Eigen Class

Eigen Class

Collection of Eigen System functions.

Inheritance Hierarchy

SystemObject
Imsl.MathEigen

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class Eigen

<SerializableAttribute>
Public Class Eigen

[SerializableAttribute]
public ref class Eigen

[<SerializableAttribute>]
type Eigen =  class end

The Eigen type exposes the following members.

Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	GetValues	Returns the eigenvalues of a matrix of type double.
	GetVectors	Returns the eigenvectors.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	PerformanceIndex	Returns the performance index of a real eigensystem.
	Solve	Solves for the eigenvalues and (optionally) the eigenvectors of a real square matrix.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	MaxIterations	The maximum number of iterations.
	NumberOfProcessors	Perform the parallel calculations with the maximum possible number of processors set to NumberOfProcessors.

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Remarks

Eigen computes the eigenvalues and eigenvectors of a real matrix. The matrix is first balanced. Orthogonal similarity transformations are used to reduce the balanced matrix to a real upper Hessenberg matrix. The implicit double-shifted QR algorithm is used to compute the eigenvalues and eigenvectors of this Hessenberg matrix. The eigenvectors are normalized such that each has Euclidean length of value one. The largest component is real and positive.

The balancing routine is based on the EISPACK routine BALANC. The reduction routine is based on the EISPACK routines ORTHES and ORTRAN. The QR algorithm routine is based on the EISPACK routine HQR2. See Smith et al. (1976) for the EISPACK routines. Further details, some timing data, and credits are given in Hanson et al. (1990).

While the exact value of the performance index, $\tau$ , is highly machine dependent, the performance of Eigen is considered excellent if $\tau \lt 1$ , good if $1 \le \tau \le 100$ , and poor if $\tau \gt 100$ .

The performance index was first developed by the EISPACK project at Argonne National Laboratory; see Smith et al. (1976, pages 124-125).

Reference

Imsl.Math Namespace

Other Resources

Example