def compute_critical_values(P, Q, p, q):
"""
Usage
-----
Compute all the critical values between trajectories P and Q
Parameters
----------
param P : px2 numpy_array, Trajectory P
param Q : qx2 numpy_array, Trajectory Q
param p : float, number of points in Trajectory P
param q : float, number of points in Trajectory Q
Returns
-------
cc : list, all critical values between trajectories P and Q
"""
origin = eucl_dist(P[0], Q[0])
end = eucl_dist(P[-1], Q[-1])
end_point = max(origin, end)
cc = set([end_point])
for i in range(p - 1):
for j in range(q - 1):
Lij = point_to_seg(Q[j], P[i], P[i + 1])
if Lij > end_point:
cc.add(Lij)
Bij = point_to_seg(P[i], Q[j], Q[j + 1])
if Bij > end_point:
cc.add(Bij)
return sorted(list(cc))
def _c(ca, i, j, P, Q):
if ca[i, j] > -1:
return ca[i, j]
elif i == 0 and j == 0:
ca[i, j] = eucl_dist(P[0], Q[0])
elif i > 0 and j == 0:
ca[i, j] = max(_c(ca, i - 1, 0, P, Q), eucl_dist(P[i], Q[0]))
elif i == 0 and j > 0:
ca[i, j] = max(_c(ca, 0, j - 1, P, Q), eucl_dist(P[0], Q[j]))
elif i > 0 and j > 0:
ca[i, j] = max(
min(_c(ca, i - 1, j, P, Q), _c(ca, i - 1, j - 1, P, Q),
_c(ca, i, j - 1, P, Q)), eucl_dist(P[i], Q[j]))
else:
ca[i, j] = float("inf")
return ca[i, j]
def e_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 eucl_dist(t0[i - 1], t1[j - 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 e_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] = eucl_dist(t0[i - 1], t1[j - 1]) + min(
C[i, j - 1], C[i - 1, j - 1], C[i - 1, j])
dtw = C[n0, n1]
return dtw
def e_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 eucl_dist(t0[i - 1], t1[j - 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 free_line(p, eps, s):
"""
Usage
-----
Return the free space in the segment s, from point p.
This free space is the set of all point in s whose distance from p is at most eps.
Since s is a segment, the free space is also a segment.
We return a 1x2 array whit the fraction of the segment s which are in the free space.
If no part of s are in the free space, return [-1,-1]
Parameters
----------
param p : 1x2 numpy_array, centre of the circle
param eps : float, radius of the circle
param s : 2x2 numpy_array, line
Returns
-------
lf : 1x2 numpy_array
fraction of segment which is in the free space (i.e [0.3,0.7], [0.45,1], ...)
If no part of s are in the free space, return [-1,-1]
"""
px = p[0]
py = p[1]
s1x = s[0, 0]
s1y = s[0, 1]
s2x = s[1, 0]
s2y = s[1, 1]
if s1x == s2x and s1y == s2y:
if eucl_dist(p, s[0]) > eps:
lf = [-1, -1]
else:
lf = [0, 1]
else:
if point_to_seg(p, s[0], s[1]) > eps:
#print("No Intersection")
lf = [-1, -1]
else:
segl = eucl_dist(s[0], s[1])
segl2 = segl * segl
intersect = circle_line_intersection(px, py, s1x, s1y, s2x, s2y,
eps)
if intersect[0][0] != intersect[1][0] or intersect[0][
1] != intersect[1][1]:
i1x = intersect[0, 0]
i1y = intersect[0, 1]
u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) *
(s2y - s1y))) / segl2
i2x = intersect[1, 0]
i2y = intersect[1, 1]
u2 = (((i2x - s1x) * (s2x - s1x)) + ((i2y - s1y) *
(s2y - s1y))) / segl2
ordered_point = sorted((0, 1, u1, u2))
lf = ordered_point[1:3]
else:
if px == s1x and py == s1y:
lf = [0, 0]
elif px == s2x and py == s2y:
lf = [1, 1]
else:
i1x = intersect[0][0]
i1y = intersect[0][1]
u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) *
(s2y - s1y))) / segl2
if 0 <= u1 <= 1:
lf = [u1, u1]
else:
lf = [-1, -1]
return lf