SOR
82 lines
2.6 KiB
Python
82 lines
2.6 KiB
Python
import math
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from decimal import Decimal
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from utils import (
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parse_angle_to_minutes,
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format_minutes_as_angle,
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scientific_round
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)
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def calc_uncertainty(data_strs, res_str="1"):
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# 转换为分钟进行高精度计算
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data = [parse_angle_to_minutes(s) for s in data_strs]
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res = Decimal(res_str) # 仪器误差，单位：分
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n = len(data)
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# 1. 计算平均值
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sum_val = sum(data)
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mean = sum_val / n
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# 2. 计算标准差 s
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if n > 1:
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variance = sum((x - mean) ** 2 for x in data) / (n - 1)
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s = Decimal(str(math.sqrt(float(variance))))
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else:
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s = Decimal('0')
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# 3. A类不确定度 u_A
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u_A = s / Decimal(str(math.sqrt(n)))
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# 4. B类不确定度 u_B (仪器误差)
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u_B = res / Decimal(str(math.sqrt(3)))
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# 5. 合成不确定度 u
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u = Decimal(str(math.sqrt(float(u_A**2 + u_B**2))))
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return mean, s, u_A, u_B, u
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def format_final_result(mean_minutes, u_minutes):
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"""
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按照“四舍六入五凑偶”修约：
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1. 不确定度 u 保留一位有效数字
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2. 平均值末位与 u 对齐
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"""
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u_float = float(u_minutes)
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if u_float == 0:
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return f"θ = {format_minutes_as_angle(mean_minutes)} ± 0'"
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first_digit_pos = math.floor(math.log10(u_float))
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prec = Decimal('1e' + str(first_digit_pos))
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mean_final_val, u_final = scientific_round(mean_minutes, u_minutes)
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mean_str = format_minutes_as_angle(mean_final_val, prec)
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u_str = f"{u_final}'"
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return f"θ = {mean_str} ± {u_str}"
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if __name__ == "__main__":
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print("=== 角度不确定度计算器 ===")
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print("输入格式: '度.分' (如 120.15 表示 120°15')，多个数据用空格隔开。")
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try:
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user_input = input("请输入数据：").split()
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if not user_input:
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print("未输入数据！")
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else:
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res_input = input("请输入仪器分度值 (单位: 分，默认 1)：").strip() or "1"
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mean_v, s, u_A, u_B, u = calc_uncertainty(user_input, res_input)
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print("\n--- 中间计算过程 ---")
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print(f"平均值: {format_minutes_as_angle(mean_v)} ({mean_v:.4f}')")
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print(f"标准差 s: {s:.6f}'")
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print(f"A类不确定度 u_A: {u_A:.6f}'")
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print(f"B类不确定度 u_B: {u_B:.6f}'")
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print(f"合成不确定度 u: {u:.6f}'")
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print("\n--- 最终修约结果 (四舍六入五凑偶) ---")
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print(format_final_result(mean_v, u))
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except Exception as e:
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print(f"错误: {e}") |