mathtool/lib/tools/convolution_calculator.dart

// tools/convolution_calculator.dart
import 'package:flutter/material.dart';
import 'package:rational/rational.dart';

class ConvolutionCalculatorPage extends StatefulWidget {
  @override
  _ConvolutionCalculatorPageState createState() => _ConvolutionCalculatorPageState();
}

class _ConvolutionCalculatorPageState extends State<ConvolutionCalculatorPage> {
  final List<TextEditingController> _xValueControllers = [];
  final List<TextEditingController> _xProbControllers = [];
  final List<TextEditingController> _yValueControllers = [];
  final List<TextEditingController> _yProbControllers = [];
  
  List<Map<String, Rational>> _convolutionResult = [];
  bool _showResult = false;

  @override
  void initState() {
    super.initState();
    // 初始化默认数据
    _initializeDefaultData();
  }

  void _initializeDefaultData() {
    // 添加X的默认数据
    _addXRow(value: '0', prob: '1/2');
    _addXRow(value: '1', prob: '1/2');
    
    // 添加Y的默认数据
    _addYRow(value: '0', prob: '1/3');
    _addYRow(value: '1', prob: '1/3');
    _addYRow(value: '2', prob: '1/3');
  }

  void _addXRow({String value = '', String prob = ''}) {
    setState(() {
      _xValueControllers.add(TextEditingController(text: value));
      _xProbControllers.add(TextEditingController(text: prob));
    });
  }

  void _removeXRow(int index) {
    setState(() {
      _xValueControllers.removeAt(index);
      _xProbControllers.removeAt(index);
    });
  }

  void _addYRow({String value = '', String prob = ''}) {
    setState(() {
      _yValueControllers.add(TextEditingController(text: value));
      _yProbControllers.add(TextEditingController(text: prob));
    });
  }

  void _removeYRow(int index) {
    setState(() {
      _yValueControllers.removeAt(index);
      _yProbControllers.removeAt(index);
    });
  }

  Rational _parseRational(String input) {
    try {
      if (input.contains('/')) {
        List<String> parts = input.split('/');
        if (parts.length == 2) {
          return Rational.parse(parts[0].trim()) / Rational.parse(parts[1].trim());
        }
      }
      return Rational.parse(input.trim());
    } catch (e) {
      throw FormatException('无效的概率格式: $input');
    }
  }

  void _calculateConvolution() {
    try {
      // 解析X分布
      Map<Rational, Rational> xDistribution = {};
      Rational xSum = Rational.zero;
      for (int i = 0; i < _xValueControllers.length; i++) {
        Rational value = _parseRational(_xValueControllers[i].text);
        Rational prob = _parseRational(_xProbControllers[i].text);
        xDistribution[value] = prob;
        xSum += prob;
      }

      // 解析Y分布
      Map<Rational, Rational> yDistribution = {};
      Rational ySum = Rational.zero;
      for (int i = 0; i < _yValueControllers.length; i++) {
        Rational value = _parseRational(_yValueControllers[i].text);
        Rational prob = _parseRational(_yProbControllers[i].text);
        yDistribution[value] = prob;
        ySum += prob;
      }

      // 验证概率和是否为1
      if (xSum != Rational.one) {
        throw FormatException('X的概率和必须为1，当前为: $xSum');
      }
      if (ySum != Rational.one) {
        throw FormatException('Y的概率和必须为1，当前为: $ySum');
      }

      // 计算卷积
      Map<Rational, Rational> convolution = {};
      for (var xEntry in xDistribution.entries) {
        for (var yEntry in yDistribution.entries) {
          Rational sumValue = xEntry.key + yEntry.key;
          Rational prob = xEntry.value * yEntry.value;
          convolution[sumValue] = (convolution[sumValue] ?? Rational.zero) + prob;
        }
      }

      // 转换为列表并排序
      _convolutionResult = convolution.entries
          .map((entry) => {'value': entry.key, 'probability': entry.value})
          .toList();
      
      _convolutionResult.sort((a, b) => a['value']!.compareTo(b['value']!));

      setState(() {
        _showResult = true;
      });

    } catch (e) {
      _showErrorDialog(e.toString());
    }
  }

  void _showErrorDialog(String message) {
    showDialog(
      context: context,
      builder: (context) => AlertDialog(
        title: Text('计算错误'),
        content: Text(message),
        actions: [
          TextButton(
            onPressed: () => Navigator.of(context).pop(),
            child: Text('确定'),
          ),
        ],
      ),
    );
  }

  void _clearAll() {
    setState(() {
      _xValueControllers.clear();
      _xProbControllers.clear();
      _yValueControllers.clear();
      _yProbControllers.clear();
      _convolutionResult.clear();
      _showResult = false;
      _initializeDefaultData();
    });
  }

  @override
  void dispose() {
    for (var controller in _xValueControllers) {
      controller.dispose();
    }
    for (var controller in _xProbControllers) {
      controller.dispose();
    }
    for (var controller in _yValueControllers) {
      controller.dispose();
    }
    for (var controller in _yProbControllers) {
      controller.dispose();
    }
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('卷积分布列计算'),
        backgroundColor: Colors.white,
        elevation: 1,
        actions: [
          IconButton(
            icon: Icon(Icons.clear_all),
            onPressed: _clearAll,
            tooltip: '清空所有',
          ),
        ],
      ),
      body: SingleChildScrollView(
        padding: EdgeInsets.all(16),
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.start,
          children: [
            _buildDistributionInput('随机变量 X 的分布列', _xValueControllers, _xProbControllers, _addXRow, _removeXRow),
            SizedBox(height: 24),
            _buildDistributionInput('随机变量 Y 的分布列', _yValueControllers, _yProbControllers, _addYRow, _removeYRow),
            SizedBox(height: 24),
            Center(
              child: ElevatedButton.icon(
                onPressed: _calculateConvolution,
                icon: Icon(Icons.calculate),
                label: Text('计算卷积分布列'),
                style: ElevatedButton.styleFrom(
                  padding: EdgeInsets.symmetric(horizontal: 24, vertical: 12),
                ),
              ),
            ),
            SizedBox(height: 24),
            if (_showResult) _buildResultTable(),
          ],
        ),
      ),
    );
  }

  Widget _buildDistributionInput(
    String title,
    List<TextEditingController> valueControllers,
    List<TextEditingController> probControllers,
    VoidCallback onAdd,
    Function(int) onRemove,
  ) {
    return Card(
      elevation: 2,
      child: Padding(
        padding: EdgeInsets.all(16),
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.start,
          children: [
            Text(
              title,
              style: TextStyle(fontSize: 18, fontWeight: FontWeight.bold),
            ),
            SizedBox(height: 16),
            _buildTableHeader(),
            SizedBox(height: 8),
            ...List.generate(valueControllers.length, (index) {
              return _buildInputRow(
                valueControllers[index],
                probControllers[index],
                index,
                onRemove,
                valueControllers.length,
              );
            }),
            SizedBox(height: 16),
            Center(
              child: OutlinedButton.icon(
                onPressed: onAdd,
                icon: Icon(Icons.add, size: 18),
                label: Text('添加一行'),
              ),
            ),
          ],
        ),
      ),
    );
  }

  Widget _buildTableHeader() {
    return Row(
      children: [
        Expanded(
          flex: 2,
          child: Text('取值', style: TextStyle(fontWeight: FontWeight.bold)),
        ),
        SizedBox(width: 16),
        Expanded(
          flex: 3,
          child: Text('概率 (支持分数如 1/2)', style: TextStyle(fontWeight: FontWeight.bold)),
        ),
        SizedBox(width: 16),
        Expanded(
          flex: 1,
          child: Text('操作', style: TextStyle(fontWeight: FontWeight.bold)),
        ),
      ],
    );
  }

  Widget _buildInputRow(
    TextEditingController valueController,
    TextEditingController probController,
    int index,
    Function(int) onRemove,
    int totalRows,
  ) {
    return Padding(
      padding: EdgeInsets.symmetric(vertical: 8),
      child: Row(
        children: [
          Expanded(
            flex: 2,
            child: TextField(
              controller: valueController,
              decoration: InputDecoration(
                hintText: '如: 0, 1, 2...',
                border: OutlineInputBorder(),
                contentPadding: EdgeInsets.symmetric(horizontal: 12, vertical: 8),
              ),
              keyboardType: TextInputType.numberWithOptions(signed: true, decimal: true),
            ),
          ),
          SizedBox(width: 16),
          Expanded(
            flex: 3,
            child: TextField(
              controller: probController,
              decoration: InputDecoration(
                hintText: '如: 1/2, 0.25, 0.3',
                border: OutlineInputBorder(),
                contentPadding: EdgeInsets.symmetric(horizontal: 12, vertical: 8),
              ),
            ),
          ),
          SizedBox(width: 16),
          Expanded(
            flex: 1,
            child: IconButton(
              icon: Icon(Icons.remove_circle, color: Colors.red),
              onPressed: totalRows > 1 ? () => onRemove(index) : null,
              tooltip: '删除此行',
            ),
          ),
        ],
      ),
    );
  }

  Widget _buildResultTable() {
    return Card(
      elevation: 2,
      color: Colors.green[50],
      child: Padding(
        padding: EdgeInsets.all(16),
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.start,
          children: [
            Text(
              '卷积分布列 X + Y',
              style: TextStyle(
                fontSize: 18,
                fontWeight: FontWeight.bold,
                color: Colors.green[800],
              ),
            ),
            SizedBox(height: 16),
            _buildResultTableHeader(),
            ..._convolutionResult.map(_buildResultRow).toList(),
            SizedBox(height: 16),
            _buildProbabilitySum(),
          ],
        ),
      ),
    );
  }

  Widget _buildResultTableHeader() {
    return Container(
      padding: EdgeInsets.symmetric(vertical: 12, horizontal: 16),
      decoration: BoxDecoration(
        color: Colors.green[100],
        borderRadius: BorderRadius.vertical(top: Radius.circular(8)),
      ),
      child: Row(
        children: [
          Expanded(
            child: Text('X + Y 取值', style: TextStyle(fontWeight: FontWeight.bold)),
          ),
          Expanded(
            child: Text('概率 (分数)', style: TextStyle(fontWeight: FontWeight.bold)),
          ),
          Expanded(
            child: Text('概率 (小数)', style: TextStyle(fontWeight: FontWeight.bold)),
          ),
        ],
      ),
    );
  }

  Widget _buildResultRow(Map<String, Rational> entry) {
    Rational value = entry['value']!;
    Rational probability = entry['probability']!;
    double decimalProb = probability.toDouble();

    return Container(
      padding: EdgeInsets.symmetric(vertical: 12, horizontal: 16),
      decoration: BoxDecoration(
        border: Border(bottom: BorderSide(color: Colors.green[100]!)),
      ),
      child: Row(
        children: [
          Expanded(
            child: Text(
              value.toString(),
              style: TextStyle(fontSize: 16),
            ),
          ),
          Expanded(
            child: Text(
              _toFractionString(probability),
              style: TextStyle(fontSize: 16, fontFamily: 'Monospace'),
            ),
          ),
          Expanded(
            child: Text(
              decimalProb.toStringAsFixed(6),
              style: TextStyle(fontSize: 16, fontFamily: 'Monospace'),
            ),
          ),
        ],
      ),
    );
  }

  String _toFractionString(Rational rational) {
    if (rational.denominator == BigInt.one) {
      return rational.numerator.toString();
    }
    return '${rational.numerator}/${rational.denominator}';
  }

  Widget _buildProbabilitySum() {
    Rational total = _convolutionResult.fold(
      Rational.zero,
      (sum, entry) => sum + entry['probability']!,
    );

    return Container(
      padding: EdgeInsets.all(12),
      decoration: BoxDecoration(
        color: Colors.green[100],
        borderRadius: BorderRadius.circular(8),
      ),
      child: Row(
        mainAxisAlignment: MainAxisAlignment.spaceBetween,
        children: [
          Text('概率总和:', style: TextStyle(fontWeight: FontWeight.bold)),
          Text(
            '${_toFractionString(total)} = ${total.toDouble().toStringAsFixed(6)}',
            style: TextStyle(fontWeight: FontWeight.bold, fontFamily: 'Monospace'),
          ),
        ],
      ),
    );
  }
}