Re: [OctDev] Test failures due to tolerance in fftfilt.m

[Ed M. <ee...@gm...>]

On Fri, Sep 7, 2012 at 2:12 PM, Daniel J Sebald <dan...@ie...>wrote:

> On 09/06/2012 02:59 PM, Daniel J Sebald wrote:
>
>> I'll toss this one to Ed and Rik, since we were just talking about
>> precision issues for svds test failures...
>>
>> I checked the current state of tests and found this failure:
>>
>>  processing
>>>>>>> /usr/local/src/octave/octave/**octave/scripts/signal/fftfilt.**m
>>>>>>>
>>>>>> ***** test
>>
>
> There is a bit more to this, and I've put a patch on Savannah:
>
> https://savannah.gnu.org/bugs/**index.php?37297<https://savannah.gnu.org/bugs/index.php?37297>
>
> The routine will round the output if the inputs are integers and will
> truncate the imaginary component if both inputs are real.  That seems fair,
> I suppose.  (I do wonder though if there should be an option to remove this
> behavior because some might not want such a thing.  Any thoughts
> maintainers or OctDev?)  I've extended that concept to account for the
> other cases of real*imaginary, imaginary*real, and imaginary*imaginary.  I
> don't see why only the real*real case should be done...all or nothing, as I
> see it.  These conditions now have tests, and there are a couple more tests
> for tolerance on the imaginary/imaginary scenario, as well as the
> complex/complex scenario.
>
> By making the integerization (rounding) test more stringent, I uncovered a
> bug whereby only the first element of the output single row vector was
> rounded.
>
> Dan
>

I just ran into the fftfilt test failure again (bugs 37297 & 35959)
and I narrowed it down to differences between FFTPACK and fftw3.
octave with FFTPACK gets the test error:

!!!!! test failed
assert (fftfilt (b, r * x),r * r * [1, 1, 0, 0, 0, 0, 0, 0, 0, 0],eps)
expected
 Columns 1 through 3:
     ...
 maximum absolute error 2.22478e-16 exceeds tolerance 2.22045e-16

rebuilding with fftw3 makes the error go away. Then I looked
at the errors with fftpack and fftw3, ie the difference between
the fftfilt output (a 10-element complex vector) and the expected vector:

                fftpack                                                fftw3
                -------                                                -----
   3.4694469519536142e-18 + 2.2204460492503131e-16i
0.0000000000000000e+00 - 0.0000000000000000e+00i
   1.3877787807814457e-17 + 2.2204460492503131e-16i
0.0000000000000000e+00 - 2.2204460492503131e-16i
   3.1892503067014210e-17 + 2.0395767215548695e-17i
0.0000000000000000e+00 - 0.0000000000000000e+00i
  -1.5476803848138888e-17 - 1.1721501528016046e-17i
0.0000000000000000e+00 - 0.0000000000000000e+00i
  -5.5511151231257827e-17 - 5.2041704279304213e-17i
0.0000000000000000e+00 + 2.7755575615628914e-17i
   0.0000000000000000e+00 - 6.9388939039072284e-17i
0.0000000000000000e+00 + 2.7755575615628914e-17i
  -3.1892503067014198e-17 - 3.5115384015709088e-17i
0.0000000000000000e+00 - 0.0000000000000000e+00i
   1.0999025841583994e-18 + 1.0166004376210030e-17i
0.0000000000000000e+00 + 5.5511151231257827e-17i
  -3.4694469519536142e-18 - 0.0000000000000000e+00i
0.0000000000000000e+00 - 0.0000000000000000e+00i
  -1.3877787807814457e-17 - 0.0000000000000000e+00i
0.0000000000000000e+00 - 5.5511151231257827e-17i

some things to notice about these:

1) the largest error in both is in the imag part of the 2nd element
   and is exactly eps, i.e. one ulp; no big surprise

2) the fftpack result has more "garbage" numbers but roughly the
   same size as the garbage from fftw3 and all smaller than eps.

3) the reason the test fails with fftpack is that it was unlucky enough
   to have put a bit of garbage in the real part of the second element
   which made the abs of the element slightly larger than eps. Otherwise
   the two results should be considered equivalent.

4) the fftw3 result passes the test because assert() uses the infinity
   norm; had it used, e.g. the 2-norm the test would have failed.
   These tests should not depend on which norm is used.

I propose fixing this test by replacing the tolerance eps with something
like 2*eps*norm(z) where z = r*r*[1 1 0 0 0 0 0 0 0 0]. Just multiplying
eps by 2 would fix this problem but tests like these should always account
for the size of the things being tested.

I put a modified version of Dan's patch for bug #37297 on the tracker.
In it I added norms to the test tolerances, so for example instead of

assert (y0, y, 55*eps);

I substituted

assert (y0, y, 4*eps*norm(y));

and it passes 10000 passes with both fftpack and fftw3.

-- 
Ed Meyer