test_matrix fails on i386

[olebole]

On i386, I get the following failure:

    def test_matrix():
        m = Minuit(lambda x, y: x**2 + (y / 2) ** 2 + 1, x=0, y=0)
        m.errordef = 1
        m.migrad()
>       assert (
            framed(tab.tabulate(*m.covariance.to_table()))
            == """
             x       y
    --  ------  ------
    x    1      -0.643
    y   -0.643   4
    """
        )
E       AssertionError: assert '\n      x   ...     0    4\n' == '\n         x... -0.643   4\n'
E           
E         -          x       y
E         ? ---       ---
E         +       x    y
E         - --  ------  ------
E         + --  ---  ---
E         - x    1      -0.643
E         ?           --- ----
E         + x     1    0
E         ?      +
E         - y   -0.643   4
E         + y     0    4
tests/test_tabulate.py:33: AssertionError

I am unsure what the cause is; earlier compilations do not show this behavior. This appeards independent of whether the change taken from #776 (see #830) was applied or not.

[HDembinski]

Looking at the code, I am surprised why this test ever passed?! The answer you got is correct, the off-diagonal elements of the covariance matrix for this cost function should be zero, not -0.643. I will fix this.

[HDembinski]

🤦 That was an ugly bug in the formatting code which tries to produce a matrix that looks reasonable for humans instead of something like [[1, 1.23e-16], [1.23e-16, 4]]. The numerical result was actually correct.

[stephanlachnit]

Unfortunately, it still fails on i386 (2.21.3):

          x    y
    --  ---  ---
  - x     1   -0
  ?           ^
  + x     1    0
  ?           ^
  - y    -0    4
  ?      ^
  + y     0    4
  ?      ^

I guess it's a precision problem on i386?

[HDembinski]

Due to differences in library implementations, it is possible that positive numbers near zero come out negative. I think this should be fixed in the pdf_format function, it should remove the minus sign if the number after rounding is zero.