Decomposition<T> Class

Represents a matrix decomposition.

Definition

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

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: Extreme.Mathematics.LinearAlgebra.CholeskyDecomposition<T>
Extreme.Mathematics.LinearAlgebra.ComplexSingularValueDecomposition<T>
Extreme.Mathematics.LinearAlgebra.EigenvalueDecomposition<T>
Extreme.Mathematics.LinearAlgebra.LQDecomposition<T>
Extreme.Mathematics.LinearAlgebra.LUDecomposition<T>
Extreme.Mathematics.LinearAlgebra.NonNegativeMatrixFactorization<T>
Extreme.Mathematics.LinearAlgebra.QLDecomposition<T>
Extreme.Mathematics.LinearAlgebra.QRDecomposition<T>
Extreme.Mathematics.LinearAlgebra.RQDecomposition<T>
Extreme.Mathematics.LinearAlgebra.SingularValueDecomposition<T>
Extreme.Mathematics.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 a value indicating 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

AddProductToVector	Multiplies a Vector<T> by this instance and stores the result in a second vector of type DenseVector<T>. (Inherited from LinearOperator<T>) Obsolete.
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>)
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 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>)
Multiply(TransposeOperation, Matrix<T>)	Multiplies a matrix on the left by this matrix. (Inherited from LinearOperator<T>) Obsolete.
Multiply(TransposeOperation, Vector<T>)	Multiplies a vector on the left by this vector. (Inherited from LinearOperator<T>) Obsolete.
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)