Eigenvalue decomposition of a matrix. Calculates eigenvectors and eigenvalues of a real matrix.Objects of this class are immutable. Decomposition is calculated at initialization, and the decomposed matrix can not be replaced later. More...

Inheritance diagram for IG::Num::EigenValueDecomposition:

Collaboration diagram for IG::Num::EigenValueDecomposition:

List of all members.

Public Member Functions
	EigenValueDecomposition (Matrix_MathNetNumerics A)
	Constructor.
	EigenValueDecomposition (Matrix A)
	Constructor.
void	GetProduct (ref IMatrix product)
	Calculates the product (i.e. the original matrix of coefficients of a linear system of equations) of the current decomposition, and stores it to the specified matrix.
IMatrix	GetProduct ()
	Calculates and returns the product (i.e. the original matrix of coefficients of a linear system of equations) of the current decomposition.
void	Inverse (ref IMatrix inv)
	Calculates inverse of the decomposed matrix represented by the current object, and stores it in the specified matrix.
IMatrix	Inverse ()
	Calculates and returns inverse of the decomposed matrix represented by the current object.
Protected Member Functions
override MatrixBase_MathNetNumerics	SolveMathNetNumerics (IMatrix righthandSides)
	Solves systems of linear equations with the specified right-hand sides and the current matrix decomposition by using the Math.Net Numerics library, and returns the result in Math.Net matrix form.
override VectorBase_MathNetNumerics	SolveMathNetNumerics (IVector rightHandSides)
	Solves the system of linear equations with the specified right-hand sides and the current matrix decomposition by using the Math.Net Numerics library, and returns the result in Math.Net matrix form.
Protected Attributes
internal EigenValueDecomposition_MathNetNumerics	Base = null
double	_determinant
bool	_determinantCalculated = false
Properties
bool	IsNonSingular `[get]`
	Indicates whether the matrix of coefficients of a linear system is nonsingular.
Matrix	Eigenvectors `[get]`
	Returns the right eigenvectors.
System.Numerics.Complex[]	EigenValues `[get]`
	Returns the eigen values as a an array of complex numbers.
double	Determinant `[get]`
	Returns the determinant.
Private Attributes
MatrixBase_MathNetNumerics	_inverse

Detailed Description

Eigenvalue decomposition of a matrix.

Calculates eigenvectors and eigenvalues of a real matrix.

Objects of this class are immutable. Decomposition is calculated at initialization, and the decomposed matrix can not be replaced later.

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V*D*V' and V*VT=I. If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*Inverse(V) depends upon V.Condition().

$A Igor Feb09;

Constructor & Destructor Documentation

IG::Num::EigenValueDecomposition::EigenValueDecomposition ( Matrix_MathNetNumerics A ) [inline]

Constructor.

Parameters:

A	Matrix to be decomposed.

IG::Num::EigenValueDecomposition::EigenValueDecomposition ( Matrix A ) [inline]

Constructor.

Parameters:

A	Matrix to be decomposed.

Member Function Documentation

void IG::Num::EigenValueDecomposition::GetProduct ( ref IMatrix product ) [inline]

Calculates the product (i.e. the original matrix of coefficients of a linear system of equations) of the current decomposition, and stores it to the specified matrix.

Parameters:

product Matrix where re-calculated product of the decomposed matrix is stored.

Implements IG::Num::ILinearSolver.

IMatrix IG::Num::EigenValueDecomposition::GetProduct ( ) [inline]

Calculates and returns the product (i.e. the original matrix of coefficients of a linear system of equations) of the current decomposition.

Implements IG::Num::ILinearSolver.

void IG::Num::EigenValueDecomposition::Inverse ( ref IMatrix inv ) [inline]

Calculates inverse of the decomposed matrix represented by the current object, and stores it in the specified matrix.

Parameters:

inv	Matrix where calculated inverse is stored.

Implements IG::Num::ILinearSolver.

IMatrix IG::Num::EigenValueDecomposition::Inverse ( ) [inline]

Calculates and returns inverse of the decomposed matrix represented by the current object.

Implements IG::Num::ILinearSolver.

override MatrixBase_MathNetNumerics IG::Num::EigenValueDecomposition::SolveMathNetNumerics ( IMatrix righthandSides ) [inline, protected, virtual]

Solves systems of linear equations with the specified right-hand sides and the current matrix decomposition by using the Math.Net Numerics library, and returns the result in Math.Net matrix form.

Parameters:

righthandSides Matrix that contains right-hand sides of the linear equations to be solved as its columns.

Returns:: The Math.Net Numerics matrix whose columns contains solutions to the systems of linear equations whose right-hand sides are specified by yhe righthandSides parameter.

Reimplemented from IG::Num::LinearSolverBase.

override VectorBase_MathNetNumerics IG::Num::EigenValueDecomposition::SolveMathNetNumerics ( IVector rightHandSides ) [inline, protected, virtual]

Solves the system of linear equations with the specified right-hand sides and the current matrix decomposition by using the Math.Net Numerics library, and returns the result in Math.Net matrix form.

Parameters:

righthandSides Vector of right-hand sides of the linear equations to be solved.

Returns:: The Math.Net Numerics vector whose columns contains solutions to the systems of linear equations whose right-hand sides are specified by yhe righthandSides parameter.

Reimplemented from IG::Num::LinearSolverBase.