mathtool2/lib/tools/bisection_method.dart

// tools/bisection_method.dart
import 'package:flutter/material.dart';
import 'package:math_expressions/math_expressions.dart';

class BisectionMethodPage extends StatefulWidget {
  @override
  _BisectionMethodPageState createState() => _BisectionMethodPageState();
}

class _BisectionMethodPageState extends State<BisectionMethodPage> {
  final TextEditingController _functionController = TextEditingController(text: 'x^3 - x - 2');
  final TextEditingController _aController = TextEditingController(text: '1');
  final TextEditingController _bController = TextEditingController(text: '2');
  final TextEditingController _toleranceController = TextEditingController(text: '0.0001');
  final TextEditingController _maxIterationsController = TextEditingController(text: '100');

  List<String> _iterations = [];
  String _result = '';
  bool _isCalculating = false;

  // 使用 math_expressions 库计算数学表达式
  double _evaluateFunction(String function, double x) {
    try {
      // 预处理函数表达式
      String exprString = function
          .replaceAll(' ', '')
          .replaceAll('×', '*')
          .replaceAll('÷', '/');
      
      // 创建解析器
      Parser p = Parser();
      
      // 解析表达式
      Expression expression = p.parse(exprString);
      
      // 创建上下文并绑定变量 x
      ContextModel contextModel = ContextModel()
        ..bindVariable(Variable('x'), Number(x));
      
      // 计算表达式
      double result = expression.evaluate(EvaluationType.REAL, contextModel);
      
      return result;
    } catch (e) {
      throw Exception('函数表达式解析错误: $e\n请检查表达式格式是否正确');
    }
  }

  void _calculate() {
    setState(() {
      _isCalculating = true;
      _iterations.clear();
      _result = '';
    });

    try {
      double a = double.parse(_aController.text);
      double b = double.parse(_bController.text);
      double tolerance = double.parse(_toleranceController.text);
      int maxIterations = int.parse(_maxIterationsController.text);
      String function = _functionController.text;

      if (a >= b) {
        throw Exception('区间左端点必须小于右端点');
      }

      double fa = _evaluateFunction(function, a);
      double fb = _evaluateFunction(function, b);

      if (fa.isNaN || fb.isNaN) {
        throw Exception('函数在端点处计算失败，请检查表达式');
      }

      if (fa * fb > 0) {
        throw Exception('函数在区间两端点必须异号\nf(a) = $fa, f(b) = $fb');
      }

      int iteration = 0;
      double c = a;

      while ((b - a).abs() > tolerance && iteration < maxIterations) {
        c = (a + b) / 2;
        double fc = _evaluateFunction(function, c);

        if (fc.isNaN) {
          throw Exception('迭代过程中函数计算失败');
        }

        _iterations.add('迭代 ${iteration + 1}: a=${a.toStringAsFixed(6)}, b=${b.toStringAsFixed(6)}, c=${c.toStringAsFixed(6)}, f(c)=${fc.toStringAsFixed(6)}');

        if (fc.abs() < tolerance) {
          break;
        } else if (fa * fc < 0) {
          b = c;
          fb = fc;
        } else {
          a = c;
          fa = fc;
        }

        iteration++;
      }

      setState(() {
        _result = '近似解: ${c.toStringAsFixed(8)}\n'
                 '迭代次数: $iteration\n'
                 '最终误差: ${(b - a).abs().toStringAsFixed(8)}';
      });

    } catch (e) {
      setState(() {
        _result = '错误: $e';
      });
    } finally {
      setState(() {
        _isCalculating = false;
      });
    }
  }

  void _clear() {
    setState(() {
      _functionController.text = 'x^3 - x - 2';
      _aController.text = '1';
      _bController.text = '2';
      _toleranceController.text = '0.0001';
      _maxIterationsController.text = '100';
      _iterations.clear();
      _result = '';
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('二分法求根', style: TextStyle(color: Colors.black)),
        backgroundColor: Colors.white,
        elevation: 1,
        iconTheme: IconThemeData(color: Colors.black),
      ),
      body: SingleChildScrollView(
        padding: EdgeInsets.all(16),
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.start,
          children: [
            Text(
              '二分法求方程近似解',
              style: TextStyle(fontSize: 24, fontWeight: FontWeight.bold, color: Colors.deepPurple),
            ),
            SizedBox(height: 16),
            Text(
              '使用方法：\n'
              '1. 输入函数表达式（支持: +, -, *, /, ^, sin, cos, tan, ln, e, sqrt 等）\n'
              '2. 输入有根区间 [a, b]\n'
              '3. 设置精度和最大迭代次数\n'
              '4. 点击计算获取近似解\n\n'
              '示例表达式:\n'
              '• x^3 - x - 2\n'
              '• sin(x) + cos(x)\n'
              '• e^x - 2\n'
              '• ln(x) + sqrt(x)',
              style: TextStyle(fontSize: 14, color: Colors.grey[600]),
            ),
            SizedBox(height: 20),
            
            // 函数输入
            _buildInputField('函数 f(x)', '例如: x^3 - x - 2', _functionController),
            SizedBox(height: 16),
            
            Row(
              children: [
                Expanded(child: _buildInputField('区间左端点 a', '1', _aController)),
                SizedBox(width: 16),
                Expanded(child: _buildInputField('区间右端点 b', '2', _bController)),
              ],
            ),
            SizedBox(height: 16),
            
            Row(
              children: [
                Expanded(child: _buildInputField('精度 tolerance', '0.0001', _toleranceController)),
                SizedBox(width: 16),
                Expanded(child: _buildInputField('最大迭代次数', '100', _maxIterationsController)),
              ],
            ),
            SizedBox(height: 24),
            
            // 按钮
            Row(
              children: [
                Expanded(
                  child: ElevatedButton(
                    onPressed: _isCalculating ? null : _calculate,
                    style: ElevatedButton.styleFrom(
                      backgroundColor: Colors.deepPurple,
                      padding: EdgeInsets.symmetric(vertical: 16),
                    ),
                    child: _isCalculating 
                        ? SizedBox(height: 20, width: 20, child: CircularProgressIndicator(color: Colors.white))
                        : Text('计算', style: TextStyle(fontSize: 16, color: Colors.white)),
                  ),
                ),
                SizedBox(width: 16),
                Expanded(
                  child: OutlinedButton(
                    onPressed: _clear,
                    style: OutlinedButton.styleFrom(
                      padding: EdgeInsets.symmetric(vertical: 16),
                    ),
                    child: Text('清空', style: TextStyle(fontSize: 16)),
                  ),
                ),
              ],
            ),
            SizedBox(height: 24),
            
            // 结果展示
            if (_result.isNotEmpty) ...[
              Container(
                width: double.infinity,
                padding: EdgeInsets.all(16),
                decoration: BoxDecoration(
                  color: _result.contains('错误') ? Colors.red[50] : Colors.green[50],
                  borderRadius: BorderRadius.circular(8),
                  border: Border.all(color: _result.contains('错误') ? Colors.red : Colors.green),
                ),
                child: Text(
                  _result,
                  style: TextStyle(
                    fontSize: 16, 
                    fontWeight: FontWeight.bold, 
                    color: _result.contains('错误') ? Colors.red[800] : Colors.green[800]
                  ),
                ),
              ),
              SizedBox(height: 16),
            ],
            
            // 迭代过程
            if (_iterations.isNotEmpty) ...[
              Text('迭代过程:', style: TextStyle(fontSize: 18, fontWeight: FontWeight.bold)),
              SizedBox(height: 8),
              Container(
                height: 200,
                decoration: BoxDecoration(
                  border: Border.all(color: Colors.grey[300]!),
                  borderRadius: BorderRadius.circular(8),
                ),
                child: ListView.builder(
                  itemCount: _iterations.length,
                  itemBuilder: (context, index) {
                    return Container(
                      padding: EdgeInsets.symmetric(horizontal: 12, vertical: 8),
                      decoration: BoxDecoration(
                        border: index > 0 ? Border(top: BorderSide(color: Colors.grey[200]!)) : null,
                        color: index % 2 == 0 ? Colors.grey[50] : Colors.white,
                      ),
                      child: Text(
                        _iterations[index],
                        style: TextStyle(fontSize: 12, fontFamily: 'Monospace'),
                      ),
                    );
                  },
                ),
              ),
            ],
          ],
        ),
      ),
    );
  }

  Widget _buildInputField(String label, String hint, TextEditingController controller) {
    return Column(
      crossAxisAlignment: CrossAxisAlignment.start,
      children: [
        Text(label, style: TextStyle(fontWeight: FontWeight.bold)),
        SizedBox(height: 4),
        TextField(
          controller: controller,
          decoration: InputDecoration(
            hintText: hint,
            border: OutlineInputBorder(),
            contentPadding: EdgeInsets.symmetric(horizontal: 12, vertical: 8),
          ),
        ),
      ],
    );
  }
}