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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):
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 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)
opt = torch.optim.LBFGS([thetas], lr=1.0, max_iter=20, line_search_fn='strong_wolfe')
# Precompute triangulation connectivity outside the graph each outer iter
def closure_once(idx):
def _c():
opt.zero_grad(set_to_none=True)
Z_t = build_Z(thetas) # complex torch, depends on real angles
total = torch.zeros((), dtype=torch.complex128, device=thetas.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=args.series)
loss = -total.real # maximize volume
loss.backward()
return loss
return _c
hist = []; t0 = time.time()
for it in range(1, args.iters+1):
# Rebuild Delaunay triangles using current (detached) positions
with torch.no_grad():
Z_np = build_Z(thetas).detach().cpu().numpy()
idx = delaunay_triangulation_indices(Z_np)
loss = opt.step(closure_once(idx))
with torch.no_grad(): hist.append(float(-loss.item()))
if it % args.print_every == 0 or it in (1, args.iters):
print(f'[{it:03d}] fast volume ~ {hist[-1]:.10f} (tris={idx.shape[0]})')
t1 = time.time()
# Final exact eval
with torch.no_grad():
Zf = build_Z(thetas).detach().cpu().numpy()
from ideal_poly_volume_toolkit.geometry import ideal_poly_volume_via_delaunay as eval_del
vol_exact = eval_del(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 ~ {hist[-1]:.12f}')
print(f'final exact volume {vol_exact:.12f}')
print('final angles (rad):', thetas.detach().cpu().numpy())
if __name__ == '__main__':
main()
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