mathtool/lib/tools/mixed_variance.dart

// tools/mixed_variance.dart
import 'package:flutter/material.dart';
import 'package:rational/rational.dart';
import '../utils/math_utils.dart';

class MixedVariancePage extends StatefulWidget {
  @override
  _MixedVariancePageState createState() => _MixedVariancePageState();
}

class _MixedVariancePageState extends State<MixedVariancePage> {
  final TextEditingController sampleSizesController = TextEditingController();
  final TextEditingController meansController = TextEditingController();
  final TextEditingController variancesController = TextEditingController();

  String result = '';

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('混合方差')),
      body: Padding(
        padding: EdgeInsets.all(16),
        child: Column(
          children: [
            _buildInputField('各层样本量（用空格分隔）', sampleSizesController),
            _buildInputField('各层均值（用空格分隔）', meansController),
            _buildInputField('各层方差（用空格分隔）', variancesController),
            SizedBox(height: 20),
            ElevatedButton(
              onPressed: _calculate,
              child: Text('计算'),
            ),
            SizedBox(height: 20),
            if (result.isNotEmpty)
              Card(
                child: Padding(
                  padding: EdgeInsets.all(16),
                  child: Text(
                    result,
                    style: TextStyle(fontSize: 16),
                  ),
                ),
              ),
          ],
        ),
      ),
    );
  }

  Widget _buildInputField(String label, TextEditingController controller) {
    return Padding(
      padding: EdgeInsets.symmetric(vertical: 8),
      child: TextField(
        controller: controller,
        keyboardType: TextInputType.numberWithOptions(signed: true, decimal: true),
        decoration: InputDecoration(
          labelText: label,
          border: OutlineInputBorder(),
          hintText: label.contains('分隔') ? '用空格分隔多个值' : '输入分数如: 1/2 或小数',
        ),
      ),
    );
  }

  void _calculate() {
    try {
      final sizes = sampleSizesController.text.split(' ').map((s) => MathUtils.parseRational(s)).toList();
      final means = meansController.text.split(' ').map((s) => MathUtils.parseRational(s)).toList();
      final variances = variancesController.text.split(' ').map((s) => MathUtils.parseRational(s)).toList();

      if (sizes.length != means.length || sizes.length != variances.length) {
        setState(() {
          result = '错误: 输入的数据长度不一致';
        });
        return;
      }

      Rational totalSize = Rational.zero;
      Rational weightedSum = Rational.zero;

      for (int i = 0; i < sizes.length; i++) {
        totalSize += sizes[i];
        weightedSum += sizes[i] * means[i];
      }

      final overallMean = weightedSum / totalSize;

      Rational mixedVariance = Rational.zero;
      for (int i = 0; i < sizes.length; i++) {
        mixedVariance += sizes[i] * (variances[i] + (means[i] - overallMean).pow(2)) / totalSize;
      }

      // 获取近似值
      double overallMeanApprox = overallMean.toDouble();
      double mixedVarianceApprox = mixedVariance.toDouble();

      setState(() {
        result = '总均值 = ${MathUtils.rationalToString(overallMean)} (≈${overallMeanApprox.toStringAsFixed(4)})\n'
      '混合方差 = ${MathUtils.rationalToString(mixedVariance)} (≈${mixedVarianceApprox.toStringAsFixed(4)})';
      });
    } catch (e) {
      setState(() {
        result = '错误: $e';
      });
    }
  }

  @override
  void dispose() {
    sampleSizesController.dispose();
    meansController.dispose();
    variancesController.dispose();
    super.dispose();
  }
}