On Mon, Jul 19, 2010 at 6:31 PM, Ondrej Certik <ondrej@certik.cz> wrote:

Hi,

I was always using something like

abs(x-y) < eps

or

(abs(x-y) < eps).all()

but today I needed to also make sure this works for larger numbers, where I need to compare relative errors, so I found this:

http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

and wrote this:

def feq(a, b, max_relative_error=1e-12, max_absolute_error=1e-12):    a = float(a)    b = float(b)    # if the numbers are close enough (absolutely), then they are equal    if abs(a-b) < max_absolute_error:        return True    # if not, they can still be equal if their relative error is small    if abs(b) > abs(a):        relative_error = abs((a-b)/b)    else:        relative_error = abs((a-b)/a)    return relative_error <= max_relative_error

Is there any function in numpy, that implements this? Or maybe even the better, integer based version, as referenced in the link above?

I need this in tests, where I calculate something on some mesh, then compare to the correct solution projected on some other mesh, so I have to deal with accuracy issues.

Is allclose close enough? np.allclose(a, b, rtol=1.0000000000000001e-05, atol=1e-08) Returns True if two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`.

On Tue, Jul 20, 2010 at 3:31 AM, Ondrej Certik <ondrej@certik.cz> wrote:

Hi,

I was always using something like

abs(x-y) < eps

or

(abs(x-y) < eps).all()

but today I needed to also make sure this works for larger numbers, where I need to compare relative errors, so I found this:

http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

Actually, there is better, as mentioned in that same page. I implemented the functions for reliable, amplitude independent floating point comparison: assert_array_max_ulp: Given two arrays a and b, check that every item differs in at most N Unit in the Last Place. assert_array_almost_equal_nulp Compare two arrays relatively to their spacing. It is a relatively robust method to compare two arrays whose amplitude is variable. Note ---- An assertion is raised if the following condition is not met: abs(x - y) <= nulps * spacing(max(abs(x), abs(y))) Parameters ---------- x: array_like first input array y: array_like second input array nulp: int max number of unit in the last place for tolerance (see Note) I think we should go toward using those almost everywhere we need floating point comparison in testing, cheers, David