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taxi-trajectories.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Oct 23 19:02:14 2015
@author: Rory H.R.
"""
from pykalman import KalmanFilter
import pandas as pd
import numpy as np
import os
#from math import radians, cos, sin, asin, sqrt, pi
import matplotlib.pyplot as plt
# Patch to get values rather than log(10) on hexbin plot
from matplotlib.ticker import LogFormatter
class LogFormatterHB(LogFormatter):
def __call__(self, v, pos=None):
vv = self._base ** v
return LogFormatter.__call__(self, vv, pos)
#%%
def pythagoras(lat_in, lon_in):
lat = np.array(lat_in)
lon = np.array(lon_in)
lat *= np.pi/180
lon *= np.pi/180
lon1 = lon[0:-1]
lon2 = lon[1:]
lat1 = lat[0:-1]
lat2 = lat[1:]
x = (lon2-lon1) * np.cos((lat1+lat2)/2)
y = lat2-lat1
d = np.sqrt(x**2 + y**2) * 6371*1000
return d
#%% Function that return a list of files to read in a given folder
def get_files(direc):
full_files = []
for root, dirs, files in os.walk(direc):
for name in files:
full_files.append(os.path.join(root, name))
return full_files
#%% Read in data
#full_files = ['data/012/15.txt'] # 1 file: 50 KB
#full_files = get_files('data/012') # 1 folder: 30-50 MB
full_files = get_files('data') # All folders 700 MB
print "Reading in the .txt files..."
data = []
for index, file_path in enumerate(full_files):
data.append(pd.read_csv(file_path, infer_datetime_format=True,\
header=None, parse_dates = [1],\
names = ['taxi_id', 'date_time', 'longitude', 'latitude']))
data = pd.concat(data, ignore_index=True)
print "Size of data frame: ", data.shape
print "%.1f million rows" % (data.shape[0]/1.0e6)
# Drop duplicates and NAs
data.drop_duplicates(inplace=True)
data.dropna(inplace=True)
#%% Compute Time Intervals
print "Computing time intervals..."
grouped = data.sort('date_time').groupby('taxi_id')['date_time']
time_intervals = []
for group_id, times in grouped:
# times.sort(inplace=True)
time_intervals.append(times.diff())
time_intervals = pd.concat(time_intervals)
time_intervals.dropna(inplace=True)
time_intervals /= np.timedelta64(1,'s') # Divide by 1 second, for float64 data
print "Average sample interval: %.0f secs" % time_intervals[time_intervals < 1e4].mean()
time_intervals /= 60 # Convert to minutes
#%% Compute Distance Intervals
print "Computing distance intervals..."
grouped = data.sort('date_time').groupby('taxi_id')
distances = []
for g in grouped:
# Distances are given in meters
# g[1].sort(columns = 'date_time', inplace=True)
distances.append(pd.DataFrame(pythagoras(g[1].latitude.values, \
g[1].longitude.values)))
distances = pd.concat(distances)
print "Total trajectory distance: %.0f million km" % \
(distances[distances[0] < 1e5][0].sum()/1e9)
print "Average distance between samples: %.0f m" % \
(distances[(distances[0] < 1e5)][0].mean())
#%% Plotting: Time -- plots a histogram time intervals with
# proportions summing to 1
print "Plotting time intervals..."
fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10,5))
axes[0].set_xlabel('Interval (minutes)')
axes[0].set_ylabel('Frequency (proportion)')
axes[0].set_title('Time Intervals')
hist, bins = np.histogram(time_intervals[(time_intervals > 0) & \
(time_intervals < 12)].astype(np.ndarray), bins=20)
axes[0].bar(bins[:-1], hist.astype(np.float32) / hist.sum(), width=(bins[1]-bins[0]))
#% Plotting: Distance -- plots a normed histogram of distance intervals
distances.dropna(inplace=True)
hist, bins = np.histogram(distances[(distances[0] < 8000)][0].values, bins=20)
axes[1].bar(bins[:-1], hist.astype(np.float32) / hist.sum(), width=(bins[1]-bins[0]))
axes[1].set_xlabel('Distance (meters)')
axes[1].set_ylabel('Frequency (proportion)')
fig.tight_layout()
#%% Plot position density
print "Plotting position density..."
xmin, xmax = 116.1, 116.8
ymin, ymax = 39.5, 40.3
window = data[(xmin < data.longitude) & (data.longitude < xmax) & \
(ymin < data.latitude) & ( data.latitude < ymax)]
x = np.array(window.longitude)
y = np.array(window.latitude)
plt.figure(figsize = (10,7), dpi=150)
plt.hexbin(x,y,bins='log', gridsize=800, cmap=plt.cm.hot) # black -> red > white
plt.axis([xmin, xmax, ymin, ymax])
plt.title("Traffic data over Beijing")
plt.xlabel('Longitude (degrees)')
plt.ylabel('Latitude (degrees)')
cb = plt.colorbar(format=LogFormatterHB())
cb.set_label('Number of points')
plt.tight_layout()
plt.show()
#%% Make the 5th Ring Road Beijing
# Location details
xmin, xmax = 116.25, 116.5
ymin, ymax = 39.75, 40.1
window = data[(xmin < data.longitude) & (data.longitude < xmax) & \
(ymin < data.latitude) & ( data.latitude < ymax)]
x = np.array(window.longitude)
y = np.array(window.latitude)
plt.figure(figsize = (10,7), dpi=150)
plt.hexbin(x,y, bins='log', gridsize=800, cmap=plt.cm.hot) # black -> red > white
plt.axis([xmin, xmax, ymin, ymax])
plt.title("Traffic data for Beijing's 5th Ring Road")
plt.xlabel('Longitude (degrees)')
plt.ylabel('Latitude (degrees)')
cb = plt.colorbar(format=LogFormatterHB())
cb.set_label('Number of points')
plt.tight_layout()
plt.show()
#%% Select data for one taxi
one_taxi = data[data.taxi_id == 1131]
#%% Plot distance to manually identify start/stop indicies
#plt.plot(pythagoras(one_taxi.latitude[0:101], one_taxi.longitude[0:101]))
#%% Kalman Filter and plot results
#kf = KalmanFilter(transition_matrices = [[1, 1], [0, 1]], observation_matrices = [[0.1, 0.5], [-0.3, 0.0]])
start_index = 38
end_index = 69
measurements = np.asarray([one_taxi.longitude, one_taxi.latitude])
measurements = measurements.T[start_index:end_index]
kf = KalmanFilter(initial_state_mean = measurements[0], \
n_dim_obs=2, n_dim_state=2)
kf = kf.em(measurements)
#(filtered_state_means, filtered_state_covariances) = kf.filter(measurements)
(smoothed_state_means, smoothed_state_covariances) = kf.smooth(measurements)
#plt.plot(filtered_state_means.T[0],filtered_state_means.T[1])
plt.plot(smoothed_state_means.T[0],smoothed_state_means.T[1])
plt.title("One Trip smoothed with Karman Filter")
plt.xlabel('Longitude (degrees)')
plt.ylabel('Latitude (degrees)')
print "Taxi data for Taxi ID: %d" % one_taxi.taxi_id[0]
print "Start date and time: ", one_taxi.date_time[start_index]
print "Duration:", one_taxi.date_time[end_index] - one_taxi.date_time[start_index]
#%% Kalman Filter and plot results
#kf = KalmanFilter(transition_matrices = [[1, 1], [0, 1]], observation_matrices = [[0.1, 0.5], [-0.3, 0.0]])
start_index = 0
end_index = 800
measurements = np.asarray([one_taxi.longitude, one_taxi.latitude])
measurements = measurements.T[start_index:end_index]
kf = KalmanFilter(initial_state_mean = measurements[0], \
n_dim_obs=2, n_dim_state=2)
kf = kf.em(measurements)
#(filtered_state_means, filtered_state_covariances) = kf.filter(measurements)
(smoothed_state_means, smoothed_state_covariances) = kf.smooth(measurements)
#plt.plot(filtered_state_means.T[0],filtered_state_means.T[1])
plt.plot(smoothed_state_means.T[0],smoothed_state_means.T[1])
plt.title("Many trips smoothed with Karman Filter")
plt.xlabel('Longitude (degrees)')
plt.ylabel('Latitude (degrees)')
print "Taxi data for Taxi ID: %d" % one_taxi.taxi_id[0]
print "Start date and time: ", one_taxi.date_time[start_index]
print "Duration:", one_taxi.date_time[end_index] - one_taxi.date_time[start_index]
#plt.tight_layout()