qt生成n个点绘制二次函数曲线并计算出函数曲线 a b c 的值并计算出拟合值R2

以下是一个简单的用Qt绘制二次函数曲线的示例代码，并计算出函数曲线a、b、c的值和拟合值R2：

#include <QtWidgets>

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

        // 设置绘图区域大小
        setFixedSize(500, 500);

        // 生成n个点
        const int n = 20;
        for (int i = 0; i < n; ++i) {
            double x = i * 1.0 / (n - 1);
            double y = a * x * x + b * x + c;
            m_points.append(QPointF(x, y));
        }

        // 计算函数曲线的a、b、c值
        double x_sum = 0, x2_sum = 0, x3_sum = 0, x4_sum = 0;
        double y_sum = 0, xy_sum = 0, x2y_sum = 0;
        for (int i = 0; i < n; ++i) {
            double x = m_points[i].x();
            double y = m_points[i].y();
            x_sum += x;
            x2_sum += x * x;
            x3_sum += x * x * x;
            x4_sum += x * x * x * x;
            y_sum += y;
            xy_sum += x * y;
            x2y_sum += x * x * y;
        }
        double denominator = n * x2_sum * x4_sum - x3_sum * x3_sum - x2_sum * x2_sum * n
                             + 2 * x2_sum * x3_sum + x_sum * x_sum * x4_sum
                             - n * x_sum * x2_sum * x2_sum;
        a = (n * x2y_sum - x2_sum * y_sum - x_sum * xy_sum + n * x_sum * x2_sum * b) / denominator;
        b = (xy_sum - x_sum * y_sum - a * (x2_sum - n * x_sum * x_sum)) / x2_sum;
        c = (y_sum - a * x2_sum - b * x_sum) / n;

        // 计算R2值
        double y_mean = y_sum / n;
        double ss_tot = 0, ss_res = 0;
        for (int i = 0; i < n; ++i) {
            double y = m_points[i].y();
            ss_tot += (y - y_mean) * (y - y_mean);
            ss_res += (y - (a * m_points[i].x() * m_points[i].x() + b * m_points[i].x() + c))
                      * (y - (a * m_points[i].x() * m_points[i].x() + b * m_points[i].x() + c));
        }
        R2 = 1 - ss_res / ss_tot;
    }

protected:
    void paintEvent(QPaintEvent *event) override
    {
        QPainter painter(this);
        painter.setRenderHint(QPainter::Antialiasing);

        // 绘制坐标系
        painter.translate(width() / 2, height() / 2);
        painter.drawLine(QPointF(-width() / 2, 0), QPointF(width() / 2, 0));
        painter.drawLine(QPointF(0, -height() / 2), QPointF(0, height() / 2));

        // 绘制函数曲线
        painter.setPen(QPen(Qt::red, 2));
        QPainterPath path;
        for (int i = 0; i < m_points.size(); ++i) {
            QPointF p = m_points[i] * QPointF(width() / 2, -height() / 2);
            if (i == 0) {
                path.moveTo(p);
            } else {
                path.lineTo(p);
            }
        }
        painter.drawPath(path);
    }

private:
    QVector<QPointF> m_points;
    double a = 1, b = 2, c = 1; // 二次函数曲线的a、b、c值
    double R2 = 0;              // 拟合值R2
};

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    QuadraticFunctionWidget widget;
    widget.show();

    return app.exec();
}

在上面的代码中，我们生成了n个均匀分布的点，并使用这些点拟合出一个二次函数曲线。然后，我们计算出函数曲线的a、b、c值和拟合值R2，并在窗口中绘制出这个二次函数曲线。