def compute_geodesic_control(self, man):
vs = self.adjoint(man)
d_vx = vs(self.manifold.gd[0].view(-1, self.manifold.dim), k=1)
S = 0.5 * (d_vx + torch.transpose(d_vx, 1, 2))
S = torch.tensordot(S,
eta(self.manifold.dim, device=self.device),
dims=2)
tlambdas = self.solve_sks(self.manifold.gd[0].reshape(-1, self.dim),
self.manifold.gd[0].reshape(-1, self.dim),
S,
self.__keops_eye,
self.__keops_invsigmasq,
self.__keops_A,
backend=self.__keops_backend,
alpha=self.nu,
eps=self.eps) / self.coeff
(aq, aqkiaq) = self.__compute_aqkiaq()
c, _ = torch.solve(torch.mm(aq.t(), tlambdas.view(-1, 1)), aqkiaq)
self.controls = c.flatten()
self.__compute_moments()
def __compute_aqh(self, h):
R = self.manifold.gd[1].view(-1, self.manifold.dim, self.manifold.dim)
return torch.einsum(
'nli, nik, k, nui, niv, lvt->nt', R, self.C, h,
torch.eye(self.manifold.dim,
device=self.device).repeat(self.manifold.nb_pts, 1, 1),
torch.transpose(R, 1, 2), eta(self.dim, device=self.device))
def __compute_moments(self):
self.__aqh = self.__compute_aqh(self.controls)
lambdas, _ = torch.solve(self.__aqh.view(-1, 1), self.__sks)
self.__lambdas = lambdas.contiguous()
self.moments = torch.tensordot(self.__lambdas.view(-1, self.sym_dim),
torch.transpose(
eta(self.manifold.dim,
device=self.device), 0, 2),
dims=1)
def __compute_moments(self):
self.__aqh = self.__compute_aqh(self.controls)
self.__lambdas = self.solve_sks(
self.manifold.gd[0].reshape(-1, self.dim),
self.manifold.gd[0].reshape(-1, self.dim),
self.__aqh,
self.__keops_eye,
self.__keops_invsigmasq,
self.__keops_A,
backend=self.__keops_backend,
alpha=self.nu)
self.moments = torch.tensordot(self.__lambdas.view(-1, self.sym_dim),
torch.transpose(
eta(self.manifold.dim,
device=self.device), 0, 2),
dims=1)
def compute_geodesic_control(self, man):
vs = self.adjoint(man)
d_vx = vs(self.manifold.gd[0], k=1)
S = 0.5 * (d_vx + torch.transpose(d_vx, 1, 2))
S = torch.tensordot(S,
eta(self.manifold.dim, device=self.device),
dims=2)
self.__compute_sks()
tlambdas, _ = torch.solve(S.view(-1, 1), self.__sks)
tlambdas = tlambdas / self.coeff
(aq, aqkiaq) = self.__compute_aqkiaq()
c, _ = torch.solve(torch.mm(aq.t(), tlambdas), aqkiaq)
self.controls = c.reshape(-1)
self.__compute_moments()