Package xal.tools.math.r3

Class R3x3JacobiDecomposition

java.lang.Object

xal.tools.math.r3.R3x3JacobiDecomposition

public class R3x3JacobiDecomposition
extends Object

Encapsulates the results of an eigenvalue decomposition operation on a symmetric R^3×3 matrix A object using Jacobi iterations.

If the matrix is symmetric it can be factored as

A = RDR^T

where A is the target matrix, R is an orthogonal matrix in SO(3), and D is the diagonal matrix of real eigenvalues of A.

The JAMA matrix package is not explicitly used in this class.

Most of the work of the Jacobi iterations is done in the helper class JacobiIterate.

Author:

Christopher K. Allen #see xal.tools.math.r3.R3x3 #see xal.tools.math.r3.JacobiIterate

Field Summary

Fields

Modifier and Type	Field	Description
static final double	ERROR_TOLERANCE	small numerical tolerance
static final double	ONE_DEGREE	the value of one degree in radians
static final double	ROTATION_TOLERANCE	Stopping error criterion

Constructor Summary

Constructors

Constructor	Description
R3x3JacobiDecomposition(R3x3 matTarget)	Constructor for R3x3JacobiDecomposition objects.

Method Summary

Modifier and Type	Method	Description
R3x3	getDiagonalMatrix()	Return the matrix D of eigenvalues in the decomposition.
double[]	getEigenvalues()	Get the array of all eigenvalues.
int	getIterationCount()	Get the number of iterations necessary to diagonalize the matrix to give precision.
R3x3	getRotationMatrix()	Get the matrix R of eigenvectors for the decomposition.
static void	setDebug(boolean bolDebug)	Turn debugging flag on or off.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

ONE_DEGREE

public static final double ONE_DEGREE

the value of one degree in radians

See Also:

• Constant Field Values

ROTATION_TOLERANCE

public static final double ROTATION_TOLERANCE

Stopping error criterion

See Also:

• Constant Field Values

ERROR_TOLERANCE

public static final double ERROR_TOLERANCE

small numerical tolerance

See Also:

• Constant Field Values

Constructor Details

R3x3JacobiDecomposition

public R3x3JacobiDecomposition(R3x3 matTarget)
                        throws IllegalArgumentException

Constructor for R3x3JacobiDecomposition objects. The decomposition is done in the construction of this object.

Parameters:

matTarget - target matrix to factorize

Throws:

IllegalArgumentException - matrix is not symmetric

Method Details

setDebug

public static void setDebug(boolean bolDebug)

Turn debugging flag on or off. Turning on debugging flag sends debugging information to the console.

Parameters:

bolDebug - value of debugging flag.

getIterationCount

public int getIterationCount()

Get the number of iterations necessary to diagonalize the matrix to give precision.

Returns:

number of Jacobi iterations performed.

See Also:

• ROTATION_TOLERANCE

getEigenvalues

public double[] getEigenvalues()

Get the array of all eigenvalues.

Returns:

size 3 array of all the eigenvalues

getRotationMatrix

public R3x3 getRotationMatrix()

Get the matrix R of eigenvectors for the decomposition. Note that this matrix is the diagonalizing matrix for the target matrix A. Since the target matrix A is symmetric then the returned matrix R will be in the special orthogonal group SO(3). Note that, in general, this matrix could be badly conditioned.

Returns:

diagonalizing matrix of A

getDiagonalMatrix

public R3x3 getDiagonalMatrix()

Return the matrix D of eigenvalues in the decomposition. Note that since target matrix A is symmetric then this matrix will be diagonal with real elements.

Returns:

diagonal matrix D of eigenvalues of A