Eigenvalue decomposition of a matrix. More...

Inheritance diagram for IG.Num.EigenValueDecomposition:

Collaboration diagram for IG.Num.EigenValueDecomposition:

Public Member Functions
	EigenValueDecomposition (Matrix_MathNetNumerics A)
	Constructor. More...

	EigenValueDecomposition (Matrix A)
	Constructor. More...

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. More...

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

void	Inverse (ref IMatrix inv)
	Calculates inverse of the decomposed matrix represented by the current object, and stores it in the specified matrix. More...

IMatrix	Inverse ()
	Calculates and returns inverse of the decomposed matrix represented by the current object. More...

Public Member Functions inherited from IG.Num.LinearSolverBase
virtual void	Solve (IMatrix B, ref IMatrix X)
	Solves A*X = B (a set of linear systems of equations), where B is the matrix whose colums are right-hand sides of equations to be solved. Solutions are stored to the specified matrix. More...

IMatrix	Solve (IMatrix B)
	Solves A*X = B (a set of linear systems of equations), where B is the matrix whose colums are right-hand sides of equations to be solved, and returns a matrix whose columns are solutions of the specified systems of equations. More...

virtual void	Solve (IVector b, ref IVector x)
	Solves a system of linear equations A*x=b, and stores the solution in the specified vector. More...

IVector	Solve (IVector b)
	Solves a system of linear equations A*x=b, and returns the solution. More...

Public Member Functions inherited from IG.Num.ILinearSolver
void	Solve (IMatrix B, ref IMatrix X)
	Solves A*X = B (a set of linear systems of equations), where B is the matrix whose colums are right-hand sides of equations to be solved. Solutions are stored to the specified matrix. More...

IMatrix	Solve (IMatrix B)
	Solves A*X = B (a set of linear systems of equations), where B is the matrix whose colums are right-hand sides of equations to be solved, and returns a matrix whose columns are solutions of the specified systems of equations. More...

void	Solve (IVector b, ref IVector x)
	Solves a system of linear equations A*x=b, and stores the solution in the specified vector. More...

IVector	Solve (IVector b)
	Solves a system of linear equations A*x=b, and returns the solution. More...

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. More...

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. More...

Protected Attributes
double	_determinant

bool	_determinantCalculated = false

Protected Attributes inherited from IG.Num.LinearSolverBase
MatrixBase_MathNetNumerics	_matrixSolution_MathNetNumerics

Matrix_MathNetNumerics	_matrixRighthandSides_MathNetNumerics

VectorBase_MathNetNumerics	_vectorSolution_MathNetNumerics

Vector_MathNetNumerics	_vectorRighthandSides_MathNetNumerics

IVector	auxB = null

IVector	auxX = null

Properties
bool	IsNonSingular `[get]`
	Indicates whether the matrix of coefficients of a linear system is nonsingular. More...

Matrix	Eigenvectors `[get]`
	Returns the right eigenvectors. More...

System.Numerics.Complex[]	EigenValues `[get]`
	Returns the eigen values as a an array of complex numbers. More...

double	Determinant `[get]`
	Returns the determinant. More...

Properties inherited from IG.Num.LinearSolverBase
object	Lock `[get]`
	This object's central lock object to be used by other object. Do not use this object for locking in class' methods, for this you should use InternalLock. More...

Properties inherited from IG.Num.ILinearSolver
bool	IsNonSingular `[get]`
	Indicates whether the matrix of coefficients of a linear system represented by the current decomposition object, is nonsingular. More...

Properties inherited from IG.Lib.ILockable
object	Lock `[get]`

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.

References IG.Num.Matrix.Copy().

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.

References IG.Num.Matrix.Copy().

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 )

inlineprotectedvirtual

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.

References IG.Num.Matrix.Copy().

override VectorBase_MathNetNumerics IG.Num.EigenValueDecomposition.SolveMathNetNumerics ( IVector rightHandSides )

inlineprotectedvirtual

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.

References IG.Num.VectorBase.Copy().

Member Data Documentation

double IG.Num.EigenValueDecomposition._determinant

protected

bool IG.Num.EigenValueDecomposition._determinantCalculated = false

protected

MatrixBase_MathNetNumerics IG.Num.EigenValueDecomposition._inverse

private

Property Documentation

bool IG.Num.EigenValueDecomposition.IsNonSingular

get

Indicates whether the matrix of coefficients of a linear system is nonsingular.

Returns: true if U, and hence A, is nonsingular.

Matrix IG.Num.EigenValueDecomposition.Eigenvectors

get

Returns the right eigenvectors.

System.Numerics.Complex [] IG.Num.EigenValueDecomposition.EigenValues

get

Returns the eigen values as a an array of complex numbers.

Returns: The eigen values.

double IG.Num.EigenValueDecomposition.Determinant

get

Returns the determinant.

Returns: det(A)

Exceptions

System.ArgumentException Matrix must be square.

The documentation for this class was generated from the following file:

igbase/numeric/MatrixDecompositions.cs

Public Member Functions

Protected Member Functions

Protected Attributes

Properties

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation