simplify hessian matrix structure initialization

[luke-kiernan]

Currently there's some graph stuff for figuring out the sparse structure of the hessian of the homotopy function. I did some profiling a while back and found that simply computing J^T J is faster. Both give the same results: we want (2-or-fewer)-hop neighbors. Also using J^T J's structure generalizes better: e.g. proportional-to-headroom slack.

[Copilot]

Pull request overview

This PR simplifies initialization of the robust-homotopy Hessian sparse structure by deriving it directly from the Jacobian product J' * J (instead of building the structure via a graph-based neighbor traversal), motivated by profiling/performance.

Changes:

• Remove the custom graph-based _create_hessian_matrix_structure implementation.
• Allocate the Hessian sparsity pattern by temporarily filling J.Jv.nzval, computing Hv = J.Jv' * J.Jv, and zeroing stored values afterward.

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[github-actions]

Performance Results

Precompile Time

Main	This Branch	Delta
2.486 s	2.368 s	-4.7%

Solve Time

Test	Main	This Branch	Delta
matpower_ACTIVSg10k_sys-NewtonRaphsonACPowerFlow First Solve	12.012 s	11.872 s	-1.2%
matpower_ACTIVSg10k_sys-NewtonRaphsonACPowerFlow Second Solve	81.7 ms	538.6 ms	+559.4%
matpower_ACTIVSg10k_sys-RobustHomotopyPowerFlow First Solve	16.114 s	15.749 s	-2.3%
matpower_ACTIVSg10k_sys-RobustHomotopyPowerFlow Second Solve	9.623 s	9.261 s	-3.8%
matpower_ACTIVSg10k_sys-NewtonRaphsonACPowerFlow(iwamoto) First Solve	393.3 ms	202.4 ms	-48.5%
matpower_ACTIVSg10k_sys-NewtonRaphsonACPowerFlow(iwamoto) Second Solve	80.2 ms	87.0 ms	+8.5%
matpower_ACTIVSg10k_sys-TrustRegionACPowerFlow(iwamoto) First Solve	2.158 s	2.441 s	+13.1%
matpower_ACTIVSg10k_sys-TrustRegionACPowerFlow(iwamoto) Second Solve	463.7 ms	85.5 ms	-81.6%
matpower_ACTIVSg10k_sys-DCPowerFlow First Solve	5.127 s	5.088 s	-0.8%
matpower_ACTIVSg10k_sys-DCPowerFlow Second Solve	14.6 ms	14.7 ms	+0.8%
matpower_ACTIVSg10k_sys-PTDFDCPowerFlow First Solve	1.719 s	1.709 s	-0.6%
matpower_ACTIVSg10k_sys-PTDFDCPowerFlow Second Solve	65.4 ms	65.4 ms	+0.1%
matpower_ACTIVSg10k_sys-vPTDFDCPowerFlow First Solve	5.943 s	5.925 s	-0.3%
matpower_ACTIVSg10k_sys-vPTDFDCPowerFlow Second Solve	3.561 s	3.542 s	-0.5%

[luke-kiernan]

Copilot was right — verified that ac_power_flow_jacobian.jl:331-332 sets the LCC angle-constraint diagonals to 1.0 at structure creation, and _update_jacobian_matrix_values! never rewrites them, so the old nonzeros(J.Jv) .= 0.0 would corrupt them on any system with LCC. Fixed via save/restore of J.Jv's nzval in d9b58e6.

edit: turns out the RH method as written isn't compatible with LCCs anyway...but it's a one-time cost, so I'll leave the save-and-restore.

[luke-kiernan]

Turns out these safeguards aren't strictly necessary: at the moment, H = J' * J keeps structural zeros. However, nothing in the SparseArrays docs dictates that behavior, so best not to rely on it.

[luke-kiernan]

I added a "no LCCs" guard on the RH method path and a basic test that exercises said guard.

[jd-lara]

I added a "no LCCs" guard on the RH method path and a basic test that exercises said guard.

The problem is going to the that in real systems like WECC and the EI there will be LCCs in the data.

[luke-kiernan]

The problem is going to the that in real systems like WECC and the EI there will be LCCs in the data.

Sure, I can work on an LCC-compatible robust homotopy method. But I'd still vote for merging this: throwing a human-readable error is improvement over "dimension mismatch."

edit: there's a couple other things in this PR too, besides the LCC error

[jd-lara]

The problem is going to the that in real systems like WECC and the EI there will be LCCs in the data.

Sure, I can work on an LCC-compatible robust homotopy method. But I'd still vote for merging this: throwing a human-readable error is improvement over "dimension mismatch."

edit: there's a couple other things in this PR too, besides the LCC error

Yeah, I don't think is blocking. Just nothing that it will be a consideration