Re: eps function and numerical accuracy

[Daniel J Sebald]

On 07/08/2013 06:41 PM, Nir Krakauer wrote:
> As in your example, assert works element-by-element -- i.e. it will
> return an error if any two elements in the input arguments differ by
> more than the specified tolerance

Well, at first blush it seems that way, but this error:

maximum absolute error 4.44089e-16 exceeds tolerance 2.71333e-166

makes me wonder because the absolute error associated with the first 
element isn't near that magnitude.  That's actually the other end of the 
vector.

Here is a simple example:

> > assert([1 2], [0, 0], [1 2])
> > assert([1 2], [0, 0], [1 1])
error: assert ([1, 2],[0, 0],[1, 1]) expected
   0   0
but got
   1   2
maximum absolute error 2 exceeds tolerance 1maximum absolute error 1 
exceeds tolerance
error: called from:
error: 
/usr/local/src/octave/octave/build-gui-11/../octave/scripts/testfun/assert.m 
at line 235, column 5

The first test is fine.  The second error is correct, but why it is 
indicating "maximum absolute error 1 exceeds tolerance" I'm not sure... 
looking at the assert() function:

          if (tol == 0)
            err = any (A != B);
            errtype = "values do not match";
          elseif (tol >= 0)
            err = max (abs (A - B));
            errtype = "maximum absolute error %g exceeds tolerance %g";
          else
            abserr = max (abs (A(B == 0)));
            A = A(B != 0);
            B = B(B != 0);
            relerr = max (abs (A - B) ./ abs (B));
            err = max ([abserr; relerr]);
            errtype = "maximum relative error %g exceeds tolerance %g";
          endif
          if (err > abs (tol))
            iserror = 1;
            coda = sprintf (errtype, err, abs (tol));
          endif

it looks like "tol" must be a scalar in order to operate sanely.  I see 
now why the error message is coming out so strange when I provide a 
vector for tol.  The sprintf routine prints multiple lines for "tol" 
vector, even if there is no failure associated with the index in question.

It seems like it shouldn't be too difficult to alter assert(.,.,tol) so 
that tol can be a vector.  Rik (others) do we want to make this change 
so that we can fine tune tests like binocdf() and the many other similar 
types of functions?

Dan