{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 长度直接测量与不确定度评定\n",
    "\n",
    "本 Notebook 用于对多次长度直接测量数据进行 A 类不确定度、B 类不确定度及合成不确定度计算，并严格按照“四舍六入五凑偶”规则对测量结果进行科学修约与末位对齐。\n",
    "\n",
    "---\n",
    "### 实验原理与数学公式\n",
    "\n",
    "#### 1. 算术平均值与样本标准差\n",
    "对 $n$ 次独立等精度直接测量值 $x_1, x_2, \\dots, x_n$：\n",
    "$$\\bar{x} = \\frac{1}{n} \\sum_{i=1}^n x_i$$\n",
    "$$s = \\sqrt{\\frac{1}{n-1} \\sum_{i=1}^n (x_i - \\bar{x})^2}$$\n",
    "\n",
    "#### 2. A 类、B 类及合成不确定度\n",
    "* **A 类不确定度**（由有限次测量随机效应引起）：\n",
    "$$u_A = \\frac{s}{\\sqrt{n}}$$\n",
    "* **B 类不确定度**（由测量仪器极限误差 $\\Delta_{\\mathrm{inst}}$ 引起，假定均匀分布）：\n",
    "$$u_B = \\frac{\\Delta_{\\mathrm{inst}}}{\\sqrt{3}}$$\n",
    "* **合成标准不确定度**：\n",
    "$$u = \\sqrt{u_A^2 + u_B^2}$$\n",
    "\n",
    "#### 3. 修约与结果表示\n",
    "* 不确定度 $u$ 按照“四舍六入五凑偶”原则保留一位有效数字。\n",
    "* 测量平均值末位与不确定度的有效位数对齐。"
   ],
   "id": "1ed33dfddc944ff0"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from decimal import Decimal, ROUND_HALF_EVEN\n",
    "from python.utils import get_decimal_places, scientific_round\n",
    "\n",
    "print(\"工具函数加载完成。\")"
   ],
   "id": "709179017567e25d"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 测量数据与仪器参数设置\n",
    "> **提示**：直接在下方修改测量数据列表 `raw_data`（字符串或数值）与仪器分度值/允差 `res_str` 即可。"
   ],
   "id": "6e9499ceb295ab05"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 测量数据列表 (字符串格式保留输入精度)\n",
    "raw_data = [\"10.25\", \"10.24\", \"10.26\", \"10.25\", \"10.24\", \"10.25\"]\n",
    "\n",
    "# 仪器分度值 / 仪器误差限 Δ_inst\n",
    "res_str = \"0.05\"\n",
    "\n",
    "print(f\"输入测量数据 (n={len(raw_data)}): {raw_data}\")\n",
    "print(f\"仪器误差限 Δ_inst: {res_str}\")"
   ],
   "id": "722fceaefcc9ac13"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 不确定度计算与科学修约"
   ],
   "id": "376599ba7264087b"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_uncertainty(data_strs, res_str=\"0.05\"):\n",
    "    data = [Decimal(str(s)) for s in data_strs]\n",
    "    res = Decimal(str(res_str))\n",
    "    n = len(data)\n",
    "    \n",
    "    # 1. 原始精度平均值\n",
    "    places = get_decimal_places(data_strs)\n",
    "    sum_val = sum(data)\n",
    "    mean = sum_val / n\n",
    "    mean_final = mean.quantize(Decimal('1.' + '0' * places), rounding=ROUND_HALF_EVEN)\n",
    "    \n",
    "    # 2. 样本标准差 s\n",
    "    variance = sum((x - mean) ** 2 for x in data) / (n - 1) if n > 1 else Decimal(\"0\")\n",
    "    s = Decimal(str(math.sqrt(float(variance))))\n",
    "    \n",
    "    # 3. A 类不确定度\n",
    "    u_A = s / Decimal(str(math.sqrt(n))) if n > 1 else Decimal(\"0\")\n",
    "    \n",
    "    # 4. B 类不确定度\n",
    "    u_B = res / Decimal(str(math.sqrt(3)))\n",
    "    \n",
    "    # 5. 合成不确定度\n",
    "    u = Decimal(str(math.sqrt(float(u_A**2 + u_B**2))))\n",
    "    \n",
    "    return mean_final, mean, s, u_A, u_B, u\n",
    "\n",
    "mean_display, mean_raw, s, u_A, u_B, u = calc_uncertainty(raw_data, res_str)\n",
    "mean_final, u_final = scientific_round(mean_raw, u)\n",
    "\n",
    "print(\"=\" * 40)\n",
    "print(\"         长 度 测 量 不 确 定 度 分 析         \")\n",
    "print(\"=\" * 40)\n",
    "print(f\"测量次数 n         : {len(raw_data)}\")\n",
    "print(f\"算术平均值         : {mean_raw:.6f}\")\n",
    "print(f\"样本标准差 s       : {s:.6f}\")\n",
    "print(f\"A 类不确定度 u_A   : {u_A:.6f}\")\n",
    "print(f\"B 类不确定度 u_B   : {u_B:.6f}\")\n",
    "print(f\"合成不确定度 u     : {u:.6f}\")\n",
    "print(\"-\" * 40)\n",
    "print(f\"★ 最终修约结果    : L = {mean_final} ± {u_final}\")\n",
    "print(\"=\" * 40)"
   ],
   "id": "5fc60b2526bdc755"
  }
 ],
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