public abstract class ComplexCholeskyDecomposition : ComplexDecomposition

Public MustInherit Class ComplexCholeskyDecomposition
	Inherits ComplexDecomposition

public ref class ComplexCholeskyDecomposition abstract : public ComplexDecomposition

[<AbstractClassAttribute>]
type ComplexCholeskyDecomposition =  
    class
        inherit ComplexDecomposition
    end

The ComplexCholeskyDecomposition type exposes the following members.

	Name	Description
	ComplexCholeskyDecomposition	Constructs a new ComplexCholeskyDecomposition object.

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

	Name	Description
	Decompose	Performs the actual Cholesky decomposition. (Overrides ComplexDecompositionDecompose.)
	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 ComplexDenseMatrix. (Overrides ComplexLinearOperatorEstimateConditionNumber.)
	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 ComplexDenseMatrix. (Overrides ComplexLinearOperatorGetDeterminant.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from ComplexLinearOperator.)
	GetInverse(Boolean)	Calculates the inverse of the factorized ComplexHermitianMatrix. (Overrides ComplexLinearOperatorGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from ComplexLinearOperator.)
	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 ComplexDecomposition.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(ComplexMatrix)	Multiplies the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	Multiply(ComplexVector)	Applies the base matrix of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexMatrix)	Multiplies the transpose of the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexVector)	Multiplies the transpose of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	Rank	Returns the numerical rank of a matrix. (Inherited from ComplexLinearOperator.)
	Rank(Double)	Returns the numerical rank of the matrix using the specified tolerance. (Overrides ComplexLinearOperatorRank(Double).)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from ComplexDecomposition.)
	Solve(ComplexMatrix)	Solves the system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	Solve(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	Solve(ComplexDenseMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolve(ComplexDenseMatrix, Boolean).)
	Solve(ComplexDenseVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolve(ComplexDenseVector, Boolean).)
	SolveTranspose(ComplexMatrix)	Solves the transposed system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexDenseMatrix, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseMatrix, Boolean).)
	SolveTranspose(ComplexDenseVector, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseVector, Boolean).)
	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.

ComplexCholeskyDecomposition 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.

ComplexCholeskyDecomposition 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(ComplexDenseVector, 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 ComplexLUDecomposition class instead.

Numerical Libraries

Reference