SpectralDecompositionGetEigenvalues(ReadOnlyComplexMatrix, Boolean) Method

Computes the eigenvalues of the specified Hermitian complex matrix.

Definition

Namespace: Novacta.Analytics.Advanced
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a

C#

public static DoubleMatrix GetEigenvalues(
	ReadOnlyComplexMatrix matrix,
	bool lowerTriangularPart
)

VB

Public Shared Function GetEigenvalues ( 
	matrix As ReadOnlyComplexMatrix,
	lowerTriangularPart As Boolean
) As DoubleMatrix

C++

public:
static DoubleMatrix^ GetEigenvalues(
	ReadOnlyComplexMatrix^ matrix, 
	bool lowerTriangularPart
)

F#

static member GetEigenvalues : 
        matrix : ReadOnlyComplexMatrix * 
        lowerTriangularPart : bool -> DoubleMatrix

Parameters

matrix ReadOnlyComplexMatrix: The matrix containing the lower or upper triangular part of the matrix whose eigenvalues must be computed.
lowerTriangularPart Boolean: true if matrix contains the lower triangular part of the matrix to be decomposed; false if matrix contains its upper triangular part.

Return Value

DoubleMatrix
A column vector containing the eigenvalues of the decomposed matrix, in ascending order.

Example

In the following example, the eigenvalues of a matrix are computed.

Computing the eigenvalues of a matrix

using System;
using Novacta.Analytics.Advanced;

namespace Novacta.Analytics.CodeExamples.Advanced
{
    public class SpectralDecompositionExample1  
    {
        public void Main()
        {
            // Create a matrix containing the
            // lower triangular part of the Hermitian matrix
            // whose eigenvalues must be computed.
            var matrix = ComplexMatrix.Dense(2, 2, [ 
                new(1, 0), new(-3, -2),
                new(5, 4), new(-6,  0)
            ], StorageOrder.RowMajor);

            // Set the relevant triangular part.
            bool lowerTriangularPart = false;

            // Compute the eigenvalues.
            var eigenvalues = SpectralDecomposition.GetEigenvalues(
                matrix,
                lowerTriangularPart);

            Console.WriteLine("Matrix whose eigenvalues must be computed:");
            Console.WriteLine(ComplexMatrix.Dense(2, 2, [
                new( 1, 0), new(-3, -2),
                new(-3, 2), new(-6,  0)
            ], StorageOrder.RowMajor));


            Console.WriteLine("Matrix eigenvalues:");
            Console.WriteLine(eigenvalues);
        }
    }
}

// Executing method Main() produces the following output:
// 
// Matrix whose eigenvalues must be computed:
// (                1,                0) (               -3,               -2) 
// (               -3,                2) (               -6,                0) 
// 
// 
// Matrix eigenvalues:
// -7.52493781      
// 2.52493781       
// 
//

Exceptions

ArgumentNullException	matrix is null.
ArgumentException	matrix is not square.