Class SymmetricEigenSolver

Solves for eigenvalues and eigenvectors of 3x3 symmetric matrices. Uses the Symmetric QR Algorithm with Householder tridiagonalization and Wilkinson shift.

Inheritance

object

SymmetricEigenSolver

Namespace: NWH.Aerodynamics.Airfoils

Assembly: NWH.Aerodynamics.dll

Syntax

public class SymmetricEigenSolver

Remarks

Port of WildMagic5 Wm5SymmetricEigensolverGTE class from geometrictools.com. Implementation based on Algorithm 8.2.3 (Symmetric QR Algorithm) from "Matrix Computations, 2nd edition" by Golub and Van Loan. Decomposes matrix A into Q^TAQ = D where D is diagonal (eigenvalues) and Q is orthogonal (eigenvectors).

Constructors

SymmetricEigenSolver(int, int)

Creates a new eigensolver for NxN symmetric matrices.

Declaration

public SymmetricEigenSolver(int size, int maxIterations)

Parameters

Type	Name	Description
int	size	Matrix dimension (N). Must be greater than 1.
int	maxIterations	Maximum number of QR iterations allowed for convergence.

Remarks

Matrix input is stored in row-major order. Computes orthogonal matrix Q and diagonal matrix D such that Q^TAQ = D, where D contains eigenvalues and Q columns contain eigenvectors.

Fields

NO_CONVERGENCE

Declaration

public const int NO_CONVERGENCE = 2147483647

Field Value

Type	Description
int

Methods

GetEigenvalue(int)

Declaration

public double GetEigenvalue(int c)

Parameters

Type	Name	Description
int	c

Returns

Type	Description
double

GetEigenvalues()

Declaration

public double[] GetEigenvalues()

Returns

Type	Description
double[]

GetEigenvalues(double[])

Retrieves the computed eigenvalues.

Declaration

public void GetEigenvalues(double[] eigenvalues)

Parameters

Type	Name	Description
double[]	eigenvalues	Output array to receive eigenvalues. Must have size elements.

Remarks

If sorting was requested in Solve(), eigenvalues will be returned in sorted order.

GetEigenvector(int)

Declaration

public double[] GetEigenvector(int c)

Parameters

Type	Name	Description
int	c

Returns

Type	Description
double[]

GetEigenvector(int, double[])

Computes a single eigenvector corresponding to the specified eigenvalue index. More efficient than GetEigenvectors when only a subset of eigenvectors is needed.

Declaration

public void GetEigenvector(int c, double[] eigenvector)

Parameters

Type	Name	Description
int	c	Index of the eigenvector to compute (0 to size-1).
double[]	eigenvector	Output array to receive the eigenvector. Must have size elements.

GetEigenvectors()

Declaration

public double[] GetEigenvectors()

Returns

Type	Description
double[]

GetEigenvectors(double[])

Computes the orthogonal eigenvector matrix Q.

Declaration

public void GetEigenvectors(double[] eigenvectors)

Parameters

Type	Name	Description
double[]	eigenvectors	Output array to receive eigenvectors in row-major order. Must have size*size elements.

Remarks

Each column of the output matrix Q represents an eigenvector. The eigenvectors satisfy Q^TAQ = D where D is the diagonal eigenvalue matrix.

IsRotation()

Declaration

public bool IsRotation()

Returns

Type	Description
bool

Solve(double[], SortType)

Solves for eigenvalues and eigenvectors of the given symmetric matrix.

Declaration

public int Solve(double[] input, SymmetricEigenSolver.SortType eSort)

Parameters

Type	Name	Description
double[]	input	Input matrix in row-major order with size*size elements.
SymmetricEigenSolver.SortType	eSort	Sort order for eigenvalues (Decreasing, NoSorting, or Increasing).

Returns

Type	Description
int	Number of iterations until convergence, or NO_CONVERGENCE if failed to converge.