[SciPy-Dev] Should a RuntimeWarning be raised for optimize.zeros.newton if the initial guess is zero?

[Mark Alexander Mikofski]

Hi All,

I would like to solicit discussion about an issue that was raised in #8357
by one of the reviewers regarding the case when the initial guess is zero,
but the derivative is also zero - currently scipy.optmize.newton raises a
RuntimeWarning and there is also a test to check for this condition,
"scipy/optimize/tests/test_zeros.py::TestBasic::test_deriv_zero_warning"

I have created an issue #8904 for this case, but I don't know what the
SciPy community opinion is on this issue. Is the current condition the
desired outcome? Or should an exception be made for initial guess that are
already zero, even if the derivative would be zero yielding an infinite
newton step?

I'm also concerned that this issue #8904 is blocking #8357, which IMHO is
not related to this philosophical question.

Thanks for your consideration!

-- 
Mark Mikofski, PhD (2005)
*Fiat Lux*
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