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  • Extreme.Mathematics.LinearAlgebra
    • BandMatrix Class
    • BandMatrix(T) Class
    • BandVector Class
    • BlockVector(T) Class
    • CholeskyDecomposition Class
    • CholeskyDecomposition(T) Class
    • CloningMethod Enumeration
    • ColumnCollection Structure
    • ColumnCollection(T) Structure
    • ComplexEigenvalueDecomposition Class
    • ComplexSingularValueDecomposition(T) Class
    • ComponentReadOnlyException Class
    • ComposedComplexMatrix(T) Class
    • ComposedComplexVector(T) Class
    • ConstantMatrix Class
    • ConstantMatrix(T) Class
    • ConstantVector Class
    • ConstantVector(T) Class
    • Decomposition Class
    • Decomposition(T) Class
    • DenseMatrix Class
    • DenseMatrix(T) Class
    • DenseVector Class
    • DenseVector(T) Class
    • DiagonalMatrix Class
    • DiagonalMatrix(T) Class
    • EigenvalueDecomposition Class
    • EigenvalueDecomposition(T) Class
    • EigenvalueRange Enumeration
    • GeneralizedDecomposition(T) Class
    • GeneralizedEigenvalueDecomposition(T) Class
    • GeneralizedSingularValueDecomposition(T) Class
    • GeneralizedSingularValueDecompositionFactors Enumeration
    • HermitianEigenvalueDecomposition Class
    • HermitianMatrix(T) Class
    • IDoubleStorage Interface
    • ILeastSquaresSolver Interface
    • IndexedVector Class
    • IndexedVector(T) Class
    • IndexValuePair Structure
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    • IResizableMatrix Interface
    • IResizableMatrix(T) Interface
    • ISingleLeastSquaresSolver Interface
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    • Kernel Class
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    • LeastSquaresSolver Class
    • LeastSquaresSolver(T) Class
    • LinearAlgebraOperations Class
    • LinearOperator Class
    • LinearOperator(T) Class
    • LQDecomposition(T) Class
    • LUDecomposition Class
    • LUDecomposition(T) Class
    • MatrixNotPositiveDefiniteException Class
    • MatrixSingularException Class
    • MatrixStructure Enumeration
    • MatrixView Class
    • MatrixView(T) Class
    • NonHermitianEigenvalueDecomposition Class
    • NonHermitianEigenvalueDecomposition(T) Class
    • NonNegativeMatrixFactorization Class
    • NonNegativeMatrixFactorization(T) Class
    • NonsymmetricEigenvalueDecomposition Class
    • PermutationMatrix Class
    • PivotVector Structure
    • QLDecomposition(T) Class
    • QRDecomposition Class
    • QRDecomposition(T) Class
    • Range Structure
    • RowCollection Structure
    • RowCollection(T) Structure
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    • RowColumnValueTriplet(T) Structure
    • RQDecomposition(T) Class
    • SingleBandCholeskyDecomposition Class
    • SingleBandLUDecomposition Class
    • SingleBandMatrix Class
    • SingleBandVector Class
    • SingleBandVector.BandVectorEnumerator Structure
    • SingleCholeskyDecomposition Class
    • SingleColumnCollection Structure
    • SingleConstantMatrix Class
    • SingleConstantVector Class
    • SingleDecomposition Class
    • SingleDenseMatrix Class
    • SingleDenseVector Class
    • SingleDiagonalMatrix Class
    • SingleEigenvalueDecomposition Class
    • SingleIndexedVector Class
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    • SingleKernel Class
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    • SingleLUDecomposition Class
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    • SingleSparseLUDecomposition Class
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    • SymmetricIndefiniteDecomposition(T) Class
    • SymmetricMatrix Class
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  • SingleSparseLUDecomposition Class
    • SingleSparseLUDecomposition Constructors
    • Properties
    • Methods
SingleSparseLUDecomposition ClassExtreme Optimization Numerical Libraries for .NET Professional
Represents the LU decomposition of a general SingleMatrix.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.LinearAlgebraSingleLinearTransformation
    Extreme.Mathematics.LinearAlgebraSingleDecomposition
      Extreme.Mathematics.LinearAlgebraSingleSparseLUDecomposition

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

C#
VB
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F#
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public sealed class SingleSparseLUDecomposition : SingleDecomposition
Public NotInheritable Class SingleSparseLUDecomposition
	Inherits SingleDecomposition
public ref class SingleSparseLUDecomposition sealed : public SingleDecomposition
[<SealedAttribute>]
type SingleSparseLUDecomposition =  
    class
        inherit SingleDecomposition
    end

The SingleSparseLUDecomposition type exposes the following members.

Constructors

  NameDescription
Public methodSingleSparseLUDecomposition(SingleMatrix)
Constructs a new SingleSparseLUDecomposition object.,
Public methodSingleSparseLUDecomposition(SingleSparseMatrix, Boolean)
Constructs a new SingleSparseLUDecomposition object.
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Properties

  NameDescription
Public propertyBaseMatrix
Gets the underlying matrix of the decomposition.
(Inherited from SingleDecomposition.)
Public propertyColumnPermutation
Gets the column permutation of the decomposition.
Public propertyLowerTriangularFactor
Returns the lower SingleTriangularMatrix component of this SingleSparseLUDecomposition.
Public propertyOverwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
(Inherited from SingleDecomposition.)
Public propertyRowPermutation
Gets the row permutation of the decomposition.
Public propertyUpperTriangularFactor
Gets the upper SingleTriangularMatrix component of this SingleSparseLUDecomposition.
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Methods

  NameDescription
Public methodApplyP(SingleMatrix)
Applies the permutation P of the decomposition PA= LU to a SingleMatrix and returns the result as a SingleDenseMatrix.
Public methodApplyP(SingleVector)
Applies the permutation P of the decomposition PA= LU to a vector.
Public methodApplyP(SingleMatrix, Boolean)
Applies the permutation P of the decomposition PA= LU to a SingleDenseMatrix.
Public methodApplyP(SingleVector, Boolean)
Applies the permutation P of the decomposition PA= LU to a vector.
Public methodApplyP(SingleMatrix, TransposeOperation, Boolean)
Applies the permutation P of the decomposition PA= LU to a SingleDenseMatrix.
Public methodApplyP(SingleVector, TransposeOperation, Boolean)
Applies the permutation P of the decomposition PA= LU to a vector.
Public methodDecompose
Performs the actual LU decomposition.
(Overrides SingleDecompositionDecompose.)
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 matrix underlying this system of equations.
(Overrides SingleLinearTransformationEstimateConditionNumber.)
Public methodGetDeterminant
Calculates the determinant of the decomposed SingleMatrix.
(Overrides SingleLinearTransformationGetDeterminant.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetInverse
Calculates the inverse of the factorized SingleMatrix.
(Overrides SingleLinearTransformationGetInverse.)
Public methodGetObjectData
Populates a SerializationInfo with the data needed to serialize the target object.
(Inherited from SingleLinearTransformation.)
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 SingleDecomposition.)
Public methodRank
Returns the numerical rank of a matrix.
(Inherited from SingleLinearTransformation.)
Public methodRank(Single)
Returns the numerical rank of a matrix using the specified tolerance.
(Overrides SingleLinearTransformationRank(Single).)
Public methodSolve(SingleMatrix)
Solves the system of linear equations for the specified right-hand side SingleMatrix.
(Inherited from SingleLinearTransformation.)
Public methodSolve(SingleVector)
Solves the system of linear equations for the specified right-hand side SingleVector.
(Inherited from SingleLinearTransformation.)
Public methodSolve(SingleDenseMatrix, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side SingleDenseMatrix and optionally overwrites the right-hand side with the solution.
(Overrides SingleLinearTransformationSolve(SingleDenseMatrix, Boolean).)
Public methodSolve(SingleDenseVector, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side SingleVector.
(Overrides SingleLinearTransformationSolve(SingleDenseVector, Boolean).)
Public methodSolveTranspose(SingleMatrix)
Solves the transposed system of linear equations for the specified right-hand side SingleMatrix.
(Inherited from SingleLinearTransformation.)
Public methodSolveTranspose(SingleVector)
Solves the system of linear equations for the specified right-hand side SingleVector.
(Inherited from SingleLinearTransformation.)
Public methodSolveTranspose(SingleDenseMatrix, Boolean)
Solves the transposed system of linear equations for the specified right-hand side SingleDenseMatrix and optionally overwrites the right-hand side with the solution.
(Overrides SingleLinearTransformationSolveTranspose(SingleDenseMatrix, Boolean).)
Public methodSolveTranspose(SingleDenseVector, Boolean)
Solves the transposed system of linear equations for the specified right-hand side DenseVector and optionally overwrites the right-hand side with the solution.
(Overrides SingleLinearTransformationSolveTranspose(SingleDenseVector, Boolean).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The LU decomposition of a matrix A rewrites the matrix in the form A= PLU, where P is a permutation matrix, L is a unit lower-triangular matrix, and U is an upper-triangular matrix.

SingleSparseLUDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten by 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.

SingleSparseLUDecomposition inherits from SingleLinearTransformation. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(SingleDenseVector, Boolean) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber.

Version Information

Numerical Libraries

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

Reference

Extreme.Mathematics.LinearAlgebra Namespace
Extreme.Mathematics.LinearAlgebraSingleDenseMatrix
Extreme.Mathematics.LinearAlgebraSingleTriangularMatrix
Extreme.Mathematics.LinearAlgebraCholeskyDecomposition
Extreme.Mathematics.LinearAlgebraSingleLinearTransformation

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