DotNetMatrix.LUDecomposition Class Reference

LU Decomposition. 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. More...

Inheritance diagram for DotNetMatrix.LUDecomposition:

Collaboration diagram for DotNetMatrix.LUDecomposition:

Public Member Functions
	LUDecomposition (GeneralMatrix A)
	LU Decomposition More...
virtual double	Determinant ()
	Determinant More...
virtual GeneralMatrix	Solve (GeneralMatrix B)
	Solve A*X = B More...
	LUDecomposition (GeneralMatrix A)
	LU Decomposition More...
virtual double	Determinant ()
	Determinant More...
virtual GeneralMatrix	Solve (GeneralMatrix B)
	Solve A*X = B More...

Properties
virtual bool	IsNonSingular [get]
	Is the matrix nonsingular? More...
virtual GeneralMatrix	L [get]
	Return lower triangular factor More...
virtual GeneralMatrix	U [get]
	Return upper triangular factor More...
virtual int[]	Pivot [get]
	Return pivot permutation vector More...
virtual double[]	DoublePivot [get]
	Return pivot permutation vector as a one-dimensional double array More...

Private Member Functions
void ISerializable.	GetObjectData (SerializationInfo info, StreamingContext context)
void ISerializable.	GetObjectData (SerializationInfo info, StreamingContext context)

Private Attributes
double[][]	LU
	Array for internal storage of decomposition. internal array storage. More...
int	m
	Row and column dimensions, and pivot sign. column dimension. row dimension. pivot sign. More...
int	n
int	pivsign
int[]	piv
	Internal storage of pivot vector. pivot vector. More...

Detailed Description

LU Decomposition. 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 decompostion 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 IsNonSingular() returns false.

Constructor & Destructor Documentation

DotNetMatrix.LUDecomposition.LUDecomposition ( GeneralMatrix  A )

inline

LU Decomposition

Parameters

A	Rectangular matrix

Returns

Structure to access L, U and piv.

References DotNetMatrix.GeneralMatrix.ArrayCopy, DotNetMatrix.GeneralMatrix.ColumnDimension, DotNetMatrix.LUDecomposition.m, DotNetMatrix.LUDecomposition.n, DotNetMatrix.LUDecomposition.pivsign, and DotNetMatrix.GeneralMatrix.RowDimension.

DotNetMatrix.LUDecomposition.LUDecomposition ( GeneralMatrix  A )

inline

LU Decomposition

Parameters

A	Rectangular matrix

Returns

Structure to access L, U and piv.

References DotNetMatrix.GeneralMatrix.ArrayCopy, DotNetMatrix.GeneralMatrix.ColumnDimension, DotNetMatrix.LUDecomposition.m, DotNetMatrix.LUDecomposition.n, DotNetMatrix.LUDecomposition.pivsign, and DotNetMatrix.GeneralMatrix.RowDimension.

Member Function Documentation

virtual double DotNetMatrix.LUDecomposition.Determinant ( )

inlinevirtual

Determinant

Returns

det(A)

Exceptions

System.ArgumentException

Matrix must be square

References DotNetMatrix.LUDecomposition.n.

Referenced by DotNetMatrix.GeneralMatrix.Determinant().

virtual GeneralMatrix DotNetMatrix.LUDecomposition.Solve ( GeneralMatrix  B )

inlinevirtual

Solve A*X = B

Parameters

B	A Matrix with as many rows as A and any number of columns.

Returns

X so that L*U*X = B(piv,:)

Exceptions

System.ArgumentException	Matrix row dimensions must agree.
System.SystemException	Matrix is singular.

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.ColumnDimension, DotNetMatrix.GeneralMatrix.GetMatrix(), DotNetMatrix.LUDecomposition.IsNonSingular, DotNetMatrix.LUDecomposition.n, and DotNetMatrix.GeneralMatrix.RowDimension.

void ISerializable. DotNetMatrix.LUDecomposition.GetObjectData ( SerializationInfo  info, StreamingContext  context  )

inlineprivate

virtual double DotNetMatrix.LUDecomposition.Determinant ( )

inlinevirtual

Determinant

Returns

det(A)

Exceptions

System.ArgumentException

Matrix must be square

References DotNetMatrix.LUDecomposition.n.

virtual GeneralMatrix DotNetMatrix.LUDecomposition.Solve ( GeneralMatrix  B )

inlinevirtual

Solve A*X = B

Parameters

B	A Matrix with as many rows as A and any number of columns.

Returns

X so that L*U*X = B(piv,:)

Exceptions

System.ArgumentException	Matrix row dimensions must agree.
System.SystemException	Matrix is singular.

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.ColumnDimension, DotNetMatrix.GeneralMatrix.GetMatrix(), DotNetMatrix.LUDecomposition.IsNonSingular, DotNetMatrix.LUDecomposition.n, and DotNetMatrix.GeneralMatrix.RowDimension.

void ISerializable. DotNetMatrix.LUDecomposition.GetObjectData ( SerializationInfo  info, StreamingContext  context  )

inlineprivate

Member Data Documentation

double [][] DotNetMatrix.LUDecomposition.LU

private

Array for internal storage of decomposition. internal array storage.

int DotNetMatrix.LUDecomposition.m

private

Row and column dimensions, and pivot sign. column dimension. row dimension. pivot sign.

Referenced by DotNetMatrix.LUDecomposition.LUDecomposition().

int DotNetMatrix.LUDecomposition.n

private

Referenced by DotNetMatrix.LUDecomposition.Determinant(), DotNetMatrix.LUDecomposition.LUDecomposition(), and DotNetMatrix.LUDecomposition.Solve().

int DotNetMatrix.LUDecomposition.pivsign

private

Referenced by DotNetMatrix.LUDecomposition.LUDecomposition().

int [] DotNetMatrix.LUDecomposition.piv

private

Internal storage of pivot vector. pivot vector.

Property Documentation

bool DotNetMatrix.LUDecomposition.IsNonSingular

get

Is the matrix nonsingular?

Returns

true if U, and hence A, is nonsingular.

Referenced by DotNetMatrix.LUDecomposition.Solve().

GeneralMatrix DotNetMatrix.LUDecomposition.L

get

Return lower triangular factor

Returns

L

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

GeneralMatrix DotNetMatrix.LUDecomposition.U

get

Return upper triangular factor

Returns

U

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

virtual int [] DotNetMatrix.LUDecomposition.Pivot

get

Return pivot permutation vector

Returns

piv

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

virtual double [] DotNetMatrix.LUDecomposition.DoublePivot

get

Return pivot permutation vector as a one-dimensional double array

Returns

(double) piv

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The documentation for this class was generated from the following file:

• igtest/numerics/DotMatrix/Backup/LUDecomposition.cs