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ComplexDecomposition ClassExtreme Optimization Numerical Libraries for .NET Professional
Represents a matrix decomposition.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.LinearAlgebra.ComplexComplexLinearOperator
    Extreme.Mathematics.LinearAlgebra.ComplexComplexDecomposition
      Extreme.Mathematics.LinearAlgebra.ComplexComplexCholeskyDecomposition
      Extreme.Mathematics.LinearAlgebra.ComplexComplexLUDecomposition
      Extreme.Mathematics.LinearAlgebra.ComplexComplexQRDecomposition
      Extreme.Mathematics.LinearAlgebra.ComplexComplexSingularValueDecomposition
      Extreme.Mathematics.LinearAlgebraComplexEigenvalueDecomposition

Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.16312.0)
Syntax

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public abstract class ComplexDecomposition : ComplexLinearOperator
Public MustInherit Class ComplexDecomposition
	Inherits ComplexLinearOperator
public ref class ComplexDecomposition abstract : public ComplexLinearOperator
[<AbstractClassAttribute>]
type ComplexDecomposition =  
    class
        inherit ComplexLinearOperator
    end

The ComplexDecomposition type exposes the following members.

Constructors

  NameDescription
Protected methodComplexDecomposition
Constructs a new ComplexDecomposition object.
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Properties

  NameDescription
Public propertyBaseMatrix
Gets the underlying matrix of the decomposition.
Protected propertyDone
Gets or sets whether the decomposition has been performed.
Public propertyFactors
Gets a collection of the matrix factors that make up the decomposition.
Public propertyOverwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
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Methods

  NameDescription
Public methodDecompose
Performs the actual decomposition.
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Public methodEstimateConditionNumber
Calculates an estimate for the condition number of a matrix.
(Inherited from ComplexLinearOperator.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetDeterminant
Calculates the determinant of a matrix.
(Inherited from ComplexLinearOperator.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetInverse
Calculates the inverse matrix..
(Inherited from ComplexLinearOperator.)
Public methodGetInverse(Boolean)
Calculates the inverse of the factorized ComplexMatrix.
(Inherited from ComplexLinearOperator.)
Public methodGetObjectData
Populates a SerializationInfo with the data needed to serialize the target object.
(Inherited from ComplexLinearOperator.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodIsSingular
Gets a value indicating whether the BaseMatrix of this decomposition is singular.
(Overrides ComplexLinearOperatorIsSingular.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodMultiply(ComplexMatrix)
Multiplies the decomposition to a matrix.
(Overrides ComplexLinearOperatorMultiply(ComplexMatrix).)
Public methodMultiply(ComplexVector)
Applies the base matrix of the decomposition to a vector.
(Overrides ComplexLinearOperatorMultiply(ComplexVector).)
Public methodMultiplyTranspose(ComplexMatrix)
Multiplies the transpose of the decomposition to a matrix.
(Overrides ComplexLinearOperatorMultiplyTranspose(ComplexMatrix).)
Public methodMultiplyTranspose(ComplexVector)
Multiplies the transpose of the decomposition to a vector.
(Overrides ComplexLinearOperatorMultiplyTranspose(ComplexVector).)
Public methodRank
Returns the numerical rank of a matrix.
(Inherited from ComplexLinearOperator.)
Public methodRank(Double)
Returns the numerical rank of a matrix using the specified tolerance.
(Inherited from ComplexLinearOperator.)
Protected methodSetSingular
Sets a flag that indicates the underlying matrix of this decomposition is singular.
Public methodSolve(ComplexMatrix)
Solves the system of linear equations for the specified right-hand side ComplexMatrix.
(Inherited from ComplexLinearOperator.)
Public methodSolve(ComplexVector)
Solves the system of linear equations for the specified right-hand side complex vector.
(Inherited from ComplexLinearOperator.)
Public methodSolve(ComplexDenseMatrix, Boolean)
Solves the system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution.
(Inherited from ComplexLinearOperator.)
Public methodSolve(ComplexDenseVector, Boolean)
Solves the system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution.
(Inherited from ComplexLinearOperator.)
Public methodSolveTranspose(ComplexMatrix)
Solves the transposed system of linear equations for the specified right-hand side ComplexMatrix.
(Inherited from ComplexLinearOperator.)
Public methodSolveTranspose(ComplexVector)
Solves the system of linear equations for the specified right-hand side complex vector.
(Inherited from ComplexLinearOperator.)
Public methodSolveTranspose(ComplexDenseMatrix, Boolean)
Solves the transposed system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution.
(Inherited from ComplexLinearOperator.)
Public methodSolveTranspose(ComplexDenseVector, Boolean)
Solves the transposed system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution.
(Inherited from ComplexLinearOperator.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

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

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

ClassDescription
ComplexLUDecompositionRepresents a decomposition into a lower and an upper-triangular matrix.
ComplexQRDecompositionRepresents a decomposition into an orthogonal and an upper triangular matrix.
ComplexCholeskyDecompositionRepresents the decomposition of a ComplexHermitianMatrix into the product of a lower-triangular matrix and its conjugate transpose.

Notes to inheritors: When you inherit from ComplexDecomposition, you must override the following members: EstimateConditionNumber, GetDeterminant, GetInverse, Rank(Double), Solve(ComplexDenseMatrix, Boolean), Solve(ComplexDenseVector, Boolean).

Version Information

Numerical Libraries

Supported in: 5.x, 4.x
See Also

Reference

Extreme.Mathematics.LinearAlgebra.Complex Namespace
Extreme.Mathematics.LinearAlgebra.ComplexComplexLUDecomposition
Extreme.Mathematics.LinearAlgebra.ComplexComplexQRDecomposition
Extreme.Mathematics.LinearAlgebra.ComplexComplexCholeskyDecomposition

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