fix: avoid log(0) in KL divergence (Fixes #12233)

[Monasri29-hub]

Description

Fixes #12233

This PR fixes a critical bug in the kullback_leibler_divergence function where entries with y_true = 0 caused the function to return nan.

Problem

The current implementation computes y_true * np.log(y_true / y_pred) for all entries, including when y_true = 0. This results in 0 * log(0) = 0 * (-inf) = nan, which breaks the function.

Solution

Filter out zero entries from y_true before computing the logarithm. This is mathematically correct because:

• In information theory, the convention is that 0 * log(0) = 0
• Mathematical limit: lim(p→0+) p·log(p) = 0
• This is how SciPy's rel_entr and other standard implementations handle this case

Changes Made

• Added boolean masking to filter zero entries: mask = y_true != 0
• Applied mask to both arrays before logarithm computation
• Added two new doctests demonstrating correct behavior with zeros
• Added inline comment explaining the mathematical justification

Testing

New Test Cases Added:

1. Single zero in y_true: [0.0, 0.3, 0.7] → Returns 0.0237... ✓
2. Multiple zeros in y_true: [0.0, 0.0, 1.0] → Returns 0.6931... ✓

All Existing Tests Pass:

• Original non-zero case still works correctly
• Error handling for mismatched array lengths unchanged

Verification