fix(solve): 审查 mm1_metrics + 第二批入口改动（工程侧收口 + 6 条测试）
用户本轮改了 markov_simulate / markov_steady_state 的入口校验，并写完 mm1_metrics，
三处算法本体都正确（mm1 的 5 个公式经探针与闭式解逐位对拍通过，含 W = Wq + 1/mu）。
Codex 只动工程侧：
Fixed
- mm1_metrics 的稳定性分界 "<" 应为 "<="（docstring 与既有测试的口径都是 lambda >= mu 不稳定）：
lambda == mu 原先掉进 try、rho == 1.0 触发 ZeroDivisionError，被 except 吞成 success=False。
两个分支的可观测输出完全相同（success=False / metrics={} / data=None），只有 message 不同，
故按决策 31 直接修并加回归测试，未改动任何口径。
- 三处报错文案的参数名抄错：markov_steady_state 的 max_iter <= 0 写成 "tol 必须是正数"，
mm1_metrics 的 service_rate 两条报错都写成 "tol"；半角逗号统一为全角。
Changed
- mm1_metrics 的 docstring 补 Raises 与 data 说明；call_params = {...} 补空格；
ruff 6 条（W293 x5 / F541 f-string 无占位符 / W292 文件末尾无换行）。
- markov_steady_state 的 try 前 3 个空行 -> 1；"异常: " -> "异常："。
- tests/test_solve.py：摘掉 2 条 mm1_metrics 的 skip，新增 4 条（lambda == mu 的回归、
非负校验回归、max_iter=3 未收敛判 success=False）。
- STATUS.md 决策 56 / 57 更新办结项 + 新增决策 58（mm1 的 4 条待拍板）；CHANGELOG；易错点 29。
校验：pytest 202 passed / 28 skipped（230 收集）；ruff 0；pyright 0
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@@ -521,6 +521,8 @@ def markov_simulate(
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arr, _ = as_array(transition)
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if arr.ndim != 2 or arr.shape[0] != arr.shape[1]:
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raise ValueError(f"transition 必须是二维方阵，你传入的形状是 {arr.shape}")
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if np.any(arr < 0):
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raise ValueError("transition 矩阵的元素必须是非负的（概率不能为负）")
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if not np.allclose(arr.sum(axis=1), 1.0):
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raise ValueError("transition 每一行的和必须是 1.0")
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s = arr.shape[0]
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@@ -638,19 +640,30 @@ def markov_steady_state(transition: Any, max_iter: int | np.integer = 10000, tol
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arr, _ = as_array(transition)
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if arr.ndim != 2 or arr.shape[0] != arr.shape[1]:
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raise ValueError(f"transition 必须是二维方阵，你传入的形状是 {arr.shape}")
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if np.any(arr < 0):
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raise ValueError("transition 矩阵的元素必须是非负的（概率不能为负）")
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if not np.allclose(arr.sum(axis=1), 1.0):
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raise ValueError("transition 每一行的和必须是 1.0")
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if isinstance(max_iter, bool) or not isinstance(max_iter, (int, np.integer)):
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raise ValueError(f"max_iter 必须是正整数，你传入了 {type(max_iter).__name__}")
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if max_iter <= 0:
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raise ValueError(f"max_iter 必须是正整数，你传入了 {max_iter}")
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if not isinstance(tol, (int, float)) or isinstance(tol, bool):
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raise TypeError(f"tol 必须是浮点数，你传入了 {type(tol).__name__}")
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if tol <= 0:
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raise ValueError(f"tol 必须是正数，你传入了 {tol}")
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s = arr.shape[0]
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v = np.full(s, 1.0 / s)
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iterations = 0
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converged = False
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if isinstance(max_iter, bool) or not isinstance(max_iter, (int, np.integer)) or max_iter <= 0:
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raise ValueError(f"max_iter 必须是正整数，你传入了 {max_iter}")
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if not isinstance(tol, (int, float)) or tol <= 0:
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raise ValueError(f"tol 必须是正数，你传入了 {tol}")
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call_params = {
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"transition": arr.tolist(),
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"max_iter": max_iter,
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"tol": tol,
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}
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try:
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for _ in range(max_iter):
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@@ -670,21 +683,20 @@ def markov_steady_state(transition: Any, max_iter: int | np.integer = 10000, tol
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return Result(
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name="markov_steady_state",
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params={"max_iter": max_iter, "tol": tol},
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params=call_params,
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metrics=metrics,
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data=v,
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success=True,
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message=f"平稳分布求解{'成功' if converged else '未完全收敛'}，迭代 {iterations} 次。"
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success=converged,
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message=f"平稳分布求解{'成功' if converged else '失败：未在最大迭代次数内收敛'}，迭代 {iterations} 次。"
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)
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except Exception as e:
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return Result(
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name="markov_steady_state",
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params={"max_iter": max_iter, "tol": tol},
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params=call_params,
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metrics={},
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data=None,
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success=False,
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message=f"平稳分布求解失败：{type(e).__name__} - {str(e)}"
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message=f"平稳分布求解异常：{type(e).__name__} - {str(e)}"
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)
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@@ -700,7 +712,15 @@ def mm1_metrics(arrival_rate: float, service_rate: float) -> Any:
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Returns
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-------
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`Result`：`metrics={"rho", "L", "Lq", "W", "Wq"}`
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（系统利用率、系统内平均顾客数、队列长度、平均逗留时间、平均等待时间）。
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（系统利用率、系统内平均顾客数、队列长度、平均逗留时间、平均等待时间）；
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`data` 与 `metrics` 同值（闭式解没有样本数组）。
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Raises
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------
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TypeError:
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`arrival_rate` / `service_rate` 不是数值（`bool` 也判非法）。
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ValueError:
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`arrival_rate` / `service_rate` 不是正数。
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Notes
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-----
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@@ -714,5 +734,58 @@ def mm1_metrics(arrival_rate: float, service_rate: float) -> Any:
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>>> round(r.metrics["rho"], 4)
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0.6667
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"""
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# TODO(L1)
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raise NotImplementedError
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if not isinstance(arrival_rate, (int, float)) or isinstance(arrival_rate, bool):
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raise TypeError(f"arrival_rate 必须是浮点数，你传入了 {type(arrival_rate).__name__}")
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if arrival_rate <= 0:
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raise ValueError(f"arrival_rate 必须是正数，你传入了 {arrival_rate}")
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if not isinstance(service_rate, (int, float)) or isinstance(service_rate, bool):
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raise TypeError(f"service_rate 必须是浮点数，你传入了 {type(service_rate).__name__}")
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if service_rate <= 0:
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raise ValueError(f"service_rate 必须是正数，你传入了 {service_rate}")
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call_params = {"arrival_rate": arrival_rate, "service_rate": service_rate}
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if service_rate <= arrival_rate:
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return Result(
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name="mm1_metrics",
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params=call_params,
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metrics={},
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data=None,
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success=False,
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message="系统不稳定：到达率 λ 大于等于服务率 μ，队列长度无界，无法计算闭式解。"
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)
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try:
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rho = arrival_rate / service_rate
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L = rho / (1.0 - rho) # 系统内平均顾客数
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Lq = rho ** 2 / (1.0 - rho) # 队列中平均等待顾客数
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W = 1.0 / (service_rate - arrival_rate) # 平均逗留时间
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Wq = W - 1.0 / service_rate # 平均等待时间
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# 4. 封装返回
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metrics = {
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"rho": float(rho),
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"L": float(L),
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"Lq": float(Lq),
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"W": float(W),
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"Wq": float(Wq)
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}
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return Result(
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name="mm1_metrics",
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params=call_params,
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metrics=metrics,
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data=metrics,
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success=True,
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message="M/M/1 排队系统指标计算成功。"
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)
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except Exception as e:
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return Result(
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name="mm1_metrics",
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params=call_params,
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metrics={},
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data=None,
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success=False,
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message=f"计算失败：{type(e).__name__} - {str(e)}"
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)
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