C++——多项式拟合
目标：利用C++对txt或者xml中的数据，进行高阶或低阶多项式拟合
为方便以后查找，代码以及详细资料已打包，并上传至云盘（链接：https://pan.baidu.com/s/1bvUBIoxv7Avxeq_Cz6xOZQ 密码：u9qe）
打包的内容如下：
运行结果：
上图是C++代码运行的结果，在Matlab中显示的效果；下图是Matlab中利用Curve Fitting Tool拟合的效果（四阶多项式拟合）。注意横坐标与纵坐标不一样额，那是因为这里的原始数据与一般的数据不同：一个x坐标可能对应多个y值。这种情况直接将横纵坐标反着写就行了。
C++代码：
一、cpp文件
1、主函数curveFittingMain.cpp：
#include
#include
#include
#include
#include
#include
#include
using namespace std; vector
fitCurve(vector
arr_1, vector
arr_2, int n); vector
getFitPoint(vector
coArr, vector
pointArr); int main(int argc, char* argv[]) { //step1: 读取txt文件中的数据 string file_x = "C:\\Users\\Zhangwei\\Desktop\\TEST\\多坐标点\\Quadrant_finalX.txt"; string file_y = "C:\\Users\\Zhangwei\\Desktop\\TEST\\多坐标点\\Quadrant_finalY.txt"; ifstream infile_x,infile_y; infile_x.open(file_x); infile_y.open(file_y); if (!infile_x && !infile_y) cout << "error" << endl; double temp; vector
Data_x, Data_y; while (infile_x >> temp) { Data_x.push_back(temp); } while (infile_y >> temp) { Data_y.push_back(temp); } //step2:调用拟合函数 // CoArr 表示多项式拟合的系数 // myRes 表示拟合的系数与拟合前的横坐标，计算得到新的纵坐标 vector
CoArr = fitCurve(Data_y, Data_x, 4); //调用函数，4表示阶数，（可以随意取，1—线性拟合，2—平方拟合，3—立方拟合,>=4,高阶拟合） vector
myRes = getFitPoint(CoArr, Data_y); //生成拟合数据 //step3:将myRes保存为txt文档 ofstream outfile; outfile.open("C:\\Users\\Zhangwei\\Desktop\\TEST\\多坐标点\\Quadrant_Final.txt"); for (int j = 0; j < myRes.size(); j++) { outfile << myRes[j] << endl; } outfile.close(); //system("pause"); return 0; } //getFitPoint函数用于获取拟合后的数据点 vector
getFitPoint(vector
coArr, vector
pointArr) { vector
finalPoint; if (pointArr.size() == 0 || coArr.size() == 0) { cout << "数据点有误！" << endl; } if (pointArr.size() > 0 && coArr.size() > 0) { for (int i = 0; i < pointArr.size(); i++) { double temp = 0; for (int j = 0; j < coArr.size(); j++) { temp += pow(pointArr[i], j)*coArr[j]; } finalPoint.push_back(temp); } } return finalPoint; } //fitCurve函数用于曲线拟合 vector
fitCurve(vector
arr_1, vector
arr_2, int n) { CLS m_cls; vector
coefficientsSet; if (arr_1.size() != arr_2.size()) { cout << " 输入数据有误！" << endl; } if (arr_1.size() == arr_2.size()) { for (int i = 0; i < arr_1.size(); i++) { m_cls.addPoint(arr_1[i], arr_2[i]); } m_cls.setN(n); m_cls.Solve(); double *t_paracof = m_cls.getSolution(); for (int i = 0; i < n + 1; i++) { coefficientsSet.push_back(t_paracof[i]); //多项式的系数项，第一项为常数项，最后一项为x^n项 } } return coefficientsSet; }
2、Linequ.cpp
// Linequ.cpp: implementation of the CLinequ class. // // //#include "stdafx.h" #include "math.h" #include "Linequ.h" #ifdef _DEBUG #undef THIS_FILE static char THIS_FILE[] = __FILE__; //#define new DEBUG_NEW #endif // // Construction/Destruction // CLinequ::CLinequ(int dims) { index = dims; sums = new double[dims]; MatrixA = new double[dims * dims]; solu = new double[dims]; } CLinequ::~CLinequ() { delete[] sums; delete[] MatrixA; delete[] solu; } void CLinequ::setMatrix(double *rmatr) //设置矩阵 { for (int i = 0; i
d) { d = t; js[k] = j; is = i; } } if (d + 1.0 == 1.0) l = 0; else { if (js[k] != k) for (i = 0; i <= index - 1; i++){ p = i*index + k; q = i*index + js[k]; t = MatrixA[p]; MatrixA[p] = MatrixA[q]; MatrixA[q] = t; } if (is != k) { for (j = k; j <= index - 1; j++){ p = k*index + j; q = is*index + j; t = MatrixA[p]; MatrixA[p] = MatrixA[q]; MatrixA[q] = t; } t = sums[k]; sums[k] = sums[is]; sums[is] = t; } } if (l == 0) { delete[] js; //fail to solve return(0); } d = MatrixA[k*index + k]; for (j = k + 1; j <= index - 1; j++){ p = k*index + j; MatrixA[p] = MatrixA[p] / d; } sums[k] = sums[k] / d; for (i = k + 1; i <= index - 1; i++){ for (j = k + 1; j <= index - 1; j++){ p = i*index + j; MatrixA[p] = MatrixA[p] - MatrixA[i*index + k] * MatrixA[k*index + j]; } sums[i] = sums[i] - MatrixA[i*index + k] * sums[k]; } } d = MatrixA[(index - 1)*index + index - 1]; if (fabs(d) + 1.0 == 1.0) { delete[] js; //fail to solve return(0); } solu[index - 1] = sums[index - 1] / d; //回代过程 for (i = index - 2; i >= 0; i--){ t = 0.0; for (j = i + 1; j <= index - 1; j++) t = t + MatrixA[i*index + j] * solu[j]; solu[i] = sums[i] - t; } js[index - 1] = index - 1; for (k = index - 1; k >= 0; k--) if (js[k] != k) { t = solu[k]; solu[k] = solu[js[k]]; solu[js[k]] = t; } delete[] js; return(1); } double *CLinequ::getSolution() const { return solu; }
3、LS.cpp
// LS.cpp: implementation of the CLS class. // // //#include "stdafx.h" #include "LS.h" #include "Matrix.h" #include "Linequ.h" #ifdef _DEBUG #undef THIS_FILE static char THIS_FILE[] = __FILE__; //#define new DEBUG_NEW #endif // // Construction/Destruction // CLS* CLS::_instance = 0; CLS::CLS() { pSolution = 0; m = 0; n = 0; _instance = this; } CLS::~CLS() { if (pSolution) delete[] pSolution; } CLS *CLS::getInstance() { if (!_instance) new CLS(); return _instance; } void CLS::setN(int t) { n = t + 1; if (pSolution) delete[] pSolution; pSolution = new double[n]; } void CLS::addPoint(double x, double y) { pVertex[m][0] = x; pVertex[m][1] = y; m++; } bool CLS::Solve() { if (m <= 0 || n <= 0) return false; CMatrix *A = new CMatrix(m, n); int i, j; for (j = 0; j < m; j++) A->setData(j, 0, 1.0); for (i = 1; i < n; i++) { for (j = 0; j < m; j++) { A->setData(j, i, A->getData(j, i - 1) * pVertex[j][0]); } } CMatrix *B = A->getRev(); CMatrix *b = new CMatrix(m, 1); for (i = 0; i < m; i++) b->setData(i, 0, pVertex[i][1]); CMatrix *C = B->getMul(A); CMatrix *d = B->getMul(b); CLinequ *pL = new CLinequ(n); pL->setLinequ(C->getMatrix(), d->getMatrix()); pL->Solve(); double *t = pL->getSolution(); for (i = 0; i < n; i++) pSolution[i] = t[i]; return true; } double *CLS::getSolution() const { return pSolution; } double CLS::calcY(double x) { double y = 0.0, temp = 1.0; for (int i = 0; i < n; i++) { y += pSolution[i] * temp; temp *= x; } return y; } void CLS::restart() { m = 0; if (pSolution) delete[] pSolution; pSolution = 0; n = 0; } 4、Matrix.cpp
// Matrix.cpp: implementation of the CMatrix class. // // //#include "stdafx.h" #include "Matrix.h" #ifdef _DEBUG #undef THIS_FILE static char THIS_FILE[] = __FILE__; //#define new DEBUG_NEW #endif // // Construction/Destruction // void CMatrix::setMatrix(double *rmatr) //设置矩阵 { for (int i = 0; i < m * n; i++) { *(pMatrix + i) = rmatr[i]; //矩阵成员赋初值 } } CMatrix::CMatrix(int a, int b) //矩阵Matrix类的构造函数 { m = a; n = b; //保护数据赋值 pMatrix = new double[m * n]; //动态分配内存 } CMatrix::~CMatrix() //矩阵Matrix类的析构函数 { delete[] pMatrix; //内存释放 } CMatrix *CMatrix::getRev() { CMatrix *pR = new CMatrix(n, m); for (int j = 0; j < n; j++) { for (int i = 0; i < m; i++) *(pR->pMatrix + i + m * j) = *(pMatrix + i * n + j); } return pR; } CMatrix *CMatrix::getMul(CMatrix *b) { if (b->m != n) return 0; CMatrix *pR = new CMatrix(m, b->n); for (int i = 0; i < m; i++) { for (int j = 0; j < b->n; j++) { double temp = 0.0; for (int k = 0; k < n; k++) temp += *(pMatrix + i * n + k) * *(b->pMatrix + k * b->n + j); *(pR->pMatrix + i * b->n + j) = temp; } } return pR; } int CMatrix::getM() const { return m; } int CMatrix::getN() const { return n; } double *CMatrix::getMatrix() const { return pMatrix; } double CMatrix::getData(int i, int j) const { if (i < m && j < n && i >= 0 && j >= 0) return *(pMatrix + i * n + j); else return 0.0; } void CMatrix::setData(int i, int j, double t) { if (i < m && j < n && i >= 0 && j >= 0) { *(pMatrix + i * n + j) = t; } }二、头文件（.h文件）
1、Linequ.h
// Linequ.h: interface for the CLinequ class. // // #if !defined(AFX_LINEQU_H__3673E7FC_1154_436A_9D22_B472DD858F13__INCLUDED_) #define AFX_LINEQU_H__3673E7FC_1154_436A_9D22_B472DD858F13__INCLUDED_ #if _MSC_VER > 1000 #pragma once #endif // _MSC_VER > 1000 class CLinequ { public: //外部接口 CLinequ(int dims = 2); //构造函数 virtual ~CLinequ(); //析构函数 void setLinequ(double *a, double *b); //方称赋值 void setMatrix(double *rmatr); int Solve(); //全选主元高斯消去法求解方程 double *getSolution() const; private: double *sums; //方程右端项 double *MatrixA; double *solu; //方程的解 int index; }; #endif // !defined(AFX_LINEQU_H__3673E7FC_1154_436A_9D22_B472DD858F13__INCLUDED_) 2、LS.h
// LS.h: interface for the CLS class. // // #if !defined(AFX_LS_H__208D279A_F391_4DA8_BBE3_3895A9800FFE__INCLUDED_) #define AFX_LS_H__208D279A_F391_4DA8_BBE3_3895A9800FFE__INCLUDED_ #if _MSC_VER > 1000 #pragma once #endif // _MSC_VER > 1000 class CLS { private: static CLS *_instance; double pVertex[2000][2];//最多可以拟合2000个点 int m; //点的个数 int n; //多项式次数 double *pSolution; //多项式系数 public: CLS(); virtual ~CLS(); static CLS *getInstance(); void setN(int t); //n次多项式拟合 void addPoint(double x, double y); //添加一个点 void restart(); bool Solve(); double *getSolution() const; //获得多项式系数 double calcY(double x); //根据x坐标计算y }; #endif // !defined(AFX_LS_H__208D279A_F391_4DA8_BBE3_3895A9800FFE__INCLUDED_) 3、Matrix.h
// Matrix.h: interface for the CMatrix class. // // #if !defined(AFX_MATRIX_H__AEE89FA3_05E2_44AC_AA96_5FBCB3608C13__INCLUDED_) #define AFX_MATRIX_H__AEE89FA3_05E2_44AC_AA96_5FBCB3608C13__INCLUDED_ #if _MSC_VER > 1000 #pragma once #endif // _MSC_VER > 1000 class CMatrix { public: CMatrix(int a = 2, int b = 2); virtual ~CMatrix(); void setMatrix(double *rmatr); CMatrix *getRev(); CMatrix *getMul(CMatrix *b); int getM() const; //获得行数 int getN() const; //获得列数 double getData(int i, int j) const; void setData(int i, int j, double t); double *getMatrix() const; //获得矩阵 protected: int m, n; double *pMatrix; }; #endif // !defined(AFX_MATRIX_H__AEE89FA3_05E2_44AC_AA96_5FBCB3608C13__INCLUDED_)
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