{ Analytica Model Test_SipMath_3_1, encoding="UTF-8" }
SoftwareVersion 7.2.2


{ System Variables with non-default values: }
SampleSize := 1000
TypeChecking := 1
Checking := 1
SaveOptions := 2
SaveValues := 0

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{!-50299|DiagramColor LinkModule: 0x00ffffff}
{!-50299|DiagramColor Library: 0x00ffffff}
{!-50299|DiagramColor LinkLibrary: 0x00ffffff}
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Model Test_SipMath_3_1
Title: Test SipMath 3.1
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Wed, Oct 21, 2026 7:42 AM
DiagState: 2,0,1,1250,471,17,10
WindState: 2,110,416,720,350
FontStyle: Arial,15
FileInfo: 0,Model Test_SipMath_3_1,2,2,0,0,W:\Testmodels\Test SipMath 3.1.ana
{!70104|Att_GUID: c7b87b6f-57bb-4663-b87b-77926948f9e3 bc8d4963-0d86-403f-82a1-7dccbf352a0f}

Include 0,LinkLibrary SipMath_3_1,2,2,0,0,SipMath 3.1 library.ana

NodeLocation SipMath_3_1: 136,160,2
NodeSize SipMath_3_1: 88,32


Module QA_Fixtures
Title: QA Fixtures
Description: Embedded canonical JSON examples and additional deterministic test fixtures. No network dependency when tests run.
NodeLocation: 136,264,2
NodeSize: 88,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,0,1,1264,476,17,10

Constant Canonical_Single_JSON
Title: Canonical Single JSON
Description: Canonical library 01 from Probability Management (2021-08-23), whitespace compacted. Original calibration values preserved. Source: https://www.probabilitymanagement.org/s/Lib_01_Single-Variable_2021_08_23.SIPmath
Definition: '{"name":"Single Variable Library","objectType":"sipModel","libraryType":"SIPmath_3_0","dateCreated":"2021-08-17","provenance":"SLS","U01":{"rng":[{"name":"HDR101","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":1,"varId":1,"seed3":2,"seed4":2}}]},"sips":[{"name":"Unbounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","metadata":{"Average":-0.508109215629409,"Trial1":0.108155020321771,"Trial2":0.422196005333154,"Trial3":-0.0278776878964113},"arguments":{"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.46025990428473268,0.52556291243339126,2.11565238380833565]}}]}'
NodeLocation: 160,96,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Constant Canonical_Copula_JSON
Title: Canonical Copula JSON
Description: Canonical library 02 extract: exact RNGs, coefficient vectors, matrix and Trial1/2/3 calibration metadata. Display density arrays omitted. Source: https://www.probabilitymanagement.org/s/Lib_02_Gauss_2021_08_23.SIPmath
Definition: '{~
 "name":"Gaussian Copula Development Time Library","objectType":"sipModel","libraryType":"SIPmath_3_0",~
 "globalVariables":[{"name":"correlationMatrixValue","value":{"columns":["Accounts","Products","Orders","Fulfillment"],"rows":["Accounts","Products","Orders","Fulfillment"],"matrix":[{"row":"Accounts","col":"Accounts","value":1},{"row":"Accounts","col":"Products","value":0},{"row":"Accounts","col":"Orders","value":0},{"row":"Accounts","col":"Fulfillment","value":0},{"row":"Products","col":"Products","value":1},{"row":"Products","col":"Orders","value":0},{"row":"Products","col":"Fulfillment","value":0.75},{"row":"Orders","col":"Orders","value":1},{"row":"Orders","col":"Fulfillment","value":0},{"row":"Fulfillment","col":"Fulfillment","value":1}]}}],~
 "U01":{"rng":[~
 {"name":"HDR4","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":4,"seed3":0,"seed4":0}},~
 {"name":"HDR5","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":5,"seed3":0,"seed4":0}},~
 {"name":"HDR6","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":6,"seed3":0,"seed4":0}},~
 {"name":"HDR7","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":7,"seed3":0,"seed4":0}},~
 {"name":"HDR8","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":8,"seed3":0,"seed4":0}}],~
 "copula":[{"name":"Gaussian","function":"GaussianCopula","arguments":{"correlationMatrix":{"type":"globalVariables","value":"correlationMatrixValue"},"rng":["HDR4","HDR5","HDR6","HDR7"]},"copulaLayer":["cl1","cl2","cl3","cl4"]}]},~
 "sips":[~
 {"name":"Accounts","ref":{"source":"copula","name":"Gaussian","copulaLayer":"cl1"},"function":"Metalog_1_0","arguments":{"aCoefficients":[9.872717622,1.678242357,2.54967822,3.535388319,-13.40905029]},"metadata":{"Trial1":5.91064824323855,"Trial2":3.99951401423695,"Trial3":3.61593085127843}},~
 {"name":"Products","ref":{"source":"copula","name":"Gaussian","copulaLayer":"cl2"},"function":"Metalog_1_0","arguments":{"aCoefficients":[10.28359942,1.433048092,1.737463084,3.927285373,-13.45782811]},"metadata":{"Trial1":4.81850430027545,"Trial2":16.264999616127,"Trial3":9.21182344011462}},~
 {"name":"Orders","ref":{"source":"copula","name":"Gaussian","copulaLayer":"cl3"},"function":"Metalog_1_0","arguments":{"aCoefficients":[8.526657058,4.390832871,7.645594813,-11.34424622,-27.90451926]},"metadata":{"Trial1":8.84993813887317,"Trial2":5.73877017205265,"Trial3":7.90854997496018}},~
 {"name":"Fulfillment","ref":{"source":"copula","name":"Gaussian","copulaLayer":"cl4"},"function":"Metalog_1_0","arguments":{"aCoefficients":[8.93145879,3.863446641,6.494528709,-8.804090192,-25.50440804]},"metadata":{"Trial1":6.7522436646553,"Trial2":11.4933053690752,"Trial3":5.97047076730257}},~
 {"name":"Marketing","ref":{"source":"rng","name":"HDR8"},"function":"Metalog_1_0","arguments":{"aCoefficients":[9.872717622,1.678242357,2.54967822,3.535388319,-13.40905029]},"metadata":{"Trial1":4.97377773402723,"Trial2":5.26303264347232,"Trial3":11.3668582781926}}~
 ]~
}'
NodeLocation: 464,96,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Constant Canonical_Discrete_JSON
Title: Canonical Discrete JSON
Description: Canonical library 06, complete numerical table and calibration metadata, whitespace compacted. Source: https://www.probabilitymanagement.org/s/Lib_06_Poisson_2021_08_23.SIPmath
Definition: '{"name":"Discrete Poisson Variable With Lookup Library","objectType":"sipModel","libraryType":"SIPmath_3_0","U01":{"rng":[{"name":"HDR9","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":9,"seed3":0,"seed4":0}}]},"sips":[{"name":"Poisson","ref":{"source":"rng","name":"HDR9"},"function":"Lookup_Table","metadata":{"Lambda":0.5,"Trial6":1,"Trial23":2,"Trial299":3},"arguments":{"value":[[0.606530660,0],[0.909795990,1],[0.985612322,2],[0.998248377,3],[0.999827884,4],[0.999985835,5],[0.999998998,6],[0.999999938,7],[0.999999997,8],[1,9]]}}]}'
NodeLocation: 160,176,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Constant Canonical_Parameters_JSON
Title: Canonical Parameters JSON
Description: Canonical library 09 numerical extract, including duplicate environment-specific StandardNormal entries. Source: https://www.probabilitymanagement.org/s/Lib_09_Input_Param_and_Environment_Specific_2021_09_07.SIPmath. Original first-three-trial expectations are in QA.
Definition: '{"name":"Basic Library","objectType":"sipModel","libraryType":"SIPmath_3_0",~
"U01":{"rng":[~
{"name":"HDR1","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":1,"seed3":0,"seed4":0}},~
{"name":"HDR2","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":2,"seed3":{"type":"parameter","name":"User-entered Seed3"},"seed4":0}},~
{"name":"HDR3","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":9039920,"varId":3,"seed3":0,"seed4":0}}]},~
"sips":[~
{"name":"Variable1","ref":{"source":"rng","name":"HDR1"},"function":"Metalog_1_0","arguments":{"lowerBound":0,"upperBound":5,"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.4602599042847327,0.5255629124333913,2.1156523838083356]}},~
{"name":"Variable2_seed3_param","ref":{"source":"rng","name":"HDR2"},"function":"Metalog_1_0","arguments":{"aCoefficients":[10.28359942,1.433048092,1.737463084,3.927285373,-13.45782811]}},~
{"name":"StandardNormal","ref":{"source":"rng","name":"HDR3"},"function":"Metalog_1_0","arguments":{"aCoefficients":[-1.18721e-8,-108.7360185,0.000228037,437.4513354,-0.000910088,988.3027041,-3370.883493,-0.001941269,0.006475465,-2823.944368,7434.879183,0.004897097,-0.011367609,2456.743398,-3595.592826,-0.003114859]}},~
{"name":"StandardNormal","ref":{"source":"rng","name":"HDR3"},"environment":"ExcelFrontline","function":"PsiNormal","arguments":{"mean":0,"stdDev":1}},~
{"name":"StandardNormal","ref":{"source":"rng","name":"HDR3"},"environment":"ExcelPalisade","function":"RiskNormal","arguments":{"mean":0,"stdDev":1}}~
]}'
NodeLocation: 160,256,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Constant Synthetic_Stored_JSON
Title: Synthetic Stored JSON
Description: Small synthetic fixture for inline arrays, external resources and stored copula layers. External resources are explicitly provided in QA, never fetched.
Definition: '{"objectType":"sipModel","PM_Trials":3,~
"U01":{"rng":[{"name":"Counter","function":"Index","arguments":{"counter":"PM_Index"}}],~
"copula":[{"name":"Stored","function":"SIP_Array","arguments":{"type":"csv","url":"fixture:copula","value":["A","B"]},"copulaLayer":["A","B"]}]},~
"sips":[~
{"name":"Array","function":"SIP_Array","ref":{"source":"rng","name":"Counter"},"arguments":{"type":"array","value":[10,20,30]}},~
{"name":"External","function":"SIP_Array","arguments":{"type":"csv","url":"fixture:data","value":["X"]}},~
{"name":"CopulaA","function":"Metalog_2_0","ref":{"source":"copula","name":"Stored","copulaLayer":"A"},"arguments":{"aCoefficients":[0,1]}},~
{"name":"CopulaB","function":"Metalog_2_0","ref":{"source":"copula","name":"Stored","copulaLayer":"B"},"arguments":{"aCoefficients":[0,1]}}~
]}'
NodeLocation: 464,256,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Constant Canonical_Bounds_JSON
Title: Canonical Bounds JSON
Description: Canonical library 08 extract, retaining all eight coefficient/bound/rounding definitions and all 24 first-three-trial expectations. Display/average metadata omitted. Source: https://www.probabilitymanagement.org/s/Lib_08_Rounded_Bounded_Single_HDR_2021_08_23.SIPmath
Definition: '{"name":"Bounded Rounded Library","objectType":"sipModel","libraryType":"SIPmath_3_0",~
"U01":{"rng":[{"name":"HDR101","function":"HDR_2_0","arguments":{"counter":"PM_Index","entity":1,"varId":1,"seed3":2,"seed4":2}}]},~
"sips":[~
{"name":"Unbounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","arguments":{"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.46025990428473268,0.52556291243339126,2.11565238380833565]},"metadata":{"Trial1":0.108155020321771,"Trial2":0.422196005333154,"Trial3":-0.0278776878964113}},~
{"name":"LowerBounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","arguments":{"lowerBound":0,"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.46025990428473268,0.52556291243339126,2.11565238380833565]},"metadata":{"Trial1":1.11422045881313,"Trial2":1.52530746378309,"Trial3":0.972507308941779}},~
{"name":"UpperBounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","arguments":{"upperBound":5,"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.46025990428473268,0.52556291243339126,2.11565238380833565]},"metadata":{"Trial1":4.10251154330337,"Trial2":4.34439447538021,"Trial3":3.97173009312584}},~
{"name":"Bounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","arguments":{"lowerBound":0,"upperBound":5,"aCoefficients":[-0.44366710027334577,0.31428823046335125,-0.46025990428473268,0.52556291243339126,2.11565238380833565]},"metadata":{"Trial1":2.63506214351606,"Trial2":3.02004307526592,"Trial3":2.46515514678502}},~
{"name":"Unrounded","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","arguments":{"aCoefficients":[-44.366710027334577,31.428823046335125,-46.025990428473271,52.556291243339125,211.565238380833563]},"metadata":{"Trial1":10.8155020321771,"Trial2":42.2196005333154,"Trial3":-2.78776878964113}},~
{"name":"RoundNearest","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","rounding":"nearest","arguments":{"aCoefficients":[-44.366710027334577,31.428823046335125,-46.025990428473271,52.556291243339125,211.565238380833563]},"metadata":{"Trial1":11,"Trial2":42,"Trial3":-3}},~
{"name":"RoundUp","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","rounding":"up","arguments":{"aCoefficients":[-44.366710027334577,31.428823046335125,-46.025990428473271,52.556291243339125,211.565238380833563]},"metadata":{"Trial1":11,"Trial2":43,"Trial3":-3}},~
{"name":"RoundDown","ref":{"source":"rng","name":"HDR101"},"function":"Metalog_1_0","rounding":"down","arguments":{"aCoefficients":[-44.366710027334577,31.428823046335125,-46.025990428473271,52.556291243339125,211.565238380833563]},"metadata":{"Trial1":10,"Trial2":42,"Trial3":-2}}~
]}'
NodeLocation: 464,176,2
NodeSize: 120,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close QA_Fixtures

Module SIP_QA
Title: SIP QA
Description: Deterministic regression tests, canonical calibration comparisons, numerical primitive tests, array-abstraction tests, and negative validation/security tests. Every residual should be within its tolerance.
NodeLocation: 136,376,2
NodeSize: 88,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,0,1,1264,476,17,10

Function QA_Basis_Residual(n : positive atom; version : positive atom)
Title: QA Basis Residual
Description: Independent direct basis-sum oracle for unbounded Metalog quantiles. Exercises every term count 2..16, including odd legacy lengths needing padding.
Definition: LocalIndex K := 1..n;~
LocalIndex P := [0.01, 0.2, 0.5, 0.8, 0.99];~
Local a := 1 / @K^2;~
Local power := Floor((@K - 1) / 2);~
Local logTerm := If version = 1 Then~
    @K = 2 or @K = 3 or (@K >= 6 and Mod(@K, 2) = 0)~
Else Mod(@K, 4) = 2 or Mod(@K, 4) = 3;~
Local expected := Sum(a * (P - 0.5)^power * (If logTerm Then Ln(P / (1 - P)) Else 1), K);~
Max(Abs(SIP_Metalog(P, a, K, version:version) - expected), P)
NodeLocation: 128,176,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Index QA_Case
Title: QA Case
Description: Regression case names. QA_Residual reports numerical errors; expected errors return zero when correctly rejected.
Definition: [~
 'Canonical single calibration',~
 'Canonical Gaussian calibration',~
 'Canonical discrete calibration',~
 'Canonical parameter calibration',~
 'Canonical 16-term legacy calibration',~
 'Metalog 1.0 all term counts',~
 'Metalog 2.0 all term counts',~
 'Lower bound transform',~
 'Upper bound transform',~
 'Both bounds transform',~
 'Negative rounding conventions',~
 'JSON export round trip',~
 'HDR seed mapping',~
 'Explicit trial reproducibility',~
 'Run sample equals explicit trials',~
 'Mid is trial one',~
 'Caller scenario array abstraction',~
 'Copula identity matrix',~
 'Cholesky equals correlation path',~
 'Copula different index labels',~
 'Stored array positions',~
 'Lookup exact boundary',~
 'Preloaded external array',~
 'Stored copula layer',~
 'DIST native round trip',~
 'Nested array trial dimension',~
 'Environment-independent selection',~
 'Environment-specific selection',~
 'Calibration missing is not passed',~
 'Reject stored trial overflow',~
 'Reject fractional trial',~
 'Reject invalid lookup CDF',~
 'Reject asymmetric correlation',~
 'Reject missing parameter',~
 'Reject unknown function',~
 'Reject missing external resource',~
 'Reject duplicate name/environment',~
 'Reject invalid header',~
 'Reject invalid probability',~
 'Reject seed out of range'~
]
NodeLocation: 128,64,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable QA_Residual
Title: QA Residual
Description: Numerical absolute residual for every QA_Case; zero is ideal. Unexpected errors become INF. Negative tests return zero only when an error is actually raised. All tests avoid network/file access and do not change global sample settings.
Definition: Local single := SIP_Parse(Canonical_Single_JSON);~
Local gauss := SIP_Parse(Canonical_Copula_JSON);~
Local discrete := SIP_Parse(Canonical_Discrete_JSON);~
Local param := SIP_Parse(Canonical_Parameters_JSON);~
Local stored := SIP_Parse(Synthetic_Stored_JSON);~
Local params := ParseJSON('{"User-entered Seed3":1}');~
Local resources := ParseJSON('{"fixture:data":{"X":[4,5,6]},"fixture:copula":{"A":[0.2,0.5,0.8],"B":[0.8,0.5,0.2]}}');~
LocalIndex T := 1..3;~
LocalIndex Names := SIP_Names(gauss);~
LocalIndex K := 1..3;~
LocalIndex I := ['A','B'];~
LocalIndex J := ['X','Y'];~
LocalIndex Terms := 2..16;~
Local a := Array(K, [1, 0.5, 0.1]);~
Local p := Array(T, [0.2, 0.5, 0.8]);~
Local m := Array(I, J, [[1, 0.6], [0.6, 1]]);~
Local l := Decompose(m, I, J);~
Local u := SIP_Uniform(T, varId:@I);~
Local q := SIP_Metalog(p, a, K);~
Array(QA_Case, [~
    { 01: published single-variable calibration }~
    Try(Max(Abs(SIP_Evaluate(single, 'Unbounded', T)~
        - Array(T, [0.108155020321771, 0.422196005333154, -0.0278776878964113])), T), catch:Inf),~
    { 02: every Gaussian-copula SIP including independent Marketing }~
    Try(Max(Max(SIP_Calibration(gauss, Names, T)->absoluteError, T), Names), catch:Inf),~
    { 03: published discrete trials }~
    Try((LocalIndex D := [6,23,299]; Max(Abs(SIP_Evaluate(discrete, 'Poisson', D) - Array(D,[1,2,3])), D)), catch:Inf),~
    { 04: user-entered seed }~
    Try(Max(Abs(SIP_Evaluate(param, 'Variable2_seed3_param', T, params)~
        - Array(T,[11.091734,12.036073,7.760296])), T), catch:Inf),~
    { 05: published 16-term legacy coefficients }~
    Try(Max(Abs(SIP_Evaluate(param, 'StandardNormal', T)~
        - Array(T,[-0.079230,-1.046566,0.081651])), T), catch:Inf),~
    { 06,07: independent basis oracles for every length }~
    Try(Max(QA_Basis_Residual(Terms,1),Terms), catch:Inf),~
    Try(Max(QA_Basis_Residual(Terms,2),Terms), catch:Inf),~
    { 08,09,10: all bounding transformations }~
    Try(Max(Abs(SIP_Metalog(p,a,K,lowerBound:2) - (2+Exp(q))),T), catch:Inf),~
    Try(Max(Abs(SIP_Metalog(p,a,K,upperBound:5) - (5-Exp(-q))),T), catch:Inf),~
    Try(Max(Abs(SIP_Metalog(p,a,K,lowerBound:2,upperBound:5) - (2+3/(1+Exp(-q)))),T), catch:Inf),~
    { 11: canonical Excel-style negative rounding }~
    Try(Max(Abs(SIP_Round([-2.8,2.8], 'up') - [-3,3]))~
        + Max(Abs(SIP_Round([-2.8,2.8], 'down') - [-2,2]))~
        + Max(Abs(SIP_Round([-2.5,2.5], 'nearest') - [-3,3])), catch:Inf),~
    { 12: JSON export/import preserves coefficients and seeds }~
    Try(Max(Abs(SIP_Evaluate(SIP_Parse(SIP_Export_Metalog('X',a,K,entity:5,varId:9)), 'X',T)~
        - SIP_Metalog(SIP_Uniform(T,entity:5,varId:9),a,K)),T), catch:Inf),~
    { 13,14: exact seed mapping and repeatability }~
    Try(Max(Abs(SIP_Uniform(T,entity:17,varId:23,seed3:4,seed4:8) - Hubbard_HDR(T,23,17,4,8)),T), catch:Inf),~
    Try(Max(Abs(SIP_Evaluate(single,'Unbounded',T) - SIP_Evaluate(single,'Unbounded',T)),T), catch:Inf),~
    { 15,16: Analytica evaluation modes }~
    Try(Max(Abs(Sample(SIP_Sample(single,'Unbounded')) - SIP_Evaluate(single,'Unbounded',Run)),Run), catch:Inf),~
    Try(Abs(Mid(SIP_Sample(single,'Unbounded')) - SIP_Evaluate(single,'Unbounded',1)), catch:Inf),~
    { 17: scenario arrays preserve caller index identity }~
    Try(Max(Max(Abs(SIP_Metalog(p,a+@I,K) - (q + Sum(@I * (p-0.5)^Floor((@K-1)/2)~
        * (If Mod(@K,4)=2 or Mod(@K,4)=3 Then Ln(p/(1-p)) Else 1),K))),T),I), catch:Inf),~
    { 18: identity copula }~
    Try(Max(Max(Abs(SIP_Gaussian_Copula(u,If @I=@J Then 1 Else 0,I,J)-u),I),T), catch:Inf),~
    { 19: Cholesky path equals correlation path }~
    Try(Max(Max(Abs(SIP_Gaussian_Copula(u,m,I,J) - SIP_Gaussian_Copula(u,l,I,J,True)),I),T), catch:Inf),~
    { 20: distinct row and column labels, reference first output }~
    Try(Max(Abs(SIP_Gaussian_Copula(u,m,I,J)[@I=1] - u[@I=1]),T), catch:Inf),~
    { 21,22: stored trials and lookup boundary }~
    Try(Max(Abs(SIP_Evaluate(stored,'Array',T) - Array(T,[10,20,30])),T), catch:Inf),~
    Try(Abs(SIP_Lookup(0.6,Array(I,[0.6,1]),Array(I,[10,20]),I)-10), catch:Inf),~
    { 23,24: explicitly preloaded external data and stored copula }~
    Try(Max(Abs(SIP_Evaluate(stored,'External',T,resources:resources)-Array(T,[4,5,6])),T), catch:Inf),~
    Try(Max(Abs(SIP_Evaluate(stored,'CopulaA',T,resources:resources)-Ln(p/(1-p))),T), catch:Inf),~
    { 25: native DIST codec }~
    Try((Local enc:=SipEncode(T,T,type:'Double'); Max(Abs(SIP_Stored(_Struct(type:'DIST',value:enc),T)-T),T)), catch:Inf),~
    { 26: last dimension is trials }~
    Try((Local x:=SIP_Tensor_At(ParseJSON('{"v":[[1,2,3],[4,5,6]]}')->v,2);~
        Max(Abs(x-Array(x.Dim1,[2,5])),x.Dim1)), catch:Inf),~
    { 27,28: environment alternatives }~
    Try(If SIP_Field(SIP_Select(param,'StandardNormal'),'function')='Metalog_1_0' Then 0 Else 1, catch:Inf),~
    Try(Max(Abs(SIP_Evaluate(param,'StandardNormal',T,environment:'ExcelFrontline')-CumNormalInv(SIP_Rng(param,'HDR3',T))),T), catch:Inf),~
    { 29: missing calibration is explicitly Null }~
    Try(If IsNull(SIP_Calibration(stored,'Array',1)->passed) Then 0 Else 1, catch:Inf),~
    { 30..40: must fail safely, without code execution or resource downloads }~
    Try((SIP_Evaluate(stored,'Array',4); 1), catch:0),~
    Try((SIP_Evaluate(single,'Unbounded',1.5); 1), catch:0),~
    Try((SIP_Lookup(0.5,Array(I,[0.8,0.7]),I,I); 1), catch:0),~
    Try((SIP_Gaussian_Copula(u,Array(I,J,[[1,0.2],[0.6,1]]),I,J); 1), catch:0),~
    Try((SIP_Evaluate(param,'Variable2_seed3_param',1); 1), catch:0),~
    Try((SIP_Evaluate(SIP_Parse('{"objectType":"sipModel","sips":[{"name":"Bad","function":"Execute_arbitrary_code"}]}'),'Bad',1); 1), catch:0),~
    Try((SIP_Evaluate(stored,'External',1); 1), catch:0),~
    Try((SIP_Parse('{"objectType":"sipModel","sips":[{"name":"X"},{"name":"X"}]}'); 1), catch:0),~
    Try((SIP_Parse('{"objectType":"wrong","sips":[{"name":"X"}]}'); 1), catch:0),~
    Try((SIP_Metalog(0,a,K); 1), catch:0),~
    Try((SIP_Uniform(1,seed3:10000001); 1), catch:0)~
])
NodeLocation: 384,176,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable QA_Tolerance
Title: QA Tolerance
Description: Absolute error tolerance: rounded published parameter/16-term expectations use 1e-6; Gaussian published values 1e-7; other floating comparisons 1e-10. No statistical sampling acceptance tests.
Definition: If @QA_Case = 4 or @QA_Case = 5 Then 1e-6~
Else If @QA_Case = 2 Then 1e-7~
Else 1e-10
NodeLocation: 384,256,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable QA_Passed
Title: QA Passed
Description: One boolean per test. Null or nonfinite residual is a failure, not silently omitted from the overall result.
Definition: If IsNull(QA_Residual) Then False~
Else QA_Residual <= QA_Tolerance
NodeLocation: 640,216,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable QA_Bounded_Calibration
Title: QA Bounded Calibration
Description: All 24 published trial values from canonical library 08, including upper-only bounds and negative up/down rounding. Returns per-SIP per-trial calibration structs.
Definition: Local library := SIP_Parse(Canonical_Bounds_JSON);~
LocalIndex Name := SIP_Names(library);~
LocalIndex T := 1..3;~
SIP_Calibration(library, Name, T)
NodeLocation: 128,336,2
NodeSize: 112,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable QA_Extended
Title: QA Extended
Description: Four additional integration-path residuals: JSON DIST dispatch, JSON Cholesky matrix dispatch, calibrationTrials metadata arrays, and multiDimSIP_Array dispatch. Every residual should be <=1e-10.
Definition: LocalIndex Check := ['DIST JSON dispatch','Cholesky JSON dispatch','CalibrationTrials array','Multidimensional JSON dispatch'];~
LocalIndex T := 1..3;~
Array(Check, [~
    Try((~
        Local encoded := SipEncode(T,T,type:'Double');~
        Local json := MakeJSON(_Struct(objectType:'sipModel',sips:[_Struct(name:'D',function:'DIST',arguments:_Struct(value:encoded))]),flags:1);~
        Max(Abs(SIP_Evaluate(SIP_Parse(json),'D',T)-T),T)~
    ), catch:Inf),~
    Try((~
        Local lib := SIP_Parse('{"objectType":"sipModel","U01":{"rng":[{"name":"R1","function":"HDR_2_0","arguments":{"varId":1}},{"name":"R2","function":"HDR_2_0","arguments":{"varId":2}}],"copula":[{"name":"G","function":"GaussianCopula","arguments":{"rng":["R1","R2"],"choleskyMatrix":{"rows":["a","b"],"columns":["a","b"],"matrix":[{"row":"a","col":"a","value":1},{"row":"b","col":"a","value":0.6},{"row":"b","col":"b","value":0.8}]}},"copulaLayer":["A","B"]}]},"sips":[{"name":"X","function":"Metalog_2_0","ref":{"source":"copula","name":"G","copulaLayer":"B"},"arguments":{"aCoefficients":[0,1]}}]}');~
        Local z := 0.6*CumNormalInv(SIP_Uniform(T,varId:1)) + 0.8*CumNormalInv(SIP_Uniform(T,varId:2));~
        Local p := CumNormal(z);~
        Max(Abs(SIP_Evaluate(lib,'X',T)-Ln(p/(1-p))),T)~
    ), catch:Inf),~
    Try((~
        Local lib := SIP_Parse('{"objectType":"sipModel","sips":[{"name":"A","function":"SIP_Array","arguments":{"value":[10,20,30]},"metadata":{"calibrationTrials":[10,20,30]}}]}');~
        1 - Min(SIP_Calibration(lib,'A',T)->passed,T)~
    ), catch:Inf),~
    Try((~
        Local lib := SIP_Parse('{"objectType":"sipModel","sips":[{"name":"Tensor","function":"multiDimSIP_Array","arguments":{"value":[[1,2,3],[4,5,6]]}}]}');~
        Local x := SIP_Evaluate(lib,'Tensor',2);~
        Max(Abs(x - Array(x.Dim1,[2,5])),x.Dim1)~
    ), catch:Inf)~
])
NodeLocation: 384,336,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close SIP_QA

Module Native_Array_Examples
Title: Native Array Examples
Description: Examples of vectorized coefficients, seeds and explicit caller-owned dimensions, independent of JSON container identity.
NodeLocation: 624,376,2
NodeSize: 96,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,0,1,1264,476,17,10

Index Product1
Title: Product
Description: Shared model dimension used by coefficients and stream IDs.
Definition: ['A', 'B', 'C']
NodeLocation: 128,64,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Index Metalog_Term
Title: Metalog Term
Description: Coefficient dimension; consumed by SIP_Metalog.
Definition: 1..3
NodeLocation: 384,64,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable Product_Coefficients
Title: Product Coefficients
Description: Three Metalog 2.0 coefficient vectors, indexed by Product and Metalog_Term. Uses native Array; no JSON indexes leak into model.
Definition: Array(Metalog_Term, [10 * @Product1, 1 + @Product1 / 2, 0])
NodeLocation: 128,200,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable Product_Trials
Title: Product Trials
Description: Independent HDR streams across Product, sharing explicit Trial. Result dimensions are exactly Product and Trial.
Definition: SIP_Metalog(~
    SIP_Uniform(Trial, entity:9039920, varId:@Product1),~
    Product_Coefficients, Metalog_Term~
)
NodeLocation: 384,152,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Chance Product_Sample
Title: Product Sample
Description: Native Analytica uncertainty example. HDR_U gives uniform Mid=0.5; SIP_Metalog consumes coefficient dimension and retains Product and Run in Sample mode.
Definition: SIP_Metalog(~
    HDR_U(seed1:@Product1, seed2:9039920),~
    Product_Coefficients, Metalog_Term~
)
NodeLocation: 384,248,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close Native_Array_Examples

Variable Example_Library
Title: Example Library
Description: Parse once; downstream examples reuse this native JSON struct. All provenance/calibration metadata remains accessible.
Definition: SIP_Parse(Canonical_Copula_JSON)
NodeLocation: 376,216,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0
ValueState: 2,452,458,416,303,,MIDM

Index SIP_Name
Title: SIP Name
Description: Caller-owned output dimension; explicitly shared by all library outputs.
Definition: SIP_Names(Example_Library)
NodeLocation: 376,64,2
NodeSize: 80,24
NodeInfo: 1,,,,,,,0,,,,,,0

Index Trial
Title: Trial
Description: Explicit first ten SIPmath trials, independent of Analytica's sample settings.
Definition: 1..10
NodeLocation: 624,64,2
NodeSize: 80,24
NodeInfo: 1,,,,,,,0,,,,,,0

Variable Example_Trials
Title: Example Trials
Description: Deterministic coherent [SIP_Name,Trial] sample table. SIP_Name and Trial are retained; internal coefficient and copula dimensions are consumed.
Definition: SIP_Evaluate(Example_Library, SIP_Name, Trial)
NodeLocation: 624,264,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0
WindState: 2,98,82,720,350
ValueState: 2,36,42,1123,340,,MIDM

Chance Example_Sample
Title: Example Sample
Description: Coherent SIP distributions for Analytica uncertainty calculations. Sample view uses Run; Mid view returns trial 1, not a mean or median.
Definition: SIP_Sample(Example_Library, SIP_Name)
NodeLocation: 624,168,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0
ValueState: 2,388,394,660,239,,STAT
ReformVal: [Undefined,Null,Undefined,Undefined,1]
Att_ResultSliceState: [SIP_Name,5,Sys_LocalIndex('Step'),1]
Att_XRole: -1
Att_ColorRole: Null

Variable QA_All_Passed
Title: QA All Passed
Description: True only when every deterministic QA case passes. Open SIP QA for per-case residuals and tolerances.
Definition: Sum(QA_Passed, QA_Case) = IndexLength(QA_Case)~
and Min(~
    Min(QA_Bounded_Calibration->passed, QA_Bounded_Calibration.T),~
    QA_Bounded_Calibration.Name~
)~
and Max(QA_Extended, QA_Extended.Check) <= 1e-10
NodeLocation: 376,376,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0
ValueState: 2,404,410,416,303,,MIDM

Text SIP_Example_Guide
Title: SIP Example Guide
Description: Start with Example Trials (deterministic) or Example Sample (uncertainty views).~
Native Array Examples demonstrates shared model indexes and coefficient arrays.~
SIP QA contains 44 regression checks plus 24 bounded/rounding calibration checks.~
QA All Passed must be True. Fixtures are embedded; tests do not need the internet.~
SIP Sample in Mid view returns trial 1, not a mean or median.
NodeLocation: 376,520,1
NodeSize: 336,72
NodeInfo: 1,,,,,,,0,,,,,,0

{!50500|ArrowClass Ar477859243}
{!50500|Att_HeadNode: SIP_QA}
{!50500|Att_TailNode: SipMath_3_1}
{!50500|Att_ArrowWayPoints: [Null,Null,-128,0,-128,1]}
{!50500|Att_ArrowProperties: 0}

{!50500|ArrowClass Ar1551601067}
{!50500|Att_HeadNode: Native_Array_Examples}
{!50500|Att_TailNode: SipMath_3_1}
{!50500|Att_ArrowWayPoints: [Null,Null,121,-48,121,1]}
{!50500|Att_ArrowProperties: 0}

Close Test_SipMath_3_1