Matrix.CreateToeplitz Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.1.0

Overload List

CreateToeplitz<T>(ReadOnlySpan<T>, ArrayMutability) Creates a new dense symmetric Toeplitz matrix from the first column.
CreateToeplitz<T>(ReadOnlySpan<T>, ReadOnlySpan<T>, ArrayMutability) Creates a new dense Toeplitz matrix from the first column and first row.

CreateToeplitz<T>(ReadOnlySpan<T>, ArrayMutability)

Creates a new dense symmetric Toeplitz matrix from the first column.
C# 
public static DenseMatrix<T> CreateToeplitz<T>(
	ReadOnlySpan<T> firstColumn,
	ArrayMutability mutability = ArrayMutability.MutableValues
)

Parameters

firstColumn  ReadOnlySpan<T>
A span containing the elements of the first column (which also defines the first row for a symmetric Toeplitz matrix).
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 symmetric Toeplitz structure.

Remarks

A symmetric Toeplitz matrix is a special case where the first row equals the first column, resulting in a symmetric matrix.

This method creates a dense representation of the Toeplitz matrix. For large matrices where memory efficiency and specialized operations are important, consider using the structured [!:ToeplitzMatrix<T>] type.

Example

C# 
// Create a 4x4 symmetric Toeplitz matrix
var col = new double[] { 1, 2, 3, 4 };
var matrix = Matrix.CreateToeplitz(col);

// Resulting matrix:
// [ 1  2  3  4 ]
// [ 2  1  2  3 ]
// [ 3  2  1  2 ]
// [ 4  3  2  1 ]

CreateToeplitz<T>(ReadOnlySpan<T>, ReadOnlySpan<T>, ArrayMutability)

Creates a new dense Toeplitz matrix from the first column and first row.
C# 
public static DenseMatrix<T> CreateToeplitz<T>(
	ReadOnlySpan<T> firstColumn,
	ReadOnlySpan<T> firstRow,
	ArrayMutability mutability = ArrayMutability.MutableValues
)

Parameters

firstColumn  ReadOnlySpan<T>
A span containing the elements of the first column.
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 DenseMatrix<T> with the Toeplitz structure.

Remarks

A Toeplitz matrix is a matrix in which each descending diagonal from left to right is constant. The matrix is defined by its first column and first row.

This method creates a dense representation of the Toeplitz matrix. For large matrices where memory efficiency and specialized operations are important, consider using the structured [!:ToeplitzMatrix<T>] type.

The first element (top-left corner) must be the same in both firstColumn and firstRow. If they differ, an exception is thrown.

Example

C# 
// Create a 4x5 Toeplitz matrix
var col = new double[] { 1, 2, 3, 4 };
var row = new double[] { 1, 5, 6, 7, 8 };
var matrix = Matrix.CreateToeplitz(col, row);

// Resulting matrix:
// [ 1  5  6  7  8 ]
// [ 2  1  5  6  7 ]
// [ 3  2  1  5  6 ]
// [ 4  3  2  1  5 ]

Exceptions

ArgumentException The first element of firstColumn and firstRow are not equal.

See Also