model...  47.9%
Fitting model...  48.0%
Fitting model...  48.0%
Fitting model...  48.1%
Fitting model...  48.1%
Fitting model...  48.2%
Fitting model...  48.2%
Fitting model...  48.3%
Fitting model...  48.4%
Fitting model...  48.4%
Fitting model...  48.4%
Fitting model...  48.5%
Fitting model...  48.5%
Fitting model...  48.6%
Fitting model...  48.6%
Fitting model...  48.7%
Fitting model...  48.8%
Fitting model...  48.8%
Fitting model...  48.9%
Fitting model...  48.9%
Fitting model...  48.9%
Fitting model...  49.0%
Fitting model...  49.0%
Fitting model...  49.1%
Fitting model...  49.1%
Fitting model...  49.2%
Fitting model...  49.2%
Fitting model...  49.3%
Fitting model...  49.4%
Fitting model...  49.4%
Fitting model...  49.5%
Fitting model...  49.5%
Fitting model...  49.5%
Fitting model...  49.6%
Fitting model...  49.6%
Fitting model...  49.7%
Fitting model...  49.8%
Fitting model...  49.8%
Fitting model...  49.9%
Fitting model...  49.9%
Fitting model...  50.0%
Fitting model...  50.0%
Fitting model...  50.0%
Fitting model...  50.1%
Fitting model...  50.1%
Fitting model...  50.2%
Fitting model...  50.2%
Fitting model...  50.3%
Fitting model...  50.3%
Fitting model...  50.4%
Fitting model...  50.4%
Fitting model...  50.5%
Fitting model...  50.5%
Fitting model...  50.6%
Fitting model...  50.6%
Fitting model...  50.7%
Fitting model...  50.7%
Fitting model...  50.8%
Fitting model...  50.8%
Fitting model...  50.9%
Fitting model...  50.9%
Fitting model...  51.0%
Fitting model...  51.0%
Fitting model...  51.1%
Fitting model...  51.1%
Fitting model...  51.2%
Fitting model...  51.2%
Fitting model...  51.3%
Fitting model...  51.3%
Fitting model...  51.4%
Fitting model...  51.4%
Fitting model...  51.5%
Fitting model...  51.5%
Fitting model...  51.6%
Fitting model...  51.6%
Fitting model...  51.7%
Fitting model...  51.7%
Fitting model...  51.8%
Fitting model...  51.8%
Fitting model...  51.9%
Fitting model...  51.9%
Fitting model...  52.0%
Fitting model...  52.0%
Fitting model...  52.1%
Fitting model...  52.1%
Fitting model...  52.2%
Fitting model...  52.2%
Fitting model...  52.3%
Fitting model...  52.3%
Fitting model...  52.4%
Fitting model...  52.4%
Fitting model...  52.5%
Fitting model...  52.5%
Fitting model...  52.6%
Fitting model...  52.6%
Fitting model...  52.7%
Fitting model...  52.8%
Fitting model...  52.8%
Fitting model...  52.8%
Fitting model...  52.9%
Fitting model...  52.9%
Fitting model...  53.0%
Fitting model...  53.0%
Fitting model...  53.1%
Fitting model...  53.1%
Fitting model...  53.2%
Fitting model...  53.2%
Fitting model...  53.3%
Fitting model...  53.3%
Fitting model...  53.4%
Fitting model...  53.4%
Fitting model...  53.5%
Fitting model...  53.5%
Fitting model...  53.6%
Fitting model...  53.6%
Fitting model...  53.7%
Fitting model...  53.8%
Fitting model...  53.8%
Fitting model...  53.8%
Fitting model...  53.9%
Fitting model...  53.9%
Fitting model...  54.0%
Fitting model...  54.0%
Fitting model...  54.1%
Fitting model...  54.1%
Fitting model...  54.2%
Fitting model...  54.2%
Fitting model...  54.3%
Fitting model...  54.4%
Fitting model...  54.4%
Fitting model...  54.4%
Fitting model...  54.5%
Fitting model...  54.5%
Fitting model...  54.6%
Fitting model...  54.6%
Fitting model...  54.7%
Fitting model...  54.8%
Fitting model...  54.8%
Fitting model...  54.9%
Fitting model...  54.9%
Fitting model...  54.9%
Fitting model...  55.0%
Fitting model...  55.0%
Fitting model...  55.1%
Fitting model...  55.1%
Fitting model...  55.2%
Fitting model...  55.2%
Fitting model...  55.3%
Fitting model...  55.4%
Fitting model...  55.4%
Fitting model...  55.5%
Fitting model...  55.5%
Fitting model...  55.5%
Fitting model...  55.6%
Fitting model...  55.6%
Fitting model...  55.7%
Fitting model...  55.8%
Fitting model...  55.8%
Fitting model...  55.9%
Fitting model...  55.9%
Fitting model...  56.0%
Fitting model...  56.0%
Fitting model...  56.0%
Fitting model...  56.1%
Fitting model...  56.1%
Fitting model...  56.2%
Fitting model...  56.2%
Fitting model...  56.3%
Fitting model...  56.4%
Fitting model...  56.4%
Fitting model...  56.5%
Fitting model...  56.5%
Fitting model...  56.5%
Fitting model...  56.6%
Fitting model...  56.6%
Fitting model...  56.7%
Fitting model...  56.8%
Fitting model...  56.8%
Fitting model...  56.9%
Fitting model...  56.9%
Fitting model...  57.0%
Fitting model...  57.0%
Fitting model...  57.0%
Fitting model...  57.1%
Fitting model...  57.1%
Fitting model...  57.2%
Fitting model...  57.2%
Fitting model...  57.3%
Fitting model...  57.4%
Fitting model...  57.4%
Fitting model...  57.5%
Fitting model...  57.5%
Fitting model...  57.6%
Fitting model...  57.6%
Fitting model...  57.6%
Fitting model...  57.7%
Fitting model...  57.8%
Fitting model...  57.8%
Fitting model...  57.9%
Fitting model...  57.9%
Fitting model...  58.0%
Fitting model...  58.0%
Fitting model...  58.1%
Fitting model...  58.1%
Fitting model...  58.1%
Fitting model...  58.2%
Fitting model...  58.2%
Fitting model...  58.3%
Fitting model...  58.4%
Fitting model...  58.4%
Fitting model...  58.5%
Fitting model...  58.5%
Fitting model...  58.6%
Fitting model...  58.6%
Fitting model...  58.7%
Fitting model...  58.7%
Fitting model...  58.8%
Fitting model...  58.8%
Fitting model...  58.9%
Fitting model...  58.9%
Fitting model...  59.0%
Fitting model...  59.0%
Fitting model...  59.1%
Fitting model...  59.1%
Fitting model...  59.2%
Fitting model...  59.2%
Fitting model...  59.2%
Fitting model...  59.3%
Fitting model...  59.4%
Fitting model...  59.4%
Fitting model...  59.5%
Fitting model...  59.5%
Fitting model...  59.6%
Fitting model...  59.6%
Fitting model...  59.7%
Fitting model...  59.7%
Fitting model...  59.8%
Fitting model...  59.8%
Fitting model...  59.9%
Fitting model...  59.9%
Fitting model...  60.0%
Fitting model...  60.0%
Fitting model...  60.1%
Fitting model...  60.1%
Fitting model...  60.2%
Fitting model...  60.2%
Fitting model...  60.2%
Fitting model...  60.3%
Fitting model...  60.4%
Fitting model...  60.4%
Fitting model...  60.5%
Fitting model...  60.5%
Fitting model...  60.6%
Fitting model...  60.6%
Fitting model...  60.7%
Fitting model...  60.7%
Fitting model...  60.8%
Fitting model...  60.8%
Fitting model...  60.9%
Fitting model...  60.9%
Fitting model...  61.0%
Fitting model...  61.0%
Fitting model...  61.1%
Fitting model...  61.1%
Fitting model...  61.2%
Fitting model...  61.2%
Fitting model...  61.3%
Fitting model...  61.3%
Fitting model...  61.4%
Fitting model...  61.4%
Fitting model...  61.5%
Fitting model...  61.5%
Fitting model...  61.6%
Fitting model...  61.6%
Fitting model...  61.7%
Fitting model...  61.7%
Fitting model...  61.8%
Fitting model...  61.8%
Fitting model...  61.9%
Fitting model...  61.9%
Fitting model...  62.0%
Fitting model...  62.0%
Fitting model...  62.1%
Fitting model...  62.1%
Fitting model...  62.2%
Fitting model...  62.2%
Fitting model...  62.3%
Fitting model...  62.3%
Fitting model...  62.4%
Fitting model...  62.4%
Fitting model...  62.5%
Fitting model...  62.5%
Fitting model...  62.5%
Fitting model...  62.6%
Fitting model...  62.6%
Fitting model...  62.7%
Fitting model...  62.7%
Fitting model...  62.8%
Fitting model...  62.8%
Fitting model...  62.9%
Fitting model...  62.9%
Fitting model...  63.0%
Fitting model...  63.0%
Fitting model...  63.1%
Fitting model...  63.1%
Fitting model...  63.2%
Fitting model...  63.2%
Fitting model...  63.3%
Fitting model...  63.3%
Fitting model...  63.4%
Fitting model...  63.4%
Fitting model...  63.5%
Fitting model...  63.5%
Fitting model...  63.6%
Fitting model...  63.6%
Fitting model...  63.7%
Fitting model...  63.7%
Fitting model...  63.8%
Fitting model...  63.8%
Fitting model...  63.9%
Fitting model...  63.9%
Fitting model...  64.0%
Fitting model...  64.0%
Fitting model...  64.1%
Fitting model...  64.1%
Fitting model...  64.2%
Fitting model...  64.2%
Fitting model...  64.3%
Fitting model...  64.3%
Fitting model...  64.4%
Fitting model...  64.5%
Fitting model...  64.5%
Fitting model...  64.5%
Fitting model...  64.6%
Fitting model...  64.6%
Fitting model...  64.7%
Fitting model...  64.8%
Fitting model...  64.8%
Fitting model...  64.8%
Fitting model...  64.9%
Fitting model...  65.0%
Fitting model...  65.0%
Fitting model...  65.0%
Fitting model...  65.1%
Fitting model...  65.1%
Fitting model...  65.2%
Fitting model...  65.2%
Fitting model...  65.3%
Fitting model...  65.3%
Fitting model...  65.4%
Fitting model...  65.5%
Fitting model...  65.5%
Fitting model...  65.5%
Fitting model...  65.6%
Fitting model...  65.6%
Fitting model...  65.7%
Fitting model...  65.8%
Fitting model...  65.8%
Fitting model...  65.8%
Fitting model...  65.9%
Fitting model...  66.0%
Fitting model...  66.0%
Fitting model...  66.0%
Fitting model...  66.1%
Fitting model...  66.1%
Fitting model...  66.2%
Fitting model...  66.2%
Fitting model...  66.3%
Fitting model...  66.3%
Fitting model...  66.4%
Fitting model...  66.5%
Fitting model...  66.5%
Fitting model...  66.5%
Fitting model...  66.6%
Fitting model...  66.6%
Fitting model...  66.7%
Fitting model...  66.8%
Fitting model...  66.8%
Fitting model...  66.8%
Fitting model...  66.9%
Fitting model...  67.0%
Fitting model...  67.0%
Fitting model...  67.0%
Fitting model...  67.1%
Fitting model...  67.2%
Fitting model...  67.2%
Fitting model...  67.2%
Fitting model...  67.3%
Fitting model...  67.3%
Fitting model...  67.4%
Fitting model...  67.5%
Fitting model...  67.5%
Fitting model...  67.5%
Fitting model...  67.6%
Fitting model...  67.7%
Fitting model...  67.7%
Fitting model...  67.8%
Fitting model...  67.8%
Fitting model...  67.8%
Fitting model...  67.9%
Fitting model...  68.0%
Fitting model...  68.0%
Fitting model...  68.0%
Fitting model...  68.1%
Fitting model...  68.2%
Fitting model...  68.2%
Fitting model...  68.2%
Fitting model...  68.3%
Fitting model...  68.3%
Fitting model...  68.4%
Fitting model...  68.5%
Fitting model...  68.5%
Fitting model...  68.5%
Fitting model...  68.6%
Fitting model...  68.7%
Fitting model...  68.7%
Fitting model...  68.8%
Fitting model...  68.8%
Fitting model...  68.8%
Fitting model...  68.9%
Fitting model...  69.0%
Fitting model...  69.0%
Fitting model...  69.0%
Fitting model...  69.1%
Fitting model...  69.2%
Fitting model...  69.2%
Fitting model...  69.2%
Fitting model...  69.3%
Fitting model...  69.3%
Fitting model...  69.4%
Fitting model...  69.5%
Fitting model...  69.5%
Fitting model...  69.5%
Fitting model...  69.6%
Fitting model...  69.7%
Fitting model...  69.7%
Fitting model...  69.8%
Fitting model...  69.8%
Fitting model...  69.8%
Fitting model...  69.9%
Fitting model...  70.0%
Fitting model...  70.0%
Fitting model...  70.0%
Fitting model...  70.1%
Fitting model...  70.2%
Fitting model...  70.2%
Fitting model...  70.2%
Fitting model...  70.3%
Fitting model...  70.3%
Fitting model...  70.4%
Fitting model...  70.5%
Fitting model...  70.5%
Fitting model...  70.5%
Fitting model...  70.6%
Fitting model...  70.7%
Fitting model...  70.7%
Fitting model...  70.8%
Fitting model...  70.8%
Fitting model...  70.9%
Fitting model...  70.9%
Fitting model...  71.0%
Fitting model...  71.0%
Fitting model...  71.0%
Fitting model...  71.1%
Fitting model...  71.2%
Fitting model...  71.2%
Fitting model...  71.2%
Fitting model...  71.3%
Fitting model...  71.4%
Fitting model...  71.4%
Fitting model...  71.5%
Fitting model...  71.5%
Fitting model...  71.5%
Fitting model...  71.6%
Fitting model...  71.7%
Fitting model...  71.7%
Fitting model...  71.8%
Fitting model...  71.8%
Fitting model...  71.9%
Fitting model...  71.9%
Fitting model...  72.0%
Fitting model...  72.0%
Fitting model...  72.0%
Fitting model...  72.1%
Fitting model...  72.2%
Fitting model...  72.2%
Fitting model...  72.2%
Fitting model...  72.3%
Fitting model...  72.4%
Fitting model...  72.4%
Fitting model...  72.5%
Fitting model...  72.5%
Fitting model...  72.5%
Fitting model...  72.6%
Fitting model...  72.7%
Fitting model...  72.7%
Fitting model...  72.8%
Fitting model...  72.8%
Fitting model...  72.9%
Fitting model...  72.9%
Fitting model...  73.0%
Fitting model...  73.0%
Fitting model...  73.0%
Fitting model...  73.1%
Fitting model...  73.2%
Fitting model...  73.2%
Fitting model...  73.2%
Fitting model...  73.3%
Fitting model...  73.4%
Fitting model...  73.4%
Fitting model...  73.5%
Fitting model...  73.5%
Fitting model...  73.6%
Fitting model...  73.6%
Fitting model...  73.7%
Fitting model...  73.7%
Fitting model...  73.8%
Fitting model...  73.8%
Fitting model...  73.9%
Fitting model...  73.9%
Fitting model...  74.0%
Fitting model...  74.0%
Fitting model...  74.1%
Fitting model...  74.1%
Fitting model...  74.2%
Fitting model...  74.2%
Fitting model...  74.2%
Fitting model...  74.3%
Fitting model...  74.4%
Fitting model...  74.4%
Fitting model...  74.5%
Fitting model...  74.5%
Fitting model...  74.6%
Fitting model...  74.6%
Fitting model...  74.7%
Fitting model...  74.7%
Fitting model...  74.8%
Fitting model...  74.8%
Fitting model...  74.9%
Fitting model...  74.9%
Fitting model...  75.0%
Fitting model...  75.0%
Fitting model...  75.0%
Fitting model...  75.1%
Fitting model...  75.1%
Fitting model...  75.2%
Fitting model...  75.2%
Fitting model...  75.3%
Fitting model...  75.3%
Fitting model...  75.4%
Fitting model...  75.4%
Fitting model...  75.5%
Fitting model...  75.5%
Fitting model...  75.6%
Fitting model...  75.6%
Fitting model...  75.7%
Fitting model...  75.8%
Fitting model...  75.8%
Fitting model...  75.8%
Fitting model...  75.9%
Fitting model...  75.9%
Fitting model...  76.0%
Fitting model...  76.0%
Fitting model...  76.1%
Fitting model...  76.1%
Fitting model...  76.2%
Fitting model...  76.2%
Fitting model...  76.3%
Fitting model...  76.3%
Fitting model...  76.4%
Fitting model...  76.4%
Fitting model...  76.5%
Fitting model...  76.5%
Fitting model...  76.6%
Fitting model...  76.6%
Fitting model...  76.7%
Fitting model...  76.8%
Fitting model...  76.8%
Fitting model...  76.8%
Fitting model...  76.9%
Fitting model...  77.0%
Fitting model...  77.0%
Fitting model...  77.0%
Fitting model...  77.1%
Fitting model...  77.1%
Fitting model...  77.2%
Fitting model...  77.2%
Fitting model...  77.3%
Fitting model...  77.3%
Fitting model...  77.4%
Fitting model...  77.5%
Fitting model...  77.5%
Fitting model...  77.5%
Fitting model...  77.6%
Fitting model...  77.6%
Fitting model...  77.7%
Fitting model...  77.8%
Fitting model...  77.8%
Fitting model...  77.8%
Fitting model...  77.9%
Fitting model...  78.0%
Fitting model...  78.0%
Fitting model...  78.0%
Fitting model...  78.1%
Fitting model...  78.1%
Fitting model...  78.2%
Fitting model...  78.2%
Fitting model...  78.3%
Fitting model...  78.3%
Fitting model...  78.4%
Fitting model...  78.5%
Fitting model...  78.5%
Fitting model...  78.5%
Fitting model...  78.6%
Fitting model...  78.6%
Fitting model...  78.7%
Fitting model...  78.8%
Fitting model...  78.8%
Fitting model...  78.8%
Fitting model...  78.9%
Fitting model...  79.0%
Fitting model...  79.0%
Fitting model...  79.0%
Fitting model...  79.1%
Fitting model...  79.1%
Fitting model...  79.2%
Fitting model...  79.2%
Fitting model...  79.3%
Fitting model...  79.3%
Fitting model...  79.4%
Fitting model...  79.5%
Fitting model...  79.5%
Fitting model...  79.5%
Fitting model...  79.6%
Fitting model...  79.7%
Fitting model...  79.7%
Fitting model...  79.8%
Fitting model...  79.8%
Fitting model...  79.8%
Fitting model...  79.9%
Fitting model...  80.0%
Fitting model...  80.0%
Fitting model...  80.0%
Fitting model...  80.1%
Fitting model...  80.2%
Fitting model...  80.2%
Fitting model...  80.2%
Fitting model...  80.3%
Fitting model...  80.3%
Fitting model...  80.4%
Fitting model...  80.5%
Fitting model...  80.5%
Fitting model...  80.5%
Fitting model...  80.6%
Fitting model...  80.7%
Fitting model...  80.7%
Fitting model...  80.8%
Fitting model...  80.8%
Fitting model...  80.8%
Fitting model...  80.9%
Fitting model...  81.0%
Fitting model...  81.0%
Fitting model...  81.0%
Fitting model...  81.1%
Fitting model...  81.2%
Fitting model...  81.2%
Fitting model...  81.2%
Fitting model...  81.3%
Fitting model...  81.3%
Fitting model...  81.4%
Fitting model...  81.5%
Fitting model...  81.5%
Fitting model...  81.5%
Fitting model...  81.6%
Fitting model...  81.7%
Fitting model...  81.7%
Fitting model...  81.8%
Fitting model...  81.8%
Fitting model...  81.8%
Fitting model...  81.9%
Fitting model...  82.0%
Fitting model...  82.0%
Fitting model...  82.0%
Fitting model...  82.1%
Fitting model...  82.2%
Fitting model...  82.2%
Fitting model...  82.2%
Fitting model...  82.3%
Fitting model...  82.3%
Fitting model...  82.4%
Fitting model...  82.5%
Fitting model...  82.5%
Fitting model...  82.5%
Fitting model...  82.6%
Fitting model...  82.7%
Fitting model...  82.7%
Fitting model...  82.8%
Fitting model...  82.8%
Fitting model...  82.8%
Fitting model...  82.9%
Fitting model...  83.0%
Fitting model...  83.0%
Fitting model...  83.0%
Fitting model...  83.1%
Fitting model...  83.2%
Fitting model...  83.2%
Fitting model...  83.2%
Fitting model...  83.3%
Fitting model...  83.4%
Fitting model...  83.4%
Fitting model...  83.5%
Fitting model...  83.5%
Fitting model...  83.5%
Fitting model...  83.6%
Fitting model...  83.7%
Fitting model...  83.7%
Fitting model...  83.8%
Fitting model...  83.8%
Fitting model...  83.9%
Fitting model...  83.9%
Fitting model...  84.0%
Fitting model...  84.0%
Fitting model...  84.0%
Fitting model...  84.1%
Fitting model...  84.2%
Fitting model...  84.2%
Fitting model...  84.2%
Fitting model...  84.3%
Fitting model...  84.4%
Fitting model...  84.4%
Fitting model...  84.5%
Fitting model...  84.5%
Fitting model...  84.5%
Fitting model...  84.6%
Fitting model...  84.7%
Fitting model...  84.7%
Fitting model...  84.8%
Fitting model...  84.8%
Fitting model...  84.9%
Fitting model...  84.9%
Fitting model...  85.0%
Fitting model...  85.0%
Fitting model...  85.0%
Fitting model...  85.1%
Fitting model...  85.2%
Fitting model...  85.2%
Fitting model...  85.2%
Fitting model...  85.3%
Fitting model...  85.4%
Fitting model...  85.4%
Fitting model...  85.5%
Fitting model...  85.5%
Fitting model...  85.5%
Fitting model...  85.6%
Fitting model...  85.7%
Fitting model...  85.7%
Fitting model...  85.8%
Fitting model...  85.8%
Fitting model...  85.9%
Fitting model...  85.9%
Fitting model...  86.0%
Fitting model...  86.0%
Fitting model...  86.1%
Fitting model...  86.1%
Fitting model...  86.2%
Fitting model...  86.2%
Fitting model...  86.2%
Fitting model...  86.3%
Fitting model...  86.4%
Fitting model...  86.4%
Fitting model...  86.5%
Fitting model...  86.5%
Fitting model...  86.6%
Fitting model...  86.6%
Fitting model...  86.7%
Fitting model...  86.7%
Fitting model...  86.8%
Fitting model...  86.8%
Fitting model...  86.9%
Fitting model...  86.9%
Fitting model...  87.0%
Fitting model...  87.0%
Fitting model...  87.1%
Fitting model...  87.1%
Fitting model...  87.2%
Fitting model...  87.2%
Fitting model...  87.2%
Fitting model...  87.3%
Fitting model...  87.4%
Fitting model...  87.4%
Fitting model...  87.5%
Fitting model...  87.5%
Fitting model...  87.5%
Fitting model...  87.6%
Fitting model...  87.6%
Fitting model...  87.7%
Fitting model...  87.8%
Fitting model...  87.8%
Fitting model...  87.8%
Fitting model...  87.9%
Fitting model...  87.9%
Fitting model...  88.0%
Fitting model...  88.0%
Fitting model...  88.1%
Fitting model...  88.1%
Fitting model...  88.2%
Fitting model...  88.2%
Fitting model...  88.3%
Fitting model...  88.3%
Fitting model...  88.4%
Fitting model...  88.4%
Fitting model...  88.5%
Fitting model...  88.5%
Fitting model...  88.6%
Fitting model...  88.6%
Fitting model...  88.7%
Fitting model...  88.8%
Fitting model...  88.8%
Fitting model...  88.8%
Fitting model...  88.9%
Fitting model...  88.9%
Fitting model...  89.0%
Fitting model...  89.0%
Fitting model...  89.1%
Fitting model...  89.1%
Fitting model...  89.2%
Fitting model...  89.2%
Fitting model...  89.3%
Fitting model...  89.3%
Fitting model...  89.4%
Fitting model...  89.5%
Fitting model...  89.5%
Fitting model...  89.5%
Fitting model...  89.6%
Fitting model...  89.6%
Fitting model...  89.7%
Fitting model...  89.8%
Fitting model...  89.8%
Fitting model...  89.8%
Fitting model...  89.9%
Fitting model...  90.0%
Fitting model...  90.0%
Fitting model...  90.0%
Fitting model...  90.1%
Fitting model...  90.1%
Fitting model...  90.2%
Fitting model...  90.2%
Fitting model...  90.3%
Fitting model...  90.3%
Fitting model...  90.4%
Fitting model...  90.5%
Fitting model...  90.5%
Fitting model...  90.5%
Fitting model...  90.6%
Fitting model...  90.6%
Fitting model...  90.7%
Fitting model...  90.8%
Fitting model...  90.8%
Fitting model...  90.8%
Fitting model...  90.9%
Fitting model...  91.0%
Fitting model...  91.0%
Fitting model...  91.0%
Fitting model...  91.1%
Fitting model...  91.1%
Fitting model...  91.2%
Fitting model...  91.2%
Fitting model...  91.3%
Fitting model...  91.3%
Fitting model...  91.4%
Fitting model...  91.5%
Fitting model...  91.5%
Fitting model...  91.5%
Fitting model...  91.6%
Fitting model...  91.6%
Fitting model...  91.7%
Fitting model...  91.8%
Fitting model...  91.8%
Fitting model...  91.8%
Fitting model...  91.9%
Fitting model...  92.0%
Fitting model...  92.0%
Fitting model...  92.0%
Fitting model...  92.1%
Fitting model...  92.2%
Fitting model...  92.2%
Fitting model...  92.2%
Fitting model...  92.3%
Fitting model...  92.3%
Fitting model...  92.4%
Fitting model...  92.5%
Fitting model...  92.5%
Fitting model...  92.5%
Fitting model...  92.6%
Fitting model...  92.7%
Fitting model...  92.7%
Fitting model...  92.8%
Fitting model...  92.8%
Fitting model...  92.8%
Fitting model...  92.9%
Fitting model...  93.0%
Fitting model...  93.0%
Fitting model...  93.0%
Fitting model...  93.1%
Fitting model...  93.2%
Fitting model...  93.2%
Fitting model...  93.2%
Fitting model...  93.3%
Fitting model...  93.3%
Fitting model...  93.4%
Fitting model...  93.5%
Fitting model...  93.5%
Fitting model...  93.5%
Fitting model...  93.6%
Fitting model...  93.7%
Fitting model...  93.7%
Fitting model...  93.8%
Fitting model...  93.8%
Fitting model...  93.8%
Fitting model...  93.9%
Fitting model...  94.0%
Fitting model...  94.0%
Fitting model...  94.0%
Fitting model...  94.1%
Fitting model...  94.2%
Fitting model...  94.2%
Fitting model...  94.2%
Fitting model...  94.3%
Fitting model...  94.3%
Fitting model...  94.4%
Fitting model...  94.5%
Fitting model...  94.5%
Fitting model...  94.5%
Fitting model...  94.6%
Fitting model...  94.7%
Fitting model...  94.7%
Fitting model...  94.8%
Fitting model...  94.8%
Fitting model...  94.8%
Fitting model...  94.9%
Fitting model...  95.0%
Fitting model...  95.0%
Fitting model...  95.0%
Fitting model...  95.1%
Fitting model...  95.2%
Fitting model...  95.2%
Fitting model...  95.2%
Fitting model...  95.3%
Fitting model...  95.3%
Fitting model...  95.4%
Fitting model...  95.5%
Fitting model...  95.5%
Fitting model...  95.5%
Fitting model...  95.6%
Fitting model...  95.7%
Fitting model...  95.7%
Fitting model...  95.8%
Fitting model...  95.8%
Fitting model...  95.9%
Fitting model...  95.9%
Fitting model...  96.0%
Fitting model...  96.0%
Fitting model...  96.0%
Fitting model...  96.1%
Fitting model...  96.2%
Fitting model...  96.2%
Fitting model...  96.2%
Fitting model...  96.3%
Fitting model...  96.4%
Fitting model...  96.4%
Fitting model...  96.5%
Fitting model...  96.5%
Fitting model...  96.5%
Fitting model...  96.6%
Fitting model...  96.7%
Fitting model...  96.7%
Fitting model...  96.8%
Fitting model...  96.8%
Fitting model...  96.9%
Fitting model...  96.9%
Fitting model...  97.0%
Fitting model...  97.0%
Fitting model...  97.0%
Fitting model...  97.1%
Fitting model...  97.2%
Fitting model...  97.2%
Fitting model...  97.2%
Fitting model...  97.3%
Fitting model...  97.4%
Fitting model...  97.4%
Fitting model...  97.5%
Fitting model...  97.5%
Fitting model...  97.5%
Fitting model...  97.6%
Fitting model...  97.7%
Fitting model...  97.7%
Fitting model...  97.8%
Fitting model...  97.8%
Fitting model...  97.9%
Fitting model...  97.9%
Fitting model...  98.0%
Fitting model...  98.0%
Fitting model...  98.0%
Fitting model...  98.1%
Fitting model...  98.2%
Fitting model...  98.2%
Fitting model...  98.2%
Fitting model...  98.3%
Fitting model...  98.4%
Fitting model...  98.4%
Fitting model...  98.5%
Fitting model...  98.5%
Fitting model...  98.6%
Fitting model...  98.6%
Fitting model...  98.7%
Fitting model...  98.7%
Fitting model...  98.8%
Fitting model...  98.8%
Fitting model...  98.9%
Fitting model...  98.9%
Fitting model...  99.0%
Fitting model...  99.0%
Fitting model...  99.1%
Fitting model...  99.1%
Fitting model...  99.2%
Fitting model...  99.2%
Fitting model...  99.2%
Fitting model...  99.3%
Fitting model...  99.4%
Fitting model...  99.4%
Fitting model...  99.5%
Fitting model...  99.5%
Fitting model...  99.6%
Fitting model...  99.6%
Fitting model...  99.7%
Fitting model...  99.7%
Fitting model...  99.8%
Fitting model...  99.8%
Fitting model...  99.9%
Fitting model...  99.9%
Fitting model... 100.0%
iterations in  3.0768070220947266

<fadin.solver.FaDIn object at 0x7f4e69bf18e0>

Here, we print the estimated parameters of the Hawkes process.

print('Estimated baseline is:', solver.baseline_.item())
print('Estimated alpha is:', solver.alpha_.item())
print('Estimated beta parameter of the exponential kernel is:', solver.kernel_)

Estimated baseline is: 0.42343783378601074
Estimated alpha is: 0.898097574710846
Estimated beta parameter of the exponential kernel is: [tensor([[0.9752]])]

Here, we plot the values of the estimated kernel with FaDIn.

kernel = DiscreteKernelFiniteSupport(dt, n_dim, kernel='truncated_exponential',
                                     kernel_length=kernel_length)
kernel_values = kernel.kernel_eval(solver.kernel_, discretization)

plt.plot(discretization[1:], kernel_values.squeeze()[1:]/kernel_length,
         label='FaDIn\' estimated kernel')
plt.plot(discretization[1:], beta * torch.exp(-discretization[1:]*beta),
         label='True kernel', c='k')
plt.title('Hawkes influence kernel', size=20)
plt.xlabel('Time', size=20)
plt.ylabel(r'$\phi(t)$', size=25)
plt.legend(fontsize='x-large')
plt.show()