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import argparse, numpy as np, torch, time
from ideal_poly_volume_toolkit.geometry import (
delaunay_triangulation_indices,
triangle_volume_from_points_torch,
)
def random_angles(K, rng):
return 2*np.pi*rng.random(K)
def build_Z(thetas: torch.Tensor) -> torch.Tensor:
Z = torch.empty(thetas.numel() + 2, dtype=torch.complex128, device=thetas.device)
Z[0] = 1 + 0j
Z[1] = 0 + 0j
Z[2:] = torch.exp(1j * thetas.to(torch.complex128))
return Z
def torch_sum_volume(Z_t: torch.Tensor, idx, series_terms: int) -> torch.Tensor:
total = torch.zeros((), dtype=torch.float64, device=Z_t.device)
for (i, j, k) in idx:
total = total + triangle_volume_from_points_torch(
Z_t[i], Z_t[j], Z_t[k], series_terms=series_terms
)
return total
def main():
ap = argparse.ArgumentParser()
ap.add_argument('--seed', type=int, default=0)
ap.add_argument('--iters', type=int, default=75)
ap.add_argument('--series', type=int, default=96)
ap.add_argument('--print-every', type=int, default=5)
ap.add_argument('--device', type=str, default='cpu')
args = ap.parse_args()
rng = np.random.default_rng(args.seed)
K = 3
thetas = torch.tensor(
random_angles(K, rng), dtype=torch.float64, device=args.device, requires_grad=True
)
print(f"Initial thetas: {thetas.data.numpy()}")
opt = torch.optim.LBFGS([thetas], lr=1.0, max_iter=20, line_search_fn='strong_wolfe')
history = []
t0 = time.time()
for it in range(1, args.iters + 1):
with torch.no_grad():
Z_np = build_Z(thetas).detach().cpu().numpy()
idx = delaunay_triangulation_indices(Z_np)
def closure():
opt.zero_grad(set_to_none=True)
Z_t = build_Z(thetas)
total = torch_sum_volume(Z_t, idx, args.series)
loss = -total
loss.backward()
# Debug: print gradients
if it <= 3: # First few iterations
print(f" Iter {it} gradients: {thetas.grad.numpy()}")
print(f" Gradient norm: {torch.norm(thetas.grad).item():.6f}")
return loss
loss_before = closure().item()
_ = opt.step(closure)
with torch.no_grad():
Z_post = build_Z(thetas)
val_post = torch_sum_volume(Z_post, idx, args.series)
history.append(float(val_post.item()))
if it <= 3 or it % args.print_every == 0 or it in (1, args.iters):
print(f'[{it:03d}] fast volume ~ {history[-1]:.10f} (tris={idx.shape[0]})')
print(f' thetas: {thetas.data.numpy()}')
if it <= 3:
print(f' loss changed from {-loss_before:.10f} to {-history[-1]:.10f}')
t1 = time.time()
with torch.no_grad():
Zf = build_Z(thetas).detach().cpu().numpy()
from ideal_poly_volume_toolkit.geometry import ideal_poly_volume_via_delaunay
vol_exact = ideal_poly_volume_via_delaunay(Zf, mode='eval_only', dps=250)
print('\n=== Optimization (Delaunay) done ===')
print(f'iters={args.iters}, time={t1-t0:.2f}s')
print(f'final fast volume ~ {history[-1]:.12f}')
print(f'final exact volume {vol_exact:.12f}')
print('final angles (rad):', thetas.detach().cpu().numpy())
if __name__ == '__main__':
main() |