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Matrix QR Decomposition using OpenCV
Matrix QR decomposition is very useful in least square fitting model. But there is no function available to do it in OpenCV directly. So i write a function to do it myself.
It is based on the House Holder Algorithm. The defailed algorithm can be found in https://en.wikipedia.org/wiki/QR_decomposition.
The function and test code is in below.
void HouseHolderQR(const cv::Mat &A, cv::Mat &Q, cv::Mat &R){ assert ( A.channels() == 1 ); assert ( A.rows >= A.cols ); auto sign = [](float value) { return value >= 0 ? 1: -1; }; const auto totalRows = A.rows; const auto totalCols = A.cols; R = A.clone(); Q = cv::Mat::eye ( totalRows, totalRows, A.type() ); for ( int col = 0; col < A.cols; ++ col ) { cv::Mat matAROI = cv::Mat ( R, cv::Range ( col, totalRows ), cv::Range ( col, totalCols ) ); cv::Mat y = matAROI.col ( 0 ); auto yNorm = norm ( y, NORM_L2 ); cv::Mat e1 = cv::Mat::eye ( y.rows, 1, A.type() ); cv::Mat w = y + sign(y.at<float>(0,0)) * yNorm * e1; cv::Mat v = w / norm(w); cv::Mat vT; cv::transpose(v, vT ); cv::Mat I = cv::Mat::eye( matAROI.rows, matAROI.rows, A.type() ); cv::Mat I_2VVT = I - 2 * v * vT; cv::Mat matH = cv::Mat::eye ( totalRows, totalRows, A.type() ); cv::Mat matHROI = cv::Mat(matH, cv::Range ( col, totalRows ), cv::Range ( col, totalRows ) ); I_2VVT.copyTo ( matHROI ); R = matH * R; Q = Q * matH; }}void TestQRDecomposition(){ cv::Mat A, Q, R; //Test case 1 { //A = cv::Mat ( 4, 3, CV_32FC1 ); //A.at<float>(0,0) = -1.f; //A.at<float>(0,1) = -1.f; //A.at<float>(0,2) = 1.f; //A.at<float>(1,0) = 1.f; //A.at<float>(1,1) = 3.f; //A.at<float>(1,2) = 3.f; //A.at<float>(2,0) = -1.f; //A.at<float>(2,1) = -1.f; //A.at<float>(2,2) = 5.f; //A.at<float>(3,0) = 1.f; //A.at<float>(3,1) = 3.f; //A.at<float>(3,2) = 7.f; } { A = cv::Mat(5, 3, CV_32FC1); A.at<float>(0, 0) = 12.f; A.at<float>(0, 1) = -51.f; A.at<float>(0, 2) = 4.f; A.at<float>(1, 0) = 6.f; A.at<float>(1, 1) = 167.f; A.at<float>(1, 2) = -68.f; A.at<float>(2, 0) = -4.f; A.at<float>(2, 1) = 24.f; A.at<float>(2, 2) = -41.f; A.at<float>(3, 0) = -1.f; A.at<float>(3, 1) = 1.f; A.at<float>(3, 2) = 0.f; A.at<float>(4, 0) = 2.f; A.at<float>(4, 1) = 0.f; A.at<float>(4, 2) = 3.f; } std::cout << "A: " << std::endl; printfMat<float>(A); HouseHolderQR(A, Q, R); std::cout << "Q: " << std::endl; printfMat<float>(Q); std::cout << "R: " << std::endl; printfMat<float>(R); cv::Mat AVerify = Q * R; std::cout << "AVerify: " << std::endl; printfMat<float>(AVerify);}
Matrix QR Decomposition using OpenCV
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