Decomposition<T> Class

Represents a matrix decomposition.

Definition

Namespace: Numerics.NET.LinearAlgebra
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.0

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

Visual Basic

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

C++/CLI

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

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

Inheritance: Object → LinearOperator<T> → Decomposition<T>

Derived: Numerics.NET.LinearAlgebra.CholeskyDecomposition<T>
Numerics.NET.LinearAlgebra.ComplexSingularValueDecomposition<T>
Numerics.NET.LinearAlgebra.EigenvalueDecomposition<T>
Numerics.NET.LinearAlgebra.LQDecomposition<T>
Numerics.NET.LinearAlgebra.LUDecomposition<T>
Numerics.NET.LinearAlgebra.NonNegativeMatrixFactorization<T>
Numerics.NET.LinearAlgebra.QLDecomposition<T>
Numerics.NET.LinearAlgebra.QRDecomposition<T>
Numerics.NET.LinearAlgebra.RQDecomposition<T>
Numerics.NET.LinearAlgebra.SchurDecomposition<T>
Numerics.NET.LinearAlgebra.SingularValueDecomposition<T>
Numerics.NET.LinearAlgebra.SymmetricIndefiniteDecomposition<T>
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Type Parameters

T

Remarks

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

The Decomposition<T> 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<T> abstract base class.

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

Class	Description
LUDecomposition<T>	Represents a decomposition into a lower and an upper-triangular matrix.
QRDecomposition<T>	Represents a decomposition into an orthogonal and an upper triangular matrix.
CholeskyDecomposition<T>	Represents the decomposition of a SymmetricMatrix<T> into the product of a lower-triangular matrix and its transpose.

Notes to inheritors: When you inherit from Decomposition<T>, you must override the following members: EstimateConditionNumber(), GetDeterminant(), GetInverse(), Rank(T), Solve(Vector<T>).

Constructors

Decomposition<T>

Constructs a new Decomposition<T> object.

Properties

BaseMatrix	Gets the underlying matrix of the decomposition.
ColumnCount	Gets the number of columns in the matrix. (Inherited from LinearOperator<T>)
ColumnIndex	Gets or sets the index of labels for the columns of the matrix. (Inherited from LinearOperator<T>) Preliminary
Done	Gets or sets a value that indicates whether the decomposition has been performed.
ElementType	Gets the element type of the matrix. (Inherited from LinearOperator<T>)
Factors	Gets a collection of the matrix factors that make up the decomposition.
Overwrite	Gets or sets whether the BaseMatrix should be overwritten by its decomposition.
RowCount	Gets the number of rows in the matrix. (Inherited from LinearOperator<T>)
RowIndex	Gets or sets the index of labels for the rows of the matrix. (Inherited from LinearOperator<T>) Preliminary

Methods

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<T>)
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<T>)
GetHashCode	Serves as the default hash function. (Inherited from Object)
GetInverse()	Calculates the inverse matrix.. (Inherited from LinearOperator<T>)
GetInverse(Boolean)	Calculates the inverse of the factorized matrix. (Inherited from LinearOperator<T>)
GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from LinearOperator<T>) Obsolete.
GetType	Gets the Type of the current instance. (Inherited from Object)
IsSingular	Gets whether the BaseMatrix of this decomposition is singular. (Overrides LinearOperator<T>.IsSingular())
LeastSquaresSolve(Matrix<T>)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense. (Inherited from LinearOperator<T>)
LeastSquaresSolve(Vector<T>)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperator<T>)
LeastSquaresSolve(DenseMatrix<T>, 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 LinearOperator<T>)
LeastSquaresSolve(DenseVector<T>, 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 LinearOperator<T>)
LeastSquaresSolveInto(Matrix<T>, Matrix<T>)	Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense. (Inherited from LinearOperator<T>)
LeastSquaresSolveInto(Vector<T>, Vector<T>)	Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense. (Overrides LinearOperator<T>.LeastSquaresSolveInto(Vector<T>, Vector<T>))
MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
Multiply(Matrix<T>)	Applies the linear operator to a matrix. (Inherited from LinearOperator<T>)
Multiply(Vector<T>)	Applies the linear operator to a vector. (Inherited from LinearOperator<T>)
MultiplyAndAddAsLeftFactorCore	Multiplies the matrix with a vector, adds the scaled result to another scaled vector, and returns the result. (Overrides LinearOperator<T>.MultiplyAndAddAsLeftFactorCore(T, Vector<T>, T, TransposeOperation, Vector<T>, Vector<T>))
MultiplyAsLeftCore(TransposeOperation, Matrix<T>, Matrix<T>)	Multiplies a matrix by the linear operator and returns the result. (Overrides LinearOperator<T>.MultiplyAsLeftCore(TransposeOperation, Matrix<T>, Matrix<T>))
MultiplyAsLeftCore(TransposeOperation, Vector<T>, Vector<T>)	Multiplies a vector by the linear operator and returns the result. (Overrides LinearOperator<T>.MultiplyAsLeftCore(TransposeOperation, Vector<T>, Vector<T>))
MultiplyTranspose(Matrix<T>)	Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperator<T>)
MultiplyTranspose(Vector<T>)	Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperator<T>)
Rank()	Returns the numerical rank of a matrix. (Inherited from LinearOperator<T>)
Rank(T)	Returns the numerical rank of a matrix using the specified tolerance. (Inherited from LinearOperator<T>)
SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular.
Solve(Matrix<T>)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperator<T>)
Solve(Vector<T>)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperator<T>)
Solve(DenseMatrix<T>, 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<T>)
Solve(DenseVector<T>, 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<T>)
SolveInto(Matrix<T>, Matrix<T>)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperator<T>)
SolveInto(Vector<T>, Vector<T>)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperator<T>)
SolveInto(TransposeOperation, Matrix<T>, Matrix<T>)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperator<T>)
SolveInto(TransposeOperation, Vector<T>, Vector<T>)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperator<T>)
SolveTranspose(Matrix<T>)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperator<T>)
SolveTranspose(Vector<T>)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperator<T>)
SolveTranspose(DenseMatrix<T>, 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<T>)
SolveTranspose(DenseVector<T>, 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<T>)
SolveTransposeInto(Matrix<T>, Matrix<T>)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperator<T>)
SolveTransposeInto(Vector<T>, Vector<T>)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperator<T>)
ToString	Returns a string that represents the current object. (Inherited from Object)