请用C++写一份完整的Savitzky-Golay filter算法

以下是一个简单的 C++ 实现的 Savitzky-Golay filter 算法示例代码： ```cpp #include <iostream> #include <vector> // 计算卷积 std::vector<double> convolve(const std::vector<double>& data, const std::vector<double>& kernel) { int nData = data.size(); int nKernel = kernel.size(); int nOutput = nData - nKernel + 1; std::vector<double> output(nOutput); for (int i = 0; i < nOutput; ++i) { double sum = 0; for (int j = 0; j < nKernel; ++j) { sum += data[i + j] * kernel[j]; } output[i] = sum; } return output; } // Savitzky-Golay 滤波函数 std::vector<double> savitzkyGolayFilter(const std::vector<double>& data, int windowSize, int polynomialOrder) { // 生成多项式系数 std::vector<std::vector<double>> coefficients(polynomialOrder + 1, std::vector<double>(windowSize)); for (int i = 0; i <= polynomialOrder; ++i) { for (int j = 0; j < windowSize; ++j) { coefficients[i][j] = std::pow(j - (windowSize - 1) / 2.0, i); } } // 求解线性方程组得到卷积核 std::vector<double> kernel(windowSize); std::vector<std::vector<double>> A(windowSize, std::vector<double>(polynomialOrder + 1)); std::vector<double> B(windowSize); for (int i = 0; i < windowSize; ++i) { for (int j = 0; j <= polynomialOrder; ++j) { A[i][j] = coefficients[j][i]; } B[i] = 1; } // 高斯消元求解 for (int i = 0; i < windowSize; ++i) { double maxElement = std::abs(A[i][i]); int maxRow = i; for (int k = i + 1; k < windowSize; ++k) { if (std::abs(A[k][i]) > maxElement) { maxElement = std::abs(A[k][i]); maxRow = k; } } if (maxRow!= i) { std::swap(A[i], A[maxRow]); std::swap(B[i], B[maxRow]); } for (int j = i + 1; j < windowSize; ++j) { double factor = A[j][i] / A[i][i]; for (int k = i; k <= polynomialOrder; ++k) { A[j][k] -= factor * A[i][k]; } B[j] -= factor * B[i]; } } for (int i = windowSize - 1; i >= 0; --i) { kernel[i] = B[i] / A[i][i]; for (int j = i - 1; j >= 0; --j) { B[j] -= A[j][i] * kernel[i]; } } return convolve(data, kernel); } int main() { std::vector<double> data = {1.2, 2.3, 3.4, 4.5, 5.6, 6.7, 7.8, 8.9, 9.0}; int windowSize = 5; int polynomialOrder = 2; std::vector<double> filteredData = savitzkyGolayFilter(data, windowSize, polynomialOrder); for (const auto& value : filteredData) { std::cout << value << " "; } std::cout << std::endl; return 0; } ``` 额外注意的逻辑点： 1. 确保输入数据的长度足够进行滤波操作。 2. 窗口大小和多项式阶数的选择要根据具体问题和数据特点进行调整。 3. 代码中的数值计算可能存在精度问题，需要根据实际需求进行处理。 [2025-04-17 10:49:33 | AI写代码神器 | 1006点数解答]