85 lines
3.5 KiB
Python
85 lines
3.5 KiB
Python
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"""
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08_dps_level_k_bisection.py
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General, RESUMABLE bisection for the DPS level-k noise-robustness
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threshold of the Tiles state family. Each run performs STEPS_PER_RUN
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bisection steps and saves progress to a JSON state file, so you can call
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it repeatedly (e.g. in a shell loop, or across separate sessions) without
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losing progress -- useful since each SDP solve can take anywhere from
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under a second (k=2) to a few minutes (k=3, with SCS) depending on k,
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your hardware, and the solver.
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Usage:
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python3 08_dps_level_k_bisection.py
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Configure LEVEL, SOLVER, STEPS_PER_RUN, and EPS below.
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The state file is named dps_level{LEVEL}_bisection_state.json.
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--------------------------------------------------------------------
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Progress already made in the original chat session for LEVEL=3 (8 SCS
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solves, ~135-227s each) is included alongside this script as
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dps_level3_bisection_state.json:
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bracket so far: [0.90982, 0.91080] (i.e. p_c ~ 0.910-0.911)
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Just run this script (with LEVEL=3, the default) to continue narrowing
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it -- it will pick up automatically from that saved state. Delete the
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state file to start over, or change LEVEL to try a different extension
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order (4, 5, ... but see README.md for how fast the PPT-constraint size,
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and hence the cost, grows: 3*3^k).
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--------------------------------------------------------------------
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"""
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import json
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import os
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import time
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import cvxpy as cp
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from common import noisy_tiles
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from dps_hierarchy import build_dps_problem, dps_feasible
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LEVEL = 3
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SOLVER = cp.SCS # swap to cp.MOSEK if available -- likely much faster
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STEPS_PER_RUN = 1 # raise this if your machine/solver is fast enough
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EPS = 1e-5 # solver tolerance; tighten once you have a rough bracket
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DEFAULT_BRACKET = (0.70, 0.951) # 0.951 is a proven-safe upper bound (= DPS level-2 threshold,
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# since DPS level 3 can only detect at <= that noise level)
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STATE_FILE = f"dps_level{LEVEL}_bisection_state.json"
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if os.path.exists(STATE_FILE):
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with open(STATE_FILE) as f:
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state = json.load(f)
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print(f"Resuming from saved state: bracket [{state['lo']:.5f}, {state['hi']:.5f}], "
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f"{state['iter']} iterations so far.")
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else:
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state = {"lo": DEFAULT_BRACKET[0], "hi": DEFAULT_BRACKET[1], "iter": 0, "log": []}
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print(f"Starting fresh: bracket {DEFAULT_BRACKET}")
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prob, rho_param, sigma = build_dps_problem(d=3, k=LEVEL)
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print(f"sigma shape: {sigma.shape}, PPT-constraint (PSD cone) size: "
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f"{3 * 3 ** LEVEL} x {3 * 3 ** LEVEL}\n")
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for _ in range(STEPS_PER_RUN):
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lo, hi = state["lo"], state["hi"]
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mid = (lo + hi) / 2
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t0 = time.time()
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feasible = dps_feasible(prob, rho_param, noisy_tiles(mid), solver=SOLVER,
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eps=EPS, max_iters=20000, warm_start=True)
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dt = time.time() - t0
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if feasible:
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state["lo"] = mid
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else:
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state["hi"] = mid
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state["iter"] += 1
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state["log"].append({"iter": state["iter"], "p": mid, "feasible": feasible,
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"time_s": round(dt, 1), "status": prob.status})
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print(f"[iter {state['iter']}] p={mid:.5f} feasible={feasible} "
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f"status={prob.status} ({dt:.1f}s) "
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f"bracket now [{state['lo']:.5f}, {state['hi']:.5f}]")
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with open(STATE_FILE, "w") as f:
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json.dump(state, f, indent=2)
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print(f"\nCurrent bracket: [{state['lo']:.5f}, {state['hi']:.5f}] "
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f"(width {state['hi'] - state['lo']:.5f})")
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print("Run again to continue narrowing it further (progress is saved).")
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