=== Test: test_A_measurement_system ===
Timestamp: 2026-04-12 13:35:55.611597

--- Gradient Check ---
Pass: TRUE
Max error: 1.13e-06

param_idx param_value fixed analytical finite_diff abs_error rel_error pass
1 1 TRUE -153.999458177515 -153.999465942383 7.76486822928746e-06 5.04213971247965e-08 TRUE
2 2 FALSE 22.3962533949778 22.3962364196777 1.69753000669459e-05 7.57953244859976e-07 TRUE
3 0.5 FALSE 106.920211571564 106.92024230957 3.07380063730989e-05 2.874853789061e-07 TRUE
4 1.5 FALSE 15.104639397595 15.1046346028646 4.79473036740785e-06 3.17434383119638e-07 TRUE
5 1.2 FALSE -67.3364465386632 -67.3364702860514 2.37473882549466e-05 3.52667553764929e-07 TRUE
6 0.6 FALSE 111.836284724033 111.836273193359 1.15306734329579e-05 1.03103162361481e-07 TRUE
7 1 FALSE -25.627862519458 -25.6278915405273 2.90210693307813e-05 1.13240175395967e-06 TRUE
8 0.8 FALSE -156.382859769499 -156.382850646973 9.12252650664414e-06 5.83345710153208e-08 TRUE
9 0.4 FALSE 226.738851459849 226.73885345459 1.99474050077697e-06 8.79752398137828e-09 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 6.74e-06

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
3.000e-11 7.736e-09 4.903e-08 2.789e-07 1.262e-07 6.744e-06 

--- Estimation Comparison ---
Default init converged: TRUE
True init converged: TRUE
Default estimates reasonable: TRUE
True init estimates reasonable: TRUE

Parameter estimates:
parameter true_value default_init est_default se_default est_true_init se_true_init z_default z_true_init
f_var 1 1 0.911226445881204 0.0677789109116606 0.911226445806862 0.0677789109025189 -1.30975185237926 -1.30975185365274
T1_int 2 2.04653064143634 2.08445310535604 0.0478970836143775 2.08445310541466 0.0478970836098465 1.76322020012685 1.76322020151759
T1_sigma 0.5 1.09645303516447 0.519064308005067 0.0229287476953195 0.519064308020056 0.0229287476952346 0.831458754677574 0.831458755334389
T2_int 1.5 1.55327435805289 1.60084173686058 0.0580898001177371 1.60084173693319 0.0580898001117339 1.73596288257473 1.73596288400415
T2_lambda 1.2 0.5 1.25433249559986 0.0435769559222917 1.2543324956186 0.0435769559225423 1.24681714107677 1.24681714149971
T2_sigma 0.6 1.33117061718788 0.551962306445558 0.0295570709084417 0.551962306428733 0.0295570709079982 -1.62525216734931 -1.62525216794294
T3_int 1 1.02006509578485 1.05069536574027 0.038328756332046 1.05069536578627 0.0383287563283254 1.32264572586418 1.32264572719277
T3_lambda 0.8 0.5 0.807707801378054 0.0294486885372933 0.807707801391347 0.029448688537772 0.261736659963426 0.261736660410549
T3_sigma 0.4 0.876115012468385 0.398838179699003 0.0191743433116396 0.398838179687641 0.019174343311563 -0.0605924428343838 -0.0605924434271523

Likelihood comparison:
source loglik convergence
True parameters -1679.09535598629 NA
Est (default init) -1675.47932745949 0
Est (true init) -1675.47932745949 0

--- Overall Result ---
Test passed: TRUE
