public abstract class Decomposition : LinearOperator

Public MustInherit Class Decomposition
	Inherits LinearOperator

public ref class Decomposition abstract : public LinearOperator

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

The Decomposition type exposes the following members.

	Name	Description
	Decomposition	Constructs a new Decomposition object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition.
	ColumnCount	Gets the number of columns in the matrix. (Overrides LinearOperatorColumnCount.)
	Done	Gets or sets whether the decomposition has been performed.
	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. (Overrides LinearOperatorRowCount.)

	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 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 LinearOperator.)
	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 LinearOperator.)
	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 matrix. (Inherited from LinearOperator.)
	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. (Overrides LinearOperatorIsSingular.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(Matrix)	Multiplies the decomposition to a matrix. (Overrides LinearOperatorMultiply(Matrix).)
	Multiply(Vector)	Applies the base matrix of the decomposition to a vector. (Overrides LinearOperatorMultiply(Vector).)
	MultiplyTranspose(Matrix)	Multiplies the transpose of the decomposition to a matrix. (Overrides LinearOperatorMultiplyTranspose(Matrix).)
	MultiplyTranspose(Vector)	Multiplies the transpose of the decomposition to a vector. (Overrides LinearOperatorMultiplyTranspose(Vector).)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperator.)
	Rank(Double)	Returns the numerical rank of a matrix using the specified tolerance. (Inherited from LinearOperator.)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular.
	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 linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperator.)
	Solve(DenseVector, 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 LinearOperator.)
	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. (Inherited from LinearOperator.)
	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. (Inherited from LinearOperator.)
	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.)

The Decomposition class represents a decomposition of a matrix into a product of matrices with specific properties.

The Decomposition 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 LinearOperator abstract base class.

The Decomposition 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 Decomposition, you must override the following members: EstimateConditionNumber, GetDeterminant, GetInverse, Rank(Double), Solve(DenseMatrix, Boolean), Solve(DenseVector, Boolean).

Numerical Libraries

Reference