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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Public Methods

Method 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 method

Least squares solution of A * X = I
public Inverse ( ) : ].double[
return ].double[

QrDecomposition() public method

Constructs a QR decomposition.
public QrDecomposition ( double value ) : System
value double The matrix A to be decomposed.
return System

QrDecomposition() public method

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.
return System

Solve() public method

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.
return ].double[

Solve() public method

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.
return double[]

SolveTranspose() public method

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.
return ].double[