SymmetricIndefiniteDecompositionT Class

public abstract class SymmetricIndefiniteDecomposition<T> : Decomposition<T>

Public MustInherit Class SymmetricIndefiniteDecomposition(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class SymmetricIndefiniteDecomposition abstract : public Decomposition<T>

[<AbstractClassAttribute>]
type SymmetricIndefiniteDecomposition<'T> =  
    class
        inherit Decomposition<'T>
    end

Type Parameters

T

The SymmetricIndefiniteDecompositionT type exposes the following members.

	Name	Description
	SymmetricIndefiniteDecompositionT	Constructs a new SymmetricIndefiniteDecompositionT object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from DecompositionT.)
	BlockDiagonalFactor	Returns the block diagonal component of this SymmetricIndefiniteDecompositionT.
	ColumnCount	Gets the number of columns in the matrix. (Inherited from LinearOperatorT.)
	ColumnIndex	Gets or sets the index of labels for the columns of the matrix. (Inherited from LinearOperatorT.)
	Done	Gets or sets a value that indicates whether the decomposition has been performed. (Inherited from DecompositionT.)
	ElementType	Gets the element type of the matrix. (Inherited from LinearOperatorT.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides DecompositionTFactors.)
	FactorTriangle	Gets whether the first triangular factor in the decomposition is upper or lower triangular.
	LowerTriangularFactor	Returns the lower triangular component of this SymmetricIndefiniteDecompositionT.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from DecompositionT.)
	RowCount	Gets the number of rows in the matrix. (Inherited from LinearOperatorT.)
	RowIndex	Gets or sets the index of labels for the rows of the matrix. (Inherited from LinearOperatorT.)
	UpperTriangularFactor	Gets the upper triangular component of this SymmetricIndefiniteDecompositionT.

	Name	Description
	AddProductToVector	Obsolete. Multiplies a VectorT by this instance and stores the result in a second vector of type DenseVectorT. (Inherited from LinearOperatorT.)
	ComputeFactors	Computes the factors of the decomposition explicitly.
	Decompose	Performs the actual decomposition. (Inherited from DecompositionT.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	EstimateConditionNumber	Calculates an estimate for the condition number of a matrix. (Inherited from LinearOperatorT.)
	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 a matrix. (Inherited from LinearOperatorT.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from LinearOperatorT.)
	GetInverse(Boolean)	Calculates the inverse of the factorized matrix. (Inherited from LinearOperatorT.)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from LinearOperatorT.)
	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 DecompositionT.)
	LeastSquaresSolve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense. (Inherited from DecompositionT.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(MatrixT)	Applies the linear operator to a matrix. (Inherited from LinearOperatorT.)
	Multiply(VectorT)	Applies the linear operator to a vector. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, MatrixT)	Obsolete. Multiplies a matrix on the left by this matrix. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, VectorT)	Obsolete. Multiplies a vector on the left by this vector. (Inherited from LinearOperatorT.)
	MultiplyAndAddAsLeftFactorCore	Multiplies the matrix with a vector, adds the scaled result to another scaled vector, and returns the result. (Inherited from DecompositionT.)
	MultiplyAsLeftCore(TransposeOperation, MatrixT, MatrixT)	Multiplies a matrix by the linear operator and returns the result. (Inherited from DecompositionT.)
	MultiplyAsLeftCore(TransposeOperation, VectorT, VectorT)	Multiplies a vector by the linear operator and returns the result. (Inherited from DecompositionT.)
	MultiplyTranspose(MatrixT)	Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperatorT.)
	MultiplyTranspose(VectorT)	Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperatorT.)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperatorT.)
	Rank(T)	Returns the numerical rank of the matrix using the specified tolerance. (Overrides LinearOperatorTRank(T).)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from DecompositionT.)
	Solve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	Solve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	Solve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	Solve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SolveTranspose(MatrixT)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	SolveTranspose(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseMatrixT, 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. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseVectorT, 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. (Inherited from LinearOperatorT.)
	SolveTransposeInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveTransposeInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

The Bunch-Kaufman decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LDL^T or A= UDU^T, where L is a unit lower triangular matrix, U is an unit upper triangular matrix, and D is a block diagonal matrix made up of 1x1 and 2x2 blocks.

SymmetricIndefiniteDecompositionT 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.

SymmetricIndefiniteDecompositionT inherits from LinearOperatorT. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric but not necessarily. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(VectorT) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a symmetric positive definite system of equations, you can use the CholeskyDecompositionT class instead.

Reference