C# Class Accord.Math.Decompositions.QrDecomposition

QR decomposition for a rectangular matrix.

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q * R.

The QR decomposition always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if FullRank returns .

Inheritance: ISolverDecomposition

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Méthodes publiques

Méthode	Description
Inverse ( ) : ].double[	Least squares solution of `A * X = I`
QrDecomposition ( double value ) : System	Constructs a QR decomposition.
QrDecomposition ( double value, bool transpose ) : System	Constructs a QR decomposition.
Solve ( double value ) : ].double[	Least squares solution of `A * X = B`
Solve ( double value ) : double[]	Least squares solution of `A * X = B`
SolveTranspose ( double value ) : ].double[	Least squares solution of `X * A = B`

Method Details

Inverse() public méthode

Least squares solution of A * X = I

public Inverse ( ) : ].double[
Résultat	].double[

QrDecomposition() public méthode

Constructs a QR decomposition.

public QrDecomposition ( double value ) : System
value	double	The matrix A to be decomposed.
Résultat	System

QrDecomposition() public méthode

Constructs a QR decomposition.

public QrDecomposition ( double value, bool transpose ) : System
value	double	The matrix A to be decomposed.
transpose	bool	True if the decomposition should be performed on /// the transpose of A rather than A itself, false otherwise. Default is false.
Résultat	System

Solve() public méthode

Least squares solution of A * X = B

Matrix row dimensions must be the same. Matrix is rank deficient.

public Solve ( double value ) : ].double[
value	double	Right-hand-side matrix with as many rows as A and any number of columns.
Résultat	].double[

Solve() public méthode

Least squares solution of A * X = B

Matrix row dimensions must be the same. Matrix is rank deficient.

public Solve ( double value ) : double[]
value	double	Right-hand-side matrix with as many rows as A and any number of columns.
Résultat	double[]

SolveTranspose() public méthode

Least squares solution of X * A = B

Matrix column dimensions must be the same. Matrix is rank deficient.

public SolveTranspose ( double value ) : ].double[
value	double	Right-hand-side matrix with as many columns as A and any number of rows.
Résultat	].double[