mathtool2/lib/tools/mixed_variance.dart

import 'package:flutter/material.dart';

import 'tool_kit.dart';

/// 混合方差 —— 工具页改造后的样板：输入框交给 [ToolScaffold]，算式交给 Symja。
///
///   总均值   μ = Σ nᵢmᵢ / Σ nᵢ
///   混合方差   = Σ nᵢ(vᵢ + (mᵢ-μ)²) / Σ nᵢ
///
/// 两个式子都要用到 μ，所以第二个式子把 μ 的定义整个代进去 —— 表达式长一点，
/// 但省掉了"先算一次、把结果拼回表达式里"这种来回。Symja 求值一次就够。
class MixedVariancePage extends StatefulWidget {
  const MixedVariancePage({super.key});

  @override
  State<MixedVariancePage> createState() => _MixedVariancePageState();
}

class _MixedVariancePageState extends State<MixedVariancePage> {
  // 字段要在 State 里建：主题一变（E-Ink、键盘弹出）页面会重建，
  // 建在 build 里的话控制器会被换掉，用户打的字就没了。
  final _sizes = ToolField('各层样本量 nᵢ', hint: '用空格分隔多个值');
  final _means = ToolField('各层均值 mᵢ', hint: '用空格分隔多个值');
  final _variances = ToolField('各层方差 vᵢ', hint: '用空格分隔多个值');

  @override
  Widget build(BuildContext context) => ToolScaffold(
        title: '混合方差',
        fields: [_sizes, _means, _variances],
        compute: (session) async {
          if (_sizes.count != _means.count ||
              _sizes.count != _variances.count) {
            throw Exception(
              '三组数据的个数必须一致（现在是 ${_sizes.count}、'
              '${_means.count}、${_variances.count}）',
            );
          }
          final n = _sizes.list;
          final m = _means.list;
          final v = _variances.list;
          final mu = 'Total[$n*$m]/Total[$n]';
          final mixed = 'Total[$n*($v+($m-($mu))^2)]/Total[$n]';
          return [
            ...await exactAndApprox(session, '总均值 μ', mu),
            ...await exactAndApprox(session, '混合方差', mixed),
          ];
        },
      );
}