ComplexMatrixInPlaceConjugate Method

Transforms the entries of this instance in their complex conjugates.

Definition

Namespace: Novacta.Analytics
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a
C#
public void InPlaceConjugate()

Remarks

Let LaTeX equation be a matrix, and consider its generic entry

LaTeX equation

where LaTeX equation and LaTeX equation are the number of rows and columns of LaTeX equation, respectively.

The conjugate of LaTeX equation is the matrix LaTeX equation having LaTeX equation rows and LaTeX equation columns, whose generic entry is:

LaTeX equation

where LaTeX equation is the conjugate of complex LaTeX equation.

The method transforms this instance in its conjugate.

Example

In the following example, entries of a matrix are transformed in their corresponding complex conjugates.

C#
using System;
using System.Numerics;

namespace Novacta.Analytics.CodeExamples
{
    public class ComplexInPlaceConjugateExample0  
    {
        public void Main()
        {
            // Create a matrix.
            var data = new Complex[6] {
                new(1, -1), new(5, -5),
                new(2, -2), new(6, -6),
                new(3, -3), new(7, -7)
            };
            var matrix = ComplexMatrix.Dense(3, 2, data, StorageOrder.RowMajor);
            Console.WriteLine("Initial data matrix:");
            Console.WriteLine(matrix);

            // Transform in the conjugate matrix.
            matrix.InPlaceConjugate();

            Console.WriteLine();
            Console.WriteLine("Conjugate data matrix:");
            Console.WriteLine(matrix);
        }
    }
}

// Executing method Main() produces the following output:
// 
// Initial data matrix:
// (                1,               -1) (                5,               -5) 
// (                2,               -2) (                6,               -6) 
// (                3,               -3) (                7,               -7) 
// 
// 
// 
// Conjugate data matrix:
// (                1,                1) (                5,                5) 
// (                2,                2) (                6,                6) 
// (                3,                3) (                7,                7) 
// 
//

See Also