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    • Extreme.Mathematics Namespace
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    • Extreme.Mathematics.Generic.LinearAlgebra Namespace
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  • Extreme.Mathematics.Generic.LinearAlgebra Namespace
    • BandVector(T) Class
    • BandVector(T).BandVectorEnumerator Structure
    • CholeskyDecomposition(T) Class
    • ColumnCollection(T) Structure
    • ConstantVector(T) Class
    • Decomposition(T) Class
    • DenseMatrix(T) Class
    • DenseVector(T) Class
    • GenericKernel(T) Class
    • GenericKernel(T).Specialization Class
    • ILinearStorage(T) Interface
    • IndexValuePair(T) Structure
    • LinearOperator(T) Class
    • LUDecomposition(T) Class
    • MatrixView(T) Class
    • QRDecomposition(T) Class
    • RowCollection(T) Structure
    • RowColumnValueTriplet(T) Structure
    • SingularValueDecomposition(T) Class
    • SymmetricEigenvalueDecomposition(T) Class
    • SymmetricMatrix(T) Class
    • TriangularMatrix(T) Class
  • Decomposition(T) Class
    • Members
    • Constructors
    • Methods
    • Properties
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Decomposition<(Of <(<'T>)>)> Class

Members See Also 
Represents a matrix decomposition.

Namespace: Extreme.Mathematics.Generic.LinearAlgebra
Assembly: Extreme.Generic.Net40 (in Extreme.Generic.Net40.dll) Version: 4.0.10170.0 (4.0.10322.0)

Syntax

C#
                      public abstract class Decomposition<T> : LinearOperator<T>
Visual Basic (Declaration)
                      Public MustInherit Class Decomposition(Of T) _
	Inherits LinearOperator(Of T)
Visual C++
                      generic<typename T>
public ref class Decomposition abstract : public LinearOperator<T>
F#
[<AbstractClassAttribute>]
type Decomposition<'T> =  
    class
        inherit LinearOperator<'T>
    end

Type Parameters

T

Remarks

The Decomposition<(Of <(<'T>)>)> class represents a decomposition of a matrix into a product of matrices with specific properties.

The Decomposition<(Of <(<'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<(Of <(<'T>)>)> abstract base class.

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

ClassDescription
LUDecomposition<(Of <(<'T>)>)>Represents a decomposition into a lower and an upper-triangular matrix.
QRDecomposition<(Of <(<'T>)>)>Represents a decomposition into an orthogonal and an upper triangular matrix.
CholeskyDecomposition<(Of <(<'T>)>)>Represents the decomposition of a SymmetricMatrix<(Of <(<'T>)>)> into the product of a lower-triangular matrix and its transpose.

Notes to inheritors: When you inherit from Decomposition<(Of <(<'T>)>)>, you must override the following members: EstimateConditionNumber()()()(), GetDeterminant()()()(), GetInverse()()()(), [!:LinearOperator<T>.Rank(LinearOperator)], [!:LinearOperator<T>.Solve(DenseMatrix<LinearOperator>, bool)], [!:LinearOperator<T>.Solve(DenseVector<LinearOperator>, bool)].

Inheritance Hierarchy

System..::..Object
  Extreme.Mathematics.Generic.LinearAlgebra..::..LinearOperator<(Of <(<'T>)>)>
    Extreme.Mathematics.Generic.LinearAlgebra..::..Decomposition<(Of <(<'T>)>)>
      Extreme.Mathematics.Generic.LinearAlgebra..::..CholeskyDecomposition<(Of <(<'T>)>)>
      Extreme.Mathematics.Generic.LinearAlgebra..::..LUDecomposition<(Of <(<'T>)>)>
      Extreme.Mathematics.Generic.LinearAlgebra..::..QRDecomposition<(Of <(<'T>)>)>
      Extreme.Mathematics.Generic.LinearAlgebra..::..SingularValueDecomposition<(Of <(<'T>)>)>
      Extreme.Mathematics.Generic.LinearAlgebra..::..SymmetricEigenvalueDecomposition<(Of <(<'T>)>)>

See Also

Decomposition<(Of <(<'T>)>)> Members
Extreme.Mathematics.Generic.LinearAlgebra Namespace
Extreme.Mathematics.Generic.LinearAlgebra..::..LUDecomposition<(Of <(<'T>)>)>
Extreme.Mathematics.Generic.LinearAlgebra..::..QRDecomposition<(Of <(<'T>)>)>
Extreme.Mathematics.Generic.LinearAlgebra..::..CholeskyDecomposition<(Of <(<'T>)>)>

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