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

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

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

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

Type Parameters

T

The DecompositionT type exposes the following members.

	Name	Description
	DecompositionT	Constructs a new DecompositionT object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition.
	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.
	ElementType	Gets the element type of the matrix. (Inherited from LinearOperatorT.)
	Factors	Gets a collection of the matrix factors that make up the decomposition.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
	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.)

	Name	Description
	AddProductToVector	Obsolete. Multiplies a VectorT by this instance and stores the result in a second vector of type DenseVectorT. (Inherited from LinearOperatorT.)
	Decompose	Performs the actual decomposition.
	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 a hash function for a particular type. (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. (Overrides LinearOperatorTIsSingular.)
	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. (Overrides LinearOperatorTLeastSquaresSolveInto(VectorT, VectorT).)
	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. (Overrides LinearOperatorTMultiplyAndAddAsLeftFactorCore(T, VectorT, T, TransposeOperation, VectorT, VectorT).)
	MultiplyAsLeftCore(TransposeOperation, MatrixT, MatrixT)	Multiplies a matrix by the linear operator and returns the result. (Overrides LinearOperatorTMultiplyAsLeftCore(TransposeOperation, MatrixT, MatrixT).)
	MultiplyAsLeftCore(TransposeOperation, VectorT, VectorT)	Multiplies a vector by the linear operator and returns the result. (Overrides LinearOperatorTMultiplyAsLeftCore(TransposeOperation, VectorT, VectorT).)
	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 a matrix using the specified tolerance. (Inherited from LinearOperatorT.)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular.
	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 DecompositionT class represents a decomposition of a matrix into a product of matrices with specific properties.

The DecompositionT class defines methods and properties that are shared by all decomposition classes. This includes methods related to solving systems of simultaneous linear equations defined by the LinearOperatorT abstract base class.

The DecompositionT class is an abstract base class and cannot be instantiated directly. Instead, use one of its derived classes. These are:

Notes to inheritors: When you inherit from DecompositionT, you must override the following members: EstimateConditionNumber, GetDeterminant, GetInverse, Rank(T), Solve(VectorT).

Numerical Libraries

Reference