Class JaggedLuDecomposition

LU decomposition of a jagged rectangular matrix.

Inheritance

System.Object

JaggedLuDecomposition

Implements

ISolverArrayDecomposition<System.Double>

Namespace: ISynergy.Framework.Mathematics.Decompositions

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public sealed class JaggedLuDecomposition : ICloneable, ISolverArrayDecomposition<double>

Remarks

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decomposition with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if Nonsingular returns false.

If you need to compute a LU decomposition for matrices with data types other than double, see JaggedLuDecomposition. If you need to compute a LU decomposition for a multidimensional matrix, see LuDecomposition, LuDecomposition.

Constructors

JaggedLuDecomposition(Double[][], Boolean, Boolean)

Constructs a new LU decomposition.

Declaration

public JaggedLuDecomposition(double[][] value, bool transpose = false, bool inPlace = false)

Parameters

Type	Name	Description
System.Double[][]	value	The matrix A to be decomposed.
System.Boolean	transpose	True if the decomposition should be performed on the transpose of A rather than A itself, false otherwise. Default is false.
System.Boolean	inPlace	True if the decomposition should be performed over the value matrix rather than on a copy of it. If true, the matrix will be destroyed during the decomposition. Default is false.

Properties

Determinant

Returns the determinant of the matrix.

Declaration

public double Determinant { get; }

Property Value

Type	Description
System.Double

LogDeterminant

Returns the log-determinant of the matrix.

Declaration

public double LogDeterminant { get; }

Property Value

Type	Description
System.Double

LowerTriangularFactor

Returns the lower triangular factor L with A=LU.

Declaration

public double[][] LowerTriangularFactor { get; }

Property Value

Type	Description
System.Double[][]

Nonsingular

Returns if the matrix is non-singular (i.e. invertible).

Declaration

public bool Nonsingular { get; }

Property Value

Type	Description
System.Boolean

PivotPermutationVector

Returns the pivot permutation vector.

Declaration

public int[] PivotPermutationVector { get; }

Property Value

Type	Description
System.Int32[]

UpperTriangularFactor

Returns the lower triangular factor L with A=LU.

Declaration

public double[][] UpperTriangularFactor { get; }

Property Value

Type	Description
System.Double[][]

Methods

Clone()

Creates a new object that is a copy of the current instance.

Declaration

public object Clone()

Returns

Type	Description
System.Object	A new object that is a copy of this instance.

GetInformationMatrix()

Computes (Xt * X)^1 (the inverse of the covariance matrix). This matrix can be used to determine standard errors for the coefficients when solving a linear set of equations through any of the methods.

Declaration

public double[][] GetInformationMatrix()

Returns

Type	Description
System.Double[][]

Inverse()

Solves a set of equation systems of type A * X = I.

Declaration

public double[][] Inverse()

Returns

Type	Description
System.Double[][]

Reverse()

Reverses the decomposition, reconstructing the original matrix X.

Declaration

public double[][] Reverse()

Returns

Type	Description
System.Double[][]

Solve(Double[])

Solves a set of equation systems of type A * X = B.

Declaration

public double[] Solve(double[] value)

Parameters

Type	Name	Description
System.Double[]	value	Right hand side column vector with as many rows as A.

Returns

Type	Description
System.Double[]	Matrix X so that L * U * X = B.

Solve(Double[][])

Solves a set of equation systems of type A * X = B.

Declaration

public double[][] Solve(double[][] value)

Parameters

Type	Name	Description
System.Double[][]	value	Right hand side matrix with as many rows as A and any number of columns.

Returns

Type	Description
System.Double[][]	Matrix X so that L * U * X = B.

SolveForDiagonal(Double[])

Solves a set of equation systems of type A * X = B where B is a diagonal matrix.

Declaration

public double[][] SolveForDiagonal(double[] diagonal)

Parameters

Type	Name	Description
System.Double[]	diagonal	Diagonal fo the right hand side matrix with as many rows as A.

Returns

Type	Description
System.Double[][]	Matrix X so that L * U * X = B.

SolveTranspose(Double[][])

Solves a set of equation systems of type X * A = B.

Declaration

public double[][] SolveTranspose(double[][] value)

Parameters

Type	Name	Description
System.Double[][]	value	Right hand side matrix with as many columns as A and any number of rows.

Returns

Type	Description
System.Double[][]	Matrix X so that X * L * U = A.

Implements

ISolverArrayDecomposition<T>

Extension Methods

Matrix.Replace<T>(T, Object, Object)

Matrix.IsEqual(Object, Object, Decimal, Decimal)

EntityBaseExtensions.HasProperty(Object, String)

ArrayExtensions.Concatenate<T>(T, T[])

CollectionExtensions.FromHierarchy<TSource>(TSource, Func<TSource, TSource>, Func<TSource, Boolean>)

CollectionExtensions.FromHierarchy<TSource>(TSource, Func<TSource, TSource>)

ObjectExtensions.Clone<T>(T)

ObjectExtensions.To<T>(Object)

ObjectExtensions.To(Object, Type)

ObjectExtensions.HasMethod(Object, String)

ObjectExtensions.AddressOf<T>(T)

ReflectionExtensions.GetIdentityValue<T>(T)

ReflectionExtensions.GetIdentityValue<T, TResult>(T)

ReflectionExtensions.GetIdentityProperty<T>(T)

ReflectionExtensions.HasIdentityProperty<T>(T)

ReflectionExtensions.GetPropertyValue<T, TResult>(T, String, TResult)

ReflectionExtensions.GetPropertyInfo<T, TValue>(T, Expression<Func<T, TValue>>)

ReflectionExtensions.GetTitleValue<T>(T)

ReflectionExtensions.HasParentIdentityProperty<T>(T)

ReflectionExtensions.GetParentIdentityProperty<T>(T)

ReflectionExtensions.IsFreeApplication<T>(T)

See Also

CholeskyDecomposition

EigenvalueDecomposition

SingularValueDecomposition

JaggedEigenvalueDecomposition

JaggedSingularValueDecomposition