On Wed, Feb 24, 2021 at 11:29 AM Bernard Knaepen <bknae...@gmail.com> wrote:
> Hi all, > > We are developing a code that heavily relies on NumPy. Some of our > regression tests rely on floating point number comparisons and we are a bit > lost in determining how to choose atol and rtol (we are trying to do all > operations in double precision). We would like to set atol and rtol as low > as possible but still have the tests pass if we run on different > architectures or introduce some ‘cosmetic’ changes like using different > similar NumPy routines. > > For example, let’s say we want some powers of the matrix A and compute > them as: > > A = np.array(some_array) > A2 = np.dot(A, A) > A3 = np.dot(A2, A) > A4 = np.dot(A3, A) > > If we alternatively computed A4 like: > > A4 = np.linalg.matrix_power(A, 4), > > we get different values in our final outputs because obviously the > operations are not equivalent up to machine accuracy. > > Is there any reference that one could share providing guidelines on how to > choose reasonable values for atol and rtol in this kind of situation? For > example, does the NumPy package use a fixed set of values for its own > development? the default ones? > I don't think there's a clear guide in docs or blog post anywhere. You can get a sense of what works by browsing the unit tests for numpy and scipy. numpy.linalg, scipy.linalg and scipy.special are particularly relevant probably. For a rough rule of thumb: if you test on x86_64 and precision is on the order of 1e-13 to 1e-16, then set a relative tolerance 10 to 100 times higher to account for other hardware, BLAS implementations, etc. Cheers, Ralf > Thanks in advance for any help, > Cheers, > Bernard. > > > > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@python.org > https://mail.python.org/mailman/listinfo/numpy-discussion >
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