CholeskyDecomposition Class

Represents the Cholesky Decomposition of a symmetric, positive definite matrix.

Inheritance Hierarchy

SystemObject
Meta.Numerics.MatricesCholeskyDecomposition

Namespace: Meta.Numerics.Matrices
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4

Syntax

C++

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public sealed class CholeskyDecomposition

Public NotInheritable Class CholeskyDecomposition

public ref class CholeskyDecomposition sealed

[<SealedAttribute>]
type CholeskyDecomposition =  class end

The CholeskyDecomposition type exposes the following members.

Properties

	Name	Description
	Dimension	Gets the dimension of the system.

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Methods

	Name	Description
	Determinant	Computes the determinant of the original matrix.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Inverse	Computes the inverse of the original matrix.
	Solve	Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector.
	SquareRootMatrix	Returns the Cholesky square root matrix.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Remarks

A Cholesky decomposition represents a matrix as the product of a lower-left triangular matrix and its transpose. For example:

The Choleksy decomposition of a symmetric, positive definite matrix can be obtained using the CholeskyDecomposition method of the SymmetricMatrix class.

Examples

Here is an example that uses a Cholesky decomposition to solve a linear algebra problem.

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// Solve Ax = b via Cholesky decomposition
CholeskyDecomposition CD = A.CholsekyDecomposition();
ColumnVector b = new ColumnVector(1.0, 2.0, 3.0);
ColumnVector x CD.Solve(b);

Reference

Meta.Numerics.Matrices Namespace

SymmetricMatrixCholeskyDecomposition