ILMatheigGen Method (InArrayDouble, InArrayDouble, OutArrayDouble, GenEigenType, Boolean)

ILNumerics Ultimate VS Documentation

ILNumerics - Technical Application Development

Computes eigenvalues and eigenvectors (optional) of symmetric/hermitian inputs A and B: A*V=lamda*B*V.

[ILNumerics Computing Engine]

Namespace: ILNumerics
Assembly: ILNumerics.Computing (in ILNumerics.Computing.dll) Version: 5.5.0.0 (5.5.7503.3146)

Syntax

Copy

public static RetArray<double> eigGen(
	InArray<double> A,
	InArray<double> B,
	OutArray<double> V = null,
	GenEigenType type = GenEigenType.Ax_eq_lambBx,
	bool skipSymmCheck = false
)

Public Shared Function eigGen ( 
	A As InArray(Of Double),
	B As InArray(Of Double),
	Optional V As OutArray(Of Double) = Nothing,
	Optional type As GenEigenType = GenEigenType.Ax_eq_lambBx,
	Optional skipSymmCheck As Boolean = false
) As RetArray(Of Double)

Dim A As InArray(Of Double)
Dim B As InArray(Of Double)
Dim V As OutArray(Of Double)
Dim type As GenEigenType
Dim skipSymmCheck As Boolean
Dim returnValue As RetArray(Of Double)

returnValue = ILMath.eigGen(A, B, V, 
	type, skipSymmCheck)

Parameters

A: Type: ILNumericsInArrayDouble
Square, symmetric/hermitian input matrix, size [n x n].
B: Type: ILNumericsInArrayDouble
Square, symmetric/hermitian and positive definite matrix, size [n x n].
V (Optional): Type: ILNumericsOutArrayDouble
[Output, optional] Returns the eigenvectors in columns (size [n x n]). Default: (null) eigenvectors are not returned.
type (Optional): Type: ILNumericsGenEigenType
[Optional] Determines the eigen problem type. Default: (null) Ax_eq_lambBx: A*V = r*B*V.
skipSymmCheck (Optional): Type: SystemBoolean
[Optional] true: skip tests for A and B being hermitian. Default: false.

Return Value

Type: RetArrayDouble
Vector [n] of eigenvalues or a diagonal matrix [n,n] with the eigenvalues on the main diagonal if V is not null.

Exceptions

Exception	Condition
ArgumentException	if B was not positive definite, if A and B was not of the same size, if either A and/or B was found not to be symmetric/hermitian, or if the algorithm did not converge. All exceptions will give additional error details in their exception message.

Remarks

This function solves the generalized eigenproblem A*V=lamda*B*V or the problem as specified by type.

Eigenvectors in V are not normalized! See details about the normalization performed by the underlying Lapack routines.

Internally, the generalized eigenproblem A*V = r*B*V will be reduced to B^-1*A*V = r*V using cholesky factorization. The computations are handled by LAPACK functions DSYGV,SSYGV,CHEGV and ZHEGV respectively.

[ILNumerics Computing Engine]

Reference

ILMath Class

eigGen Overload

ILNumerics Namespace

ILNumericsGenEigenType

MathInternal.eigSymm(InArrayDouble)

MathInternal.eig(InArrayDouble, OutArraycomplex, MatrixProperties, Boolean)

MathInternal.chol(InArrayDouble, Boolean)