def barycenter(z,
wik=None,
lr=5e-3,
tau=5e-3,
max_iter=math.inf,
distance=pf.distance,
normed=False):
if (wik is None):
wik = 1.
else:
wik = wik.unsqueeze(-1).expand_as(z)
if (z.dim() > 1):
barycenter = z.mean(0, keepdim=True)
else:
barycenter = z.mean(0, keepdim=True)
if (len(z) == 1):
return z
iteration = 0
cvg = math.inf
while (cvg > tau and max_iter > iteration):
iteration += 1
grad_tangent = pf.log(barycenter.expand_as(z), z) * wik
if (normed):
if (type(wik) != float):
grad_tangent /= wik.sum(0, keepdim=True).expand_as(wik)
else:
grad_tangent /= len(z)
cc_barycenter = pf.exp(barycenter, lr * grad_tangent.sum(0))
cvg = distance(cc_barycenter, barycenter).max().item()
barycenter = cc_barycenter
return barycenter
def _optimization_method(self, p, d_p, lr):
p.copy_(pf.exp(p, lr * d_p))
def _optimization_method(self, p, d_p, lr):
p.copy_(
pf.add(pf.renorm_projection(p.data),
-lr * pf.exp(d_p.new(d_p.size()).zero_(), d_p)))
def test():
import numpy as np
from torch import nn
from function_tools import poincare_function as tf
from function_tools.numpy_function import RiemannianFunction as nf
import cmath
def sigmoid(x):
return 1 / (1 + cmath.exp(-x))
x = torch.rand(3, 2) / 1.5
y = torch.rand(3, 2) / 1.5
xn = x[:, 0].detach().numpy() + x[:, 1].detach().numpy() * 1j
yn = y[:, 0].detach().numpy() + y[:, 1].detach().numpy() * 1j
x = nn.Parameter(x)
y = nn.Parameter(y)
print("LOG : ")
print(" Torch version")
print(" " + str(tf.log(x, y)))
print(" numpy version")
print(" " + str(nf.log(xn, yn)))
print("EXP: ")
print(" Torch version")
print(" " + str(tf.exp(x, y)))
print(" numpy version")
print(" " + str(
np.array(
[nf.exp(xn[0], yn[0]),
nf.exp(xn[1], yn[1]),
nf.exp(xn[2], yn[2])])))
print("Poincare DIST : ")
print(" Torch version")
print(" " + str(tf.riemannian_distance(x, y)))
print(" numpy version")
print(" " + str(nf.riemannian_distance(xn, yn)))
print("Poincare Grad : ")
print(" Torch version")
x = torch.rand(1, 2) / 1.5
y = torch.rand(1, 2) / 1.5
xn = x[:, 0].detach().numpy() + x[:, 1].detach().numpy() * 1j
yn = y[:, 0].detach().numpy() + y[:, 1].detach().numpy() * 1j
x = nn.Parameter(x)
y = nn.Parameter(y)
l = tf.riemannian_distance(x, y)
l.backward()
print(" Gradient Angle")
print(" " + str(x.grad / x.grad.norm(2, -1)))
print(" numpy version")
print(" " + str(
nf.riemannian_distance_grad(xn, yn) /
abs(nf.riemannian_distance_grad(xn, yn))))
print(" Real value not angle")
print(x.grad)
g_xn = nf.riemannian_distance_grad(xn, yn)
print(nf.riemannian_distance_grad(xn, yn))
print("factor ", g_xn[0].real / x.grad[0, 0].item())
print(
nf.riemannian_distance_grad(xn, yn) /
(g_xn[0].real / x.grad[0, 0].item()))
ln = nf.riemannian_distance_grad(xn, yn)
#* -sigmoid(nf.riemannian_distance(xn, yn))
print(ln)
print("new num", nf.exp(xn, -ln))
xr = ((1 - torch.sum(x.data**2, dim=-1))) / 4
print(-x.grad * xr)
print(x - (x.grad * xr))
print("new num", tf.exp(x, -x.grad))
def barycenter(z,
wik=None,
lr=5e-2,
tau=5e-3,
max_iter=math.inf,
distance=pf.distance,
normed=False,
init_method="default"):
if (wik is None):
wik = 1.
# barycenter = z.mean(0, keepdim=True)
barycenter = z.mean(0, keepdim=True) * 0
else:
wik = wik.unsqueeze(-1).expand_as(z)
if (init_method == "global_mean"):
print("Bad init selected")
barycenter = z.mean(0, keepdim=True)
else:
barycenter = (z * wik).sum(0, keepdim=True) / wik.sum(0)
if (len(z) == 1):
return z
iteration = 0
cvg = math.inf
# print("barycenter_init", barycenter)
while (cvg > tau and max_iter > iteration):
iteration += 1
if (type(wik) != float):
grad_tangent = 2 * pf.log(barycenter.expand_as(z), z) * wik
if ((barycenter == barycenter).float().mean() != 1):
print("\n\n At least one barycenter is Nan : ")
print(barycenter)
print(wik.sum(0))
print(wik.mean(0))
print(wik.sum(1))
print(wik.mean(1))
print(iteration)
exit()
else:
grad_tangent = 2 * pf.log(barycenter.expand_as(z), z)
#print(type(wik))
if (normed):
# print(grad_tangent.size())
if (type(wik) != float):
# print(wik.sum(0, keepdim=True))
grad_tangent /= wik.sum(0, keepdim=True).expand_as(wik)
else:
grad_tangent /= len(z)
cc_barycenter = pf.exp(barycenter,
lr * grad_tangent.sum(0, keepdim=True))
cvg = distance(cc_barycenter, barycenter).max().item()
# print(cvg)
barycenter = cc_barycenter
if (type(wik) != float):
# # to debug ponderate version
# print(cvg, iteration, max_iter)
pass
# print("BARYCENTERS -> ", barycenter)
return barycenter