Added LinearODE

internbootcamp/bootcamp/linearODE/linearODE.py

@@ -0,0 +1,78 @@
+import re
+import json
+import numpy as np
+from scipy.integrate import odeint
+from internbootcamp.bootcamp.base import Basebootcamp
+
+
+class LinearODEBootcamp(Basebootcamp):
+    def __init__(
+        self,
+        k_range=(0.1, 1.0),
+        x0_range=(0.5, 2.0),
+        t_span=(0, 5),
+        n_points=50,
+        seed=None
+    ):
+        self.k_range, self.x0_range = k_range, x0_range
+        self.t0, self.t1 = t_span
+        self.n_points = n_points
+        if seed is not None:
+            np.random.seed(seed)
+
+    def case_generator(self):
+        # 1. 随机采样参数 k 和初始值 x0
+        k = float(np.random.uniform(*self.k_range))
+        x0 = float(np.random.uniform(*self.x0_range))
+        # 2. 构造时间序列并模拟 dx/dt = -k * x
+        t = np.linspace(self.t0, self.t1, self.n_points).tolist()
+        def model(x, t_val):
+            return -k * x
+        x = odeint(model, x0, t).flatten().tolist()
+        return {"t": t, "x": x, "k": k}
+
+    def prompt_func(self, identity) -> str:
+        # 将 (t, x) 对格式化为提示
+        points = ", ".join(f"({t:.2f}, {x:.2f})"
+                           for t, x in zip(identity["t"], identity["x"]))
+        return (
+            f"下面给出变量 x(t) 的观测数据点：\n{points}\n\n"
+            "请找出其满足的微分方程，形式为：dx/dt = f(x)。\n"
+            "只需返回 “dx/dt = <表达式>”。"
+        )
+
+    @staticmethod
+    def extract_output(output: str) -> str:
+        # 用正则提取“dx/dt = …”右侧的表达式
+        m = re.search(r"dx/dt\s*=\s*([^\n\r]+)", output)
+        return m.group(1).strip() if m else None
+
+    @classmethod
+    def _verify_correction(cls, solution: str, identity: dict) -> bool:
+        # 解析 LLM 给出的系数 c，形如 “c*x”
+        sol = solution.replace(" ", "")
+        match = re.fullmatch(r"([\-0-9\.eE]+)\*x", sol)
+        if not match:
+            return False
+        c = float(match.group(1))
+        # 验证 c ≈ -k
+        return abs(c + identity["k"]) < 1e-2
+
+
+if __name__ == "__main__":
+    bootcamp = LinearODEBootcamp(seed=123)
+    # 生成几个样例
+    examples = [bootcamp.case_generator() for _ in range(3)]
+
+    for identity in examples:
+        # 构造“模型”返回答案，模拟 LLM 的输出
+        coeff = -identity["k"]
+        sol = f"{coeff:.4f}*x"
+        # 调用 Basebootcamp 提供的 verify_score 接口进行验证
+        score = bootcamp.verify_score(sol, identity, short_threshold=1e-2)
+        # 打印结果
+        print(json.dumps({
+            "identity": identity,
+            "solution": sol,
+            "verify_score": score
+        }, ensure_ascii=False, indent=2))