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- // 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),
- ),
- ),
- ],
- );
- }
- }
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