CholeskyDecompositionD Class

Cholesky Decomposition of a symmetric, positive definite matrix.

Inheritance Hierarchy

SystemObject
Accord.Math.DecompositionsCholeskyDecompositionD

Namespace: Accord.Math.Decompositions
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

Copy

[SerializableAttribute]
public sealed class CholeskyDecompositionD : ICloneable, 
	ISolverMatrixDecomposition<decimal>

<SerializableAttribute>
Public NotInheritable Class CholeskyDecompositionD
	Implements ICloneable, ISolverMatrixDecomposition(Of Decimal)

Request Example View Source

The CholeskyDecompositionD type exposes the following members.

Constructors

	Name	Description
	CholeskyDecompositionD	Constructs a new Cholesky Decomposition.

Top

Properties

	Name	Description
	Determinant	Gets the determinant of the decomposed matrix.
	Diagonal	Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
	DiagonalMatrix	Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
	IsPositiveDefinite	Gets whether the decomposed matrix was positive definite.
	IsUndefined	Gets a value indicating whether the LDLt factorization has been computed successfully or if it is undefined.
	LeftTriangularFactor	Gets the left (lower) triangular factor L so that A = L * D * L'.
	LogDeterminant	If the matrix is positive-definite, gets the log-determinant of the decomposed matrix.
	Nonsingular	Gets a value indicating whether the decomposed matrix is non-singular (i.e. invertible).

Top

Methods

	Name	Description
	Clone	Creates a new object that is a copy of the current instance.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FromLeftTriangularMatrix	Creates a new Cholesky decomposition directly from an already computed left triangular matrix L.
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetInformationMatrix	Computes (Xt * X)^1 (the inverse of the covariance matrix). This matrix can be used to determine standard errors for the coefficients when solving a linear set of equations through any of the Solve(Decimal) methods.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Inverse	Solves a set of equation systems of type A * X = I.
	InverseDiagonal(Boolean)	Computes the diagonal of the inverse of the decomposed matrix.
	InverseDiagonal(Decimal, Boolean)	Computes the diagonal of the inverse of the decomposed matrix.
	InverseTrace	Computes the trace of the inverse of the decomposed matrix.
	Reverse	Reverses the decomposition, reconstructing the original matrix X.
	Solve(Decimal)	Solves a set of equation systems of type A * X = B.
	Solve(Decimal)	Solves a set of equation systems of type A * x = b.
	Solve(Decimal, Boolean)	Solves a set of equation systems of type A * X = B.
	Solve(Decimal, Boolean)	Solves a set of equation systems of type A * x = b.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

Top

Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

Top

Remarks

For a symmetric, positive definite matrix A, the Cholesky decomposition is a lower triangular matrix L so that A = L * L'. If the matrix is not positive definite, the constructor returns a partial decomposition and sets two internal variables that can be queried using the IsUndefined and IsPositiveDefinite properties.

Any square matrix A with non-zero pivots can be written as the product of a lower triangular matrix L and an upper triangular matrix U; this is called the LU decomposition. However, if A is symmetric and positive definite, we can choose the factors such that U is the transpose of L, and this is called the Cholesky decomposition. Both the LU and the Cholesky decomposition are used to solve systems of linear equations.

When it is applicable, the Cholesky decomposition is twice as efficient as the LU decomposition.

Reference

Accord.Math.Decompositions Namespace