使用最小二乘法擬合二次函數

原理：

主要二次函數擬合算法，目前項目需要4組x,y擬合二次函數
mainwindow.h

#ifndef MAINWINDOW_H #define MAINWINDOW_H#include <QMainWindow>QT_BEGIN_NAMESPACE namespace Ui { class MainWindow; } QT_END_NAMESPACEclass MainWindow : public QMainWindow {Q_OBJECTpublic:MainWindow(QWidget *parent = nullptr);~MainWindow();void EMatrix(QVector<double> Vx, QVector<double> Vy, int n, int ex, double coefficient[]);void CalEquation(int exp, double coefficient[]);double Em[100][100];double RelatePow(QVector<double> Vx, int n, int ex);double RelateMutiXY(QVector<double> Vx, QVector<double> Vy, int n, int ex);double F(double c[],int l,int m); public slots:void quadraticcal();private:Ui::MainWindow *ui; }; #endif // MAINWINDOW_H

mainwindow.cpp

#include "mainwindow.h" #include "ui_mainwindow.h" #include "qmath.h" #include <QDebug>#define N 1e-13MainWindow::MainWindow(QWidget *parent): QMainWindow(parent), ui(new Ui::MainWindow) {ui->setupUi(this);QObject::connect(ui->pushButton,SIGNAL(clicked()),this,SLOT(quadraticcal()));this->setWindowTitle("二次方程擬合");}MainWindow::~MainWindow() {delete ui; }void MainWindow::quadraticcal() {QVector<double> vx,vy;double coefficient[5];vx.push_back(ui->lineEdit->text().toDouble());vx.push_back(ui->lineEdit_2->text().toDouble());vx.push_back(ui->lineEdit_3->text().toDouble());vx.push_back(ui->lineEdit_4->text().toDouble());vy.push_back(ui->lineEdit_6->text().toDouble());vy.push_back(ui->lineEdit_7->text().toDouble());vy.push_back(ui->lineEdit_9->text().toDouble());vy.push_back(ui->lineEdit_8->text().toDouble());EMatrix(vx,vy,4,3,coefficient);QString str_1=QString::number(coefficient[1]);QString str_2=QString::number(coefficient[2]);QString str_3=QString::number(coefficient[3]);ui->lineEdit_10->setText(str_3);ui->lineEdit_11->setText(str_2);ui->lineEdit_12->setText(str_1);}void MainWindow::EMatrix(QVector<double> Vx, QVector<double> Vy, int n, int ex, double coefficient[]) {for (int i=1; i<=ex; i++){for (int j=1; j<=ex; j++){Em[i][j]=RelatePow(Vx,n,i+j-2);}Em[i][ex+1]=RelateMutiXY(Vx,Vy,n,i-1);}Em[1][1]=n;CalEquation(ex,coefficient); } //求解方程 void MainWindow::CalEquation(int exp, double coefficient[]) {for(int k=1;k<exp;k++) //消元{for(int i=k+1;i<exp+1;i++){double p1=0;if(Em[k][k]!=0)p1=Em[i][k]/Em[k][k];for(int j=k;j<exp+2;j++)Em[i][j]=Em[i][j]-Em[k][j]*p1;}}coefficient[exp]=Em[exp][exp+1]/Em[exp][exp];for(int l=exp-1;l>=1;l--) //回代求解coefficient[l]=(Em[l][exp+1]-F(coefficient,l+1,exp))/Em[l][l]; }double MainWindow::RelatePow(QVector<double> Vx, int n, int ex) {double ReSum=0;for (int i=0; i<n; i++){ReSum+=pow(Vx[i],ex);}return ReSum; } //x的ex次方與y的乘積的累加 double MainWindow::RelateMutiXY(QVector<double> Vx, QVector<double> Vy, int n, int ex) {double dReMultiSum=0;for (int i=0; i<n; i++){dReMultiSum+=pow(Vx[i],ex)*Vy[i];}return dReMultiSum; }double MainWindow::F(double c[],int l,int m) {double sum=0;for(int i=l;i<=m;i++)sum+=Em[l-1][i]*c[i];return sum; }

結果圖示：

算法借鑒自"采用最小二乘法擬合二次、三次、四次曲線"

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