96 lines
2.7 KiB
C++
96 lines
2.7 KiB
C++
/** @file jacobi.cpp
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* @brief Implementation of the jacobi rotation method
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*
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* @author Cory Alexander Balaton (coryab)
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* @author Janita Ovidie Sandtrøen Willumsen (janitaws)
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* @bug The eigenvalues fail the test. When comparing them to arma::eigsym
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* there is one value that is way off when testing with a 6x6 matrix.
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*/
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#include <algorithm>
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#include <cmath>
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#include <utility>
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#include "utils.hpp"
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#include "jacobi.hpp"
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#include "matrix.hpp"
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void jacobi_rotate(arma::mat& A, arma::mat& R, int k, int l)
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{
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double tau, t, c, s, sr, a_kk, a_ik, r_ik;
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tau = (A(l,l) - A(k,k))/(2.*A(k,l));
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sr = sqrt(1 + tau*tau);
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t = - tau + (tau > 0. ? sr : -sr);
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c = 1. / std::sqrt(1. + t*t);
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s = c*t;
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// Calculating the diagonal elements at index k an l
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a_kk = A(k,k);
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A(k,k) = a_kk*c*c - 2.*A(k,l)*c*s + A(l,l)*s*s;
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A(l,l) = A(l,l)*c*c + 2.*A(k,l)*c*s + a_kk*s*s;
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A(k,l) = A(l,k) = 0.; // These are 0 by definition
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// Calculating the other values on rows/cols k and l of A
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for (int i=0; i < A.n_rows; i++) {
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if (i == k || i == l) {
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continue;
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}
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a_ik = A(i,k);
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A(i,k) = a_ik*c - A(i,l)*s;
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A(k,i) = A(i,k);
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A(i,l) = A(i,l)*c + a_ik*s;
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A(l,i) = A(i,l);
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}
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// Calculate the values for R
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for (int i=0; i < R.n_rows; i++) {
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r_ik = R(i,k);
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R(i,k) = r_ik*c - R(i,l)*s;
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R(i,l) = R(i,l)*c + r_ik*s;
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}
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}
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void jacobi_eigensolver(const arma::mat& A,
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double eps,
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arma::vec& eigenvalues,
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arma::mat& eigenvectors,
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const int maxiter,
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int& iterations,
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bool& converged)
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{
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int k, l;
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double max_offdiag;
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// Initialize matrices
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arma::mat A_m = A;
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arma::mat R = arma::mat(A.n_rows, A.n_cols, arma::fill::eye);
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iterations = 0;
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// Use a do while so that max_offdiag gets a value before doing a comparison
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do {
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max_offdiag = max_offdiag_symmetric(A_m, k, l);
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jacobi_rotate(A_m, R, k, l);
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} while (max_offdiag >= eps && ++iterations < maxiter);
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// Get the diagonal of A
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arma::vec res = arma::diagvec(A_m);
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// Get the indeces of res in sorted order
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arma::uvec sorted_indeces = arma::sort_index(res);
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eigenvalues.resize(res.n_elem);
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eigenvectors.resize(res.n_elem, res.n_elem);
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// Set the eigenvalues and their corresponding vectors in order
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for (int i=0; i < res.n_elem; i++) {
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eigenvalues[i] = res[sorted_indeces[i]];
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eigenvectors.insert_cols(i, R.col(sorted_indeces[i]));
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}
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converged = max_offdiag < eps;
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}
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