SOR
60 lines
1.8 KiB
Python
60 lines
1.8 KiB
Python
import math
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from decimal import Decimal
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def calculate_stats(data_list, delta_inst):
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"""
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计算一组数据的平均值、A类、B类及合成不确定度。
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支持输入 list of Decimal 或 list of float/str/int。
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返回: (mean, u_combined, u_a, u_b, s)
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"""
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n = len(data_list)
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decimal_data = [Decimal(str(x)) for x in data_list]
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mean = sum(decimal_data) / Decimal(n)
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if n > 1:
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variance = sum((x - mean)**2 for x in decimal_data) / Decimal(n - 1)
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s = Decimal(str(math.sqrt(float(variance))))
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u_a = s / Decimal(str(math.sqrt(n)))
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else:
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s = Decimal("0")
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u_a = Decimal("0")
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u_b = Decimal(str(delta_inst)) / Decimal(str(math.sqrt(3)))
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u_combined = Decimal(str(math.sqrt(float(u_a**2 + u_b**2))))
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return mean, u_combined, u_a, u_b, s
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def linear_regression(x_list, y_list):
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"""
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最小二乘法线性回归: y = k·x + b
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返回: (k, b, r, u_k)
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u_k = |k| · √[(1/r² − 1) / (n − 2)]
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支持 input numbers as Decimal or float.
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"""
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n = len(x_list)
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x_dec = [Decimal(str(x)) for x in x_list]
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y_dec = [Decimal(str(y)) for y in y_list]
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x_mean = sum(x_dec) / Decimal(n)
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y_mean = sum(y_dec) / Decimal(n)
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L_xx = sum((x - x_mean)**2 for x in x_dec)
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L_yy = sum((y - y_mean)**2 for y in y_dec)
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L_xy = sum((x_dec[i] - x_mean) * (y_dec[i] - y_mean) for i in range(n))
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k = L_xy / L_xx if L_xx != 0 else Decimal("0")
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b = y_mean - k * x_mean
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denom = Decimal(str(math.sqrt(float(L_xx * L_yy)))) if L_xx * L_yy > 0 else Decimal("1")
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r = L_xy / denom
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r_float = float(r)
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if abs(r_float) < 1.0 and n > 2:
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u_k_float = float(abs(k)) * math.sqrt((1.0 / (r_float**2) - 1.0) / (n - 2))
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else:
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u_k_float = 0.0
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u_k = Decimal(str(u_k_float))
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return k, b, r, u_k
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