Represents the LU decomposition of a general Matrix.

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (Extreme.Numerics)

Syntax

Visual Basic (Declaration)
Public NotInheritable Class LUDecomposition _
	Inherits Decomposition
C#
public sealed class LUDecomposition : Decomposition
C++
public ref class LUDecomposition sealed : public Decomposition

Methods

IconTypeDescription
ApplyP(Vector)
Applies the permutation P of the decomposition PA= LU to a Vector.
ApplyP(Vector, Boolean)
Applies the permutation P of the decomposition PA= LU to a Vector.
ApplyP(Matrix)
Applies the permutation P of the decomposition PA= LU to a Matrix and returns the result as a GeneralMatrix.
ApplyP(GeneralMatrix, Boolean)
Applies the permutation P of the decomposition PA= LU to a GeneralMatrix.
Decompose()
Performs the actual LU decomposition.
Equals(Object)
Determines whether the specified Object is equal to the current Object.
EstimateConditionNumber()
Calculates an estimate for the condition number of the matrix underlying this system of equations.
Finalize()
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
GetDeterminant()
Calculates the determinant of the decomposed Matrix.
GetHashCode()
Serves as a hash function for a particular type.
GetInverse()
Calculates the inverse of the factorized Matrix.
GetInverse(Boolean)
Calculates the inverse of the factorized Matrix.
GetObjectData(SerializationInfo, StreamingContext)
Populates a SerializationInfo with the data needed to serialize the target object.
GetType()
Gets the Type of the current instance.
IsSingular()
Gets a value indicating whether the BaseMatrix of this decomposition is singular.
MemberwiseClone()
Creates a shallow copy of the current Object.
Rank(Double)
Returns the numerical rank of a matrix using the specified tolerance.
SetSingularFlag()
Sets a flag that indicates the underlying matrix of this decomposition is singular.
Solve(GeneralVector, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side Vector.
Solve(GeneralMatrix, Boolean)
Solves the system of simultaneous linear equations for the specified right-hand side GeneralMatrix and optionally overwrites the right-hand side with the solution.
Solve(Vector)
Solves the system of linear equations for the specified right-hand side Vector.
Solve(Matrix)
Solves the system of linear equations for the specified right-hand side Matrix.
ToString()
Returns a String that represents the current Object.

Constructors

IconTypeDescription
LUDecompositionNew(Matrix)
Constructs a new LUDecomposition object.,
LUDecompositionNew(GeneralMatrix, Boolean)
Constructs a new LUDecomposition object.

Properties

IconTypeDescription
BaseMatrix
Gets the underlying matrix of the decomposition.
Done
Gets or sets a value that indicates whether the decomposition has been performed.
LowerTriangularFactor
Returns the lower TriangularMatrix component of this LUDecomposition.
Overwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
UpperTriangularFactor
Gets the upper TriangularMatrix component of this LUDecomposition.

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 TriangularMatrix, and U is an TriangularMatrix.

LUDecomposition 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.

LUDecomposition inherits from LinearTransformation. 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(GeneralVector, Boolean) method. You can also calculate the GetDeterminant(), the GetInverse(), and an estimate for the EstimateConditionNumber().

Inheritance Hierarchy

See Also