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774 lines
26 KiB
C++
774 lines
26 KiB
C++
#ifndef DLS_H_
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#define DLS_H_
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#include "precomp.hpp"
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#include <iostream>
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using namespace std;
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using namespace cv;
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class dls
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{
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public:
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dls(const cv::Mat& opoints, const cv::Mat& ipoints);
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~dls();
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bool compute_pose(cv::Mat& R, cv::Mat& t);
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private:
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// initialisation
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template <typename OpointType, typename IpointType>
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void init_points(const cv::Mat& opoints, const cv::Mat& ipoints)
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{
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for(int i = 0; i < N; i++)
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{
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p.at<double>(0,i) = opoints.at<OpointType>(i).x;
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p.at<double>(1,i) = opoints.at<OpointType>(i).y;
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p.at<double>(2,i) = opoints.at<OpointType>(i).z;
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// compute mean of object points
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mn.at<double>(0) += p.at<double>(0,i);
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mn.at<double>(1) += p.at<double>(1,i);
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mn.at<double>(2) += p.at<double>(2,i);
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// make z into unit vectors from normalized pixel coords
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double sr = std::pow(ipoints.at<IpointType>(i).x, 2) +
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std::pow(ipoints.at<IpointType>(i).y, 2) + (double)1;
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sr = std::sqrt(sr);
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z.at<double>(0,i) = ipoints.at<IpointType>(i).x / sr;
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z.at<double>(1,i) = ipoints.at<IpointType>(i).y / sr;
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z.at<double>(2,i) = (double)1 / sr;
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}
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mn.at<double>(0) /= (double)N;
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mn.at<double>(1) /= (double)N;
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mn.at<double>(2) /= (double)N;
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}
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// main algorithm
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cv::Mat LeftMultVec(const cv::Mat& v);
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void run_kernel(const cv::Mat& pp);
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void build_coeff_matrix(const cv::Mat& pp, cv::Mat& Mtilde, cv::Mat& D);
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void compute_eigenvec(const cv::Mat& Mtilde, cv::Mat& eigenval_real, cv::Mat& eigenval_imag,
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cv::Mat& eigenvec_real, cv::Mat& eigenvec_imag);
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void fill_coeff(const cv::Mat * D);
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// useful functions
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cv::Mat cayley_LS_M(const std::vector<double>& a, const std::vector<double>& b,
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const std::vector<double>& c, const std::vector<double>& u);
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cv::Mat Hessian(const double s[]);
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cv::Mat cayley2rotbar(const cv::Mat& s);
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cv::Mat skewsymm(const cv::Mat * X1);
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// extra functions
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cv::Mat rotx(const double t);
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cv::Mat roty(const double t);
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cv::Mat rotz(const double t);
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cv::Mat mean(const cv::Mat& M);
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bool is_empty(const cv::Mat * v);
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bool positive_eigenvalues(const cv::Mat * eigenvalues);
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cv::Mat p, z, mn; // object-image points
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int N; // number of input points
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std::vector<double> f1coeff, f2coeff, f3coeff, cost_; // coefficient for coefficients matrix
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std::vector<cv::Mat> C_est_, t_est_; // optimal candidates
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cv::Mat C_est__, t_est__; // optimal found solution
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double cost__; // optimal found solution
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};
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class EigenvalueDecomposition {
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private:
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// Holds the data dimension.
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int n;
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// Stores real/imag part of a complex division.
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double cdivr, cdivi;
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// Pointer to internal memory.
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double *d, *e, *ort;
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double **V, **H;
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// Holds the computed eigenvalues.
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Mat _eigenvalues;
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// Holds the computed eigenvectors.
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Mat _eigenvectors;
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// Allocates memory.
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template<typename _Tp>
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_Tp *alloc_1d(int m) {
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return new _Tp[m];
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp *alloc_1d(int m, _Tp val) {
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_Tp *arr = alloc_1d<_Tp> (m);
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for (int i = 0; i < m; i++)
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arr[i] = val;
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return arr;
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp **alloc_2d(int m, int _n) {
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_Tp **arr = new _Tp*[m];
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for (int i = 0; i < m; i++)
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arr[i] = new _Tp[_n];
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return arr;
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp **alloc_2d(int m, int _n, _Tp val) {
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_Tp **arr = alloc_2d<_Tp> (m, _n);
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for (int i = 0; i < m; i++) {
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for (int j = 0; j < _n; j++) {
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arr[i][j] = val;
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}
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}
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return arr;
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}
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void cdiv(double xr, double xi, double yr, double yi) {
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double r, dv;
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if (std::abs(yr) > std::abs(yi)) {
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r = yi / yr;
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dv = yr + r * yi;
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cdivr = (xr + r * xi) / dv;
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cdivi = (xi - r * xr) / dv;
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} else {
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r = yr / yi;
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dv = yi + r * yr;
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cdivr = (r * xr + xi) / dv;
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cdivi = (r * xi - xr) / dv;
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}
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}
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// Nonsymmetric reduction from Hessenberg to real Schur form.
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void hqr2() {
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// This is derived from the Algol procedure hqr2,
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// by Martin and Wilkinson, Handbook for Auto. Comp.,
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// Vol.ii-Linear Algebra, and the corresponding
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// Fortran subroutine in EISPACK.
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// Initialize
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int nn = this->n;
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int n1 = nn - 1;
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int low = 0;
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int high = nn - 1;
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double eps = std::pow(2.0, -52.0);
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double exshift = 0.0;
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double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
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// Store roots isolated by balanc and compute matrix norm
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double norm = 0.0;
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for (int i = 0; i < nn; i++) {
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if (i < low || i > high) {
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d[i] = H[i][i];
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e[i] = 0.0;
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}
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for (int j = std::max(i - 1, 0); j < nn; j++) {
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norm = norm + std::abs(H[i][j]);
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}
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}
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// Outer loop over eigenvalue index
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int iter = 0;
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while (n1 >= low) {
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// Look for single small sub-diagonal element
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int l = n1;
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while (l > low) {
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s = std::abs(H[l - 1][l - 1]) + std::abs(H[l][l]);
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if (s == 0.0) {
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s = norm;
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}
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if (std::abs(H[l][l - 1]) < eps * s) {
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break;
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}
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l--;
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}
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// Check for convergence
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// One root found
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if (l == n1) {
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H[n1][n1] = H[n1][n1] + exshift;
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d[n1] = H[n1][n1];
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e[n1] = 0.0;
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n1--;
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iter = 0;
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// Two roots found
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} else if (l == n1 - 1) {
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w = H[n1][n1 - 1] * H[n1 - 1][n1];
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p = (H[n1 - 1][n1 - 1] - H[n1][n1]) / 2.0;
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q = p * p + w;
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z = std::sqrt(std::abs(q));
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H[n1][n1] = H[n1][n1] + exshift;
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H[n1 - 1][n1 - 1] = H[n1 - 1][n1 - 1] + exshift;
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x = H[n1][n1];
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// Real pair
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if (q >= 0) {
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if (p >= 0) {
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z = p + z;
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} else {
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z = p - z;
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}
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d[n1 - 1] = x + z;
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d[n1] = d[n1 - 1];
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if (z != 0.0) {
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d[n1] = x - w / z;
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}
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e[n1 - 1] = 0.0;
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e[n1] = 0.0;
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x = H[n1][n1 - 1];
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s = std::abs(x) + std::abs(z);
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p = x / s;
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q = z / s;
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r = std::sqrt(p * p + q * q);
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p = p / r;
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q = q / r;
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// Row modification
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for (int j = n1 - 1; j < nn; j++) {
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z = H[n1 - 1][j];
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H[n1 - 1][j] = q * z + p * H[n1][j];
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H[n1][j] = q * H[n1][j] - p * z;
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}
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// Column modification
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for (int i = 0; i <= n1; i++) {
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z = H[i][n1 - 1];
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H[i][n1 - 1] = q * z + p * H[i][n1];
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H[i][n1] = q * H[i][n1] - p * z;
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}
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// Accumulate transformations
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for (int i = low; i <= high; i++) {
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z = V[i][n1 - 1];
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V[i][n1 - 1] = q * z + p * V[i][n1];
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V[i][n1] = q * V[i][n1] - p * z;
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}
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// Complex pair
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} else {
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d[n1 - 1] = x + p;
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d[n1] = x + p;
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e[n1 - 1] = z;
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e[n1] = -z;
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}
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n1 = n1 - 2;
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iter = 0;
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// No convergence yet
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} else {
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// Form shift
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x = H[n1][n1];
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y = 0.0;
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w = 0.0;
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if (l < n1) {
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y = H[n1 - 1][n1 - 1];
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w = H[n1][n1 - 1] * H[n1 - 1][n1];
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}
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// Wilkinson's original ad hoc shift
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if (iter == 10) {
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exshift += x;
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for (int i = low; i <= n1; i++) {
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H[i][i] -= x;
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}
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s = std::abs(H[n1][n1 - 1]) + std::abs(H[n1 - 1][n1 - 2]);
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x = y = 0.75 * s;
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w = -0.4375 * s * s;
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}
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// MATLAB's new ad hoc shift
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if (iter == 30) {
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s = (y - x) / 2.0;
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s = s * s + w;
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if (s > 0) {
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s = std::sqrt(s);
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if (y < x) {
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s = -s;
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}
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s = x - w / ((y - x) / 2.0 + s);
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for (int i = low; i <= n1; i++) {
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H[i][i] -= s;
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}
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exshift += s;
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x = y = w = 0.964;
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}
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}
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iter = iter + 1; // (Could check iteration count here.)
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// Look for two consecutive small sub-diagonal elements
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int m = n1 - 2;
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while (m >= l) {
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z = H[m][m];
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r = x - z;
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s = y - z;
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p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
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q = H[m + 1][m + 1] - z - r - s;
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r = H[m + 2][m + 1];
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s = std::abs(p) + std::abs(q) + std::abs(r);
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p = p / s;
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q = q / s;
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r = r / s;
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if (m == l) {
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break;
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}
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if (std::abs(H[m][m - 1]) * (std::abs(q) + std::abs(r)) < eps * (std::abs(p)
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* (std::abs(H[m - 1][m - 1]) + std::abs(z) + std::abs(
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H[m + 1][m + 1])))) {
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break;
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}
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m--;
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}
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for (int i = m + 2; i <= n1; i++) {
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H[i][i - 2] = 0.0;
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if (i > m + 2) {
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H[i][i - 3] = 0.0;
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}
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}
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// Double QR step involving rows l:n and columns m:n
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for (int k = m; k <= n1 - 1; k++) {
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bool notlast = (k != n1 - 1);
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if (k != m) {
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p = H[k][k - 1];
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q = H[k + 1][k - 1];
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r = (notlast ? H[k + 2][k - 1] : 0.0);
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x = std::abs(p) + std::abs(q) + std::abs(r);
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if (x != 0.0) {
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p = p / x;
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q = q / x;
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r = r / x;
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}
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}
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if (x == 0.0) {
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break;
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}
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s = std::sqrt(p * p + q * q + r * r);
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if (p < 0) {
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s = -s;
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}
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if (s != 0) {
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if (k != m) {
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H[k][k - 1] = -s * x;
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} else if (l != m) {
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H[k][k - 1] = -H[k][k - 1];
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}
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p = p + s;
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x = p / s;
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y = q / s;
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z = r / s;
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q = q / p;
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r = r / p;
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// Row modification
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for (int j = k; j < nn; j++) {
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p = H[k][j] + q * H[k + 1][j];
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if (notlast) {
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p = p + r * H[k + 2][j];
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H[k + 2][j] = H[k + 2][j] - p * z;
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}
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H[k][j] = H[k][j] - p * x;
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H[k + 1][j] = H[k + 1][j] - p * y;
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}
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// Column modification
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for (int i = 0; i <= std::min(n1, k + 3); i++) {
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p = x * H[i][k] + y * H[i][k + 1];
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if (notlast) {
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p = p + z * H[i][k + 2];
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H[i][k + 2] = H[i][k + 2] - p * r;
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}
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H[i][k] = H[i][k] - p;
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H[i][k + 1] = H[i][k + 1] - p * q;
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}
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// Accumulate transformations
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for (int i = low; i <= high; i++) {
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p = x * V[i][k] + y * V[i][k + 1];
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if (notlast) {
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p = p + z * V[i][k + 2];
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V[i][k + 2] = V[i][k + 2] - p * r;
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}
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V[i][k] = V[i][k] - p;
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V[i][k + 1] = V[i][k + 1] - p * q;
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}
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} // (s != 0)
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} // k loop
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} // check convergence
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} // while (n1 >= low)
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// Backsubstitute to find vectors of upper triangular form
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if (norm == 0.0) {
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return;
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}
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for (n1 = nn - 1; n1 >= 0; n1--) {
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p = d[n1];
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q = e[n1];
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// Real vector
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if (q == 0) {
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int l = n1;
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H[n1][n1] = 1.0;
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for (int i = n1 - 1; i >= 0; i--) {
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w = H[i][i] - p;
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r = 0.0;
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for (int j = l; j <= n1; j++) {
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r = r + H[i][j] * H[j][n1];
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}
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if (e[i] < 0.0) {
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z = w;
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s = r;
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} else {
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l = i;
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if (e[i] == 0.0) {
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if (w != 0.0) {
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H[i][n1] = -r / w;
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} else {
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H[i][n1] = -r / (eps * norm);
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}
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// Solve real equations
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} else {
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x = H[i][i + 1];
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y = H[i + 1][i];
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q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
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t = (x * s - z * r) / q;
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H[i][n1] = t;
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if (std::abs(x) > std::abs(z)) {
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H[i + 1][n1] = (-r - w * t) / x;
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} else {
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H[i + 1][n1] = (-s - y * t) / z;
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}
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}
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// Overflow control
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t = std::abs(H[i][n1]);
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if ((eps * t) * t > 1) {
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for (int j = i; j <= n1; j++) {
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H[j][n1] = H[j][n1] / t;
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}
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}
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}
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}
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// Complex vector
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} else if (q < 0) {
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int l = n1 - 1;
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// Last vector component imaginary so matrix is triangular
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if (std::abs(H[n1][n1 - 1]) > std::abs(H[n1 - 1][n1])) {
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H[n1 - 1][n1 - 1] = q / H[n1][n1 - 1];
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H[n1 - 1][n1] = -(H[n1][n1] - p) / H[n1][n1 - 1];
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} else {
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cdiv(0.0, -H[n1 - 1][n1], H[n1 - 1][n1 - 1] - p, q);
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H[n1 - 1][n1 - 1] = cdivr;
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H[n1 - 1][n1] = cdivi;
|
|
}
|
|
H[n1][n1 - 1] = 0.0;
|
|
H[n1][n1] = 1.0;
|
|
for (int i = n1 - 2; i >= 0; i--) {
|
|
double ra, sa;
|
|
ra = 0.0;
|
|
sa = 0.0;
|
|
for (int j = l; j <= n1; j++) {
|
|
ra = ra + H[i][j] * H[j][n1 - 1];
|
|
sa = sa + H[i][j] * H[j][n1];
|
|
}
|
|
w = H[i][i] - p;
|
|
|
|
if (e[i] < 0.0) {
|
|
z = w;
|
|
r = ra;
|
|
s = sa;
|
|
} else {
|
|
l = i;
|
|
if (e[i] == 0) {
|
|
cdiv(-ra, -sa, w, q);
|
|
H[i][n1 - 1] = cdivr;
|
|
H[i][n1] = cdivi;
|
|
} else {
|
|
|
|
// Solve complex equations
|
|
|
|
x = H[i][i + 1];
|
|
y = H[i + 1][i];
|
|
double vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
|
|
double vi = (d[i] - p) * 2.0 * q;
|
|
if (vr == 0.0 && vi == 0.0) {
|
|
vr = eps * norm * (std::abs(w) + std::abs(q) + std::abs(x)
|
|
+ std::abs(y) + std::abs(z));
|
|
}
|
|
cdiv(x * r - z * ra + q * sa,
|
|
x * s - z * sa - q * ra, vr, vi);
|
|
H[i][n1 - 1] = cdivr;
|
|
H[i][n1] = cdivi;
|
|
if (std::abs(x) > (std::abs(z) + std::abs(q))) {
|
|
H[i + 1][n1 - 1] = (-ra - w * H[i][n1 - 1] + q
|
|
* H[i][n1]) / x;
|
|
H[i + 1][n1] = (-sa - w * H[i][n1] - q * H[i][n1
|
|
- 1]) / x;
|
|
} else {
|
|
cdiv(-r - y * H[i][n1 - 1], -s - y * H[i][n1], z,
|
|
q);
|
|
H[i + 1][n1 - 1] = cdivr;
|
|
H[i + 1][n1] = cdivi;
|
|
}
|
|
}
|
|
|
|
// Overflow control
|
|
|
|
t = std::max(std::abs(H[i][n1 - 1]), std::abs(H[i][n1]));
|
|
if ((eps * t) * t > 1) {
|
|
for (int j = i; j <= n1; j++) {
|
|
H[j][n1 - 1] = H[j][n1 - 1] / t;
|
|
H[j][n1] = H[j][n1] / t;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Vectors of isolated roots
|
|
|
|
for (int i = 0; i < nn; i++) {
|
|
if (i < low || i > high) {
|
|
for (int j = i; j < nn; j++) {
|
|
V[i][j] = H[i][j];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Back transformation to get eigenvectors of original matrix
|
|
|
|
for (int j = nn - 1; j >= low; j--) {
|
|
for (int i = low; i <= high; i++) {
|
|
z = 0.0;
|
|
for (int k = low; k <= std::min(j, high); k++) {
|
|
z = z + V[i][k] * H[k][j];
|
|
}
|
|
V[i][j] = z;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Nonsymmetric reduction to Hessenberg form.
|
|
void orthes() {
|
|
// This is derived from the Algol procedures orthes and ortran,
|
|
// by Martin and Wilkinson, Handbook for Auto. Comp.,
|
|
// Vol.ii-Linear Algebra, and the corresponding
|
|
// Fortran subroutines in EISPACK.
|
|
int low = 0;
|
|
int high = n - 1;
|
|
|
|
for (int m = low + 1; m <= high - 1; m++) {
|
|
|
|
// Scale column.
|
|
|
|
double scale = 0.0;
|
|
for (int i = m; i <= high; i++) {
|
|
scale = scale + std::abs(H[i][m - 1]);
|
|
}
|
|
if (scale != 0.0) {
|
|
|
|
// Compute Householder transformation.
|
|
|
|
double h = 0.0;
|
|
for (int i = high; i >= m; i--) {
|
|
ort[i] = H[i][m - 1] / scale;
|
|
h += ort[i] * ort[i];
|
|
}
|
|
double g = std::sqrt(h);
|
|
if (ort[m] > 0) {
|
|
g = -g;
|
|
}
|
|
h = h - ort[m] * g;
|
|
ort[m] = ort[m] - g;
|
|
|
|
// Apply Householder similarity transformation
|
|
// H = (I-u*u'/h)*H*(I-u*u')/h)
|
|
|
|
for (int j = m; j < n; j++) {
|
|
double f = 0.0;
|
|
for (int i = high; i >= m; i--) {
|
|
f += ort[i] * H[i][j];
|
|
}
|
|
f = f / h;
|
|
for (int i = m; i <= high; i++) {
|
|
H[i][j] -= f * ort[i];
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i <= high; i++) {
|
|
double f = 0.0;
|
|
for (int j = high; j >= m; j--) {
|
|
f += ort[j] * H[i][j];
|
|
}
|
|
f = f / h;
|
|
for (int j = m; j <= high; j++) {
|
|
H[i][j] -= f * ort[j];
|
|
}
|
|
}
|
|
ort[m] = scale * ort[m];
|
|
H[m][m - 1] = scale * g;
|
|
}
|
|
}
|
|
|
|
// Accumulate transformations (Algol's ortran).
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
for (int j = 0; j < n; j++) {
|
|
V[i][j] = (i == j ? 1.0 : 0.0);
|
|
}
|
|
}
|
|
|
|
for (int m = high - 1; m >= low + 1; m--) {
|
|
if (H[m][m - 1] != 0.0) {
|
|
for (int i = m + 1; i <= high; i++) {
|
|
ort[i] = H[i][m - 1];
|
|
}
|
|
for (int j = m; j <= high; j++) {
|
|
double g = 0.0;
|
|
for (int i = m; i <= high; i++) {
|
|
g += ort[i] * V[i][j];
|
|
}
|
|
// Double division avoids possible underflow
|
|
g = (g / ort[m]) / H[m][m - 1];
|
|
for (int i = m; i <= high; i++) {
|
|
V[i][j] += g * ort[i];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Releases all internal working memory.
|
|
void release() {
|
|
// releases the working data
|
|
delete[] d;
|
|
delete[] e;
|
|
delete[] ort;
|
|
for (int i = 0; i < n; i++) {
|
|
delete[] H[i];
|
|
delete[] V[i];
|
|
}
|
|
delete[] H;
|
|
delete[] V;
|
|
}
|
|
|
|
// Computes the Eigenvalue Decomposition for a matrix given in H.
|
|
void compute() {
|
|
// Allocate memory for the working data.
|
|
V = alloc_2d<double> (n, n, 0.0);
|
|
d = alloc_1d<double> (n);
|
|
e = alloc_1d<double> (n);
|
|
ort = alloc_1d<double> (n);
|
|
// Reduce to Hessenberg form.
|
|
orthes();
|
|
// Reduce Hessenberg to real Schur form.
|
|
hqr2();
|
|
// Copy eigenvalues to OpenCV Matrix.
|
|
_eigenvalues.create(1, n, CV_64FC1);
|
|
for (int i = 0; i < n; i++) {
|
|
_eigenvalues.at<double> (0, i) = d[i];
|
|
}
|
|
// Copy eigenvectors to OpenCV Matrix.
|
|
_eigenvectors.create(n, n, CV_64FC1);
|
|
for (int i = 0; i < n; i++)
|
|
for (int j = 0; j < n; j++)
|
|
_eigenvectors.at<double> (i, j) = V[i][j];
|
|
// Deallocate the memory by releasing all internal working data.
|
|
release();
|
|
}
|
|
|
|
public:
|
|
EigenvalueDecomposition()
|
|
: n(0) { }
|
|
|
|
// Initializes & computes the Eigenvalue Decomposition for a general matrix
|
|
// given in src. This function is a port of the EigenvalueSolver in JAMA,
|
|
// which has been released to public domain by The MathWorks and the
|
|
// National Institute of Standards and Technology (NIST).
|
|
EigenvalueDecomposition(InputArray src) {
|
|
compute(src);
|
|
}
|
|
|
|
// This function computes the Eigenvalue Decomposition for a general matrix
|
|
// given in src. This function is a port of the EigenvalueSolver in JAMA,
|
|
// which has been released to public domain by The MathWorks and the
|
|
// National Institute of Standards and Technology (NIST).
|
|
void compute(InputArray src)
|
|
{
|
|
/*if(isSymmetric(src)) {
|
|
// Fall back to OpenCV for a symmetric matrix!
|
|
cv::eigen(src, _eigenvalues, _eigenvectors);
|
|
} else {*/
|
|
Mat tmp;
|
|
// Convert the given input matrix to double. Is there any way to
|
|
// prevent allocating the temporary memory? Only used for copying
|
|
// into working memory and deallocated after.
|
|
src.getMat().convertTo(tmp, CV_64FC1);
|
|
// Get dimension of the matrix.
|
|
this->n = tmp.cols;
|
|
// Allocate the matrix data to work on.
|
|
this->H = alloc_2d<double> (n, n);
|
|
// Now safely copy the data.
|
|
for (int i = 0; i < tmp.rows; i++) {
|
|
for (int j = 0; j < tmp.cols; j++) {
|
|
this->H[i][j] = tmp.at<double>(i, j);
|
|
}
|
|
}
|
|
// Deallocates the temporary matrix before computing.
|
|
tmp.release();
|
|
// Performs the eigenvalue decomposition of H.
|
|
compute();
|
|
// }
|
|
}
|
|
|
|
~EigenvalueDecomposition() {}
|
|
|
|
// Returns the eigenvalues of the Eigenvalue Decomposition.
|
|
Mat eigenvalues() { return _eigenvalues; }
|
|
// Returns the eigenvectors of the Eigenvalue Decomposition.
|
|
Mat eigenvectors() { return _eigenvectors; }
|
|
};
|
|
|
|
#endif // DLS_H
|