7.2 Using the Eigenvalue Classes

The NMath Matrix eigenvalue classes solve symmetric, Hermitian, and nonsymmetric eigenvalue problems.

Constructing Eigenvalue Objects

Instances of the eigenvalue classes are constructed from matrices of the appropriate type. For example, this code creates a FloatSymEigDecomp from a FloatSymmetricMatrix:

FloatMatrix A = new FloatMatrix( "4x4 [ 0 1.73205080756888 0 0
                                        1.73205080756888 0 2 0 
                                        0 2 0 1.73205080756888 
                                        0 0 1.73205080756888 0 ]");
FloatSymmetricMatrix Asym = new FloatSymmetricMatrix( A );
FloatSymEigDecomp eig = new FloatSymEigDecomp( Asym );

Similarly, if A is a DoubleHermitianMatrix, this code creates a DoubleHermitianEigDecomp object from A:

DoubleHermitianEigDecomp eig = new DoubleHermitianEigDecomp( A );

Testing for Goodness

All eigenvalue classes provide an IsGood property that returns true if all the eigenvalues and eigenvectors were successfully computed:

DoubleComplexEigDecomp eig = new DoubleComplexEigDecomp( A );
if ( eig.IsGood )
{
  // Do something here...
}

Retrieving Eigenvalues and Eigenvectors

All eigenvalue classes provide read-only properties and member functions for retrieving eigenvalues and eigenvectors.

• NumberOfEigenValues gets the number of eigenvalues computed.
• EigenValues gets the vector of computed eigenvalues.
• EigenValue() returns the specified eigenvalue.
• NumberOfLeftEigenVectors gets the number of left eigenvectors.
• LeftEigenVectors gets the matrix of left eigenvectors.
• LeftEigenVector() returns the specified left eigenvector.
• NumberOfRightEigenVectors gets the number of right eigenvectors.
• RightEigenVectors gets the matrix of right eigenvectors.
• RightEigenVector() returns the specified right eigenvector.

For example:

FloatEigDecomp decomp = new FloatEigDecomp( A );
Console.WriteLine( "Eigenvalues = " +
  decomp.EigenValues );
Console.WriteLine( "Left eigenvectors = " +
  decomp.LeftEigenVectors );
Console.WriteLine( "Right eigenvectors = " + 
  decomp.RightEigenVectors );

Retrieving Information About the Original Matrix

Read-only properties are also provided for retrieving information about the original matrix A:

• Rows gets the number of rows.
• Cols gets the number of columns.

Reusing Eigenvalue Decompositions

An existing eigenvalue object can be reused with another matrix using the Factor() method:

FloatSymEigDecomp eig = new FloatSymEigDecomp( A );
if ( eig.IsGood )
{
  // Do something here...
}

eig.Factor( B );
if ( eig.IsGood )
{
  // Do something here...
}

TOC |  Previous |  Next |  Index