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import argparse, numpy as np, torch, time
from ideal_poly_volume_toolkit.geometry import triangle_volume_from_points_torch
def build_Z_simplex(theta: torch.Tensor) -> torch.Tensor:
"""Build points for a single triangle: 0, 1, infinity, and one movable point"""
Z = torch.empty(4, dtype=torch.complex128, device=theta.device)
Z[0] = 0 + 0j # origin
Z[1] = 1 + 0j # unit point
Z[2] = 1e10 + 0j # effectively infinity (large number)
Z[3] = torch.exp(1j * theta) # movable point on unit circle
return Z
def simplex_volume(theta: torch.Tensor, series_terms: int) -> torch.Tensor:
"""Compute volume of the single triangle formed by 0, 1, infinity, and exp(i*theta)"""
Z = build_Z_simplex(theta)
# Triangle vertices: 0, 1, exp(i*theta) (skipping infinity)
return triangle_volume_from_points_torch(Z[0], Z[1], Z[3], series_terms=series_terms)
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 = []
t0 = time.time()
for it in range(1, args.iters + 1):
def closure():
opt.zero_grad(set_to_none=True)
volume = simplex_volume(theta, args.series)
loss = -volume # maximize volume
loss.backward()
return loss
opt.step(closure)
# Log progress
with torch.no_grad():
vol = simplex_volume(theta, args.series)
history.append(vol.item())
if it % args.print_every == 0 or it in (1, args.iters):
grad_val = theta.grad.item() if theta.grad is not None else 0
print(f'[{it:03d}] volume = {history[-1]:.10f}, theta = {theta.item():.6f} rad ({theta.item() * 180/np.pi:.2f}°), grad = {grad_val:.6f}')
t1 = time.time()
# Final exact evaluation
with torch.no_grad():
from ideal_poly_volume_toolkit.geometry import triangle_volume_from_points
z0, z1, z3 = 0+0j, 1+0j, np.exp(1j * theta.item())
vol_exact = triangle_volume_from_points(z0, z1, z3, mode='exact', dps=250)
print('\n=== Simplex optimization done ===')
print(f'iters={args.iters}, time={t1-t0:.2f}s')
print(f'initial volume ~ {history[0] if history else args.init_angle:.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')
if __name__ == '__main__':
main() |