一、多项式拟合用途

当前有一组对应的x、y数据，希望通过这些数据点做出近似的多项式曲线：Y=···+nX^2+mX+c
其中多项式最高次数可调，返回各个参数及曲线的拟合度R^2

二、函数实现

参数中的order为设置的多项式最高次次数，coefficients为各次的系数

double polynomialFit(vector<double>& x, vector<double>& y, unsigned char order, vector<double>& coefficients){if (x.size() <= order || y.size() <= order) {return 0;}// 构建矩阵A和向量bint m = x.size();int n = order + 1;vector<vector<double>> A(n, vector<double>(n, 0));vector<double> b(n, 0);for (int i = 0; i < n; i++) {for (int j = 0; j < n; j++) {for (int k = 0; k < m; k++) {A[i][j] += pow(x[k], i+j);}}for (int k = 0; k < m; k++) {b[i] += y[k] * pow(x[k], i);}}n = A.size();for (int i = 0; i < n; i++) {// 列主元素消去int maxRow = i;double maxVal = fabs(A[i][i]);for (int k = i + 1; k < n; k++) {if (fabs(A[k][i]) > maxVal) {maxVal = fabs(A[k][i]);maxRow = k;}}if (maxRow != i) {std::swap(A[i], A[maxRow]);std::swap(b[i], b[maxRow]);}// 消元过程for (int k = i + 1; k < n; k++) {double factor = A[k][i] / A[i][i];for (int j = i; j < n; j++) {A[k][j] -= factor * A[i][j];}b[k] -= factor * b[i];}}// 回代求解vector<double> result(n, 0);for (int i = n - 1; i >= 0; i--) {double temp = b[i];for (int j = i + 1; j < n; j++) {temp -= A[i][j] * result[j];}result[i] = temp / A[i][i];}coefficients = result;double SSR=0;double SST=0;double sumY = std::accumulate(std::begin(y),std::end(y),0.0);double avgY = sumY/y.size();for(uint16_t i=0;i<y.size();i++){double actY=0;for(unsigned char j=0;j<=order;j++){actY+=pow(x[i],j)*result[j];}SSR += pow(actY-y[i],2);SST += pow(y[i]-avgY,2);}double R = 1-SSR/SST;return R;
}

三、函数调用

vector<double> xs{0,0,0,0};
vector<double> selectX;
vector<double> selectY;
selectX.push_back(..);
...
selectY.push_back(..);
...
double R = polynomialFit(selectX,selectY,3,xs);