QRRegressionCalculation Class

Class QRRegressionCalculation computes linear regression parameters by the method of least squares using a QR decomposition.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreQRRegressionCalculation

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

C++

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[SerializableAttribute]
public class QRRegressionCalculation : IRegressionCalculation, 
	ICloneable

<SerializableAttribute>
Public Class QRRegressionCalculation
	Implements IRegressionCalculation, ICloneable

[SerializableAttribute]
public ref class QRRegressionCalculation : IRegressionCalculation, 
	ICloneable

[<SerializableAttribute>]
type QRRegressionCalculation = 
    class
        interface IRegressionCalculation
        interface ICloneable
    end

The QRRegressionCalculation type exposes the following members.

Constructors

	Name	Description
	QRRegressionCalculation	Constrcts a QRRegressionCalculation instance with all sizes equal to zero.
	QRRegressionCalculation(DoubleMatrix)	Constructs a QRRegressionCalculation instance from the given matrix.
	QRRegressionCalculation(DoubleMatrix, Double)	Constructs a QRRegressionCalculation instance from the given matrix. The specified tolerance is used in computing the numerical rank of the matrix.

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Properties

	Name	Description
	Cols	Gets the number of columns in the matrix.
	IsGood	Returns true if the QR decomposition may be used to solve least squares problems; otherwise false.
	Rank	Gets the numerical rank of the matrix.
	RankAvailable	Returns the rank if it was calculated as a byproduct of the parameter calculation.
	Rows	Gets the number of rows in the matrix.
	Tolerance	Gets and sets the tolerance used for computing the numerical rank of the regression matrix.
	XTXInv	Gets the matrix formed by taking the inverse of the product of the transpose of the regression matrix with itself, if available.
	XTXInvAvailable	Gets a boolean value indicating whether or not the matrix formed by taking the inverse of the product of the transpose of the regression matrix with itself is available.

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Methods

	Name	Description
	CalculateParameters(DoubleMatrix, DoubleVector)	Calculates the parameters for the regression using a QR decomposition of the regression matrix to solve the least squares problem.
	CalculateParameters(DoubleMatrix, DoubleVector, Boolean)	Calculates the parameters for the regression using a QR decomposition of the regression matrix to solve the least squares problem.
	Clone	Creates a deep copy of this regression calculator instance.
	Factor(DoubleMatrix)	Factors a given matrix so that it may be used to solve least squares problems.
	Factor(DoubleMatrix, Double)	Factors a given matrix so that it may be used to solve least squares problems. The specified tolerance is used in computing the numerical rank of the matrix.
	Factor(DoubleMatrix, Double, Boolean)	Factors a given matrix so that it may be used to solve least squares problems. The specified tolerance is used in computing the numerical rank of the matrix.
	ResidualNormSqr	Computes the 2-norm squared of the residual vector.
	ResidualVector	Computes and returns the residual vector.
	Solve	Computes the solution to the least squares problem Ax = b.

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Remarks

Class QRRegressionCalculation finds the minimal norm solution to the overdetermined linear system:

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Ax = b

That is, this class finds the vector x that minimizes the 2-norm of the residual vector Ax - b. Prerequisites on the matrix A are that it has more rows than columns, and is of full rank.

Reference

CenterSpace.NMath.Core Namespace