QrDecomposition Class

QR decomposition for a rectangular matrix.

Inheritance Hierarchy

SystemObject
Accord.Math.DecompositionsQrDecomposition

Namespace: Accord.Math.Decompositions
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

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public sealed class QrDecomposition : ICloneable, 
	ISolverMatrixDecomposition<double>

Public NotInheritable Class QrDecomposition
	Implements ICloneable, ISolverMatrixDecomposition(Of Double)

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The QrDecomposition type exposes the following members.

Constructors

	Name	Description
	QrDecomposition	Constructs a QR decomposition.

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Properties

	Name	Description
	Diagonal	Returns the diagonal of R.
	FullRank	Shows if the matrix A is of full rank.
	OrthogonalFactor	Returns the (economy-size) orthogonal factor Q.
	UpperTriangularFactor	Returns the upper triangular factor R.

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Methods

	Name	Description
	Clone	Creates a new object that is a copy of the current instance.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	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 Solve(Double) methods.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Inverse	Least squares solution of A * X = I
	Reverse	Reverses the decomposition, reconstructing the original matrix X.
	Solve(Double)	Least squares solution of A * X = B
	Solve(Double)	Least squares solution of A * X = B
	SolveTranspose	Least squares solution of X * A = B
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

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Remarks

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 .

Reference

Accord.Math.Decompositions Namespace