mathtool2/lib/tools/histogram.dart

// tools/histogram.dart
import 'package:fl_chart/fl_chart.dart';
import 'package:flutter/material.dart';

import 'tool_kit.dart';

/// 直方图统计。
///
///   组中值 midᵢ = a + i·d + d/2（i 从 0 起）
///   均值 = Σ midᵢfᵢ
///   方差 = Σ (midᵢ-均值)²fᵢ
///   中位数 / 百分位数：累计频率首次超过目标 p 的那一组内插
///
/// 频率和、均值、方差、分位数全部交给 Symja 求精确值；图表要 double，
/// 才另跑一份 `N[...]` 的数值版。
class HistogramPage extends StatefulWidget {
  const HistogramPage({super.key});

  @override
  State<HistogramPage> createState() => _HistogramPageState();
}

class _HistogramPageState extends State<HistogramPage> {
  final _a = ToolField('左端点 a', hint: '如 0');
  final _d = ToolField('组距 d', hint: '如 1');
  final _f = ToolField('各组频率（用空格分隔）', hint: '用空格分隔多个值，和为 1');
  final _pct = ToolField('百分位数（可选）', hint: '留空则不算，如 3/4 或 0.75');

  @override
  Widget build(BuildContext context) => ToolScaffold(
    title: '直方图统计',
    fields: [_a, _d, _f, _pct],
    compute: (session) async {
      final a = _a.text, d = _d.text;
      if (a.isEmpty || d.isEmpty) throw Exception('请填写左端点 a 和组距 d');
      if (_f.count == 0) throw Exception('请至少填一个频率');
      final f = _f.list;

      // 频率之和必须为 1：交给 Symja 求 Total，再让 Symja 判等。
      //
      // 判等也要走 Symja：频率填小数时 `Total` 回的是 `1.0`，拿 Dart 的
      // 字符串去比 `1` 会把合法输入判成错的（用户实测反馈过）。
      final ok = await session.compute('Total[$f] == 1');
      if (ok.text != 'True') {
        final sum = await session.compute('Total[$f]');
        throw Exception('各组频率之和必须为 1，当前为 ${sum.text}');
      }

      // mid 在均值和方差两个式子里都要用，用嵌套 With 定义一次，避免重复一大串。
      final mean =
          'With[{a=$a,d=$d,f=$f}, '
          'With[{mid=Table[a+i*d+d/2,{i,0,Length[f]-1}]}, Total[mid*f]]]';
      final variance =
          'With[{a=$a,d=$d,f=$f}, '
          'With[{mid=Table[a+i*d+d/2,{i,0,Length[f]-1}]}, '
          'Total[(mid-Total[mid*f])^2*f]]]';

      final outputs = <ToolOutput>[
        ...await exactAndApprox(session, '均值', mean),
        ...await exactAndApprox(session, '方差', variance),
        ...await exactAndApprox(session, '中位数', _quantile(a, d, f, '1/2')),
      ];

      if (_pct.text.isNotEmpty) {
        outputs.addAll(
          await exactAndApprox(
            session,
            '${_pct.text} 百分位数',
            _quantile(a, d, f, _pct.text),
          ),
        );
      }

      // 图表：横轴标签 [左, 右)，左端点/右端点用精确值；柱高是频率密度 f/d，用数值。
      final lr = parseSymjaList(
        (await session.compute(
          'With[{a=$a,d=$d,f=$f}, Table[{a+i*d, a+(i+1)*d}, {i,0,Length[f]-1}]]',
        )).text,
      );
      final dens = parseSymjaList(
        (await session.compute(
          'With[{a=$a,d=$d,f=$f}, N[Table[f[[i+1]]/d, {i,0,Length[f]-1}], 8]]',
        )).text,
      ).map(asNumber).whereType<double>().toList(growable: false);
      if (lr.length == dens.length && dens.isNotEmpty) {
        outputs.add(ToolChart('直方图', _histChart(lr, dens)));
      }
      return outputs;
    },
  );

  /// 累计频率首次超过 p 的那一组内插。中位数把 p 取 1/2。
  String _quantile(String a, String d, String f, String p) =>
      'With[{a=$a,d=$d,f=$f,p=$p}, '
      'Module[{cum=Accumulate[f],k}, '
      'k=First[FirstPosition[cum, q_ /; q>p]]; '
      'a+(k-1)*d+(p-If[k==1,0,cum[[k-1]]])/f[[k]]*d]]';

  Widget _histChart(List<Object> lr, List<double> dens) {
    var maxD = 0.0;
    for (final v in dens) {
      if (v > maxD) maxD = v;
    }
    final labels = <String>[
      for (final item in lr)
        if (item is List && item.length == 2)
          '[${item[0]}, ${item[1]})'
        else
          '$item',
    ];

    return SizedBox(
      height: 400,
      child: BarChart(
        BarChartData(
          alignment: BarChartAlignment.spaceBetween,
          groupsSpace: 0,
          maxY: maxD == 0 ? 1.0 : maxD * 1.1,
          barTouchData: BarTouchData(enabled: false),
          borderData: FlBorderData(show: true),
          gridData: FlGridData(show: false),
          titlesData: FlTitlesData(
            bottomTitles: AxisTitles(
              sideTitles: SideTitles(
                showTitles: true,
                reservedSize: 40,
                getTitlesWidget: (value, meta) {
                  final i = value.toInt();
                  if (i < 0 || i >= labels.length) return const Text('');
                  return Padding(
                    padding: const EdgeInsets.only(top: 8),
                    child: Text(
                      labels[i],
                      style: const TextStyle(
                        fontSize: 10,
                        fontWeight: FontWeight.bold,
                      ),
                      textAlign: TextAlign.center,
                    ),
                  );
                },
              ),
            ),
            leftTitles: AxisTitles(
              sideTitles: SideTitles(
                showTitles: true,
                reservedSize: 40,
                getTitlesWidget: (value, meta) =>
                    Text(value.toStringAsFixed(2)),
              ),
            ),
            topTitles: AxisTitles(sideTitles: SideTitles(showTitles: false)),
            rightTitles: AxisTitles(sideTitles: SideTitles(showTitles: false)),
          ),
          barGroups: [
            for (var i = 0; i < dens.length; i++)
              BarChartGroupData(
                x: i,
                barRods: [
                  BarChartRodData(
                    toY: dens[i],
                    width: 16,
                    color: Colors.blue,
                    borderRadius: BorderRadius.zero,
                  ),
                ],
              ),
          ],
        ),
      ),
    );
  }
}