Re: tol in rank function

[José Luis García Pallero]

2016-10-22 13:09 GMT+02:00 siko1056 <address@hidden>:
> Hi,
>
> Octave's [simplified rank function][1] is
>
> s = svd (A);
> tol = max (size (A)) * s(1) * eps;
> r = sum (s > tol);
>
> and [Matlab's][2]
>
> s = svd(A);
> tol = max (size(A)) * eps (max(s));  % effectively only "max (size(A)) * eps
> ('double')"
> r = sum(s > tol);
>
> So maybe Octave should revisit the default tolerance for matlab
> compatibiliy. References I found go to the [SVD error bound estimation of
> LAPACK][3] and [here][4] comes close to the Octave implementation using the
> largest singular value.
>
> Two other comprehensive sources for matrix computation I would look at are
> [Golub & Van Loan 1996][5] or [Higham 2002][6].

Thank you very much for your answer

>
> Kai
>
> [1]:
> http://hg.savannah.gnu.org/hgweb/octave/file/tip/scripts/linear-algebra/rank.m
> [2]: https://www.mathworks.com/help/matlab/ref/rank.html
> [3]: http://www.netlib.org/lapack/lug/node96.html
> [4]: http://www.netlib.org/lapack/lug/node97.html
> [5]:
> http://web.mit.edu/ehliu/Public/sclark/Golub%20G.H.,%20Van%20Loan%20C.F.-%20Matrix%20Computations.pdf
> [6]:
> http://servidor.demec.ufpr.br/CFD/bibliografia/Higham_2002_Accuracy%20and%20Stability%20of%20Numerical%20Algorithms.pdf
>
>
>
> --
> View this message in context: 
> http://octave.1599824.n4.nabble.com/tol-in-rank-function-tp4680288p4680298.html
> Sent from the Octave - Maintainers mailing list archive at Nabble.com.
>



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