Set WtW block of KKT matrix to -I in initialize_ipm

[govindchari]

When qoco currently solves a problem and then qoco_solve is called again, the KKT system contains the NT scaling from the final iteration of the first solve. Since the NT block of the KKT matrix is not reset, this leads to the behavior seen here: #45.

This fix sets the NT block to -I in initialize_ipm which fixes this issue.

[github-actions]

Download benchmark artifacts

Benchmark Summary

• Baseline solved: 129 problems
• Diff branch solved: 129 problems

Runtime regressions (> 5.0%)

• AUG2DC: diff=0.0084s, baseline=0.0079s, Δ=+6.3%
• DUAL2: diff=0.0021s, baseline=0.0018s, Δ=+16.1%
• DUALC2: diff=0.0012s, baseline=0.0009s, Δ=+35.5%
• GOULDQP3: diff=0.0019s, baseline=0.0015s, Δ=+30.0%
• HS51: diff=0.0000s, baseline=0.0000s, Δ=+600.0%
• HS76: diff=0.0000s, baseline=0.0000s, Δ=+7.1%
• LASER: diff=0.0034s, baseline=0.0031s, Δ=+7.4%
• LOTSCHD: diff=0.0001s, baseline=0.0000s, Δ=+10.2%
• PRIMAL1: diff=0.0045s, baseline=0.0042s, Δ=+7.3%
• PRIMALC8: diff=0.0040s, baseline=0.0038s, Δ=+6.4%
• QGROW7: diff=0.0042s, baseline=0.0040s, Δ=+5.7%
• QRECIPE: diff=0.0014s, baseline=0.0011s, Δ=+30.9%
• QSCTAP1: diff=0.0027s, baseline=0.0022s, Δ=+23.3%

Runtime improvements (> 5.0%)

• CONT-200: diff=4.6637s, baseline=4.9928s, Δ=-6.6%
• CONT-300: diff=20.5352s, baseline=22.5014s, Δ=-8.7%
• CVXQP1_M: diff=0.0581s, baseline=0.0634s, Δ=-8.4%
• CVXQP1_S: diff=0.0005s, baseline=0.0006s, Δ=-18.5%
• CVXQP2_M: diff=0.0410s, baseline=0.0510s, Δ=-19.7%
• CVXQP2_S: diff=0.0004s, baseline=0.0005s, Δ=-25.9%
• CVXQP3_M: diff=0.1138s, baseline=0.1265s, Δ=-10.0%
• DUAL4: diff=0.0010s, baseline=0.0013s, Δ=-20.2%
• DUALC1: diff=0.0012s, baseline=0.0013s, Δ=-7.6%
• DUALC5: diff=0.0007s, baseline=0.0009s, Δ=-25.3%
• DUALC8: diff=0.0015s, baseline=0.0016s, Δ=-7.3%
• EXDATA: diff=6.1708s, baseline=7.1061s, Δ=-13.2%
• HS118: diff=0.0001s, baseline=0.0001s, Δ=-41.5%
• HS21: diff=0.0000s, baseline=0.0000s, Δ=-39.1%
• HS35MOD: diff=0.0000s, baseline=0.0000s, Δ=-6.2%
• HS53: diff=0.0000s, baseline=0.0000s, Δ=-11.1%
• HUESTIS: diff=0.0156s, baseline=0.0168s, Δ=-7.3%
• PRIMAL2: diff=0.0054s, baseline=0.0057s, Δ=-5.7%
• PRIMALC1: diff=0.0022s, baseline=0.0028s, Δ=-22.4%
• PRIMALC2: diff=0.0017s, baseline=0.0022s, Δ=-22.4%
• Q25FV47: diff=0.2224s, baseline=0.2410s, Δ=-7.7%
• QBEACONF: diff=0.0024s, baseline=0.0026s, Δ=-9.3%
• QBORE3D: diff=0.0022s, baseline=0.0025s, Δ=-13.5%
• QETAMACR: diff=0.0767s, baseline=0.0836s, Δ=-8.2%
• QFFFFF80: diff=0.1114s, baseline=0.1191s, Δ=-6.4%
• QPCBLEND: diff=0.0006s, baseline=0.0008s, Δ=-27.2%
• QSCAGR7: diff=0.0005s, baseline=0.0009s, Δ=-40.6%
• QSCFXM1: diff=0.0065s, baseline=0.0071s, Δ=-7.5%
• QSCFXM3: diff=0.0259s, baseline=0.0274s, Δ=-5.2%
• QSHARE2B: diff=0.0008s, baseline=0.0011s, Δ=-31.2%
• QSHELL: diff=0.1178s, baseline=0.1306s, Δ=-9.8%
• QSHIP08L: diff=0.1445s, baseline=0.1559s, Δ=-7.3%
• QSHIP12L: diff=0.2843s, baseline=0.3084s, Δ=-7.8%
• STCQP1: diff=0.0489s, baseline=0.0531s, Δ=-8.0%
• STCQP2: diff=0.1118s, baseline=0.1240s, Δ=-9.8%
• UBH1: diff=0.0293s, baseline=0.0317s, Δ=-7.5%
• VALUES: diff=0.0016s, baseline=0.0019s, Δ=-16.8%

[github-actions]

Download benchmark artifacts

Benchmark Summary

• Baseline solved: 129 problems
• Diff branch solved: 129 problems

Runtime regressions (> 5.0%)

• DUALC5: diff=0.0007s, baseline=0.0006s, Δ=+10.0%
• HS35MOD: diff=0.0000s, baseline=0.0000s, Δ=+6.3%
• QBORE3D: diff=0.0024s, baseline=0.0022s, Δ=+6.6%
• QPTEST: diff=0.0000s, baseline=0.0000s, Δ=+9.1%

Runtime improvements (> 5.0%)

• GENHS28: diff=0.0000s, baseline=0.0000s, Δ=-16.7%
• HS268: diff=0.0000s, baseline=0.0000s, Δ=-61.4%
• HS53: diff=0.0000s, baseline=0.0000s, Δ=-5.6%
• LOTSCHD: diff=0.0000s, baseline=0.0000s, Δ=-5.4%