def s_erp(t0, t1, g):
"""
Usage
-----
The Edit distance with Real Penalty between trajectory t0 and t1.
Parameters
----------
param t0 : len(t0)x2 numpy_array
param t1 : len(t1)x2 numpy_array
Returns
-------
dtw : float
The Dynamic-Time Warping distance between trajectory t0 and t1
"""
n0 = len(t0)
n1 = len(t1)
C = np.zeros((n0 + 1, n1 + 1))
C[1:, 0] = sum(
map(lambda x: abs(great_circle_distance(g[0], g[1], x[0], x[1])), t0))
C[0, 1:] = sum(
map(lambda y: abs(great_circle_distance(g[0], g[1], y[0], y[1])), t1))
for i in np.arange(n0) + 1:
for j in np.arange(n1) + 1:
derp0 = C[i - 1, j] + great_circle_distance(
t0[i - 1][0], t0[i - 1][1], g[0], g[1])
derp1 = C[i, j - 1] + great_circle_distance(
g[0], g[1], t1[j - 1][0], t1[j - 1][1])
derp01 = C[i - 1, j - 1] + great_circle_distance(
t0[i - 1][0], t0[i - 1][1], t1[j - 1][0], t1[j - 1][1])
C[i, j] = min(derp0, derp1, derp01)
erp = C[n0, n1]
return erp
def s_sspd(t0, t1):
"""
Usage
-----
The sspd-distance between trajectories t1 and t2.
The sspd-distance is the mean of the spd-distance between of t1 from t2 and the spd-distance of t2 from t1.
Parameters
----------
param t0 : len(t0)x2 numpy_array
param t1 : len(t1)x2 numpy_array
Returns
-------
sspd : float
sspd-distance of trajectory t2 from trajectory t1
"""
n0 = len(t0)
n1 = len(t1)
lats0 = t0[:, 1]
lons0 = t0[:, 0]
lats1 = t1[:, 1]
lons1 = t1[:, 0]
mdist = great_circle_distance_traj(lons0, lats0, lons1, lats1, n0, n1)
t0_dist = map(lambda it0: great_circle_distance(lons0[it0], lats0[it0], lons0[it0 + 1], lats0[it0 + 1]),
range(n0 - 1))
t1_dist = map(lambda it1: great_circle_distance(lons1[it1], lats1[it1], lons1[it1 + 1], lats1[it1 + 1]),
range(n1 - 1))
dist = s_spd(lons0, lats0, lons1, lats1, n0, n1, mdist, t0_dist) + s_spd(lons1, lats1, lons0, lats0, n1, n0,
mdist.T, t1_dist)
return dist
def s_dtw(t0, t1):
"""
Usage
-----
The Dynamic-Time Warping distance between trajectory t0 and t1.
Parameters
----------
param t0 : len(t0)x2 numpy_array
param t1 : len(t1)x2 numpy_array
Returns
-------
dtw : float
The Dynamic-Time Warping distance between trajectory t0 and t1
"""
n0 = len(t0)
n1 = len(t1)
C = np.zeros((n0 + 1, n1 + 1))
C[1:, 0] = float('inf')
C[0, 1:] = float('inf')
for i in np.arange(n0) + 1:
for j in np.arange(n1) + 1:
C[i, j] = great_circle_distance(t0[i - 1][0], t0[i - 1][1], t1[j - 1][0], t1[j - 1][1]) + \
min(C[i, j - 1], C[i - 1, j - 1], C[i - 1, j])
dtw = C[n0, n1]
return dtw
def s_edr(t0, t1, eps):
"""
Usage
-----
The Edit Distance on Real sequence between trajectory t0 and t1.
Parameters
----------
param t0 : len(t0)x2 numpy_array
param t1 : len(t1)x2 numpy_array
eps : float
Returns
-------
edr : float
The Longuest-Common-Subsequence distance between trajectory t0 and t1
"""
n0 = len(t0)
n1 = len(t1)
# An (m+1) times (n+1) matrix
C = [[0] * (n1 + 1) for _ in range(n0 + 1)]
for i in range(1, n0 + 1):
for j in range(1, n1 + 1):
if great_circle_distance(t0[i - 1][0], t0[i - 1][1], t1[j - 1][0], t1[j - 1][1]) < eps:
subcost = 0
else:
subcost = 1
C[i][j] = min(C[i][j - 1] + 1, C[i - 1][j] + 1, C[i - 1][j - 1] + subcost)
edr = float(C[n0][n1]) / max([n0, n1])
return edr
def s_lcss(t0, t1, eps):
"""
Usage
-----
The Longuest-Common-Subsequence distance between trajectory t0 and t1.
Parameters
----------
param t0 : len(t0)x2 numpy_array
param t1 : len(t1)x2 numpy_array
eps : float
Returns
-------
lcss : float
The Longuest-Common-Subsequence distance between trajectory t0 and t1
"""
n0 = len(t0)
n1 = len(t1)
# An (m+1) times (n+1) matrix
C = [[0] * (n1 + 1) for _ in range(n0 + 1)]
for i in range(1, n0 + 1):
for j in range(1, n1 + 1):
if great_circle_distance(t0[i - 1, 0], t0[i - 1, 1], t1[j - 1, 0],
t1[j - 1, 1]) < eps:
C[i][j] = C[i - 1][j - 1] + 1
else:
C[i][j] = max(C[i][j - 1], C[i - 1][j])
lcss = 1 - float(C[n0][n1]) / min([n0, n1])
return lcss
def s_hausdorff(t0, t1):
"""
Usage
-----
hausdorff distance between trajectories t1 and t2.
Parameters
----------
param lons0 : n0 x 1 numpy_array, longitudes of trajectories t0
param lats0 : n0 x 1 numpy_array, lattitudes of trajectories t0
param lons1 : n1 x 1 numpy_array, longitudes of trajectories t1
param lats1 : n1 x 1 numpy_array, lattitudes of trajectories t1
param n0: int, length of lons0 and lats0
param n1: int, length of lons1 and lats1
mdist : len(t0) x len(t1) numpy array, pairwise distance between points of trajectories t0 and t1
param t0_dist: l_t1 x 1 numpy_array, distances between consecutive points in t0
Returns
-------
h : float, hausdorff from trajectories t1 and t2
"""
n0 = len(t0)
n1 = len(t1)
lats0 = t0[:, 1]
lons0 = t0[:, 0]
lats1 = t1[:, 1]
lons1 = t1[:, 0]
mdist = great_circle_distance_traj(lons0, lats0, lons1, lats1, n0, n1)
t0_dist = map(
lambda it0: great_circle_distance(lons0[it0], lats0[it0], lons0[
it0 + 1], lats0[it0 + 1]), range(n0 - 1))
t1_dist = map(
lambda it1: great_circle_distance(lons1[it1], lats1[it1], lons1[
it1 + 1], lats1[it1 + 1]), range(n1 - 1))
h = max(
s_directed_hausdorff(lons0, lats0, lons1, lats1, n0, n1, mdist,
t0_dist),
s_directed_hausdorff(lons1, lats1, lons0, lats0, n1, n0, mdist.T,
t1_dist))
return h