=== Test: test_A_measurement_system ===
Timestamp: 2026-01-03 11:03:21.215248

--- 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 7.76486828613088e-06 5.04213974939109e-08 TRUE
2 2 FALSE 22.3962533949778 22.3962326049805 2.07899973467818e-05 9.2828100660816e-07 TRUE
3 0.5 FALSE 106.920211571564 106.920234680176 2.31086117423729e-05 2.16129452123785e-07 TRUE
4 1.5 FALSE 15.104639397595 15.1046295166016 9.88099341014959e-06 6.54169862245833e-07 TRUE
5 1.2 FALSE -67.3364465386632 -67.3364702860514 2.37473881981032e-05 3.52667552920759e-07 TRUE
6 0.6 FALSE 111.836284724033 111.83625793457 2.67894624954579e-05 2.39541835449564e-07 TRUE
7 1 FALSE -25.627862519458 -25.6278915405273 2.90210693165704e-05 1.13240175340516e-06 TRUE
8 0.8 FALSE -156.382859769499 -156.382858276367 1.49313203223755e-06 9.54792647157542e-09 TRUE
9 0.4 FALSE 226.738851459849 226.73885345459 1.99474044393355e-06 8.79752373067833e-09 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 5.45e-06

Summary of relative errors:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
2.800e-11 7.215e-09 3.991e-08 2.445e-07 1.011e-07 5.446e-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 0.911226445881203 0.0677789109116605 0.911226445806862 0.0677789109025189 -1.30975185237927 -1.30975185365275
T1_int 2 2.04653064143634 2.08445310535604 0.0478970836143775 2.08445310541466 0.0478970836098466 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 0.058089800111734 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 0.0383287563320459 1.05069536578627 0.0383287563283255 1.32264572586418 1.32264572719276
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
