DoubleQRLeastSq Class

Class DoubleQRLeastSq solves least squares problems by using a QR decomposition.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreDoubleQRLeastSq

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

Syntax

C++

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[SerializableAttribute]
public class DoubleQRLeastSq : ICloneable

<SerializableAttribute>
Public Class DoubleQRLeastSq
	Implements ICloneable

[SerializableAttribute]
public ref class DoubleQRLeastSq : ICloneable

[<SerializableAttribute>]
type DoubleQRLeastSq =  
    class
        interface ICloneable
    end

The DoubleQRLeastSq type exposes the following members.

Constructors

	Name	Description
	DoubleQRLeastSq	Constrcts a DoubleQRLeastSq instance with all sizes zero.
	DoubleQRLeastSq(DoubleMatrix)	Constructs a DoubleQRLeastSq instance from the given matrix.
	DoubleQRLeastSq(DoubleMatrix, Double)	Constructs a DoubleQRLeastSq 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	Gets a boolean value that is true if the QR decomposition may be used to solve least squares problems; otherwise false.
	Rank	Gets the numerical rank of the matrix.
	Rows	Gets the number of rows in the matrix.

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Methods

	Name	Description
	Clone	Creates a deep copy of this least squares instance.
	Factor(DoubleMatrix)	Factors a given matrix so that it may be used to solve least squares problems.
	Factor(DoubleMatrix, 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.
	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, Boolean, 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.
	OnSerializing	processing following deserialization
	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

Use class DoubleQRLeastSq to find the minimal norm solution to the overdetermined linear system:

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Ax = b

That is, find 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