Re: 2x2 orthogonal matrix multiplication error

[Marco Atzeri]

On 12/15/2014 6:04 AM, s.jo wrote:
> Hello all,
>
> In octave(3.8.2), 2x2 orthogonal matrix M shows numerical error after
> multiplied by own transpose.
>
> Say,
>     M*M' is not equal to eye(2)!
>
> There are errors in off-diagonal entries.
> But, if we try it with element-wise multiplication, it works well.
>
> Say,
> Mt = M';
> [Mt(1, :) * M(:, 1), Mt(1, :) * M(:, 2); Mt(2, :) * M(:, 1), Mt(2, :) * M(:,
> 2)] is equal to eye(2)!!
>
> I check this also with matlab, but it works well.
> I suspect that octave has some unreliable routine with
> matrix-multiplication.
> Or, is this only problem with my cygwin machine?

Hi s.jo,
Is it your own build or my cygwin package ?

I can not replicate with my package.
If is your own build please configure with
  --enable-float-truncate

see also
https://savannah.gnu.org/bugs/?func=detailitem&item_id=35024

> I also try it with the complex rotation matrix (say Hermittian 2x2 matrix).
> It also fails.
> I generate rotation matrix with cos and sin functions:
>
> M = [cs sn; -sn' cs']
>
> The following script shows these result.

the script should be attached.
Copy and past from your output is time wasting to replicate.

> Such matrix orthogonality easily fails with large size matrix due to
> numerical errors.
> But 2x2 matrix is so small. It should work always with such orthogonality
> like matlab do, I guess.
>
> Can somebody help this how it figure out?
>
> Many thanks,
>
> jo

attached your test script.
And here below my output on 32bit.
64 bit output is similar

ans = 3.8.2
cs =  0.65235
sn =  0.73407 + 0.18862i
M =

   0.65235 + 0.00000i   0.73407 + 0.18862i
  -0.73407 + 0.18862i   0.65235 + 0.00000i

ans = 0
ans =

   1.00000   0.00000
   0.00000   1.00000

ans =

   1.00000   0.00000
   0.00000   1.00000

ans =

   1.00000   0.00000

ans =

   0.00000   1.00000

ans =

   1.00000
   0.00000

ans =

   0.00000
   1.00000

ans =

   1.00000   0.00000
   0.00000   1.00000

cs =  0.37938
sn = -0.92524
M =

   0.37938  -0.92524
   0.92524   0.37938

ans =  1
ans =

   1   0
   0   1

ans =

   1   0
   0   1

ans =

   1   0

ans =

   0   1

ans =

   1
   0
ans =

   0
   1

ans =

   1   0
   0   1

test_complex_mat.m
Description: Text document