Re: Issues with eigs

[Thomas D. Dean]

On 09/08/18 12:13, Thomas D. Dean wrote:
> There is a problem here.  I know about roundoff error, etc.  Even with
> roundoff error, I believe I should get the same result every time I run
> this.
>
> octave:722> eigs(m1,m0)
> ans =
>
>           0.00026 - 2672325.75636i
>           0.00026 + 2672325.75636i
>           0.00000 + 2639890.67488i
>           0.00000 - 2639890.67488i
>          -0.00007 - 2587678.50828i
>          -0.00007 + 2587678.50828i
>
> octave:723> eigs(m1,m0)
> ans =
>
>           0.00050 - 2672274.01721i
>           0.00050 + 2672274.01721i
>          -0.00058 + 2639991.91956i
>          -0.00058 - 2639991.91956i
>          -0.00005 - 2587660.78340i
>          -0.00005 + 2587660.78340i
>
> octave:724> eigs(m1,m0)
> ans =
>
>           0.00014 + 2672332.27197i
>           0.00014 - 2672332.27197i
>          -0.00030 - 2639921.38497i
>          -0.00030 + 2639921.38497i
>           0.00001 - 2587707.77163i
>           0.00001 + 2587707.77163i
>
> With Scipy, I get the same result every time I run it.  I verified that
> both octave and numpy read the matrix the same way - non-zero values are
> the same and in the same location.
<snip>

If I ask eigs to return more than size(m1,1)/2 eigenvectors, I get the
same values each time.  If I choose the default, or, less than
size(m1,1)/2, the values do not repeat.

eigs(m1, m0, floor(size(m1,1)/2)) ## returns the same values.
eigs(m1, m0, size(m1,1)) ## returns the same values.

eigs(m1, m0, floor(size(m1,1)/3)) ## does NOT return the same values.
eigs(m1, m0, 6) ## default.  does NOT return the same values.

I can not verify the values returned are correct.
eigs(m1, m0, size(m1,1)) returns
  real(e) == 0 and abs(imag(e)) > 200
  paired, imag() alternating signs?
scipy returns
  abs(real(e)) < 1e-11 and abs(imag(e)) < 1e-3
  paired, imag() alternating signs
maple, using float approximation returns
  abs(real(e)) < 1e-9 and abs(imag(e)) < 1e-3

Some of the imag() values in scipy and maple match to 6 or 8 digits.

Tom Dean