[Octave-patch-tracker] [patch #10067] [octave forge] (linear-algebra) Improvement of funm

[Simon]

Follow-up Comment #9, patch #10067 (project octave):

Assume that input matrix A has the Schur decomposition A = QTQ* with upper
triangular matrix T. The algorithm groups the eigenvalues of T into clusters.
Eigenvalues in each cluster have similar absolute values. In order to create
these clusters eigenvalues must be moved on the diagonal of T. E.g.,
eigenvalue T(i,i) has to be moved to an arbitrary position T(j,j).
In the original code on the homepage of Prof. Higham (Funm_files.tar
<https://www.maths.manchester.ac.uk/~higham/NAMF/Funm_files.tar>) this moving
is done with trexc, see files swap.c and swapping.m in the code. And in this
paper <https://www.maths.manchester.ac.uk/~higham/narep/narep404.pdf> (p. 475)
Higham also suggests to use trexc. 
ordschur moves a list of eingenvalues to the upper left of the diagonal of T.
Quote from help string:  
> Reorders the real Schur factorization (U,S) obtained with the 'schur'
function, so that selected eigenvalues appear in the upper left diagonal
blocks of the quasi triangular Schur matrix.
But the algorithm does not always move eingenvalues to the upper left of the
diagonal.


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