{ Analytica Model SipMath_3_1, encoding="UTF-8" }
SoftwareVersion 7.2.2




LinkLibrary SipMath_3_1
Title: SipMath 3.1
Description: SIPmath 3.1 reader and array-native numerical toolkit for Analytica 7.2. Uses the existing Hubbard HDR library, native Metalog 2.0 quantiles, normal inverse/CDF, Cholesky decomposition and DIST codec. Explicit trial API and Run sampling preserve coherence. Main model contains offline canonical regression tests and examples. Supported: Metalog 1.0/2.0, bounded/rounded quantiles, Gaussian and stored copulas, discrete lookup, arrays and XML DIST; external data must be explicitly preloaded. GeneralizedMetalog application-specific lookup and full external JSON Schema validation are not implemented.
NodeSize: 88,32
DiagState: 2,0,1,796,451,17,10
WindState: 2,98,82,720,350
FontStyle: Arial,15
FileInfo: 0,LinkLibrary SipMath_3_1,2,2,0,0,SipMath 3.1 library.ana
{!40600|Att_WikiHelpURL: [wiki]SipMath_3.1_library}

Include 0,LinkLibrary Hubbard_HDR_Library,2,2,0,0,Hubbard_HDR_Library.ana

NodeLocation Hubbard_HDR_Library: 128,272,2
NodeSize Hubbard_HDR_Library: 88,32


Library SIP_Numeric
Title: SIP Numeric
Description: Array-native SIPmath primitives: explicit trials, HDR seeds, Metalog quantiles, lookup tables, rounding and Gaussian copulas. No file access.
NodeLocation: 128,368,2
NodeSize: 88,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,276,186,1264,476,17,10
WindState: 2,98,82,720,350

Function SIP_Uniform(trial : positive; entity : nonNegative = 1; varId : positive = 1; seed3, seed4 : nonNegative = 0)
Title: SIP Uniform
Description: HDR_2_0 uniform for explicit positive integer trial numbers. SIPmath entity maps to Hubbard_HDR seed2; varId maps to seed1. Extra indexes on trials or seeds are preserved. This is deterministic in both Mid and Sample modes.
Definition: If trial <> Floor(trial) or entity <> Floor(entity) or varId <> Floor(varId)~
    or seed3 <> Floor(seed3) or seed4 <> Floor(seed4)~
    or entity > 100M or varId > 100M or seed3 > 10M or seed4 > 10M~
Then Error('SIP Uniform: trials and seeds must be integers within HDR seed limits.')~
Else Hubbard_HDR(trial, varId, entity, seed3, seed4)
NodeLocation: 128,96,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0
WindState: 2,659,71,720,350

Function SIP_Metalog(p : numeric; a : numeric [K]; K : Index; lowerBound, upperBound : optional numeric atom orNull = Null; version : numeric atom = 2)
Title: SIP Metalog
Description: Quantile from 2..16 coefficients on K using native CumKeelinFromAInv (Metalog 2.0). version=1 explicitly converts the legacy basis, zero-padding odd legacy terms when needed; does NOT rely on native flag 64, which is ineffective in FromA inverse on 7.2.2. Bounds use SIPmath exponential/logistic transforms. p must lie in (0,1). K is consumed and extra indexes propagate.
Definition: If IndexLength(K) < 2 or IndexLength(K) > 16 Then~
    Error('SIP Metalog: supply 2 through 16 coefficients.')~
Else If p <= 0 or p >= 1 Then~
    Error('SIP Metalog: probability must be strictly between zero and one.')~
Else If version <> 1 and version <> 2 Then~
    Error('SIP Metalog: version must be 1 or 2.')~
Else If not IsNull(lowerBound) and not IsNull(upperBound) and lowerBound >= upperBound Then~
    Error('SIP Metalog: lowerBound must be below upperBound.')~
Else (~
    Local q := If version = 2 Then CumKeelinFromAInv(p, a, K)~
    Else (~
        { Convert legacy coefficients; FromA inverse ignores flag 64 in 7.2.2. }~
        Local n := IndexLength(K);~
        LocalIndex B := 1..(If n >= 7 and Mod(n, 4) = 3 Then n + 1 Else n);~
        Local oldPosition :=~
            If B >= 7 and Mod(B, 4) = 3 Then B + 1~
            Else If B >= 8 and Mod(B, 4) = 0 Then B - 1~
            Else B;~
        Local coefficients := a[@K = oldPosition, defVal:0];~
        CumKeelinFromAInv(p, coefficients, B)~
    );~
    { Use SIPmath bound conventions, especially upper-only UB-Exp(-q). }~
    If IsNull(lowerBound) and IsNull(upperBound) Then q~
    Else If IsNull(upperBound) Then lowerBound + Exp(q)~
    Else If IsNull(lowerBound) Then upperBound - Exp(-q)~
    Else lowerBound + (upperBound - lowerBound) * CumLogistic(q, 0, 1)~
)
NodeLocation: 384,96,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0
WindState: 2,98,82,1166,657

Function SIP_Round(x; rounding : text atom = 'none')
Title: SIP Round
Description: Apply canonical SIPmath integer rounding: down=toward zero, up=away from zero, nearest=half away from zero, matching Excel ROUND/ROUNDUP/ROUNDDOWN and canonical library 08. This differs from floor/ceiling for negative values. Precision metadata is not silently interpreted as a rounding increment.
Definition: Local r := TextLowerCase(rounding);~
If r = 'none' or r = '' Then x~
Else If r = 'down' Then Sign(x) * Floor(Abs(x))~
Else If r = 'up' Then Sign(x) * Ceil(Abs(x))~
Else If r = 'nearest' Then Sign(x) * Floor(Abs(x) + 0.5)~
Else Error('SIP Round: unknown rounding mode ' & rounding)
NodeLocation: 384,256,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Lookup(p : numeric; cumulative : numeric [I]; values : [I]; I : Index)
Title: SIP Lookup
Description: Discrete inverse CDF: first value with cumulative probability >= p. CDF must be nondecreasing in [0,1], finish at 1, and have no missing values. p in [0,1]. Values can be numeric or textual; category index I is consumed, extra indexes propagate.
Definition: If IndexLength(I) = 0 Then Error('SIP Lookup: empty table.')~
Else If p < 0 or p > 1 Then Error('SIP Lookup: probability outside [0,1].')~
Else If Min(cumulative, I) < 0 or Max(cumulative, I) > 1~
    or cumulative[@I = IndexLength(I)] <> 1~
    or Sum(IsNull(cumulative), I) > 0~
    or Min(cumulative - cumulative[@I = @I - 1, defVal:0], I) < 0~
Then Error('SIP Lookup: invalid cumulative probability table.')~
Else~
    Local pos := Min(If cumulative >= p Then @I Else IndexLength(I) + 1, I);~
    values[@I = pos]
NodeLocation: 128,176,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Gaussian_Copula(u : numeric [I]; matrix : numeric [I,J]; I, J : Index; isCholesky : boolean atom = False)
Title: SIP Gaussian Copula
Description: Transform independent uniforms on I using a latent-normal correlation matrix on [I,J]. Uses native Decompose, CumNormalInv and CumNormal. Output is on I; J is consumed. Trial/scenario indexes are preserved. With isCholesky=True matrix must be lower triangular L, C=L L-transpose. Does not draw or rank-reorder samples. Rejects invalid matrices.
Definition: If IndexLength(I) <> IndexLength(J) Then~
    Error('SIP Gaussian Copula: matrix must be square.')~
Else If u <= 0 or u >= 1 Then~
    Error('SIP Gaussian Copula: uniforms must be strictly inside (0,1).')~
Else (~
    Local L := If isCholesky Then matrix Else (~
        If Max(Max(Abs(matrix - Transpose(matrix, I, J)), I), J) > 1e-10~
            or Max(Max(Abs(matrix), I), J) > 1 + 1e-10~
            or Max(Abs(Sum(If @I = @J Then matrix Else 0, J) - 1), I) > 1e-10~
        Then Error('SIP Gaussian Copula: invalid correlation matrix.')~
        Else Decompose(matrix, I, J)~
    );~
    If Max(Max(If @J > @I Then Abs(L) Else 0, I), J) > 1e-10~
        or Max(Abs(Sum(L^2, J) - 1), I) > 1e-8~
    Then Error('SIP Gaussian Copula: expected a lower Cholesky factor with unit row variance.')~
    Else CumNormal(Sum(L * CumNormalInv(u[@I = @J]), J))~
)
NodeLocation: 384,176,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Array_At(data : [T]; T : Index; trial : positive)
Title: SIP Array At
Description: Select stored SIP trials by 1-based position, regardless of T labels. Preserves other indexes. Errors beyond stored trials; never wraps, resamples or independently permutes coherent SIPs.
Definition: If trial <> Floor(trial) or trial > IndexLength(T) Then~
    Error('SIP Array At: requested trial exceeds stored trials or is not an integer.')~
Else data[@T = trial]
NodeLocation: 128,256,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close SIP_Numeric

Library SIP_JSON
Title: SIP JSON
Description: Safe interpretation of SIPmath JSON libraries. No evaluation of text as Analytica code and no automatic external downloads.
NodeLocation: 344,368,2
NodeSize: 88,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,0,1,1264,476,17,10
WindState: 2,98,82,720,350

Function SIP_Parse(json : text atom)
Title: SIP Parse
Description: Parse SIPmath JSON into native _JSON structs and preserve metadata. Validate sipModel header and unique nonempty name/environment pairs. Environment alternatives may share a name. This is runtime validation, not full external JSON Schema certification. Keep the parsed library in a variable and reuse it. No external URLs or files are read.
Definition: Local lib := ParseJSON(json);~
If SIP_Field(lib, 'objectType', '') <> 'sipModel' Then~
    Error('SIP Parse: objectType must be sipModel.')~
Else (~
    LocalIndex S := SIP_Field(lib, 'sips', []);~
    Local keys := SIP_Field(S, 'name', '') & ':' & SIP_Field(S, 'environment', '');~
    If IndexLength(S) = 0 or Sum(SIP_Field(S, 'name', '') = '', S) > 0~
        or Size(Unique(keys)) <> IndexLength(S)~
    Then Error('SIP Parse: sips must have unique nonempty name/environment pairs.')~
    Else lib~
)
NodeLocation: 128,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Module SIP_JSON_Data
Title: SIP JSON Data
Description: Helpers for safe JSON list, parameter, matrix, and stored-data access.
NodeLocation: 384,352,2
NodeSize: 88,32
NodeInfo: 1,,,,,,,0,,,,,,0
DiagState: 2,0,1,1264,476,17,10

Function SIP_Field(obj : atom; field : text atom; default : optional = Null)
Title: SIP Field
Description: Internal helper: case-sensitive JSON member access, with default for missing member or Null container. Uses native struct member access; does not execute text.
Definition: If IsNull(obj) Then default~
Else `->`(obj, field, defVal:default)
NodeLocation: 128,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Find(items : List; name : text atom)
Title: SIP Find
Description: Internal helper: unique named object lookup in a JSON list. Missing or duplicate names produce an error.
Definition: LocalIndex N := items;~
Local matches := SIP_Field(N, 'name', '') = name;~
If Sum(matches, N) <> 1 Then~
    Error('SIP Find: missing or duplicate name ' & name)~
Else N[@N = Sum(If matches Then @N Else 0, N)]
NodeLocation: 384,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Resolve(value : atom; library : atom; parameters : atom = Null)
Title: SIP Resolve
Description: Resolve a canonical parameter or globalVariables reference. Parameter names are JSON member names in parameters. Unknown reference types fail; plain objects/numbers are returned unchanged. Does not evaluate code or fetch resources.
Definition: Local kind := Try(SIP_Field(value, 'type', ''), catch:'');~
If kind = 'parameter' Then (~
    Local name := SIP_Field(value, 'name');~
    Local result := SIP_Field(parameters, name);~
    If IsNull(result) Then Error('SIP Resolve: missing parameter ' & name)~
    Else result~
)~
Else If kind = 'globalVariables' Then~
    SIP_Field(SIP_Find(SIP_Field(library, 'globalVariables', []), SIP_Field(value, 'value')), 'value')~
Else value
NodeLocation: 640,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Matrix(value : atom; I, J : Index; symmetric : boolean atom = True)
Title: SIP Matrix
Description: Map canonical sparse {rows,columns,matrix:[{row,col,value},...]} to caller indexes I,J in declared row/column order. For correlations, fill an omitted triangular entry from its transpose. Cholesky factors use symmetric=False. Duplicate cells and dimension mismatches error.
Definition: LocalIndex Rows := SIP_Field(value, 'rows');~
LocalIndex Cols := SIP_Field(value, 'columns');~
LocalIndex E := SIP_Field(value, 'matrix');~
If IndexLength(Rows) <> IndexLength(I) or IndexLength(Cols) <> IndexLength(J) Then~
    Error('SIP Matrix: declared matrix size does not match copula inputs.')~
Else (~
    Local matches := SIP_Field(E, 'row') = Rows[@Rows = @I]~
        and SIP_Field(E, 'col') = Cols[@Cols = @J];~
    Local count := Sum(matches, E);~
    Local m := Sum(If matches Then SIP_Field(E, 'value') Else 0, E);~
    If Max(Max(count, I), J) > 1 Then Error('SIP Matrix: duplicate matrix entries.')~
    Else If symmetric Then (~
        If Min(Min(count + Transpose(count, I, J), I), J) = 0 Then~
            Error('SIP Matrix: correlation entry missing from both triangles.')~
        Else If count = 0 Then Transpose(m, I, J) Else m~
    )~
    Else m~
)
NodeLocation: 128,176,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Stored(arguments : atom; trial : positive; resources : atom = Null)
Title: SIP Stored
Description: Read array/DIST stored trials. type=array consumes value list; type=csv/xlsx resolves explicitly supplied resources by URL to a parsed JSON-style table struct {columnName:[trials]}. Resources must be preloaded by caller; never auto-fetches. value selects columns. Error on trial overflow. For DIST use type=DIST and XML value.
Definition: Local kind := SIP_Field(arguments, 'type', 'array');~
Local value := SIP_Field(arguments, 'value');~
If kind = 'DIST' Then (~
    Local data := SipDecode(value, localIndexName:'Stored_trial');~
    SIP_Array_At(data, data.Stored_trial, trial)~
)~
Else If kind = 'array' Then (~
    LocalIndex T := value;~
    SIP_Array_At(T, T, trial)~
)~
Else If kind = 'csv' or kind = 'xlsx' Then (~
    Local url := SIP_Field(arguments, 'url', '');~
    Local table := SIP_Field(resources, url);~
    If IsNull(table) Then Error('SIP Stored: preload external resource ' & url)~
    Else (~
        LocalIndex Column := value;~
        Local values := (~
            Local col[] := Column;~
            Local data := SIP_Field(table, col);~
            If IsNull(data) Then Error('SIP Stored: missing resource column ' & col)~
            Else (~
                LocalIndex T := data;~
                SIP_Array_At(T, T, trial)~
            )~
        );~
        If IndexLength(Column) = 1 Then values[@Column = 1] Else values~
    )~
)~
Else Error('SIP Stored: unsupported stored-data type ' & kind)
NodeLocation: 384,176,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Tensor_At(value : List; trial : positive)
Title: SIP Tensor At
Description: Select the last (trial) dimension of an inline nested JSON array. Earlier dimensions remain local Dim1, Dim2,... indexes. Rectangular numeric arrays only. Use caller-owned indexes and native SIP_Array_At instead when dimension identities must be shared with other model arrays.
Definition: Local data := ParseJSON(MakeJSON(_Struct(value:value), flags:1), flags:1)->value;~
LocalIndex D := IndexesOf(data);~
LocalAlias T := D[@D = IndexLength(D)];~
SIP_Array_At(data, T, trial)
NodeLocation: 640,176,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close SIP_JSON_Data

Function SIP_Names(library : atom)
Title: SIP Names
Description: Return unique SIP names as a list, collapsing environment-specific alternatives. Use as a model Index definition to choose the output dimension identity.
Definition: LocalIndex S := SIP_Field(library, 'sips', []);~
Unique(SIP_Field(S, 'name'))
NodeLocation: 384,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Select(library : atom; name : text atom; environment : text atom = 'Analytica')
Title: SIP Select
Description: Select named SIP: prefer an exact environment entry; otherwise use the environment-independent entry. Never silently use another environment. Missing or ambiguous names error.
Definition: LocalIndex S := SIP_Field(library, 'sips', []);~
Local matches := SIP_Field(S, 'name', '') = name;~
Local env := SIP_Field(S, 'environment', '');~
Local exact := matches and env = environment;~
Local choose := If Sum(exact, S) > 0 Then exact Else matches and env = '';~
If Sum(choose, S) <> 1 Then~
    Error('SIP Select: missing or ambiguous SIP/environment ' & name & '/' & environment)~
Else S[@S = Sum(If choose Then @S Else 0, S)]
NodeLocation: 640,96,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Rng(library : atom; name : text atom; trial : positive; parameters : atom = Null)
Title: SIP Rng
Description: Evaluate a named U01.rng HDR_2_0 or Index generator. counter=PM_Index uses explicit trial; other numeric/parameter counters are supported. Unknown functions fail closed. Native HDR mapping preserves stream identity.
Definition: Local rng := SIP_Find(SIP_Field(SIP_Field(library, 'U01'), 'rng', []), name);~
Local kind := SIP_Field(rng, 'function', '');~
Local a := SIP_Field(rng, 'arguments');~
Local c := SIP_Field(a, 'counter', 'PM_Index');~
Local counter := If IsText(c) and c = 'PM_Index' Then trial Else SIP_Resolve(c, library, parameters);~
If kind = 'Index' Then counter~
Else If kind = 'HDR_2_0' Then~
    SIP_Uniform(~
        counter,~
        SIP_Resolve(SIP_Field(a, 'entity', 1), library, parameters),~
        SIP_Resolve(SIP_Field(a, 'varId', 1), library, parameters),~
        SIP_Resolve(SIP_Field(a, 'seed3', 0), library, parameters),~
        SIP_Resolve(SIP_Field(a, 'seed4', 0), library, parameters)~
    )~
Else Error('SIP Rng: unsupported generator ' & kind)
NodeLocation: 128,256,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Copula(library : atom; name, layer : text atom; trial : positive; parameters : atom = Null; resources : atom = Null)
Title: SIP Copula
Description: Evaluate a named GaussianCopula or SIP_Array copula layer. Gaussian input order follows arguments.rng; output order follows copulaLayer. Matrix refs resolve globalVariables. Cholesky factors are interpreted lower triangular. Stored copulas use explicitly supplied external resources or inline arrays.
Definition: Local cop := SIP_Find(SIP_Field(SIP_Field(library, 'U01'), 'copula', []), name);~
Local kind := SIP_Field(cop, 'function');~
Local a := SIP_Field(cop, 'arguments');~
LocalIndex Layers := SIP_Field(cop, 'copulaLayer');~
Local pos := Sum(If Layers = layer Then @Layers Else 0, Layers);~
If Sum(Layers = layer, Layers) <> 1 Then Error('SIP Copula: unknown or duplicate layer ' & layer)~
Else If kind = 'GaussianCopula' Then (~
    LocalIndex I := SIP_Field(a, 'rng');~
    LocalIndex J := CopyIndex(I);~
    Local u := SIP_Rng(library, I, trial, parameters);~
    Local chol := SIP_Field(a, 'choleskyMatrix');~
    Local isChol := not IsNull(chol);~
    Local raw := SIP_Resolve(If isChol Then chol Else SIP_Field(a, 'correlationMatrix'), library, parameters);~
    Local m := SIP_Matrix(raw, I, J, not isChol);~
    Local result := SIP_Gaussian_Copula(u, m, I, J, isChol);~
    If IndexLength(Layers) <> IndexLength(I) Then Error('SIP Copula: layer count differs from input count.')~
    Else result[@I = pos]~
)~
Else If kind = 'SIP_Array' Then (~
    Local storage := SIP_Field(a, 'type', 'array');~
    If storage = 'array' Then (~
        Local values := SIP_Tensor_At(SIP_Field(a, 'value'), trial);~
        SIP_Array_At(values, values.Dim1, pos)~
    )~
    Else (~
        Local url := SIP_Field(a, 'url', '');~
        Local table := SIP_Field(resources, url);~
        If IsNull(table) Then Error('SIP Copula: preload external resource ' & url)~
        Else (~
            LocalIndex Columns := SIP_Field(a, 'value');~
            Local data := SIP_Field(table, Columns[@Columns = pos]);~
            If IsNull(data) Then Error('SIP Copula: missing copula resource column.')~
            Else (~
                LocalIndex T := data;~
                SIP_Array_At(T, T, trial)~
            )~
        )~
    )~
)~
Else Error('SIP Copula: unsupported copula ' & kind)
NodeLocation: 384,256,2
NodeSize: 88,24
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Function SIP_Source(library : atom; ref : atom; trial : positive; parameters : atom = Null; resources : atom = Null)
Title: SIP Source
Description: Resolve a SIP ref to its specified HDR/Index stream or copula layer. Does not substitute another RNG or reorder samples.
Definition: Local source := SIP_Field(ref, 'source', '');~
Local name := SIP_Field(ref, 'name', '');~
If source = 'rng' Then SIP_Rng(library, name, trial, parameters)~
Else If source = 'copula' Then~
    SIP_Copula(library, name, SIP_Field(ref, 'copulaLayer'), trial, parameters, resources)~
Else Error('SIP Source: unsupported reference source ' & source)
NodeLocation: 640,256,2
NodeSize: 88,24
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Function SIP_Evaluate(library : atom; name : text atom; trial : positive; parameters : atom = Null; resources : atom = Null; environment : text atom = 'Analytica')
Title: SIP Evaluate
Description: Evaluate a parsed library SIP at finite positive 1-based trial numbers. Array-abstracts over caller name/trial/scenario indexes. Supports Metalog_1_0/2_0, Lookup_Table, SIP_Array, inline multiDimSIP_Array, XML DIST and whitelisted Normal/CumNormalInv/PsiNormal/RiskNormal. Parameters/resources are structs. Unknown functions (including application-specific GeneralizedMetalog) error; imported text is never executed. Metadata precision is retained, not used to silently round results.
Definition: If trial <> Floor(trial) or trial >= Inf Then Error('SIP Evaluate: trial numbers must be finite positive integers.')~
Else (~
    Local sip := SIP_Select(library, name, environment);~
    Local kind := SIP_Field(sip, 'function', '');~
    Local a := SIP_Field(sip, 'arguments');~
    Local ref := SIP_Field(sip, 'ref');~
    Local result := If kind = 'SIP_Array' Then (~
        Local counter := If IsNull(ref) Then trial Else SIP_Source(library, ref, trial, parameters, resources);~
        SIP_Stored(a, counter, resources)~
    )~
    Else If kind = 'multiDimSIP_Array' Then~
        SIP_Tensor_At(SIP_Field(a, 'value'), trial)~
    Else If kind = 'DIST' Then (~
        Local data := SipDecode(SIP_Field(a, 'value'), localIndexName:'Stored_trial');~
        SIP_Array_At(data, data.Stored_trial, trial)~
    )~
    Else (~
        Local p := SIP_Source(library, ref, trial, parameters, resources);~
        If kind = 'Metalog_1_0' or kind = 'Metalog_2_0' Then (~
            Local coeff := SIP_Resolve(SIP_Field(a, 'aCoefficients'), library, parameters);~
            LocalIndex K := coeff;~
            SIP_Metalog(~
                p, K, K,~
                SIP_Resolve(SIP_Field(a, 'lowerBound'), library, parameters),~
                SIP_Resolve(SIP_Field(a, 'upperBound'), library, parameters),~
                If kind = 'Metalog_1_0' Then 1 Else 2~
            )~
        )~
        Else If kind = 'Lookup_Table' Then (~
            LocalIndex Row := SIP_Resolve(SIP_Field(a, 'value'), library, parameters);~
            LocalIndex Pair := [1, 2];~
            Local table := Local entry[] := Row Do Array(Pair, #entry);~
            SIP_Lookup(p, table[Pair = 1], table[Pair = 2], Row)~
        )~
        Else If kind = 'Normal' or kind = 'PsiNormal' or kind = 'RiskNormal' or kind = 'CumNormalInv' Then (~
            Local mean := SIP_Resolve(SIP_Field(a, 'mean', 0), library, parameters);~
            Local sd := SIP_Resolve(SIP_Field(a, 'stdDev', 1), library, parameters);~
            If sd <= 0 Then Error('SIP Evaluate: Normal stdDev must be positive.')~
            Else CumNormalInv(p, mean, sd)~
        )~
        Else If kind = 'GeneralizedMetalog' Then~
            Error('SIP Evaluate: GeneralizedMetalog requires an application-specific coefficient lookup; use SIP_Metalog after resolving that lookup.')~
        Else Error('SIP Evaluate: unsupported function ' & kind)~
    );~
    SIP_Round(result, SIP_Field(sip, 'rounding', 'none'))~
)
NodeLocation: 128,176,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Sample(library : atom; name : text atom; parameters : atom = Null; resources : atom = Null; environment : text atom = 'Analytica')
Title: SIP Sample
Description: Normal Analytica uncertainty interface. In Sample mode evaluates explicit Run trials; in Mid mode evaluates trial 1 (a reproducible representative trial, NOT a mean or median). Global sample size selects virtual trial count. Stored arrays error on overflow. Extra name/scenario indexes are retained.
Definition: SIP_Evaluate(~
    library, name,~
    If IsSampleEvalMode Then Run Else 1,~
    parameters, resources, environment~
)
NodeLocation: 384,176,2
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Function SIP_Export_Metalog(name : text atom; a : numeric [K]; K : Index; entity : nonNegative atom = 1; varId : positive atom = 1; seed3, seed4 : nonNegative atom = 0; lowerBound, upperBound : optional numeric atom orNull = Null; version : numeric atom = 2)
Title: SIP Export Metalog
Description: Construct one-variable virtual-SIP JSON using existing coefficient vectors, not refitting them. Explicit version controls coefficient convention. Seed mapping matches SIP_Uniform. Extra scenario indexes produce one JSON text per scenario. Metadata can be added using native structs/MakeJSON.
Definition: Local check := SIP_Metalog(0.5, a, K, lowerBound, upperBound, version)~
    + SIP_Uniform(1, entity, varId, seed3, seed4);~
If IsNull(check) Then Error('SIP Export Metalog: invalid parameters.')~
Else MakeJSON(~
    _Struct(~
        objectType:'sipModel', libraryType:'SIPmath_3_1',~
        name:name,~
        U01:_Struct(rng:[_Struct(~
            name:'HDR1', function:'HDR_2_0',~
            arguments:_Struct(counter:'PM_Index', entity:entity, varId:varId, seed3:seed3, seed4:seed4)~
        )]),~
        sips:[_Struct(~
            name:name,~
            ref:_Struct(source:'rng', name:'HDR1'),~
            function:If version = 1 Then 'Metalog_1_0' Else 'Metalog_2_0',~
            arguments:_Struct(aCoefficients:a, lowerBound:lowerBound, upperBound:upperBound)~
        )]~
    ),~
    flags:33~
)
NodeLocation: 128,352,2
NodeSize: 96,24
NodeInfo: 1,,,,,,,0,,,,,,0

Function SIP_Calibration(library : atom; name : text atom; trial : positive atom; parameters : atom = Null; resources : atom = Null; atol : nonNegative atom = 1e-6; rtol : nonNegative atom = 1e-8; environment : text atom = 'Analytica')
Title: SIP Calibration
Description: Compare one trial against metadata.TrialN or metadata.calibrationTrials. Returns a struct with name, trial, actual, expected, absoluteError and passed. Missing expectation gives Null passed, never a false success. Array-abstracts over name and trial indexes.
Definition: Local sip := SIP_Select(library, name, environment);~
Local meta := SIP_Field(sip, 'metadata');~
Local expected := SIP_Field(meta, 'Trial' & trial);~
If IsNull(expected) Then (~
    Local values := SIP_Field(meta, 'calibrationTrials');~
    If not IsNull(values) Then (~
        LocalIndex T := values;~
        expected := If trial <= IndexLength(T) Then T[@T = trial] Else Null~
    )~
);~
Local actual := SIP_Evaluate(library, name, trial, parameters, resources, environment);~
Local err := Abs(actual - expected);~
_Struct(~
    name:name, trial:trial, actual:actual, expected:expected,~
    absoluteError:err,~
    passed:If IsNull(expected) Then Null Else err <= atol + rtol * Abs(expected)~
)
NodeLocation: 640,176,2
NodeSize: 88,24
NodeInfo: 1,,,,,,,0,,,,,,0

Close SIP_JSON

Text SIP_Read_me
Title: SIP Read me
Description: SIPmath 3.1 for Analytica 7.2~
~
SIP Numeric: array-native primitives with caller-owned indexes.~
SIP JSON: Parse -> Names -> Evaluate or Sample.~
Explicit trials preserve coherent cross-platform streams.~
External data must be preloaded; imported code is never executed.~
~
Tests and worked examples are in the parent model.~
GeneralizedMetalog lookup and full schema certification are not included.
NodeLocation: 352,120,1
NodeSize: 320,96
NodeInfo: 1,,,,,,,0,,,,,,0

Close SipMath_3_1