Fix topology update gradient application

[QuentinWach]

Summary

• add a reusable apply_density_update helper with masked box blur support for topology optimisation updates
• rewrite the 4_topo example to use the helper and report the magnitude of every design-density change
• add unit tests that validate density updates occur inside the masked design region

Testing

• PYTHONPATH=. pytest tests/test_topology_updates.py

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https://chatgpt.com/codex/tasks/task_e_68dd6b6627d08326b90b34c6270f1b33

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Negate gradient before density update

The new apply_density_update helper adds the update as density + learning_rate * gradient, i.e. it assumes the passed gradient already points in the descent direction. In the topology example the raw overlap gradient is passed directly, whereas the previous implementation negated it before applying the optimizer. Because the objective being printed is the negative transmission, this change flips the optimization into gradient ascent and will push the design densities the wrong way, preventing the loop from improving the device. Pass -normalized_gradient (or otherwise negate the gradient) when calling apply_density_update so the update reduces the objective instead of increasing it.

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