﻿DoubleCOWeightedLeastSq Class   # DoubleCOWeightedLeastSq Class

Class DoubleCOWeightedLeastSq solves weighted least squares problems by using a Complete Orthogonal (CO) decomposition technique. Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreDoubleCOWeightedLeastSq

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.4 Syntax
`public class DoubleCOWeightedLeastSq`

The DoubleCOWeightedLeastSq type exposes the following members. Constructors
NameDescription DoubleCOWeightedLeastSq
Default constructor. Instances created with this constructor will be empty and unsuable until the Factor method is called. DoubleCOWeightedLeastSq(DoubleMatrix, DoubleVector)
Constructucts a DoubleCOWeightedLeastSq instance from the given matrix and weights. DoubleCOWeightedLeastSq(DoubleMatrix, DoubleVector, Boolean)
Constructucts a DoubleCOWeightedLeastSq instance from the given matrix and weights.
Top Properties
NameDescription A
Gets the matrix A used in the calculation.
Top Methods
NameDescription Clone
Creates a deep copy of this weighted least squares instance. Factor(DoubleMatrix, DoubleVector)
Performs any factorization on the matrix A necessary before computing a solution to the weighted least squares problem. Factor(DoubleMatrix, DoubleVector, Boolean)
Performs any factorization on the matrix A necessary before computing a solution to the weighted least squares problem. ResidualNormSqr
Computes the 2-norm squared of the residual vector. ResidualVector
Computes and returns the residual vector. Reweight
Performs necessary computations for a change of weights. Solve
Compute the solution to the weighted least squares problem.
Top Remarks
Use class DoubleCOWeightedLeastSq to find the minimal weighted norm solution to the overdetermined linear system:
`Ax = b`
That is, find the vector x that minimizes the 2-norm of the weighted residual vector (D^-1/2)*(Ax - b). Where D is a digaonal matrix with non-negative values on the diagonal. Prerequisites on the matrix A are that it has more rows than columns, and is of full rank. The Alogorithm satisfies an accuracy bound that is not affected by ill conditioning in the weight matrix D.
Reference: Complete Orthogonal Decomposition For Weighted Least Squares Patricia D. Hough and Stephen A. Vavasis SIAM J. Matrix Anal. Appl. Vol. 18, No. 2, pp 369-392, April 1997 See Also