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utils.py
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utils.py
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"""
code modified from constrained-hamiltonian-neural-networks
https://github.com/mfinzi/constrained-hamiltonian-neural-networks
"""
import matplotlib.animation as animation
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
from torch.utils import data as data
from scipy.spatial.transform import Rotation
class Animation():
def __init__(self, qt, body=None):
self.qt = qt.detach().cpu().numpy()
T, n, d = qt.shape
assert d in (2, 3)
self.fig = plt.figure()
self.ax = self.fig.add_axes([0, 0, 1, 1], projection='3d') if d==3 else self.fig.add_axes([0,0,1,1])
# xyzmin = self.qt.min(0).min(0)
# xyzmax = self.qt.max(0).max(0)
# delta = xyzmax - xyzmin
# lower = xyzmin - 0.1 * delta; upper = xyzmax + 0.1 * delta
# self.ax.set_xlim((min(lower), max(upper)))
# self.ax.set_ylim((min(lower), max(upper)))
# if d==3: self.ax.set_zlim((min(lower), max(upper)))
if d!=3: self.ax.set_aspect("equal")
empty = d * [[]]
# self.colors = np.random.choice([f"C{i}" for i in range(15)], size=n, replace=False)
self.colors = [f"C{i}" for i in range(15)]
self.objects = {
'pts': sum([self.ax.plot(*empty, ms=6, color=self.colors[i]) for i in range(n)], []),
'trails': sum([self.ax.plot(*empty, "-", color=self.colors[i]) for i in range(n)], [])
}
def init(self):
empty = np.array(2 * [[]])
for obj in self.objects.values():
for elem in obj:
elem.set_data(*empty)
if self.qt.shape[-1]==3: elem.set_3d_properties([])
return sum(self.objects.values(), [])
def update(self, i=0):
T, n, d = self.qt.shape
qt = self.qt.reshape(T, self.n_o, self.n_p, d)
trail_len = 150
for j in range(self.n_o):
# draw trails
xyz = qt[max(i-trail_len, 0): i+1, j, 0, :]
self.objects["trails"][j].set_data(*xyz[...,:2].T)
if d==3: self.objects["trails"][j].set_3d_properties(xyz[...,2].T)
# draw points
self.objects['pts'][j].set_data(*xyz[-1:,...,:2].T)
if d==3: self.objects['pts'][j].set_3d_properties(xyz[-1:,...,2].T)
return sum(self.objects.values(), [])
def animate(self):
return animation.FuncAnimation(self.fig, self.update, frames=self.qt.shape[0],
interval=33, init_func=self.init, blit=True,)#.save("test.gif")#.to_html5_video()
def dummy_dataloader():
# dummy dataloader for Lightning Module
dummy = data.DataLoader(
data.TensorDataset(
torch.Tensor(1, 1),
torch.Tensor(1, 1)
),
batch_size=1,
shuffle=False
)
return dummy
def Linear(chin, chout, zero_bias=False, orthogonal_init=False):
linear = nn.Linear(chin, chout)
if zero_bias:
torch.nn.init.zeros_(linear.bias)
if orthogonal_init:
torch.nn.init.orthogonal_(linear.weight)
return linear
def mlp(sizes, activation, output_activation=nn.Identity, orthogonal_init=True):
layers = []
for i in range(len(sizes)-1):
act = activation if i < len(sizes)-2 else output_activation
layers += [Linear(sizes[i], sizes[i+1], orthogonal_init=orthogonal_init), act()]
return nn.Sequential(*layers)
class Reshape(nn.Module):
def __init__(self, *args):
super().__init__()
self.shape = args
def forward(self, x):
return x.view(self.shape)
class CosSin(nn.Module):
def __init__(self, q_ndim, angular_dims, only_q=True):
super().__init__()
self.q_ndim = q_ndim
self.angular_dims = tuple(angular_dims)
self.non_angular_dims = tuple(set(range(q_ndim)) - set(angular_dims))
self.only_q = only_q
def forward(self, q_or_qother):
if self.only_q:
q = q_or_qother
else:
q, other = q_or_qother.chunk(2, dim=-1)
assert q.shape[-1] == self.q_ndim
q_angular = q[..., self.angular_dims]
q_not_angular = q[..., self.non_angular_dims]
cos_ang_q, sin_ang_q = q_angular.cos(), q_angular.sin()
q = torch.cat([cos_ang_q, sin_ang_q, q_not_angular], dim=-1)
if self.only_q:
res = q
else:
res = torch.cat([q, other], dim=-1)
return res
def cross_matrix(k):
"""Application of hodge star on R3, mapping Λ^1 R3 -> Λ^2 R3"""
K = torch.zeros(*k.shape[:-1],3,3,device=k.device,dtype=k.dtype)
K[...,0,1] = -k[...,2]
K[...,0,2] = k[...,1]
K[...,1,0] = k[...,2]
K[...,1,2] = -k[...,0]
K[...,2,0] = -k[...,1]
K[...,2,1] = k[...,0]
return K
def uncross_matrix(K):
k = torch.zeros(*K.shape[:-1],device=K.device,dtype=K.dtype)
k[...,0] = (K[...,2,1] - K[...,1,2])/2
k[...,1] = (K[...,0,2] - K[...,2,0])/2
k[...,2] = (K[...,1,0] - K[...,0,1])/2
return k
def eulerdot_to_omega_matrix(euler):
"""(*bsT, 3) -> (*bsT, 3, 3) matrix"""
*bsT,_ = euler.shape
M = torch.zeros(*bsT,3,3,device=euler.device,dtype=euler.dtype)
phi,theta,psi = euler.unbind(-1)
M[...,0,0] = theta.sin()*psi.sin()
M[...,0,1] = psi.cos()
M[...,1,0] = theta.sin()*psi.cos()
M[...,1,1] = -psi.sin()
M[...,2,0] = theta.cos()
M[...,2,2] = 1
return M
def euler_to_frame(euler_and_dot):
""" input: (*bsT, 2, 3)
output: (*bsT, 2, 3, 3) """
*bsT, _, _ = euler_and_dot.shape
euler, eulerdot = euler_and_dot.unbind(dim=-2) # (*bsT, 3)
omega = (eulerdot_to_omega_matrix(euler) @ eulerdot.unsqueeze(-1)).squeeze(-1) # (*bsT, 3)
RT_Rdot = cross_matrix(omega)
# Rdot_RT = cross_matrix(omega) # (*bsT, 3, 3)
R = Rotation.from_euler("ZXZ", euler.reshape(-1, 3).detach().cpu().numpy()).as_matrix()
R = torch.from_numpy(R).reshape(*bsT, 3, 3).to(euler.device, euler.dtype)
Rdot = R @ RT_Rdot
# Rdot = Rdot_RT @ R
return torch.stack([R, Rdot], dim=-3).transpose(-2, -1) # (bs, 2, d, n) -> (bs, 2, n, d)
def frame_to_euler(frame):
""" input: (*bsT, 2, 3, 3) output: (*bsT, 2, 3) """
*bsT, _, _, _ = frame.shape
R, Rdot = frame.transpose(-2, -1).unbind(-3) # (*bsT, 3, 3)
omega = uncross_matrix(R.transpose(-2, -1) @ Rdot)
# omega = uncross_matrix(Rdot @ R.transpose(-2, -1)) # (*bsT, 3)
angles = Rotation.from_matrix(R.reshape(-1, 3, 3).detach().cpu().numpy()).as_euler("ZXZ")
angles = torch.from_numpy(angles).reshape(*bsT, 3).to(R.device, R.dtype) # (*bsT, 3)
eulerdot = torch.solve(omega.unsqueeze(-1), eulerdot_to_omega_matrix(angles))[0].squeeze(-1) # (*bsT, 3)
return torch.stack([angles, eulerdot], dim=-2) # (*bsT, 2, 3)
def com_euler_to_bodyX(com_euler):
""" input (*bsT, 2, 6), output (*bsT, 2, 4, 3) """
com = com_euler[..., :3] # (*bsT, 2, 3)
frame = euler_to_frame(com_euler[..., 3:]) # (*bsT, 2, 3, 3)
# in C frame, com would be zero
shifted_frame = frame + com[..., None, :]
return torch.cat([com[..., None, :], shifted_frame], dim=-2)
def bodyX_to_com_euler(X):
""" input: (*bsT, 2, 4, 3) output: (*bsT, 2, 6) """
com = X[..., 0, :] # (*bsT, 2, 3)
euler = frame_to_euler(X[..., 1:, :] - com[..., None, :]) # (*bsT, 2, 3, 3) -> (*bsT, 2, 3)
return torch.cat([com, euler], dim=-1)