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https://issues.apache.org/jira/browse/MATH-664?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13183293#comment-13183293
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Gilles commented on MATH-664:
-----------------------------

In the current design, it is difficult to allow a custom algorithm because the 
constructor of a decomposition class takes the matrix as an argument, while the 
Jacobian matrix is constructed internally (which would be _after_ the 
instantiation of the decomposition class if created by the caller).

A clean way would be to have a new "Decomposition" interface, with a 
{{decompose(RealMatrix m)}} method. That would entail moving code that is 
currently in the decomposition classes' constructors over to implementations of 
that new method.
Since that's unlikely to occur before 3.0, I'll just change the internal 
algorithm to QR, for now.

                
> Replace "LUDecompostionImpl" with "QRDecompositionImpl" in 
> "AbstractLeastSquaresOptimizer"
> ------------------------------------------------------------------------------------------
>
>                 Key: MATH-664
>                 URL: https://issues.apache.org/jira/browse/MATH-664
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Gilles
>            Assignee: Gilles
>            Priority: Minor
>             Fix For: 3.0
>
>
> In some cases, the "getCovariances()" method throws a 
> "SingularMatrixException". This can be avoided by using "QR" instead of "LU" 
> decomposition.

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