Add Hawkes earthquake aftershocks study example

We need to install basemap to make it work

examples/earthquakes.csv

@@ -0,0 +1 @@
+../doc/_static/example_data/earthquakes.csv

examples/plot_hawkes_earthquake_example.py

@@ -0,0 +1,111 @@
+"""
+==============================================================
+Study earthquake aftershocks propagation with Hawkes processes
+==============================================================
+
+This experiments aims to detect how aftershocks propagate near Japan. A Hawkes
+process has been fit on data from
+
+Ogata, Y., 1988.
+Statistical models for earthquake occurrences and residual analysis
+for point processes.
+Journal of the American Statistical association, 83(401), pp.9-27.
+
+On the left we can see where earthquakes have occurred and on the right
+the propagation matrix, i.e. how likely a earthquake in a given zone will
+trigger an aftershock in another zone.
+We can observe than zone 1, 2 and 3 are tightly linked while zone 4 and
+5 are more self-excited.
+Note that this Hawkes process does not take the location of an earthquake
+to recover this result.
+
+Dataset `'earthquakes.csv'` is available
+`here <../_static/example_data/earthquakes.csv>`_.
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from mpl_toolkits.basemap import Basemap
+
+from tick.hawkes import HawkesEM
+from tick.plot import plot_hawkes_kernel_norms
+from tick.plot.plot_utilities import get_plot_color
+
+df = pd.read_csv('earthquakes.csv')
+
+lats = df.Latitude.values
+lons = df.Longitude.values
+
+# put timestamps in minutes and remove minimum
+timestamps = pd.to_datetime(df.DateTime).values.astype(np.float64)
+timestamps *= 1e-9 / 60
+timestamps -= min(timestamps)
+
+fig, ax_list = plt.subplots(1, 2, figsize=(8, 3.4))
+ax_list[0].set_title('Earthquakes near Japan')
+
+# Draw map
+lon0, lat0 = (139, 34)
+lon1, lat1 = (147, 44)
+m = Basemap(projection='merc', llcrnrlon=lon0, llcrnrlat=lat0, urcrnrlon=lon1,
+            urcrnrlat=lat1, resolution='l', ax=ax_list[0])
+m.drawmapboundary(fill_color='#99ffff')
+m.fillcontinents(color='#cc9966', lake_color='#99ffff')
+
+# Number of splits in the map
+n_groups_lats = 5
+
+group_lats = []
+group_lons = []
+group_timestamps = []
+group_names = []
+
+delta_lats = (lats.max() - lats.min()) / n_groups_lats
+delta_lons = lons.max() - lons.min()
+
+for group in range(n_groups_lats):
+    # Split events into groups
+    min_lat_group = lats.min() + group * delta_lats
+    max_lat_group = lats.min() + (group + 1) * delta_lats
+
+    mask = (min_lat_group <= lats) & (lats < max_lat_group)
+
+    group_lats += [lats[mask]]
+    group_lons += [lons[mask]]
+    group_timestamps += [timestamps[mask]]
+
+    # Draw earthquakes on map
+    x, y = m(group_lons[group], group_lats[group])
+    m.scatter(x, y, 0.3, marker='o', color=get_plot_color(group))
+
+    # Draw zone labels on map
+    group_name = 'Z{}'.format(group)
+    group_names += [group_name]
+
+    center_lat = 0.5 * (min_lat_group + max_lat_group)
+    x_zone, y_zone = m(lons.max() + 0.1 * delta_lons, center_lat)
+
+    zone_bbox_style = dict(boxstyle="round", ec=(0, 0, 0, 0.9), fc=(1., 1, 1,
+                                                                    0.6))
+    ax_list[0].text(x_zone, y_zone, group_name, fontsize=12, fontweight='bold',
+                    ha='left', va='center', color='k', withdash=True,
+                    bbox=zone_bbox_style)
+
+# Fit Hawkes process on events
+events = []
+for g in range(n_groups_lats):
+    events += [group_timestamps[g]]
+    events[g].sort()
+
+kernel_discretization = np.linspace(0, 10000 / 60, 6)
+em = HawkesEM(kernel_discretization=kernel_discretization, tol=1e-9,
+              max_iter=1000, print_every=200)
+em.fit(events)
+
+plot_hawkes_kernel_norms(em, ax=ax_list[1], node_names=group_names)
+ax_list[1].set_xticklabels(ax_list[1].get_xticklabels(), fontsize=11)
+ax_list[1].set_yticklabels(ax_list[1].get_yticklabels(), fontsize=11)
+
+fig.tight_layout()
+plt.show()

tick/plot/plot_hawkes.py

@@ -8,7 +8,7 @@
 
 
 def plot_hawkes_kernel_norms(kernel_object, show=True, pcolor_kwargs=None,
-                             node_names=None):
+                             node_names=None, ax=None):
     """Generic function to plot Hawkes kernel norms.
 
     Parameters
@@ -33,6 +33,10 @@ def plot_hawkes_kernel_norms(kernel_object, show=True, pcolor_kwargs=None,
         node names that will be displayed on axis.
         If `None`, node index will be used.
 
+    ax : `matplotlib.axes`, default=None
+        If not None, the figure will be plot on this axis and show will be
+        set to False. Used only with matplotlib
+
     Notes
     -----
     Kernels are displayed such that it shows norm of column influence's
@@ -50,7 +54,12 @@ def plot_hawkes_kernel_norms(kernel_object, show=True, pcolor_kwargs=None,
     column_labels = ['$\\rightarrow {}$'.format(i) for i in node_names]
 
     norms = kernel_object.get_kernel_norms()
-    fig, ax = plt.subplots()
+
+    if ax is None:
+        fig, ax = plt.subplots(1, 1, figsize=(6, 4))
+    else:
+        fig = ax.figure
+        show = False
 
     if pcolor_kwargs is None:
         pcolor_kwargs = {}

tools/travis/docker_run.sh

@@ -6,11 +6,15 @@ set -e -x
 cp -R /io src
 cd src
 
+apt-get update;
+apt-get install -y libgeos*;
+
 eval "$(pyenv init -)"
 
 pyenv global ${PYVER}
 pyenv local ${PYVER}
 
+python -m pip install  https://github.com/matplotlib/basemap/archive/v1.1.0.tar.gz
 python -m pip install yapf --upgrade
 python -m yapf --style tools/code_style/yapf.conf -i tick --recursive
 

tools/travis/osx_install.sh

@@ -31,5 +31,7 @@ python -m pip install -r requirements.txt
 python -m pip install sphinx pillow
 python -m pip install cpplint
 python -m pip install tensorflow
+brew install geos
+python -m pip install  https://github.com/matplotlib/basemap/archive/v1.1.0.tar.gz
 pyenv rehash