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= Matlab eigs() Problem Description (applies to <R2017b due to a non-fixed seed) =

For a rather large matrix (e.g 101x101) Matlab eigs() intermittently returns 2 different sets of eigenvalues when called repeatedly without changing input parameters. E.g.

[w,d]=eigs(a',10,'LM',opts);    (with opts containing disp:0) can produce outputs like below (with difference being hihglighted):

K>> [www,ddd]   = eigs(a',10,'LM',opts);

K>> sort(abs(diag(ddd)))'
ans =
    0.9914  '''0.9914''' 1.1139 1.1139
    1.2212 1.2212  1.2229 1.2229 1.2506
    1.2506

K>> [www,ddd]   = eigs(a',10,'LM',opts);

K>> sort(abs(diag(ddd)))'
ans =
    0.9914  '''1.0147''' 1.1139
    1.1139
    1.2212
    1.2212
    1.2229
    1.2229
    1.2506
    1.2506

We reported the probelm to Mathworks and got a reply (see below).

== Possible quick work-around ==

use '''eig()''' instead '''eigs()''' when possible.

== Mathworks suggested solution ==

"The behaviour you are seeing is actually not a bug, but expected behaviour. EIGS uses an iterative method of finding the eigenvalues for a matrix and starts off by choosing a starting vector completely randomly. An iterative process which starts in a different location might have completely different convergence properties and therefore might come up with a (slightly) different answer.... this kind of irregular behaviour only occurs with ill-conditioned matrices.

The best way to work around this behaviour is to specify a fixed starting vector from which the iterative process will start, i.e. by specifying the 'v0' field of the options structure that is passed into the EIGS command...."


== Problem Impact ==

E.g., when running stoch_simul, system will intermittently faill B&K test and simul too for no real or apparent reason.

Consequently, when running estimations, the eigs() problem was causing
very many AIM errors of type 4 - too few big roots.- to be reported during
the ML and MCMC estimation but none of that type 4 appeared when I rerun the same estimation after blocking eigs() and using eig() instead.

Also, it then affected the results of the  estimation : the likelihood was rather lower before the change than the likelihood after the modification and the estimated parameters were different.

=== Critical test data ===

Below .mat file contains matrix a which causes the above problem:
[[attachment:eigs_bug.mat]]