public abstract class CholeskyDecomposition : Decomposition

Public MustInherit Class CholeskyDecomposition
	Inherits Decomposition

public ref class CholeskyDecomposition abstract : public Decomposition

[<AbstractClassAttribute>]
type CholeskyDecomposition =  
    class
        inherit Decomposition
    end

The CholeskyDecomposition type exposes the following members.

	Name	Description
	CholeskyDecomposition	Constructs a new CholeskyDecomposition object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from Decomposition.)
	ColumnCount	Gets the number of columns in the matrix. (Inherited from Decomposition.)
	Done	Gets or sets whether the decomposition has been performed. (Inherited from Decomposition.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides DecompositionFactors.)
	LowerTriangularFactor	Returns the lower triangular component of this CholeskyDecomposition.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from Decomposition.)
	Permutation	Gets the permutation that is applied to both the rows and the columns of the base matrix before the decomposition.
	RowCount	Gets the number of rows in the matrix. (Inherited from Decomposition.)
	UpperTriangularFactor	Gets the upper triangular component of this CholeskyDecomposition.

	Name	Description
	AddProductToVector	Multiplies a Vector by this Matrix and stores the result in a second vector of type DenseVector. (Inherited from LinearOperator.)
	Decompose	Performs the actual Cholesky decomposition. (Overrides DecompositionDecompose.)
	Equals	Determines whether the specified Object is equal to the current Object. (Inherited from Object.)
	EstimateConditionNumber	Calculates an estimate for the condition number of the decomposed dense matrix. (Overrides LinearOperatorEstimateConditionNumber.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetDeterminant	Calculates the determinant of the factorized dense matrix. (Overrides LinearOperatorGetDeterminant.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from LinearOperator.)
	GetInverse(Boolean)	Calculates the inverse of the factorized symmetric matrix. (Overrides LinearOperatorGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from LinearOperator.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	IsSingular	Gets a value indicating whether the BaseMatrix of this decomposition is singular. (Inherited from Decomposition.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(Matrix)	Multiplies the decomposition to a matrix. (Inherited from Decomposition.)
	Multiply(Vector)	Applies the base matrix of the decomposition to a vector. (Inherited from Decomposition.)
	MultiplyTranspose(Matrix)	Multiplies the transpose of the decomposition to a matrix. (Inherited from Decomposition.)
	MultiplyTranspose(Vector)	Multiplies the transpose of the decomposition to a vector. (Inherited from Decomposition.)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperator.)
	Rank(Double)	Returns the numerical rank of the matrix using the specified tolerance. (Overrides LinearOperatorRank(Double).)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from Decomposition.)
	Solve(Matrix)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperator.)
	Solve(Vector)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperator.)
	Solve(DenseMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Overrides LinearOperatorSolve(DenseMatrix, Boolean).)
	Solve(DenseVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Overrides LinearOperatorSolve(DenseVector, Boolean).)
	SolveTo(DenseVector, DenseVector)	Solves the system for the specified right-hand side. (Inherited from LinearOperator.)
	SolveTo(Vector, DenseVector)	Solves the system for the specified right-hand side. (Inherited from LinearOperator.)
	SolveTranspose(Matrix)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperator.)
	SolveTranspose(Vector)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperator.)
	SolveTranspose(DenseMatrix, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Overrides LinearOperatorSolveTranspose(DenseMatrix, Boolean).)
	SolveTranspose(DenseVector, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Overrides LinearOperatorSolveTranspose(DenseVector, Boolean).)
	SolveTransposeTo	Solves the transposed system for the specified right-hand side. (Inherited from LinearOperator.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	TryDecompose	Attempts to perform the actual Cholesky decomposition.

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

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 LinearOperator. 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(DenseVector, Boolean) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

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

Numerical Libraries

Reference