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  • Extreme.Mathematics.LinearAlgebra.Complex
    • ComplexBandVector Class
    • ComplexCholeskyDecomposition Class
    • ComplexColumnCollection Structure
    • ComplexConstantMatrix Class
    • ComplexConstantVector Class
    • ComplexDecomposition Class
    • ComplexDenseMatrix Class
    • ComplexDenseVector Class
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    • ComposedComplexVector Class
    • IComplexLeastSquaresSolver Interface
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    • SingleComplexBandVector Class
    • SingleComplexCholeskyDecomposition Class
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  • SingleComplexCholeskyDecomposition Class
    • SingleComplexCholeskyDecomposition Constructors
    • Properties
    • Methods
SingleComplexCholeskyDecomposition ClassExtreme Optimization Numerical Libraries for .NET Professional
Represents the Cholesky decomposition of a positive-definite SingleComplexHermitianMatrix.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexLinearTransformation
    Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexDecomposition
      Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexCholeskyDecomposition

Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics.Version4x.Net40 (in Extreme.Numerics.Version4x.Net40.dll) Version: 4.2.11333.0 (5.0.12317.0)
Syntax

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public sealed class SingleComplexCholeskyDecomposition : SingleComplexDecomposition
Public NotInheritable Class SingleComplexCholeskyDecomposition
	Inherits SingleComplexDecomposition
public ref class SingleComplexCholeskyDecomposition sealed : public SingleComplexDecomposition
[<SealedAttribute>]
type SingleComplexCholeskyDecomposition =  
    class
        inherit SingleComplexDecomposition
    end

The SingleComplexCholeskyDecomposition type exposes the following members.

Constructors

  NameDescription
Public methodSingleComplexCholeskyDecomposition(SingleComplexHermitianMatrix)
Constructs a new ComplexCholeskyDecomposition object.
Public methodSingleComplexCholeskyDecomposition(SingleComplexHermitianMatrix, Boolean)
Constructs a new ComplexCholeskyDecomposition object.
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Properties

  NameDescription
Public propertyBaseMatrix
Gets the underlying matrix of the decomposition.
(Inherited from SingleComplexDecomposition.)
Public propertyOverwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
(Inherited from SingleComplexDecomposition.)
Public propertyTriangularFactor
Gets the SingleComplexTriangularMatrix component of this ComplexCholeskyDecomposition.
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Methods

  NameDescription
Public methodDecompose
Performs the actual Cholesky decomposition.
(Overrides SingleComplexDecompositionDecompose.)
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 the decomposed SingleComplexDenseMatrix.
(Overrides SingleComplexLinearTransformationEstimateConditionNumber.)
Public methodGetDeterminant
Calculates the determinant of the factorized SingleComplexDenseMatrix.
(Overrides SingleComplexLinearTransformationGetDeterminant.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetInverse
Calculates the inverse of the factorized SingleComplexHermitianMatrix.
(Overrides SingleComplexLinearTransformationGetInverse.)
Public methodGetObjectData
Populates a SerializationInfo with the data needed to serialize the target object.
(Inherited from SingleComplexLinearTransformation.)
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.
(Inherited from SingleComplexDecomposition.)
Public methodRank
Returns the numerical rank of a matrix.
(Inherited from SingleComplexLinearTransformation.)
Public methodRank(Single)
Returns the numerical rank of the matrix using the specified tolerance.
(Overrides SingleComplexLinearTransformationRank(Single).)
Public methodSolve(SingleComplexMatrix)
Solves the system of linear equations for the specified right-hand side SingleComplexMatrix.
(Inherited from SingleComplexLinearTransformation.)
Public methodSolve(SingleComplexVector)
Solves the system of linear equations for the specified right-hand side ComplexVector.
(Inherited from SingleComplexLinearTransformation.)
Public methodSolve(SingleComplexDenseMatrix, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side SingleComplexDenseMatrix and optionally overwrites the right-hand side with the solution.
(Overrides SingleComplexLinearTransformationSolve(SingleComplexDenseMatrix, Boolean).)
Public methodSolve(SingleComplexDenseVector, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution.
(Overrides SingleComplexLinearTransformationSolve(SingleComplexDenseVector, Boolean).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The Cholesky decomposition of a real hermitian positive definite matrix A rewrites the matrix in the form A= LLH, where L is a lower-triangular matrix or in the form A= UHU, where U is a upper-triangular matrix.. Which form depends on whether the elements of the Hermitian matrix are stored in the lower or upper triangular part.

ComplexCholeskyDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten with the result of the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

ComplexCholeskyDecomposition inherits from SingleLinearTransformation. This means you can use it to solve systems of linear equations where the matrix of the system is hermitian and positive definite. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(SingleComplexDenseVector, Boolean) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a general (non-hermitian or non-positive definite)system of equations, use the ComplexLUDecomposition class instead.

Version Information

Numerical Libraries

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

Reference

Extreme.Mathematics.LinearAlgebra.Complex Namespace
Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexHermitianMatrix
Extreme.Mathematics.LinearAlgebra.ComplexSingleComplexTriangularMatrix
Extreme.Mathematics.LinearAlgebra.ComplexComplexLUDecomposition
Extreme.Mathematics.LinearAlgebraSingleLinearTransformation

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