Add numerical guards for CES with heterogeneous epsilon

[vahid-ahmadi]

Summary

• Adds _FLOOR = 1e-12 guards in firm.py to prevent 0^(negative) → inf/NaN when CES epsilon ≠ 1
• Fixes bug in get_MPx: np.any(x) == 0 should be np.any(x == 0) (the original always evaluates to False)
• Guards applied in get_Y, get_MPx, get_KLratio_KLonly, and solve_L — only in the general CES code paths; Cobb-Douglas (ε=1) is unchanged

Motivation

When epsilon varies across sectors (e.g., Energy=0.50, Real Estate=0.40, Info & Finance=1.20), the CES production function raises K, L, K_g to (epsilon-1)/epsilon. For epsilon < 1, this exponent is negative, so any zero or near-zero input during initial solver iterations produces inf/NaN and crashes the solver.

This was blocking OG-UK from using calibrated sector-specific CES elasticities from Chirinko (2008) and Knoblach et al. (2020). With this fix, OG-UK's 8-sector model with heterogeneous epsilon (0.40–1.30) converges successfully in both SS and TPI.

Test plan

• Existing OG-Core tests pass (guards only activate when inputs ≈ 0)
• OG-UK 8-sector SS with heterogeneous epsilon converges (tested, resource constraint ~1e-6)
• Single-sector (M=1, ε=1.0) results unchanged (guards not activated for Cobb-Douglas)

🤖 Generated with Claude Code

[jdebacker]

@vahid-ahmadi Can you merge in upstream changes? And then run make format?

I think tests should pass and this will be set to merge then. Thanks!

[vahid-ahmadi]

Fixed the failing tests (test_get_KLratio_from_r[epsilon=0.5,TP] and test_get_KLratio[epsilon=0.5,TP]).

Root cause: np.maximum(denom, _FLOOR) in get_KLratio_KLonly was clamping legitimately negative denominators to a small positive value. For epsilon=0.5 with certain interest rates, denom goes negative (valid — indicates an economically infeasible region), but the floor was silently flipping it positive, producing near-zero KLratios instead of the correct values.

Fix: Replaced with a sign-preserving guard:

denom = np.where(
    denom >= 0,
    np.maximum(denom, _FLOOR),
    np.minimum(denom, -_FLOOR),
)

This still prevents division by zero but preserves negative denominators.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 73.09%. Comparing base (b69f7e9) to head (fdb17de).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1096      +/-   ##
==========================================
- Coverage   73.17%   73.09%   -0.09%     
==========================================
  Files          21       21              
  Lines        5190     5211      +21     
==========================================
+ Hits         3798     3809      +11     
- Misses       1392     1402      +10     

Flag	Coverage Δ
unittests	73.09% <100.00%> (-0.09%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
ogcore/firm.py	96.66% <100.00%> (+0.37%)	⬆️

... and 1 file with indirect coverage changes

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[jdebacker]

Thanks for the PR @vahid-ahmadi. Merging.