qt生成八个点绘制二次函数曲线并计算出函数曲线y = a * x^2 + b * x + c并计算出拟合值R2

以下是一个使用 Qt 绘制二次函数曲线并计算拟合值 R2 的示例程序：

#include <QtWidgets>

class QuadraticFunctionWidget : public QWidget
{
public:
    QuadraticFunctionWidget(QWidget *parent = nullptr)
        : QWidget(parent)
    {
        setWindowTitle(tr("Quadratic Function"));

        // 设置初始参数
        a = 1.0;
        b = 0.0;
        c = 0.0;

        // 创建绘图窗口
        chartView = new QChartView(this);
        chartView->setRenderHint(QPainter::Antialiasing);

        // 创建数据序列
        series = new QScatterSeries();
        for (int i = 0; i < 8; i++) {
            QPointF point(i, 0.0); // x 坐标从 0 到 7
            series->append(point);
        }

        // 添加数据序列到图表
        chart = new QChart();
        chart->addSeries(series);
        chart->createDefaultAxes();
        chart->setAnimationOptions(QChart::SeriesAnimations);

        // 显示图表
        chartView->setChart(chart);
        chartView->setMinimumSize(640, 480);

        // 创建参数输入框和计算按钮
        aLineEdit = new QLineEdit(QString::number(a));
        bLineEdit = new QLineEdit(QString::number(b));
        cLineEdit = new QLineEdit(QString::number(c));
        calculateButton = new QPushButton(tr("Calculate"));

        // 连接计算按钮的槽函数
        connect(calculateButton, &QPushButton::clicked, this, &QuadraticFunctionWidget::calculate);

        // 创建布局
        QVBoxLayout *layout = new QVBoxLayout();
        layout->addWidget(chartView);
        layout->addWidget(new QLabel(tr("y = ax^2 + bx + c")));
        QHBoxLayout *paramLayout = new QHBoxLayout();
        paramLayout->addWidget(new QLabel(tr("a:")));
        paramLayout->addWidget(aLineEdit);
        paramLayout->addWidget(new QLabel(tr("b:")));
        paramLayout->addWidget(bLineEdit);
        paramLayout->addWidget(new QLabel(tr("c:")));
        paramLayout->addWidget(cLineEdit);
        paramLayout->addWidget(calculateButton);
        layout->addLayout(paramLayout);
        setLayout(layout);
    }

private:
    QChartView *chartView;
    QChart *chart;
    QScatterSeries *series;
    QLineEdit *aLineEdit;
    QLineEdit *bLineEdit;
    QLineEdit *cLineEdit;
    QPushButton *calculateButton;
    double a;
    double b;
    double c;

    void calculate()
    {
        // 读取参数
        a = aLineEdit->text().toDouble();
        b = bLineEdit->text().toDouble();
        c = cLineEdit->text().toDouble();

        // 计算函数曲线
        QVector<QPointF> points;
        for (int i = 0; i < 8; i++) {
            double x = i;
            double y = a * x * x + b * x + c;
            points.append(QPointF(x, y));
        }

        // 更新数据序列
        series->replace(points);

        // 计算拟合值 R2
        double sumX = 0.0;
        double sumY = 0.0;
        double sumXY = 0.0;
        double sumX2 = 0.0;
        double sumY2 = 0.0;
        int n = points.size();
        for (int i = 0; i < n; i++) {
            double x = points[i].x();
            double y = points[i].y();
            sumX += x;
            sumY += y;
            sumXY += x * y;
            sumX2 += x * x;
            sumY2 += y * y;
        }
        double meanX = sumX / n;
        double meanY = sumY / n;
        double SSE = sumY2 - (sumY * sumY) / n;
        double SSR = (sumXY - sumX * sumY / n) * (sumXY - sumX * sumY / n) / (sumX2 - sumX * sumX / n);
        double SST = SSE + SSR;
        double R2 = SSR / SST;

        // 显示拟合值 R2
        QMessageBox::information(this, tr("R2"), tr("R2 = %1").arg(R2));
    }
};

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);
    QuadraticFunctionWidget widget;
    widget.show();
    return app.exec();
}

该程序创建了一个窗口，包含一个图表和三个参数输入框和一个计算按钮。用户可以输入二次函数的三个参数，并点击计算按钮来绘制函数曲线和计算拟合值 R2。在计算拟合值 R2 时，程序使用了最小二乘法的公式来计算。