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Matching-based 2×2 pairs (algo5) cost ~2.1× nnz(L) on MadNLP K2 systems #96

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Matching-based 2×2 pairs (algo5) cost ~2.1× nnz(L) on MadNLP K2 systems#96
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found-by-agentOpened by an implementing agent for an out-of-scope findingtriagedOwner has looked at this found-by-agent issue; it no longer holds the task chain

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@claude
claude
bot
opened on Oct 7, 2026

Found while working on: T21 (#21, branch task/T21-matching-scaling)

What: With matching_alg = "algo5" the "S"/"H" analysis pairs every 2×2 candidate of the scaled matrix that lies on a cycle of the symmetric matching (matching_pairs, src/matching/mc64.jl). On the K2 dumps of bench/pivot_pairs.jl this is nearly every candidate (case118: 1539 pairs; case1354: 16646), so nnz(L) is 2.09–2.19× the unpaired ordering, against 1.25–1.31× for the default structurally-zero pairs without matching (#66). Accuracy is excellent (case118: 0 perturbed pivots, max|L| ≤ 9.7, relres 5.6e-14 before refinement; case1354: 5–6 perturbed, relres ≤ 3.9e-6, 1e-15 after 5 IR steps; cuDSS algo5: 0/14 perturbed, 5.4e-13/7.7e-3), but the factor and the update stack are ~1.7× larger than needed for the default pairs. On the converged case14 iterate the matching pairs cost 2.06× (default pairs 1.91×) with 0 perturbed pivots instead of 9.

Why it is out of scope: T21 asked for the matching-based pairs; reducing their fill is a tuning question for the owner (T25 performance pass, or a refinement of the pair selection).

Suggested fix or plan change: Apply the structurally-zero test of zero_pivot_pairs! to the matching's cycle pairs (pair a matched 2-cycle only when its candidate's pivot is structurally zero or the scaled diagonal is below a much smaller tolerance), and measure fill vs perturbed pivots on the K2 dumps with bench/pivot_pairs.jl.

Activity

  1. claude
    added
    found-by-agentOpened by an implementing agent for an out-of-scope finding
    on Oct 7, 2026
  2. michel2323
    added 2 commits that reference this issue on Oct 7, 2026

    PLAN.md: refresh to the implemented design after T21 [skip ci]

    e5d8ed8

    PLAN.md: refresh to the implemented design after T21 [skip ci] (#99)

    00e6e4e

  3. michel2323 commented on Oct 7, 2026

    @michel2323
    michel2323
    on Oct 7, 2026 – with Claude
    Member

    Triage of #96 by measurement. Host only, KA CPU backend, Julia 1.13.1. The nine K2 dumps were regenerated with bench/dump_madnlp_kkt.jl (MadNLP, ExaModels and ExaModelsPower in a scratch env): case14 iterations 1, 10 and 15 (15 is the converged iterate), and case118 and case1354 at iterations 1, 10 and 20.

    Conclusion: no rule meets the bar. The fill is the price of the accuracy. No code change.

    The bar on case1354: nperturbed within a few of T21's 5–6, relres after 5 IR steps ≤ 1e-10, and nnz(L) ≤ 1.5× the unpaired ordering.

    rule (algo5) case118 k2_1/10/20: ratio, perturbed, relres+5 case1354 k2_1: ratio, perturbed, relres+5 case1354 k2_10 case1354 k2_20 case14 k2_15 (converged)
    T21 (cycle pairs with a candidate) 2.09–2.19, 0, ≤ 9.8e-16 2.18, 5, 7.4e-16 2.17, 5, 1.3e-15 2.15, 6, 1.2e-15 2.06, 0
    a: structurally zero pivots, paired with their matching mate 1.24, 0, ≤ 9.6e-16 1.34, 5, 7.9e-16 1.31, 32, 4e5 1.31, 28, 1.5 (max abs L 2.6e18) 2.06, 0
    b: scaled diagonal ≤ τ·row max, τ = 1e-2, 1e-4, 1e-8 identical to T21 identical identical identical identical
    c: a ∪ b identical to T21 for every τ identical identical identical identical

    What the table shows:

    • b and c select nothing new. The K2 dual rows have an exactly zero diagonal. Every matched cycle therefore contains a candidate at any τ > 0, and the value rule keeps every cycle. With τ = 0 it keeps none, which is pivot_pairs = "none".
    • a reaches the "default" fill (1.24–1.34×) and keeps the T21 accuracy on case14, case118 and case1354 k2_1 (relres before refinement ≤ 1.8e-10 instead of 5.6e-14).
    • a fails on the later case1354 iterates. k2_10 and k2_20 end with 28–32 perturbed pivots and the refinement diverges (relres+5 = 4e5 and 1.5). The device and the reference also disagree there (Device LDLᵀ differs from ref_ldlt! on the K2 dumps (pivot sequence, nperturbed; inertia equal) #86).
      • The broken pivots are structurally nonzero but cancel numerically. No structural rule can see them; only a value-aware choice can, which here means pairing every cycle (T21), or the a-posteriori pivoting of T27.
    • On the converged case14 iterate, a pairs 167 of the 169 cycles, since almost every pivot is structurally zero there. The fill stays 2.06×.
    • Variants tested along the way, also without success:
      • a with zero_pivot_pairs!'s greedy partner as a fallback when the mate is taken: never triggered, identical to a.
      • The structurally-zero rule with the greedy partners instead of the mates, on the scaled matrix: 13–125 perturbed pivots, relres+5 up to 1.1 on case1354.

    The fill numbers of PLAN §2.3 step 2 do not change.

    Next step: TASKS.md T25 gets the note "re-measure after the level merging whether the extra fronts matter; otherwise accepted" (docs-only PR, Refs #96). Owner: please label this issue triaged.

    Full tables follow. Columns: nnz(L) ratio to "none"; zero and perturbed pivots; 2×2 pivots; max abs L and factor error ‖A[p,p] − LDLᵀ‖_F/‖A‖_F, both of the scaled matrix under matching; relres = ‖b − Ax‖/‖b‖ with b = A·1, before refinement and after 2 and 5 IR steps; inertia; dev=ref = device and CPU reference agree on inertia and nperturbed (the reference count is in parentheses when they disagree). The "a'"/"a''" rows are the two variants above.

    Measured tables (nine K2 dumps)

    kkt_pglib_opf_case118_ieee_k2_1.mtx (n = 3150)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 16375 1.0 90 125 94 1.3e+15 0.0058 0.11 9.3e-05 6.8e-09 (1611, 1539) yes
    default 205 21032 1.28 0 5 99 1.4e+15 0.0017 0.023 5.6e-10 1.1e-15 (1611, 1539) yes
    all 1480 35708 2.18 49 69 341 1.3e+15 0.0035 0.053 2.1e-05 4.8e-10 (1611, 1539) yes
    algo5/none 0 16375 1.0 70 143 216 3.3e+13 0.0017 1.5 0.028 0.00027 (1611, 1539) yes
    algo5/default (T21) 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    algo5/all 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    a: algo5 struct-zero, mate 252 20346 1.24 0 0 363 5.8e+04 2.9e-13 1.8e-10 1.4e-15 9.6e-16 (1611, 1539) yes
    a': a + greedy fallback 252 20346 1.24 0 0 363 5.8e+04 2.9e-13 1.8e-10 1.4e-15 9.6e-16 (1611, 1539) yes
    a'': struct-zero, greedy (scaled) 249 20724 1.27 13 13 341 2.8e+13 0.00033 0.31 0.00014 5.2e-09 (1611, 1539) yes
    b: τ=1e-2 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    b: τ=1e-4 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    b: τ=1e-8 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    c: a ∪ b(1e-4) 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes
    c: a ∪ b(1e-8) 1539 35796 2.19 0 0 957 9.7 1.5e-16 5.6e-14 1.1e-15 9.8e-16 (1611, 1539) yes

    kkt_pglib_opf_case118_ieee_k2_10.mtx (n = 3150)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 16375 1.0 74 147 255 1.4e+15 0.0023 0.0029 3.4e-05 5.8e-08 (1611, 1539) no (146)
    default 208 20542 1.25 0 3 297 2.1e+14 1.3e-05 1.7e-05 1e-11 3.5e-17 (1611, 1539) yes
    all 1412 35711 2.18 55 65 787 1.3e+15 0.0017 0.0025 2e-06 3.8e-10 (1611, 1539) yes
    algo5/none 0 16375 1.0 54 139 264 3e+13 0.0014 0.019 0.00022 8.8e-07 (1611, 1539) no (140)
    algo5/default (T21) 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    algo5/all 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    a: algo5 struct-zero, mate 258 20383 1.24 0 0 452 7.6e+04 1.5e-12 5.6e-12 3e-17 2.7e-17 (1611, 1539) yes
    a': a + greedy fallback 258 20383 1.24 0 0 452 7.6e+04 1.5e-12 5.6e-12 3e-17 2.7e-17 (1611, 1539) yes
    a'': struct-zero, greedy (scaled) 249 20412 1.25 15 21 399 3.4e+13 0.00033 0.0066 5.8e-05 2.2e-07 (1611, 1539) yes
    b: τ=1e-2 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    b: τ=1e-4 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    b: τ=1e-8 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    c: a ∪ b(1e-4) 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes
    c: a ∪ b(1e-8) 1539 34698 2.12 0 0 1137 5.1 1.3e-16 4.4e-16 2.7e-17 2.9e-17 (1611, 1539) yes

    kkt_pglib_opf_case118_ieee_k2_20.mtx (n = 3150)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 16375 1.0 76 137 324 1.5e+15 7.7e-05 7.7e-05 2.2e-07 6.3e-11 (1611, 1539) yes
    default 223 20507 1.25 0 3 390 2.1e+14 3.4e-07 5.3e-07 1.1e-13 8.1e-19 (1611, 1539) yes
    all 1404 35563 2.17 56 67 1037 1.4e+15 4.7e-05 5.2e-05 1.5e-06 4.5e-08 (1611, 1539) yes
    algo5/none 0 16375 1.0 54 101 336 2.9e+13 0.00095 0.00017 4.8e-06 1.8e-07 (1611, 1539) no (98)
    algo5/default (T21) 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    algo5/all 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    a: algo5 struct-zero, mate 257 20385 1.24 0 0 559 1.1e+05 3.3e-13 1.4e-14 1.1e-18 7.5e-19 (1611, 1539) yes
    a': a + greedy fallback 257 20385 1.24 0 0 559 1.1e+05 3.3e-13 1.4e-14 1.1e-18 7.5e-19 (1611, 1539) yes
    a'': struct-zero, greedy (scaled) 251 20345 1.24 15 25 515 2.5e+13 0.00032 2.3e-05 1.8e-08 1.3e-13 (1611, 1539) yes
    b: τ=1e-2 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    b: τ=1e-4 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    b: τ=1e-8 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    c: a ∪ b(1e-4) 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes
    c: a ∪ b(1e-8) 1539 34260 2.09 0 0 1444 3.3 1.1e-16 2.2e-17 1.2e-18 5.7e-19 (1611, 1539) yes

    kkt_pglib_opf_case1354_pegase_k2_1.mtx (n = 33811)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 169033 1.0 1134 2061 2360 3.6e+16 3.5 21 19 2.9e+02 (17161, 16650) no (2060)
    default 3268 215953 1.28 14 34 3646 3.6e+15 0.021 0.12 0.00071 5.1e-07 (17165, 16646) no (33)
    all 15071 305110 1.81 1032 1541 8338 9.9e+15 0.31 2 15 67 (17165, 16646) no (1547)
    algo5/none 0 169033 1.0 1087 2119 2626 1.6e+14 0.0046 85 7.7e+04 2e+09 (17161, 16650) no (2117)
    algo5/default (T21) 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    algo5/all 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    a: algo5 struct-zero, mate 3780 225908 1.34 2 5 5181 1e+13 1.4e-05 0.029 1.9e-08 7.9e-16 (17165, 16646) yes
    a': a + greedy fallback 3780 225908 1.34 2 5 5181 1e+13 1.4e-05 0.029 1.9e-08 7.9e-16 (17165, 16646) yes
    a'': struct-zero, greedy (scaled) 3875 223938 1.32 77 114 5236 2e+14 0.0012 2.2 0.82 1.1 (17165, 16646) yes
    b: τ=1e-2 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    b: τ=1e-4 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    b: τ=1e-8 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    c: a ∪ b(1e-4) 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes
    c: a ∪ b(1e-8) 16646 368439 2.18 2 5 12189 1e+13 3.3e-06 3.9e-06 7.4e-16 7.4e-16 (17165, 16646) yes

    kkt_pglib_opf_case1354_pegase_k2_10.mtx (n = 33811)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 169033 1.0 1060 2072 2285 3.7e+16 0.071 0.53 2 58 (17162, 16649) no (2066)
    default 3170 220146 1.3 16 48 2985 8.1e+15 0.002 0.041 0.0027 5.3e-05 (17165, 16646) yes
    all 14564 349154 2.07 547 1005 6558 9.7e+16 0.28 2.2 1 3.7 (17163, 16648) no (1009)
    algo5/none 0 169033 1.0 1019 2152 2435 1.8e+14 0.013 1.1 1.2e+03 5.4e+07 (17155, 16656) no (2143)
    algo5/default (T21) 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    algo5/all 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    a: algo5 struct-zero, mate 3763 221485 1.31 14 32 4953 3.5e+13 0.0002 1.7 1.7e+02 4e+05 (17164, 16647) no (32)
    a': a + greedy fallback 3763 221485 1.31 14 32 4953 3.5e+13 0.0002 1.7 1.7e+02 4e+05 (17164, 16647) no (32)
    a'': struct-zero, greedy (scaled) 3677 224634 1.33 56 96 4822 5e+14 0.0042 0.046 0.045 0.044 (17165, 16646) yes
    b: τ=1e-2 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    b: τ=1e-4 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    b: τ=1e-8 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    c: a ∪ b(1e-4) 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes
    c: a ∪ b(1e-8) 16646 366592 2.17 0 5 11770 1e+13 2.9e-06 5.2e-08 1.3e-15 1.3e-15 (17165, 16646) yes

    kkt_pglib_opf_case1354_pegase_k2_20.mtx (n = 33811)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 169033 1.0 1075 2046 2385 3.8e+16 0.029 1.7 53 2.4e+04 (17162, 16649) no (2042)
    default 3468 221265 1.31 11 32 3284 4.4e+15 0.00033 0.0049 0.00013 2e-07 (17165, 16646) no (31)
    all 13950 342224 2.02 529 970 6496 9.9e+16 0.2 0.072 0.057 0.081 (17163, 16648) no (977)
    algo5/none 0 169033 1.0 1030 2141 2748 2.1e+14 0.0032 0.94 5.3e+02 3.9e+06 (17161, 16650) no (2139)
    algo5/default (T21) 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    algo5/all 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    a: algo5 struct-zero, mate 3974 221963 1.31 19 28 6051 2.6e+18 0.00016 28 0.16 1.5 (17164, 16647) no (28)
    a': a + greedy fallback 3974 221963 1.31 19 28 6051 2.6e+18 0.00016 28 0.16 1.5 (17164, 16647) no (28)
    a'': struct-zero, greedy (scaled) 3952 224333 1.33 73 125 5559 4.9e+13 0.00027 0.07 0.3 0.89 (17164, 16647) no (127)
    b: τ=1e-2 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    b: τ=1e-4 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    b: τ=1e-8 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    c: a ∪ b(1e-4) 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes
    c: a ∪ b(1e-8) 16646 363172 2.15 1 6 13469 1e+13 3.7e-06 3.2e-07 1.4e-15 1.2e-15 (17165, 16646) yes

    kkt_pglib_opf_case14_ieee_k2_1.mtx (n = 344)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 1712 1.0 7 13 15 1.5e+14 0.00023 0.00093 1.5e-09 3.6e-16 (175, 169) yes
    default 23 2139 1.25 0 0 16 7.4e+07 2.4e-10 8.2e-10 3.1e-16 2.2e-16 (175, 169) yes
    all 160 3559 2.08 9 11 28 1.7e+14 0.00014 0.00056 1.8e-10 2.7e-16 (175, 169) yes
    algo5/none 0 1712 1.0 4 14 35 2.8e+13 0.0017 0.12 7.1e-06 3.4e-11 (175, 169) yes
    algo5/default (T21) 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    algo5/all 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    a: algo5 struct-zero, mate 25 2119 1.24 0 0 57 3.9e+03 5e-14 1.1e-11 2.9e-16 3.2e-16 (175, 169) yes
    a': a + greedy fallback 25 2119 1.24 0 0 57 3.9e+03 5e-14 1.1e-11 2.9e-16 3.2e-16 (175, 169) yes
    a'': struct-zero, greedy (scaled) 28 2091 1.22 3 3 51 1.9e+13 0.00056 0.07 1.4e-05 3.4e-10 (175, 169) yes
    b: τ=1e-2 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    b: τ=1e-4 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    b: τ=1e-8 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    c: a ∪ b(1e-4) 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes
    c: a ∪ b(1e-8) 169 3651 2.13 0 0 116 28 1.3e-16 1.1e-14 2.5e-16 3.3e-16 (175, 169) yes

    kkt_pglib_opf_case14_ieee_k2_10.mtx (n = 344)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 1712 1.0 8 15 50 1.6e+14 8.1e-08 1.3e-07 2.8e-17 2.4e-20 (175, 169) yes
    default 25 2154 1.26 0 0 52 2.6e+10 2.5e-11 5.7e-11 5.1e-20 1.3e-20 (175, 169) yes
    all 157 3640 2.13 6 14 114 1.5e+14 4.2e-08 6e-08 5.4e-16 1.4e-20 (175, 169) yes
    algo5/none 0 1712 1.0 4 8 50 1.9e+13 0.0006 5.7e-07 1.2e-12 2.3e-20 (175, 169) no (7)
    algo5/default (T21) 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    algo5/all 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    a: algo5 struct-zero, mate 28 2142 1.25 0 0 80 5.9e+04 3.3e-13 7.9e-16 3.7e-20 1.8e-20 (175, 169) yes
    a': a + greedy fallback 28 2142 1.25 0 0 80 5.9e+04 3.3e-13 7.9e-16 3.7e-20 1.8e-20 (175, 169) yes
    a'': struct-zero, greedy (scaled) 28 2041 1.19 3 4 72 1.9e+13 0.0008 4.9e-07 3.5e-14 2.1e-20 (175, 169) yes
    b: τ=1e-2 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    b: τ=1e-4 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    b: τ=1e-8 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    c: a ∪ b(1e-4) 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes
    c: a ∪ b(1e-8) 169 3519 2.06 0 0 162 1.7 1e-16 5.2e-19 2.5e-20 1.1e-20 (175, 169) yes

    kkt_pglib_opf_case14_ieee_k2_15.mtx (n = 344)

    rule pairs nnz(L) ratio zero perturbed 2×2 max abs L error relres relres+2 relres+5 inertia dev=ref
    none 0 1712 1.0 9 9 51 1.6e+14 6.3e-13 5e-13 4.7e-18 6.9e-26 (175, 169) no (10)
    default 156 3273 1.91 7 8 120 4.9e+14 4.2e-12 6.8e-12 1.5e-16 6.6e-26 (175, 169) no (9)
    all 32 2545 1.49 10 11 44 1.5e+14 3.7e-13 6.9e-13 3.7e-20 5e-26 (175, 169) yes
    algo5/none 0 1712 1.0 9 9 50 1.9e+13 0.00058 3.7e-12 4.7e-18 8.2e-26 (175, 169) no (8)
    algo5/default (T21) 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    algo5/all 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    a: algo5 struct-zero, mate 167 3519 2.06 0 0 167 1.7 9e-17 1.5e-16 7.5e-26 4e-26 (175, 169) yes
    a': a + greedy fallback 167 3519 2.06 0 0 167 1.7 9e-17 1.5e-16 7.5e-26 4e-26 (175, 169) yes
    a'': struct-zero, greedy (scaled) 162 3393 1.98 4 4 154 1.8e+13 0.00031 1.3e-11 3e-19 6.8e-26 (175, 169) yes
    b: τ=1e-2 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    b: τ=1e-4 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    b: τ=1e-8 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    c: a ∪ b(1e-4) 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes
    c: a ∪ b(1e-8) 169 3529 2.06 0 0 167 1.7 9e-17 1.5e-16 1.6e-25 5.9e-26 (175, 169) yes

    Generated by Claude Code

  4. github-actions
    added a commit that references this issue on Oct 8, 2026

    Docs: accept the fill of matching-based pairs (#96) (#104)

    73f186c
  5. michel2323
    added
    triagedOwner has looked at this found-by-agent issue; it no longer holds the task chain
    on Oct 9, 2026

  6. michel2323 commented on Oct 9, 2026

    @michel2323
    michel2323
    on Oct 9, 2026 – with Claude
    Member

    Triaged: accepted as documented in #104. The re-measurement after level merging is an item of T26 (segmented fused factorization) in TASKS.md.

    Generated by Claude Code

  7. michel2323
    added 2 commits that reference this issue on Oct 9, 2026

    Docs: split T25 into T22/T24-T26 after PR #107, renumber the post-v1 …

    7af9d99

    Docs: split T25 into T22/T24–T26 after PR #107, renumber the post-v1 …

    584e57c
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