[SciPy-Dev] Return residual and derivative in gradient descent methods like Newton

[Mark Alexander Mikofski]

Hi,

Would anyone disagree or would anyone be interested in a proposal to allow
the derivative to be returned from the user supplied function as an
optional second argument in gradient search method like Newton? EG

>>> lambda x,a: (x**3-a, 3*x*"2)
>>> newton(f, x0, fprime='f2', args=(a,))

Some simple tests show that this may have a 2X speed in cases where the
derivative expression requires the value of the original function call.

See this issue in which I proposed this idea and wore a sample test script
https://github.com/scipy/scipy/issues/8354

I proposed a way to keep the existing API and add this new feature.
* If `fprime` is a callable, then same as before
* If it's a string like "f2" the get fprime from second output

Thanks,
Mark
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