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From Gilles <gil...@harfang.homelinux.org>
Subject [Math] Covariance matrix (in least-squares optimization)
Date Tue, 17 Mar 2015 15:56:42 GMT
Hi.

In interface "LeastSquaresProblem.Evaluation" (in package 
"o.a.c.m.fitting.leastsquares"),
the argument to method "getCovariances(double)" defines the condition 
for an exception to
be thrown when the product of the Jacobian matrix with its transpose is 
deemed singular.

The Javadoc does not specify the meaning of the singularity 
"threshold".
If I'm not mistaken, the value for the threshold should be different 
whether we consider
the product above, or the Jacobian matrix itself.  Also, the meaning of 
the threshold seems
tied to the QR decomposition.

I wonder whether we should not select a "more objective" criterion to 
determine when
the Jacobian should be considered singular.
Is it possible to assert that below a certain threshold, the inversion 
is bound to
produce garbage and thus set a hard-coded default?


Best regards,
Gilles


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