Matrix.CreateCirculant<T> Method

Creates a new dense circulant matrix from the first row.

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.3.0

public static DenseMatrix<T> CreateCirculant<T>(
	ReadOnlySpan<T> firstRow,
	ArrayMutability mutability = ArrayMutability.MutableValues
)

Visual Basic

Public Shared Function CreateCirculant(Of T) ( 
	firstRow As ReadOnlySpan(Of T),
	Optional mutability As ArrayMutability = ArrayMutability.MutableValues
) As DenseMatrix(Of T)

C++/CLI

public:
generic<typename T>
static DenseMatrix<T>^ CreateCirculant(
	ReadOnlySpan<T> firstRow, 
	ArrayMutability mutability = ArrayMutability::MutableValues
)

static member CreateCirculant : 
        firstRow : ReadOnlySpan<'T> * 
        ?mutability : ArrayMutability 
(* Defaults:
        let _mutability = defaultArg mutability ArrayMutability.MutableValues
*)
-> DenseMatrix<'T>

Parameters

firstRow ReadOnlySpan<T>: A span containing the elements of the first row.
mutability ArrayMutability (Optional): Specifies how the matrix's values may be changed. The default is mutable values.

Type Parameters

T: The element type of the matrix.

Return Value

DenseMatrix<T>
A new square DenseMatrix<T> with the circulant structure.

Remarks

A circulant matrix is a special kind of Toeplitz matrix where each row is a cyclic right shift of the previous row. It is fully determined by its first row.

Circulant matrices have special properties: they are diagonalized by the discrete Fourier transform, making certain operations very efficient.

Example


            // Create a 4x4 circulant matrix
            var row = new double[] { 1, 2, 3, 4 };
            var matrix = Matrix.CreateCirculant(row);
            
            // Resulting matrix:
            // [ 1  2  3  4 ]
            // [ 4  1  2  3 ]
            // [ 3  4  1  2 ]
            // [ 2  3  4  1 ]