"""
07_dps_level3_single.py

A single DPS level-3 feasibility check on the pure Tiles state, to confirm
the construction works and see its cost before committing to a full
noise-threshold bisection (see 08_dps_level_k_bisection.py).

In the original sandbox this took ~137s with SCS (single solve, cold
start). Expect similar or better on a modern laptop; likely far faster
with an interior-point solver (MOSEK, if you have a license) since the
PSD cone here (81x81 complex Hermitian) is small by modern SDP standards
-- SCS is a first-order method tuned for large sparse problems and is not
especially fast on small/dense feasibility problems like this one.

Expected result: status "infeasible" (i.e. entanglement IS detected).
"""
import time
import cvxpy as cp
from common import RHO_TILES
from dps_hierarchy import build_dps_problem, dps_feasible

SOLVER = cp.SCS  # try cp.MOSEK if available -- likely much faster at this size

prob, rho_param, sigma = build_dps_problem(d=3, k=3)
print(f"sigma shape: {sigma.shape}   "
      f"PPT-constraint (PSD cone) size: {3 * 3 ** 3} x {3 * 3 ** 3}")

t0 = time.time()
ok = dps_feasible(prob, rho_param, RHO_TILES, solver=SOLVER, eps=1e-6, max_iters=20000)
print(f"DPS level-3 feasible: {ok}  status={prob.status}  [{time.time() - t0:.1f}s]")