# TAB013-G-003 Smoke Testg0 解析锚点校验 # 校验目标 # 1. β1s≫1段线性衰减 ds/dt ≈ -1 # 2. β1s≫1区间 log(s) ~ log(t) 幂律斜率 ≈ -1/(β-1)容差±0.05 # 3. 提取过渡时间 t_transition验证β越大过渡越晚 # 4. 校验 T_half^m T_half^S分离随β增大 # 5. 顺带检验μ_debt饱和区行为 # 依赖numpy, scipy.integrate, scipy.stats import numpy as np from scipy.integrate import solve_ivp from scipy.stats import linregress # 全局参数和主扫描脚本保持完全一致 s_c 1.0 s_floor 1e-12 def ode_rhs(tau_tilde, s, beta): # g0版本 ODE rhs -s * (1.0 / ((1.0 s)**beta)) return rhs def mu_debt(s): return s / (s s_c) def solve_single_g0(beta, s0, t_end200, n_eval2000): t_eval np.linspace(0, t_end, n_eval) sol solve_ivp( funode_rhs, t_span(0, t_end), y0[s0], args(beta,), t_evalt_eval, methodLSODA, atol1e-9, rtol1e-7 ) if not sol.success: raise RuntimeError(fIntegration failed for beta{beta}) t sol.t s sol.y[0,:] mu mu_debt(s) return t, s, mu def calc_half_time(t_arr, val_arr, init_val): 求衰减到初值一半的时间 half_target init_val / 2 idx np.argmin(np.abs(val_arr - half_target)) return t_arr[idx] def smoke_g0_powerlaw(): print( START SMOKE TEST g0 ANALYTIC ANCHOR ) beta_list [1.0, 1.2, 1.5, 2.0, 3.0] s0 100.0 t_end 200.0 slope_tol 0.05 smoke_records [] for beta in beta_list: t, s, mu solve_single_g0(beta, s0, t_endt_end) # 半衰时间 T_half_S calc_half_time(t, s, s0) mu0 mu_debt(s0) T_half_m calc_half_time(t, mu, mu0) delta_T T_half_m - T_half_S # 定义幂律拟合窗口s0/10 s 10 mask_fit (s s0 / 10) (s 10) t_fit t[mask_fit] s_fit s[mask_fit] # 过渡时间t_transition首次满足 s s0/10 的时刻 trans_idx np.argmax(s s0/10) t_transition t[trans_idx] if np.any(s s0/10) else np.nan print(f --- beta {beta} ---) print(fT_half_S {T_half_S:.4f}, T_half_m {T_half_m:.4f}, ΔT {delta_T:.4f}) print(ft_transition {t_transition:.4f}) slope None theory_slope None fit_ok False if beta 1.0: # β1s1段线性衰减 ds/dt≈-1不做log-log拟合 print(β1 branch: linear decay regime (not powerlaw)) if len(t_fit) 10: # 线性拟合 s ~ t res linregress(t_fit, s_fit) slope_lin res.slope print(fLinear fit slope s~t: {slope_lin:.4f}, expected ~ -1.0) fit_ok True else: # β1log-log拟合 log(s) ~ log(t) theory_slope -1.0 / (beta - 1.0) if len(t_fit) 10: logt np.log10(t_fit) logs np.log10(s_fit) res linregress(logt, logs) slope res.slope print(fLog-log slope: {slope:.4f}, theoretical slope: {theory_slope:.4f}) # 断言校验 if np.abs(slope - theory_slope) slope_tol: fit_ok True print(f✓ Slope passed tolerance ±{slope_tol}) else: print(f✗ Slope OUTSIDE tolerance!) else: print(⚠️ Not enough points in power-law fitting window) smoke_records.append({ beta: beta, T_half_S: T_half_S, T_half_m: T_half_m, delta_T: delta_T, t_transition: t_transition, slope: slope, theory_slope: theory_slope, fit_ok: fit_ok }) # 全局校验β1ΔT随β单调递增 print( GLOBAL CHECK: ΔT separation trend ) high_beta_recs [r for r in smoke_records if r[beta]1.0] deltas [r[delta_T] for r in high_beta_recs] beta_vals [r[beta] for r in high_beta_recs] print(fβ sequence: {beta_vals}) print(fΔT sequence: {[f{d:.4f} for d in deltas]}) is_monotonic_inc np.all(np.diff(deltas) 0) if is_monotonic_inc: print(✓ ΔT T_half^m - T_half^S is monotonically increasing with β) else: print(✗ ΔT not monotonic increasing with β!) return smoke_records if __name__ __main__: rec smoke_g0_powerlaw()