SOR
78 lines
2.5 KiB
Python
78 lines
2.5 KiB
Python
import math
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from decimal import Decimal, ROUND_HALF_EVEN
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def get_decimal_places(data_strings):
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"""获取输入数据中小数点后的位数"""
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max_places = 0
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for s in data_strings:
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if '.' in s:
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places = len(s.split('.')[1])
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max_places = max(max_places, places)
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return max_places
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def calc_uncertainty(data_strs, res_str="0.05"):
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# 转换为 Decimal 进行高精度计算
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data = [Decimal(s) for s in data_strs]
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res = Decimal(res_str)
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n = len(data)
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# 1. 计算平均值
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places = get_decimal_places(data_strs)
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sum_val = sum(data)
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mean = sum_val / n
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# 修改：平均值修约使用“四舍六入五凑偶”
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mean_final = mean.quantize(Decimal('1.' + '0' * places), rounding=ROUND_HALF_EVEN)
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# 2. 计算标准差 s
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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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# 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_final, s, u_A, u_B, u
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def format_final_result(mean, u):
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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)
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# 找到第一位非零数字的位置
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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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# 修改：不确定度 u 的修约改为 ROUND_HALF_EVEN
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u_final = u.quantize(prec, rounding=ROUND_HALF_EVEN)
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# 修改：平均值修约保持一致
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mean_final = mean.quantize(prec, rounding=ROUND_HALF_EVEN)
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return f"f = {mean_final} ± {u_final}"
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if __name__ == "__main__":
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# ... (后续输入输出逻辑保持不变)
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print("请输入数据，用空格分隔：")
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raw_input = input().split()
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print("请输入仪器分度值（默认 0.05）：")
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res_input = input().strip() or "0.05"
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mean_f, s, u_A, u_B, u = calc_uncertainty(raw_input, res_input)
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print("\n--- 中间计算过程 (高精度展示) ---")
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print(f"平均值 (原始精度): {mean_f}")
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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_f, u)) |