提取工具函数

utils/__init__.py

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+from utils.formatting import (
+    get_decimal_places,
+    scientific_round,
+    parse_angle_to_minutes,
+    format_minutes_as_angle
+)
+from utils.stats import (
+    calculate_stats,
+    linear_regression
+)
+from utils.io import (
+    input_float,
+    input_decimal,
+    input_int,
+    input_data_group
+)

utils/formatting.py

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+import math
+from decimal import Decimal, ROUND_HALF_EVEN
+
+def get_decimal_places(data_strings):
+    """获取输入数据中小数点后的位数，用于自适应展示"""
+    max_places = 0
+    for s in data_strings:
+        if '.' in s:
+            places = len(s.split('.')[1])
+            max_places = max(max_places, places)
+    return max_places
+
+def scientific_round(value, uncertainty):
+    """
+    按照“四舍六入五凑偶”修约：
+    1. 不确定度 u 保留一位有效数字
+    2. 平均值/结果末位与 u 对齐
+    """
+    if uncertainty <= 0:
+        return str(value), "0"
+    
+    d_val = Decimal(str(value))
+    d_unc = Decimal(str(uncertainty))
+    
+    u_float = float(d_unc)
+    first_digit_pos = math.floor(math.log10(u_float))
+    prec = Decimal('1e' + str(first_digit_pos))
+    
+    u_final = d_unc.quantize(prec, rounding=ROUND_HALF_EVEN)
+    val_final = d_val.quantize(prec, rounding=ROUND_HALF_EVEN)
+    
+    return val_final, u_final
+
+def parse_angle_to_minutes(s):
+    """
+    将输入解析为内部统一单位：分钟（Decimal）。
+    支持格式：
+    1. 'D.M' -> D度M分 (例如 '120.15' -> 120*60 + 15 = 7215分)
+    2. 'D' (纯数字无点) -> D度 (例如 '120' -> 120*60 = 7200分)
+    3. 'D.M.S' -> D度M分S秒 (例如 '120.15.30' -> 7215.5分)
+    """
+    parts = s.split('.')
+    if len(parts) == 1:
+        return Decimal(parts[0]) * 60
+    elif len(parts) == 2:
+        return Decimal(parts[0]) * 60 + Decimal(parts[1])
+    else:
+        res = Decimal(parts[0]) * 60 + Decimal(parts[1])
+        if len(parts) >= 3:
+            res += Decimal(parts[2]) / 60
+        return res
+
+def format_minutes_as_angle(minutes, prec=None):
+    """
+    将总分钟数转换为 D° M' 格式，支持保持对齐精度。
+    """
+    neg = minutes < 0
+    minutes = abs(minutes)
+    
+    d = int(minutes // 60)
+    m = minutes % 60
+    
+    if m >= 60:
+        d += 1
+        m -= 60
+        
+    if prec is not None and prec < 1:
+        places = abs(prec.as_tuple().exponent)
+        m_str = format(m, f'.{places}f')
+    else:
+        if m == int(m):
+            m_str = str(int(m))
+        else:
+            m_str = format(m, 'f').rstrip('0').rstrip('.')
+            
+    return f"{'-' if neg else ''}{d}°{m_str}'"

utils/io.py

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+from decimal import Decimal
+
+def input_float(prompt, default=None):
+    """输入一个浮点数值，支持默认值"""
+    while True:
+        try:
+            suffix = f" (默认 {default})" if default is not None else ""
+            val = input(f"{prompt}{suffix}: ").strip()
+            if not val and default is not None:
+                return float(default)
+            if not val:
+                continue
+            return float(val)
+        except Exception:
+            print("  输入无效，请输入数字。")
+
+def input_decimal(prompt, default=None):
+    """输入一个 Decimal 值，支持默认值"""
+    while True:
+        try:
+            suffix = f" (默认 {default})" if default is not None else ""
+            val = input(f"{prompt}{suffix}: ").strip()
+            if not val and default is not None:
+                return Decimal(str(default))
+            if not val:
+                continue
+            return Decimal(val)
+        except Exception:
+            print("  输入无效，请输入数字。")
+
+def input_int(prompt, default=None):
+    """输入一个整数，支持默认值"""
+    while True:
+        try:
+            suffix = f" (默认 {default})" if default is not None else ""
+            val = input(f"{prompt}{suffix}: ").strip()
+            if not val and default is not None:
+                return default
+            if not val:
+                continue
+            return int(val)
+        except Exception:
+            print("  输入无效，请输入整数。")
+
+def input_data_group(name, count, unit=""):
+    """输入一组重复测量的数值"""
+    prompt_unit = f" (单位: {unit})" if unit else ""
+    print(f"\n请输入 {name} 的 {count} 次测量值{prompt_unit}:")
+    data = []
+    for i in range(count):
+        while True:
+            try:
+                val = input(f"第 {i+1} 次 = ").strip()
+                if not val: continue
+                data.append(Decimal(val))
+                break
+            except Exception:
+                print("输入无效，请输入数字。")
+    return data

utils/stats.py

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