`RuntimeWarning: invalid value encountered in divide` when using `singlediode()`

[jwhitaker-gridcog]

Describe the bug
Since version 0.14, calling singediode() sometimes results in

/home/jarrad/src/.../.venv/lib/python3.12/site-packages/scipy/optimize/_chandrupatla.py:437: RuntimeWarning: invalid value encountered in divide
  C = A / (A + B)

To Reproduce

import pvlib
import numpy as np

pvlib.pvsystem.singlediode(0., 1e-12, 0.5, np.inf, 1.8)

Expected behavior
No warning.

Screenshots

Versions:

• pvlib.__version__: 0.4.0
• pandas.__version__: 2.3.
• python: 3.12
• numpy.__version__: 2.3.5
• scipy.__version__: 1.17.0

Additional context

Poking a little bit, it looks like your call to scipy find_minimum may not obey the constraints they require. Scipy doco states (https://docs.scipy.org/doc/scipy-1.17.0/reference/generated/scipy.optimize.elementwise.find_minimum.html)

init:
The abscissae of a standard scalar minimization bracket. A bracket is valid if arrays x1, x2, x3 = init satisfy x1 < x2 < x3 and func(x1) >= func(x2) <= func(x3), where one of the inequalities is strict. Arrays must be broadcastable with one another and the arrays of args.

Looking at the PR where this was implemented, it looks like care was taken to obey the second invariant, but the first might have gotten missed. When you set init = (-1, 0.8*v_oc, v_oc), if v_oc == 0 then x2 < x3 gets broken. I haven't proven that this is the cause of the warning, but I am suspicious...

Thanks!

[cwhanse]

Verified that the warning raises when v_oc = 0.. As for what to do about it, three options come to mind:

1. ignore it with no action. I'd like to think v_oc = 0 is operationally irrelevant, but perhaps it's a common irritant to have the warning raised.
2. wrap the call to find_minimum with with np.errstate(divide='ignore') I'm on the fence here, I'd hate to unintentionally cover up some bug we want to detect. But I think the risk of hiding a bug is small. Division by zero would happen in the optimized function, which uses singlediode._lambertw_i_from_v. There's plenty of divisions in that function, but all the calculations are simple arithmetic, or handled by scipy's lambertw.
3. change to init = (-1., 0.8*v_oc - 0.2, v_oc). 0.8*v_oc - 0.2 is the point that is 80% of the distance along the interval (-1., v_oc) and that should be safe even for v_oc <= 0.

We don't want to add a small positive number to v_oc, e.g., init = (-1., 0.8*v_oc, v_oc + 1e-10) that could return positive voltages for v_mp.

I'll note that the current function returns a reasonable result despite the division by 0 warning.