import math
import torch
def cos_sim(v):
v_inner = inner_product(v)
v_size = vec_size(v)
v_cos = v_inner / torch.mm(v_size, v_size.t())
return v_cos
def vec_size(v):
return v.norm(dim=-1, keepdim=True)
def inner_product(v):
return torch.mm(v, v.t())
def euclidean_dist(v, eps=1e-10):
v_norm = (v**2).sum(-1, keepdim=True)
dist = v_norm + v_norm.t() - 2.0 * torch.mm(v, v.t())
dist = torch.sqrt(torch.abs(dist) + eps)
return dist
def theta(v, eps=1e-5):
v_cos = cos_sim(v).clamp(-1. + eps, 1. - eps)
x = torch.acos(v_cos) + math.radians(10)
return x
def triangle(v):
theta_ = theta(v)
theta_rad = theta_ * math.pi / 180.
vs = vec_size(v)
x = (vs.mm(vs.t())) * torch.sin(theta_rad)
return x / 2.
def magnitude_dif(v):
vs = vec_size(v)
return (vs - vs.t()).abs()
def sector(v):
ed = euclidean_dist(v)
md = magnitude_dif(v)
sec = math.pi * torch.pow((ed + md), 2) * theta(v)/360.
return sec
def ts_ss(v):
tri = triangle(v)
sec = sector(v)
return tri * sec
def ts_ss_(v, eps=1e-15, eps2=1e-4):
# reusable compute
v_inner = torch.mm(v, v.t())
vs = v.norm(dim=-1, keepdim=True)
vs_dot = vs.mm(vs.t())
# compute triangle(v)
v_cos = v_inner / vs_dot
v_cos = v_cos.clamp(-1. + eps2, 1. - eps2) # clamp to avoid backprop instability
theta_ = torch.acos(v_cos) + math.radians(10)
theta_rad = theta_ * math.pi / 180.
tri = (vs_dot * torch.sin(theta_rad)) / 2.
# compute sector(v)
v_norm = (v ** 2).sum(-1, keepdim=True)
euc_dist = v_norm + v_norm.t() - 2.0 * v_inner
euc_dist = torch.sqrt(torch.abs(euc_dist) + eps) # add epsilon to avoid srt(0.)
magnitude_diff = (vs - vs.t()).abs()
sec = math.pi * (euc_dist + magnitude_diff) ** 2 * theta_ / 360.
return tri * sec
vec1 = [1,2]
vec2 = [2,4]
v = torch.tensor([vec1, vec2])
print(euclidean_dist(v)
print(cos_sim(v)
print(ts_ss_(v))
