jacobi.cpp File Reference

Implementation of the jacobi rotation method. More...

#include <algorithm>
#include <cmath>
#include <utility>
#include "utils.hpp"
#include "jacobi.hpp"
#include "matrix.hpp"

Functions
void	jacobi_rotate (arma::mat &A, arma::mat &R, int k, int l)
	Computes a single rotation.
void	jacobi_eigensolver (const arma::mat &A, double eps, arma::vec &eigenvalues, arma::mat &eigenvectors, const int maxiter, int &iterations, bool &converged)
	Solves the eigenvalue problem using the jacobi rotation method.

Detailed Description

Implementation of the jacobi rotation method.

Author

Cory Alexander Balaton (coryab)

Janita Ovidie Sandtrøen Willumsen (janitaws)

Bug:

The eigenvalues fail the test. When comparing them to arma::eigsym there is one value that is way off when testing with a 6x6 matrix.

Function Documentation

jacobi_eigensolver()

void jacobi_eigensolver	(	const arma::mat &	A,
		double	eps,
		arma::vec &	eigenvalues,
		arma::mat &	eigenvectors,
		const int	maxiter,
		int &	iterations,
		bool &	converged
	)

Solves the eigenvalue problem using the jacobi rotation method.

jacobi_eigensolver Initializes matrices A_m and R before going into the main loop.

For each iteration of the loop, it finds the largest absolute off-diagonal value of A_m, and then calls jacobi_rotate. The loop stops when the largest off-diagonal is less than the tolerance (eps) or if the maximum number of iterations has been reached.

The last thing this function does is to sort the eigenvalues and the corresponding eigenvectors in ascending order.

Parameters

A	The initial matrix to be solved
eps	Tolerance
eigenvalues	A vector that will contain the computed eigenvalues
eigenvectors	A Matrix that will contain the computed eigenvectors
maxiter	The max number of iterations allowed
iterations	To keep track of how many iterations the algorithm used
converged	Tells the user if the algorithm has converged

Returns

Void

jacobi_rotate()

void jacobi_rotate	(	arma::mat &	A,
		arma::mat &	R,
		int	k,
		int	l
	)

Computes a single rotation.

jacobi_rotate computes a single rotation for Jacobi's rotation algorithm. It starts by calculating tau, t (tan), c (cos), s (sin) and then updates A and R at rows/columsn k and l.

Parameters

A	Matrix A (m)
R	The rotation matrix R (m)
k	Index of the row with the element of largest absolute value
l	Index of the column with the element of largest absolute value

Returns

Void