StressPy 0.0.9 โ€” synthetic worked example

Local geometric diagnostics ยท Residual = observed โˆ’ predicted

Summary

All scalar results and calculation status; settings and arrays follow in detail.

categoryquantityvalueinterpretation
Analysisstresspy_version0.0.9
Analysispython_version3.12.14
Analysisnumpy_version2.3.5
Analysisn_observations5
Analysisn_parameters2
Analysismetricsigma
Analysisjacobian_methodcentral
Analysisrank_rtol1.1102230246251565e-15
Analysisrank_atol0.0
Analysisrank_threshold1.7554167342926843e-14
Fitrmse_original0.6648308055437864Original observation units; not a noise-calibrated statistic
Geometrytotal_stress55.25
Geometrytangent_stress43.35000000022918
Geometrynormal_stress11.899999999770822
Geometrynormal_fraction0.21538461538046735
Geometrynormal_fraction_pct21.538461538046736
Geometryrank2
Geometrycondition_number1.4142135623717986Retained singular spectrum
Geometryrepair_norm0.5283937925425799Supplied parameter coordinates
Geometryfull_column_condition_number1.4142135623717986Infinite if full column rank is not retained
Settingssigma_floorNot appliedRequested absolute uncertainty floor; None means not applied
Settingssigma_floor_quantileNot appliedRequested quantile floor; None means not applied
Settingsapplied_sigma_floorNot appliedEffective floor value; None means not applied
Optional analysesnonlinear_repairIncluded
Optional analysescalibrationIncluded
Optional analysesrank_sensitivityIncluded
Optional analysesweighting_sensitivityIncluded
Optional analysesparameter_diagnosticsIncluded
Optional analysesjoint_compatibilityNot calculated
Optional analysesbounded_repairNot calculated
Optional analysesdeletion_influenceNot calculated
Nonlinear repairbaseline_total_stress55.25
Nonlinear repairbest_alpha1.0
Nonlinear repairbest_stress11.899999999999999
Nonlinear repairactual_reduction43.35
Nonlinear repairscaled_repair_norm0.5283937925425799
Calibrationmethodfixed_geometry_monte_carlo
Calibrationnoise_modelindependent zero-mean Gaussian
Calibrationobserved_stress11.899999999770822
Calibrationreference_mean2.9671898839174653
Calibrationn_resamples999
Calibrationexceedances5
Calibrationp_value0.006
Calibrationconfidence_level0.95
Calibrationtail_probability_interval[0.0021396770441084265, 0.01166256327907405]

Observations

Original observation coordinates; components add to residual. Stress attribution appears here only for known diagonal metrics.

indexlabelobservedpredictedresidualtangent_componentnormal_componentgrouptangent_stress_contributionnormal_stress_contributionnormal_shareleverage
0x=-20.20.00.2-0.059999999996223310.2599999999962233left0.089999999988669921.68999999995090280.142016806721298320.6000000000022
1x=-10.70.50.199999999999999960.2000000000017786-1.778621694370486e-12left1.00000000001778587.908737829213344e-236.645998175937526e-240.2999999999990832
2x=01.11.00.100000000000000090.45999999999739655-0.35999999999739646centre5.289999999940123.2399999999531360.27226890756433060.19999999999706652
3x=11.91.50.39999999999999990.719999999999615-0.31999999999961504right12.9599999999861362.559999999993840.215126050423793460.2999999999979831
4x=23.42.01.40.98000000000605040.41999999999394966right24.010000000296474.4099999998729430.37058823529057760.6000000000036669

Whitened Coordinates

Whitened-coordinate contributions sum to tangent/normal stress; dense whitening mixes original observations.

coordinateweighted_residualweighted_tangent_componentweighted_normal_componenttangent_stress_contributionnormal_stress_contributionleverage
01.0-0.299999999981116541.29999999998111650.089999999988669921.68999999995090280.6000000000022
10.99999999999999981.0000000000088929-8.893108471852429e-121.00000000001778587.908737829213344e-230.2999999999990832
20.50000000000000042.2999999999869827-1.79999999998698225.289999999940123.2399999999531360.19999999999706652
31.99999999999999963.5999999999980745-1.59999999999807512.9599999999861362.559999999993840.2999999999979831
47.04.9000000000302522.099999999969748324.010000000296474.4099999998729430.6000000000036669

Parameters

Values may be unavailable for residual-only analyses. Participation is in the retained/discarded numerical parameter subspaces; it is not a probability or uncertainty.

indexlabelvaluelocal_repairretained_participationdiscarded_participationjacobian_steptested_repairbest_parameters
0intercept1.00.45999999999921271.00.06.055454452393343e-060.45999999999921271.4599999999992126
1slope0.50.259999999996644641.00.06.055454452393343e-060.259999999996644640.7599999999966447

Singular Values

indexsingular_valueretainedrank_threshold
015.811388300880932True1.7554167342926843e-14
111.1803398875368True1.7554167342926843e-14

Tangent Basis

Retained left singular vectors in whitened observation coordinates.

whitened_coordinatedirection_0direction_1
0-0.63245553202729830.44721359551143686
1-0.316227766009590570.44721359550405765
25.218020152720572e-120.4472135954966782
30.31622776602292550.44721359549339845
40.63245553204063320.44721359549421846

Parameter Basis

Retained right singular vectors in supplied parameter coordinates.

parameter_indexdirection_0direction_1
01.6500868289262163e-111.0
11.0-1.6500868289262163e-11

Jacobian

Prediction Jacobian in supplied coordinates.

observation_indexparameter_0parameter_1
00.9999999999960519-2.000000000001271
10.9999999999960519-0.9999999999960519
20.99999999999605190.0
31.0000000000052191.000000000005219
41.00000000002355342.000000000010438

Settings

Copied inputs and effective metric/rank settings. Null settings were not applied.

settingindexvalue
metricNot calculatedsigma
sigma00.2
sigma10.2
sigma20.2
sigma30.2
sigma40.2
covarianceNot calculatedNot calculated
whitenerNot calculatedNot calculated
rank_rtolNot calculated1.1102230246251565e-15
rank_atolNot calculated0.0
weightsNot calculatedNot calculated
sigma_input00.2
sigma_input10.2
sigma_input20.2
sigma_input30.2
sigma_input40.2
sigma_floorNot calculatedNot calculated
sigma_floor_quantileNot calculatedNot calculated
applied_sigma_floorNot calculatedNot calculated

Groups

Additive contributions under the analysis metric; these do not identify a causal defective mechanism.

groupcounttangent_stressnormal_stress
left21.09000000000645561.6899999999509028
centre15.289999999940123.239999999953136
right236.97000000028266.969999999866783

Repair Steps

All attempted nonlinear steps, including rejected bounds and model errors.

alphaparametersstatustotal_stressfixed_tangent_stressfixed_normal_stresspredicted_reductionactual_reductionefficiency_ratio
1.0[1.4599999999992126, 0.7599999999966447]linear_agreement11.8999999999999994.0165672698976646e-2111.89999999999999943.3500000002291843.350.9999999999947133
0.5[1.2299999999996063, 0.6299999999983223]linear_agreement22.73750000013166810.83750000024626411.899999999885432.5125000001718832.512499999868330.9999999999906636
0.1[1.0459999999999212, 0.5259999999996645]linear_agreement47.01350000004739435.1135000002536611.8999999997937338.2365000000435458.2364999999526060.999999999988959

Calibration Quantiles

quantilereference_stress
0.0250.1910405409369134
0.52.3469913662423414
0.957.731293950276721
0.9758.957501952888789

Calibration Reference

replicatenormal_stressrank
05.5901040826048392
11.36887156035311872
20.64761364541605362
32.0378581714240922
42.1894098112971542
50.301707136996564542
64.6494148685762392
72.81847890780029032
80.92512938009264492
90.44933275723400222
101.96672050422420372
113.62420564382941952
120.49840332844082672
131.5951168180356642
140.58347455997063892
150.97292775359034962
160.51839004671513182
170.62928111555594142
180.76146256670124632
191.37936168972726962
203.0665416385137162
213.4580202782991452
221.77863077751499992
232.34144461306546072
240.78167316467174952
252.59393927159427662
262.96635797066133482
270.110764449809989582
284.1700687236353312
290.93051401672321392
301.75973812791941552
311.20425457374641082
326.0913319308576922
331.8076771923372132
341.11222706216712892
351.5638955397456262
361.85109460510428032
378.1935151323001852
384.4357816007579792
391.19787485823800992
403.61605956866723682
410.83649925536696412
422.3863139301265732
431.09669202536295972
441.14785473330664532
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487.5466521019550172
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504.1133814964496812
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520.55915634947886642
530.228713669872125822
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553.1644682329936332
565.2801384391951512
570.32674208708682532
587.7630366565832262
592.79179137455996252
605.5426108618020842
611.04966516879468432
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632.62666017513854342
641.23038515632675942
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763.00345970272563672
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Rank Sensitivity

Explicit rank cutoff sweep; no p-values are inferred.

rank_rtolranknormal_stressnormal_fractionrepair_norm
1e-12211.8999999997708220.215384615380467350.5283937925425799
1e-08211.8999999997708220.215384615380467350.5283937925425799
0.0001211.8999999997708220.215384615380467350.5283937925425799

Weighting Sensitivity

Absolute stresses under different metrics are not directly comparable.

schemeranktotal_stresstangent_stressnormal_stressnormal_fractionrepair_normanalysis_settings
equal22.20999999999999951.73400000000916690.47599999999083280.215384615380467380.5283937925425799{"metric": "euclidean", "sigma": null, "covariance": null, "whitener": null, "rank_rtol": 1.1102230246251565e-15, "rank_atol": 0.0, "weights": null, "sigma_input": null, "sigma_floor": null, "sigma_floor_quantile": null, "applied_sigma_floor": null}
sigma_0.2255.2543.3500000002291811.8999999997708220.215384615380467350.5283937925425799{"metric": "sigma", "sigma": [0.2, 0.2, 0.2, 0.2, 0.2], "covariance": null, "whitener": null, "rank_rtol": 1.1102230246251565e-15, "rank_atol": 0.0, "weights": null, "sigma_input": [0.2, 0.2, 0.2, 0.2, 0.2], "sigma_floor": null, "sigma_floor_quantile": null, "applied_sigma_floor": null}

Parameter Diagnostics

Separately supplied diagnostics; scale and truncation may differ from the main result. Retained variance factors are not full uncertainties.

indexlabelparameter_scaleidentifiable_participationnull_participationretained_variance_factorhas_null_component
0intercept1.01.00.00.007999999999945832False
1slope1.01.00.00.003999999999980249False

Parameter Diagnostic Settings

quantityvalue
rank2
singular_values[15.811388300880932, 11.1803398875368]
retained_directions[[1.6500868289262163e-11, 1.0], [1.0, -1.6500868289262163e-11]]
retained_condition_number1.4142135623717986
full_column_condition_number1.4142135623717986
condition_indices[1.0, 1.4142135623717986]

Metadata

User-supplied provenance; not independently inferred or verified.

keyvalue
dataSynthetic demonstration, not experimental evidence
modelintercept + slope * x
x[-2.0, -1.0, 0.0, 1.0, 2.0]
parameter_coordinatesraw; dimensionless example
unitsdimensionless synthetic observations
fit_protocolsupplied baseline; not fitted to these observations
calibration_seed42
calibration_resamples999
calibration_noiseindependent zero-mean Gaussian, sigma=0.2
calibration_scopeconditional fixed-geometry reference, not refitting

Interpretation and provenance