Spaces:
Sleeping
Sleeping
File size: 3,331 Bytes
82a8f4b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 |
import argparse, numpy as np, torch, time
from ideal_poly_volume_toolkit.geometry import triangle_volume_from_points_torch
def main():
ap = argparse.ArgumentParser()
ap.add_argument('--init-angle', type=float, default=0.5, help='Initial angle in radians')
ap.add_argument('--iters', type=int, default=50)
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()
# Single angle parameter
theta = torch.tensor(args.init_angle, dtype=torch.float64, device=args.device, requires_grad=True)
print(f"Initial theta: {theta.item():.6f} radians ({theta.item() * 180/np.pi:.2f} degrees)")
# Use LBFGS optimizer
opt = torch.optim.LBFGS([theta], lr=1.0, max_iter=20, line_search_fn='strong_wolfe')
history = []
grad_history = []
t0 = time.time()
for it in range(1, args.iters + 1):
def closure():
opt.zero_grad(set_to_none=True)
# Triangle vertices: 0, 1, exp(i*theta)
z0 = torch.tensor(0+0j, dtype=torch.complex128, device=theta.device)
z1 = torch.tensor(1+0j, dtype=torch.complex128, device=theta.device)
z2 = torch.exp(1j * theta.to(torch.complex128))
volume = triangle_volume_from_points_torch(z0, z1, z2, series_terms=args.series)
loss = -volume # maximize volume
loss.backward()
return loss
opt.step(closure)
# Log progress
with torch.no_grad():
z0 = torch.tensor(0+0j, dtype=torch.complex128, device=theta.device)
z1 = torch.tensor(1+0j, dtype=torch.complex128, device=theta.device)
z2 = torch.exp(1j * theta.to(torch.complex128))
vol = triangle_volume_from_points_torch(z0, z1, z2, series_terms=args.series)
history.append(vol.item())
grad_history.append(theta.grad.item() if theta.grad is not None else 0)
if it % args.print_every == 0 or it in (1, args.iters):
print(f'[{it:03d}] volume = {history[-1]:.10f}, theta = {theta.item():.6f} rad ({theta.item() * 180/np.pi:.2f}°), |grad| = {abs(grad_history[-1]):.8f}')
t1 = time.time()
# Final exact evaluation
with torch.no_grad():
from ideal_poly_volume_toolkit.geometry import triangle_volume_from_points
z0, z1, z2 = 0+0j, 1+0j, np.exp(1j * theta.item())
vol_exact = triangle_volume_from_points(z0, z1, z2, mode='exact', dps=250)
print('\n=== Simplex optimization done ===')
print(f'iters={args.iters}, time={t1-t0:.2f}s')
print(f'initial volume ~ {vol_exact if it == 1 else history[0]:.10f}')
print(f'final fast volume ~ {history[-1]:.10f}')
print(f'final exact volume {vol_exact:.12f}')
print(f'final theta: {theta.item():.6f} radians ({theta.item() * 180/np.pi:.2f} degrees)')
# The theoretical maximum for a triangle with vertices at 0, 1, exp(i*theta) occurs at theta = π/2
print(f'\nExpected optimal theta: {np.pi/2:.6f} radians (90.00 degrees)')
print(f'Distance from optimum: {abs(theta.item() - np.pi/2):.6f} radians ({abs(theta.item() - np.pi/2) * 180/np.pi:.2f} degrees)')
if __name__ == '__main__':
main() |