Represents the Cholesky decomposition of a positive-definite SymmetricMatrix.

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (Extreme.Numerics)

Syntax

Visual Basic (Declaration)
Public NotInheritable Class CholeskyDecomposition _ Inherits Decomposition

C#
public sealed class CholeskyDecomposition : Decomposition

C++
public ref class CholeskyDecomposition sealed : public Decomposition

Methods

Icon	Type	Description
	Decompose()	Performs the actual Cholesky decomposition.
	Equals(Object)	Determines whether the specified Object is equal to the current Object.
	EstimateConditionNumber()	Calculates an estimate for the condition number of the decomposed GeneralMatrix.
	Finalize()	Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
	GetDeterminant()	Calculates the determinant of the factorized GeneralMatrix.
	GetHashCode()	Serves as a hash function for a particular type.
	GetInverse()	Calculates the inverse of the factorized SymmetricMatrix.
	GetObjectData(SerializationInfo, StreamingContext)	Populates a SerializationInfo with the data needed to serialize the target object.
	GetType()	Gets the Type of the current instance.
	IsSingular()	Gets a value indicating whether the BaseMatrix of this decomposition is singular.
	MemberwiseClone()	Creates a shallow copy of the current Object.
	Rank(Double)	Returns the numerical rank of the matrix using the specified tolerance.
	SetSingularFlag()	Sets a flag that indicates the underlying matrix of this decomposition is singular.
	Solve(GeneralVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side GeneralVector and optionally overwrites the right-hand side with the solution.
	Solve(GeneralMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side GeneralMatrix and optionally overwrites the right-hand side with the solution.
	Solve(Vector)	Solves the system of linear equations for the specified right-hand side Vector.
	Solve(Matrix)	Solves the system of linear equations for the specified right-hand side Matrix.
	ToString()	Returns a String that represents the current Object.

Constructors

Icon	Type	Description
	CholeskyDecompositionNew(SymmetricMatrix)	Constructs a new CholeskyDecomposition object.
	CholeskyDecompositionNew(SymmetricMatrix, Boolean)	Constructs a new CholeskyDecomposition object.

Properties

Icon	Type	Description
	BaseMatrix	Gets the underlying matrix of the decomposition.
	Done	Gets or sets a value that indicates whether the decomposition has been performed.
	LowerTriangularFactor	Gets the lower TriangularMatrix component of this CholeskyDecomposition.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.

Remarks

The Cholesky decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LL^T, where L is a TriangularMatrix.

CholeskyDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten with the result of the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

CholeskyDecomposition inherits from LinearTransformation. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric and positive definite. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(GeneralVector, Boolean) method. You can also calculate the GetDeterminant() the GetInverse(), and an estimate for the EstimateConditionNumber().

To solve a general (non-symmetric or non-positive definite)system of equations, use the LUDecomposition class instead.

Inheritance Hierarchy

System.Object
  Extreme.Mathematics.LinearAlgebra.LinearTransformation
    Extreme.Mathematics.LinearAlgebra.Decomposition
      Extreme.Mathematics.LinearAlgebra.CholeskyDecomposition