Minor problem with "test eigs.cc"

[Ben Abbott]

Usually the tests for eigs.cc pass. However, occasionally a test fails ... 

octave:23> for n=1:10
> test eigs.cc
> end
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
PASSES 149 out of 149 tests
warning: eigs: Only 2 of the 4 requested eigenvalues converged
PASSES 149 out of 149 tests
  ***** testif HAVE_ARPACK
 [v1,d1] = eigs(A, k, 'li');
 d1 = diag(d1);
 for i=1:k
  assert(max(abs((A - d1(i)*eye(n))*v1(:,i))),0.,1e-11)
 endfor
!!!!! test failed
assert (max (abs ((A - d1 (i) * eye (n)) * v1 (:, i))),0.,1e-11) expected
0
but got
 5.4678e-10
maximum absolute error 5.46777e-10 exceeds tolerance 1e-11

The "si" case also fails occasionally.

I checked to see what v1 and d1 were equal to for the "si" case.

octave:28> test eigs.cc
v1 =

  -1.2620e-15   4.3321e-01   1.3679e-15  -8.5117e-01
   4.3321e-01   1.4068e-16  -8.5117e-01  -2.1346e-15
   3.1932e-15  -8.2468e-01  -2.2144e-16   5.0501e-01
  -8.2468e-01  -4.7564e-16   5.0501e-01   9.4326e-16
  -2.0027e-15   3.5375e-01   8.5673e-17  -1.4078e-01
   3.5375e-01   5.1071e-17  -1.4078e-01  -2.1120e-16
   6.6293e-16  -8.3095e-02  -2.6173e-17   2.5413e-02
  -8.3095e-02   5.6656e-18   2.5413e-02   3.0575e-17
  -2.5145e-16   1.3363e-02   5.7272e-17  -3.3829e-03
   1.3363e-02  -7.3601e-19  -3.3829e-03   2.5479e-17
   9.8410e-17  -1.6307e-03  -6.5828e-17   3.5633e-04
  -1.6307e-03  -7.4956e-19   3.5633e-04   2.8022e-17
   5.1545e-17   1.6021e-04  -8.7960e-17  -3.1037e-05
   1.6021e-04   2.9167e-17  -3.1037e-05  -8.0778e-17
  -4.2127e-17  -1.3167e-05  -1.0555e-16   2.3039e-06
  -1.3167e-05  -5.8575e-17   2.3039e-06  -8.9651e-17
  -6.9868e-17   9.3001e-07   5.5030e-17  -1.4898e-07
   9.3001e-07  -8.6356e-17  -1.4898e-07   6.8739e-17
   1.1556e-16  -5.7778e-08  -1.7364e-17   8.5590e-09
  -5.7778e-08  -2.1737e-16   8.5590e-09   1.7395e-16

d1 =

Diagonal Matrix

   3.9036        0        0        0
        0   2.9036        0        0
        0        0   2.5933        0
        0        0        0   1.5933

PASSES 149 out of 149 tests

Would it not be better to test a case where the imaginary part wasn't expected 
to be zero?

For example,

%!testif HAVE_ARPACK
%! [v1,d1] = eigs(1i*A, k, 'li');
%! d1 = diag(d1);
%! for i=1:k
%!  assert(max(abs((1i*A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
%! endfor
%!testif HAVE_ARPACK
%! [v1,d1] = eigs(1i*A, k, 'si');
%! d1 = diag(d1);
%! for i=1:k
%!  assert(max(abs((1i*A - d1(i)*speye(n))*v1(:,i))),0.,1e-11)
%! endfor

This doesn't fail for me.

Ben