﻿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) Constructs a DoubleCOWeightedLeastSq instance from the given matrix and weights.
DoubleCOWeightedLeastSq(DoubleMatrix, DoubleVector, Boolean) Constructs a DoubleCOWeightedLeastSq instance from the given matrix and weights.
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Properties
NameDescription
A Gets the matrix A used in the calculation.
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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.
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Remarks
Use class DoubleCOWeightedLeastSq to find the minimal weighted norm solution to the overdetermined linear system:
C#
`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