Examples with Function cbit.vcell.math.Function used on opensource projects

Example 21 with Function

use of cbit.vcell.math.Function in project vcell by virtualcell.

the class SundialsSolver method getODESolverResultSet.

/**
 * This method was created in VisualAge.
 * @return double[]
 * @param vectorIndex int
 */
public ODESolverResultSet getODESolverResultSet() {
    // 
    // read .ida file
    // 
    ODESolverResultSet odeSolverResultSet = getStateVariableResultSet();
    if (odeSolverResultSet == null) {
        return null;
    }
    // 
    // add appropriate Function columns to result set
    // 
    SimulationSymbolTable simSymbolTable = simTask.getSimulationJob().getSimulationSymbolTable();
    Function[] functions = simSymbolTable.getFunctions();
    for (int i = 0; i < functions.length; i++) {
        if (SimulationSymbolTable.isFunctionSaved(functions[i])) {
            Expression exp1 = new Expression(functions[i].getExpression());
            try {
                exp1 = simSymbolTable.substituteFunctions(exp1);
            } catch (MathException e) {
                e.printStackTrace(System.out);
                throw new RuntimeException("Substitute function failed on function " + functions[i].getName() + " " + e.getMessage());
            } catch (ExpressionException e) {
                e.printStackTrace(System.out);
                throw new RuntimeException("Substitute function failed on function " + functions[i].getName() + " " + e.getMessage());
            }
            try {
                FunctionColumnDescription cd = new FunctionColumnDescription(exp1.flatten(), functions[i].getName(), null, functions[i].getName(), false);
                odeSolverResultSet.addFunctionColumn(cd);
            } catch (ExpressionException e) {
                e.printStackTrace(System.out);
            }
        }
    }
    if (getSensitivityParameter() != null) {
        try {
            if (odeSolverResultSet.findColumn(getSensitivityParameter().getName()) == -1) {
                FunctionColumnDescription fcd = new FunctionColumnDescription(new Expression(getSensitivityParameter().getConstantValue()), getSensitivityParameter().getName(), null, getSensitivityParameter().getName(), false);
                odeSolverResultSet.addFunctionColumn(fcd);
            }
            Variable[] variables = simSymbolTable.getVariables();
            StateVariable[] stateVars = createStateVariables();
            for (int i = 0; i < variables.length; i++) {
                if (variables[i] instanceof Function && SimulationSymbolTable.isFunctionSaved((Function) variables[i])) {
                    Function depSensFunction = (Function) variables[i];
                    Expression depSensFnExpr = new Expression(depSensFunction.getExpression());
                    depSensFnExpr = simSymbolTable.substituteFunctions(depSensFnExpr);
                    depSensFnExpr = getFunctionSensitivity(depSensFnExpr, getSensitivityParameter(), stateVars);
                    // depSensFnExpr = depSensFnExpr.flatten(); 	// already bound and flattened in getFunctionSensitivity, no need here.....
                    String depSensFnName = new String("sens_" + depSensFunction.getName() + "_wrt_" + getSensitivityParameter().getName());
                    if (depSensFunction != null) {
                        FunctionColumnDescription cd = new FunctionColumnDescription(depSensFnExpr.flatten(), depSensFnName, getSensitivityParameter().getName(), depSensFnName, false);
                        odeSolverResultSet.addFunctionColumn(cd);
                    }
                }
            }
        } catch (MathException e) {
            e.printStackTrace(System.out);
            throw new RuntimeException("Error adding function to resultSet: " + e.getMessage());
        } catch (ExpressionException e) {
            e.printStackTrace(System.out);
            throw new RuntimeException("Error adding function to resultSet: " + e.getMessage());
        }
    }
    return odeSolverResultSet;
}

Example 22 with Function

use of cbit.vcell.math.Function in project vcell by virtualcell.

the class SimulationData method getVarAndFunctionDataIdentifiers.

/**
 * This method was created in VisualAge.
 * @return java.lang.String[]
 */
public synchronized DataIdentifier[] getVarAndFunctionDataIdentifiers(OutputContext outputContext) throws IOException, DataAccessException {
    // Is this zip format?
    boolean bIsChombo = false;
    try {
        bIsChombo = isChombo();
    } catch (FileNotFoundException e) {
        e.printStackTrace(System.out);
    }
    File zipFile1 = getZipFile(bIsChombo, null);
    File zipFile2 = getZipFile(bIsChombo, 0);
    bZipFormat1 = false;
    bZipFormat2 = false;
    if (zipFile1.exists()) {
        bZipFormat1 = true;
    } else if (zipFile2.exists()) {
        bZipFormat2 = true;
    }
    refreshLogFile();
    if (!isComsol()) {
        try {
            refreshMeshFile();
        } catch (MathException e) {
            e.printStackTrace(System.out);
            throw new DataAccessException(e.getMessage());
        }
    }
    if (!isRulesData && !getIsODEData() && !isComsol() && dataFilenames != null) {
        // read variables only when I have never read the file since variables don't change
        if (dataSetIdentifierList.size() == 0) {
            File file = getPDEDataFile(0.0);
            DataSet dataSet = getPDEDataSet(file, 0.0);
            String[] varNames = dataSet.getDataNames();
            int[] varTypeInts = dataSet.getVariableTypeIntegers();
            if (varNames == null) {
                return null;
            }
            dataSetIdentifierList.clear();
            for (int i = 0; i < varNames.length; i++) {
                VariableType varType = null;
                try {
                    varType = VariableType.getVariableTypeFromInteger(varTypeInts[i]);
                } catch (IllegalArgumentException e) {
                    if (LG.isEnabledFor(Level.WARN)) {
                        LG.warn("Exception typing " + varNames[i] + " has unsupported type " + varTypeInts[i] + ": " + e.getMessage());
                    }
                    varType = SimulationData.getVariableTypeFromLength(mesh, dataSet.getDataLength(varNames[i]));
                }
                Domain domain = Variable.getDomainFromCombinedIdentifier(varNames[i]);
                String varName = Variable.getNameFromCombinedIdentifier(varNames[i]);
                dataSetIdentifierList.addElement(new DataSetIdentifier(varName, varType, domain));
            }
            refreshDataProcessingOutputInfo(outputContext);
            if (dataProcessingOutputInfo != null) {
                for (int i = 0; i < dataProcessingOutputInfo.getVariableNames().length; i++) {
                    if (dataProcessingOutputInfo.getPostProcessDataType(dataProcessingOutputInfo.getVariableNames()[i]).equals(DataProcessingOutputInfo.PostProcessDataType.image)) {
                        dataSetIdentifierList.addElement(new DataSetIdentifier(dataProcessingOutputInfo.getVariableNames()[i], VariableType.POSTPROCESSING, null));
                    }
                }
            }
        }
        // always read functions file since functions might change
        getFunctionDataIdentifiers(outputContext);
    }
    if ((isRulesData || getIsODEData()) && dataSetIdentifierList.size() == 0) {
        ODEDataBlock odeDataBlock = getODEDataBlock();
        if (odeDataBlock == null) {
            throw new DataAccessException("Results are not availabe yet. Please try again later.");
        }
        ODESimData odeSimData = odeDataBlock.getODESimData();
        int colCount = odeSimData.getColumnDescriptionsCount();
        // assume index=0 is time "t"
        int DATA_OFFSET = 1;
        dataSetIdentifierList.clear();
        for (int i = 0; i < (colCount - DATA_OFFSET); i++) {
            String varName = odeSimData.getColumnDescriptions(i + DATA_OFFSET).getDisplayName();
            // TODO domain
            Domain domain = null;
            dataSetIdentifierList.addElement(new DataSetIdentifier(varName, VariableType.NONSPATIAL, domain));
        }
    }
    if (isComsol() && dataSetIdentifierList.size() == 0) {
        ComsolSimFiles comsolSimFiles = getComsolSimFiles();
        if (comsolSimFiles.simTaskXMLFile != null) {
            try {
                String xmlString = FileUtils.readFileToString(comsolSimFiles.simTaskXMLFile);
                SimulationTask simTask = XmlHelper.XMLToSimTask(xmlString);
                Enumeration<Variable> variablesEnum = simTask.getSimulation().getMathDescription().getVariables();
                while (variablesEnum.hasMoreElements()) {
                    Variable var = variablesEnum.nextElement();
                    if (var instanceof VolVariable) {
                        dataSetIdentifierList.addElement(new DataSetIdentifier(var.getName(), VariableType.VOLUME, var.getDomain()));
                    } else if (var instanceof MemVariable) {
                        dataSetIdentifierList.addElement(new DataSetIdentifier(var.getName(), VariableType.MEMBRANE, var.getDomain()));
                    } else if (var instanceof Function) {
                        VariableType varType = VariableType.UNKNOWN;
                        if (var.getDomain() != null && var.getDomain().getName() != null) {
                            SubDomain subDomain = simTask.getSimulation().getMathDescription().getSubDomain(var.getDomain().getName());
                            if (subDomain instanceof CompartmentSubDomain) {
                                varType = VariableType.VOLUME;
                            } else if (subDomain instanceof MembraneSubDomain) {
                                varType = VariableType.MEMBRANE;
                            } else if (subDomain instanceof FilamentSubDomain) {
                                throw new RuntimeException("filament subdomains not supported");
                            } else if (subDomain instanceof PointSubDomain) {
                                varType = VariableType.POINT_VARIABLE;
                            }
                        }
                        dataSetIdentifierList.addElement(new DataSetIdentifier(var.getName(), varType, var.getDomain()));
                    } else if (var instanceof Constant) {
                        System.out.println("ignoring Constant " + var.getName());
                    } else if (var instanceof InsideVariable) {
                        System.out.println("ignoring InsideVariable " + var.getName());
                    } else if (var instanceof OutsideVariable) {
                        System.out.println("ignoring OutsideVariable " + var.getName());
                    } else {
                        throw new RuntimeException("unexpected variable " + var.getName() + " of type " + var.getClass().getName());
                    }
                }
            } catch (XmlParseException | ExpressionException e) {
                e.printStackTrace();
                throw new RuntimeException("failed to read sim task file, msg: " + e.getMessage(), e);
            }
        }
    }
    DataIdentifier[] dis = new DataIdentifier[dataSetIdentifierList.size()];
    for (int i = 0; i < dataSetIdentifierList.size(); i++) {
        DataSetIdentifier dsi = (DataSetIdentifier) dataSetIdentifierList.elementAt(i);
        String displayName = dsi.getName();
        if (dsi.isFunction()) {
            AnnotatedFunction f = null;
            for (int j = 0; j < annotatedFunctionList.size(); j++) {
                AnnotatedFunction function = (AnnotatedFunction) annotatedFunctionList.elementAt(j);
                if (function.getName().equals(dsi.getName())) {
                    f = function;
                    break;
                }
            }
            if (f != null) {
                displayName = f.getDisplayName();
            }
        }
        dis[i] = new DataIdentifier(dsi.getName(), dsi.getVariableType(), dsi.getDomain(), dsi.isFunction(), displayName);
    }
    return dis;
}

Example 23 with Function

use of cbit.vcell.math.Function in project vcell by virtualcell.

the class OutputFunctionContext method computeFunctionTypeWRTExpression.

// check if the new expression is valid for outputFunction of functionType
public VariableType computeFunctionTypeWRTExpression(AnnotatedFunction outputFunction, Expression exp) throws ExpressionException, InconsistentDomainException {
    MathDescription mathDescription = getSimulationOwner().getMathDescription();
    boolean bSpatial = getSimulationOwner().getGeometry().getDimension() > 0;
    if (!bSpatial) {
        return VariableType.NONSPATIAL;
    }
    Expression newexp = new Expression(exp);
    // making sure that output function is not direct function of constant.
    newexp.bindExpression(this);
    // here use math description as symbol table because we allow
    // new expression itself to be function of constant.
    newexp = MathUtilities.substituteFunctions(newexp, this).flatten();
    String[] symbols = newexp.getSymbols();
    VariableType functionType = outputFunction.getFunctionType();
    String funcName = outputFunction.getName();
    Domain funcDomain = outputFunction.getDomain();
    VariableType[] varTypes = null;
    if (symbols != null && symbols.length > 0) {
        // making sure that new expression is defined in the same domain
        varTypes = new VariableType[symbols.length];
        for (int i = 0; i < symbols.length; i++) {
            if (ReservedMathSymbolEntries.getReservedVariableEntry(symbols[i]) != null) {
                varTypes[i] = functionType;
            } else {
                Variable var = mathDescription.getVariable(symbols[i]);
                if (var == null) {
                    var = mathDescription.getPostProcessingBlock().getDataGenerator(symbols[i]);
                }
                varTypes[i] = VariableType.getVariableType(var);
                if (funcDomain != null) {
                    if (var.getDomain() == null) {
                        // OK
                        continue;
                    }
                    GeometryClass funcGeoClass = simulationOwner.getGeometry().getGeometryClass(funcDomain.getName());
                    GeometryClass varGeoClass = simulationOwner.getGeometry().getGeometryClass(var.getDomain().getName());
                    if (varGeoClass instanceof SubVolume && funcGeoClass instanceof SurfaceClass) {
                        // seems ok if membrane refereces volume
                        if (!((SurfaceClass) funcGeoClass).isAdjacentTo((SubVolume) varGeoClass)) {
                            // but has to be adjacent
                            String errMsg = "'" + funcName + "' defined on Membrane '" + funcDomain.getName() + "' directly or indirectly references " + " variable '" + symbols[i] + "' defined on Volume '" + var.getDomain().getName() + " which is not adjacent to Membrane '" + funcDomain.getName() + "'.";
                            throw new ExpressionException(errMsg);
                        }
                    } else if (!var.getDomain().compareEqual(funcDomain)) {
                        String errMsg = "'" + funcName + "' defined on '" + funcDomain.getName() + "' directly or indirectly references " + " variable '" + symbols[i] + "' defined on '" + var.getDomain().getName() + ".";
                        throw new ExpressionException(errMsg);
                    }
                }
            }
        }
    }
    // if there are no variables (like built in function, vcRegionArea), check with flattened expression to find out the variable type of the new expression
    VariableDomain functionVariableDomain = functionType.getVariableDomain();
    Function flattenedFunction = new Function(funcName, newexp, funcDomain);
    flattenedFunction.bind(this);
    VariableType newVarType = SimulationSymbolTable.getFunctionVariableType(flattenedFunction, getSimulationOwner().getMathDescription(), symbols, varTypes, bSpatial);
    if (!newVarType.getVariableDomain().equals(functionVariableDomain)) {
        String errMsg = "The expression for '" + funcName + "' includes at least one " + newVarType.getVariableDomain().getName() + " variable. Please make sure that only " + functionVariableDomain.getName() + " variables are " + "referenced in " + functionVariableDomain.getName() + " output functions.";
        throw new ExpressionException(errMsg);
    }
    return newVarType;
}

Example 24 with Function

use of cbit.vcell.math.Function in project vcell by virtualcell.

the class MathTestingUtilities method getOutwardNormal.

/**
 * Insert the method's description here.
 * Creation date: (1/23/2003 10:30:23 PM)
 * @return cbit.vcell.parser.Expression
 * @param analyticSubDomainExp cbit.vcell.parser.Expression
 */
public static Function[] getOutwardNormal(Expression analyticSubVolume, String baseName) throws ExpressionException, MappingException, MathException {
    VariableHash varHash = new VariableHash();
    Expression[] insideOutsideFunctions = getInsideOutsideFunctions(analyticSubVolume);
    StringBuffer normalBufferX = new StringBuffer("0.0");
    StringBuffer normalBufferY = new StringBuffer("0.0");
    StringBuffer normalBufferZ = new StringBuffer("0.0");
    for (int i = 0; i < insideOutsideFunctions.length; i++) {
        // 
        // each one gets a turn being the minimum
        // 
        Function[] functions = getOutwardNormalFromInsideOutsideFunction(insideOutsideFunctions[i], baseName + i);
        for (int j = 0; j < functions.length; j++) {
            varHash.addVariable(functions[j]);
        }
        String closestName = baseName + i + "_closest";
        StringBuffer closestBuffer = new StringBuffer("1.0");
        for (int j = 0; j < insideOutsideFunctions.length; j++) {
            if (i != j) {
                closestBuffer.append(" && (" + baseName + i + "_distance < " + baseName + j + "_distance)");
            }
        }
        Expression closest = new Expression(closestBuffer.toString());
        varHash.addVariable(new Function(closestName, closest, null));
        normalBufferX.append(" + (" + baseName + i + "_closest * " + baseName + i + "_Nx)");
        normalBufferY.append(" + (" + baseName + i + "_closest * " + baseName + i + "_Ny)");
        normalBufferZ.append(" + (" + baseName + i + "_closest * " + baseName + i + "_Nz)");
    }
    varHash.addVariable(new Function(baseName + "_Nx", new Expression(normalBufferX.toString()), null));
    varHash.addVariable(new Function(baseName + "_Ny", new Expression(normalBufferY.toString()), null));
    varHash.addVariable(new Function(baseName + "_Nz", new Expression(normalBufferZ.toString()), null));
    Variable[] vars = varHash.getAlphabeticallyOrderedVariables();
    java.util.Vector<Variable> varList = new java.util.Vector<Variable>(java.util.Arrays.asList(vars));
    return (Function[]) BeanUtils.getArray(varList, Function.class);
}

Example 25 with Function

use of cbit.vcell.math.Function in project vcell by virtualcell.

the class MathTestingUtilities method constructOdesForSensitivity.

// 
// This method is used to solve for sensitivity of variables to a given parameter.
// The mathDescription and the sensitivity parameter are passed as arguments.
// New variables and ODEs are constructed according to the rule listed below and are added to the mathDescription.
// The method returns the modified mathDescription.
// 
public static MathDescription constructOdesForSensitivity(MathDescription mathDesc, Constant sensParam) throws ExpressionException, MathException, MappingException {
    // 
    // For each ODE :
    // 
    // dX/dt = F(X, P)
    // 
    // (where P is the sensitivity parameter)
    // 
    // we create two other ODEs :
    // 
    // dX_1/dt = F(X_1, P_1)    and
    // 
    // dX_2/dt = F(X_2, P_2)
    // 
    // where P_1 = P + epsilon, and
    // P_2 = P - epsilon.
    // 
    // We keep the initial conditions for both the new ODEs to be the same,
    // i.e., X_1_init = X_2_init.
    // 
    // Then, solving for X_1 & X_2, sensitivity of X wrt P can be computed as :
    // 
    // dX = (X_1 - X_2)
    // --	 -----------   .
    // dP	 (P_1 - P_2)
    // 
    // 
    // REMOVE PRINTS AFTER CHECKING !!!
    System.out.println(" \n\n------------  Old Math Description -----------------");
    System.out.println(mathDesc.getVCML_database());
    if (mathDesc.getGeometry().getDimension() > 0) {
        throw new RuntimeException("Suppport for Spatial systems not yet implemented.");
    }
    VariableHash varHash = new VariableHash();
    Enumeration<Variable> enumVar = mathDesc.getVariables();
    while (enumVar.hasMoreElements()) {
        varHash.addVariable(enumVar.nextElement());
    }
    // 
    // Get 2 values of senstivity parameter (P + epsilon) & (P - epsilon)
    // 
    Constant epsilon = new Constant("epsilon", new Expression(sensParam.getConstantValue() * 1e-3));
    Constant sensParam1 = new Constant(sensParam.getName() + "_1", new Expression(sensParam.getConstantValue() + epsilon.getConstantValue()));
    Constant sensParam2 = new Constant(sensParam.getName() + "_2", new Expression(sensParam.getConstantValue() - epsilon.getConstantValue()));
    // 
    // Iterate through each subdomain (only 1 in compartmental case), and each equation in the subdomain
    // 
    Enumeration<SubDomain> subDomainEnum = mathDesc.getSubDomains();
    // 
    // Create a vector of equations to store the 2 equations for each ODE variable in the subdomain.
    // Later, add it to the equations list in the subdomain.
    // 
    Vector<Equation> equnsVector = new Vector<Equation>();
    Vector<Variable> varsVector = new Vector<Variable>();
    Vector<Variable> var1s = new Vector<Variable>();
    Vector<Variable> var2s = new Vector<Variable>();
    while (subDomainEnum.hasMoreElements()) {
        SubDomain subDomain = subDomainEnum.nextElement();
        Enumeration<Equation> equationEnum = subDomain.getEquations();
        Domain domain = new Domain(subDomain);
        while (equationEnum.hasMoreElements()) {
            Equation equation = equationEnum.nextElement();
            if (equation instanceof OdeEquation) {
                OdeEquation odeEquation = (OdeEquation) equation;
                // Similar to substituteWithExactSolutions, to bind and substitute functions in the ODE
                Expression substitutedRateExp = substituteFunctions(odeEquation.getRateExpression(), mathDesc);
                String varName = odeEquation.getVariable().getName();
                VolVariable var = new VolVariable(varName, domain);
                varsVector.addElement(var);
                // 
                // Create the variable var1, and get the initExpr and rateExpr from the original ODE.
                // Substitute the new vars (var1 and param1) in the old initExpr and rateExpr and create a new ODE
                // 
                String varName1 = new String("__" + varName + "_1");
                Expression initExpr1 = odeEquation.getInitialExpression();
                Expression rateExpr1 = new Expression(substitutedRateExp);
                rateExpr1.substituteInPlace(new Expression(varName), new Expression(varName1));
                rateExpr1.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam1.getName()));
                VolVariable var1 = new VolVariable(varName1, domain);
                var1s.addElement(var1);
                OdeEquation odeEqun1 = new OdeEquation(var1, initExpr1, rateExpr1);
                equnsVector.addElement(odeEqun1);
                // 
                // Create the variable var2, and get the initExpr and rateExpr from the original ODE.
                // Substitute the new vars (var2 and param2) in the old initExpr and rateExpr and create a new ODE
                // 
                String varName2 = new String("__" + varName + "_2");
                Expression initExpr2 = odeEquation.getInitialExpression();
                Expression rateExpr2 = new Expression(substitutedRateExp);
                rateExpr2.substituteInPlace(new Expression(varName), new Expression(varName2));
                rateExpr2.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam2.getName()));
                VolVariable var2 = new VolVariable(varName2, domain);
                var2s.addElement(var2);
                OdeEquation odeEqun2 = new OdeEquation(var2, initExpr2, rateExpr2);
                equnsVector.addElement(odeEqun2);
                // 
                // Create a function for the sensitivity function expression (X1-X2)/(P1-P2), and save in varHash
                // 
                Expression diffVar = Expression.add(new Expression(var1.getName()), Expression.negate(new Expression(var2.getName())));
                Expression diffParam = Expression.add(new Expression(sensParam1.getName()), Expression.negate(new Expression(sensParam2.getName())));
                Expression sensitivityExpr = Expression.mult(diffVar, Expression.invert(diffParam));
                Function sens_Func = new Function("__sens" + varName + "_wrt_" + sensParam.getName(), sensitivityExpr, domain);
                varHash.addVariable(epsilon);
                varHash.addVariable(sensParam1);
                varHash.addVariable(sensParam2);
                varHash.addVariable(var1);
                varHash.addVariable(var2);
                varHash.addVariable(sens_Func);
            } else {
                // sensitivity not implemented for PDEs or other equation types.
                throw new RuntimeException("SolverTest.constructedExactMath(): equation type " + equation.getClass().getName() + " not yet implemented");
            }
        }
        // 
        // Need to substitute the new variables in the new ODEs.
        // i.e., if Rate Expr for ODE_1 for variable X_1 contains variable Y, variable Z, etc.
        // Rate Expr is already substituted with X_1, but it also needs substitute Y with Y_1, Z with Z_1, etc.
        // So get the volume variables, from the vectors for vars, var_1s and var_2s
        // Substitute the rate expressions for the newly added ODEs in equnsVector.
        // 
        Variable[] vars = (Variable[]) BeanUtils.getArray(varsVector, Variable.class);
        Variable[] var_1s = (Variable[]) BeanUtils.getArray(var1s, Variable.class);
        Variable[] var_2s = (Variable[]) BeanUtils.getArray(var2s, Variable.class);
        Vector<Equation> newEqunsVector = new Vector<Equation>();
        for (int i = 0; i < equnsVector.size(); i++) {
            Equation equn = equnsVector.elementAt(i);
            Expression initEx = equn.getInitialExpression();
            Expression rateEx = equn.getRateExpression();
            for (int j = 0; j < vars.length; j++) {
                if (equn.getVariable().getName().endsWith("_1")) {
                    rateEx.substituteInPlace(new Expression(vars[j].getName()), new Expression(var_1s[j].getName()));
                } else if (equn.getVariable().getName().endsWith("_2")) {
                    rateEx.substituteInPlace(new Expression(vars[j].getName()), new Expression(var_2s[j].getName()));
                }
            }
            OdeEquation odeEqun = new OdeEquation(equn.getVariable(), initEx, rateEx);
            newEqunsVector.addElement(odeEqun);
        }
        // 
        for (int i = 0; i < newEqunsVector.size(); i++) {
            mathDesc.getSubDomain(subDomain.getName()).addEquation((Equation) newEqunsVector.elementAt(i));
        }
        // 
        // FAST SYSTEM
        // If the subdomain has a fast system, create a new fast system by substituting the high-low variables/parameters
        // in the expressions for the fastInvariants and fastRates and adding them to the fast system.
        // 
        Vector<FastInvariant> invarsVector = new Vector<FastInvariant>();
        Vector<FastRate> ratesVector = new Vector<FastRate>();
        Enumeration<FastInvariant> fastInvarsEnum = null;
        Enumeration<FastRate> fastRatesEnum = null;
        // Get the fast invariants and fast rates in the system.
        FastSystem fastSystem = subDomain.getFastSystem();
        if (fastSystem != null) {
            fastInvarsEnum = fastSystem.getFastInvariants();
            fastRatesEnum = fastSystem.getFastRates();
            // 
            while (fastInvarsEnum.hasMoreElements()) {
                FastInvariant fastInvar = fastInvarsEnum.nextElement();
                Expression fastInvarExpr = fastInvar.getFunction();
                fastInvarExpr = MathUtilities.substituteFunctions(fastInvarExpr, mathDesc);
                Expression fastInvarExpr1 = new Expression(fastInvarExpr);
                Expression fastInvarExpr2 = new Expression(fastInvarExpr);
                for (int i = 0; i < vars.length; i++) {
                    fastInvarExpr1.substituteInPlace(new Expression(vars[i].getName()), new Expression(var_1s[i].getName()));
                    fastInvarExpr2.substituteInPlace(new Expression(vars[i].getName()), new Expression(var_2s[i].getName()));
                }
                fastInvarExpr1.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam1.getName()));
                FastInvariant fastInvar1 = new FastInvariant(fastInvarExpr1);
                invarsVector.addElement(fastInvar1);
                fastInvarExpr2.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam2.getName()));
                FastInvariant fastInvar2 = new FastInvariant(fastInvarExpr2);
                invarsVector.addElement(fastInvar2);
            }
            // Add the newly created fast invariants to the existing list of fast invariants in the fast system.
            for (int i = 0; i < invarsVector.size(); i++) {
                FastInvariant inVar = (FastInvariant) invarsVector.elementAt(i);
                fastSystem.addFastInvariant(inVar);
            }
            // 
            while (fastRatesEnum.hasMoreElements()) {
                FastRate fastRate = fastRatesEnum.nextElement();
                Expression fastRateExpr = fastRate.getFunction();
                fastRateExpr = MathUtilities.substituteFunctions(fastRateExpr, mathDesc);
                Expression fastRateExpr1 = new Expression(fastRateExpr);
                Expression fastRateExpr2 = new Expression(fastRateExpr);
                for (int i = 0; i < vars.length; i++) {
                    fastRateExpr1.substituteInPlace(new Expression(vars[i].getName()), new Expression(var_1s[i].getName()));
                    fastRateExpr2.substituteInPlace(new Expression(vars[i].getName()), new Expression(var_2s[i].getName()));
                }
                fastRateExpr1.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam1.getName()));
                FastRate fastRate1 = new FastRate(fastRateExpr1);
                ratesVector.addElement(fastRate1);
                fastRateExpr2.substituteInPlace(new Expression(sensParam.getName()), new Expression(sensParam2.getName()));
                FastRate fastRate2 = new FastRate(fastRateExpr2);
                ratesVector.addElement(fastRate2);
            }
            // Add the newly created fast rates to the existing list of fast rates in the fast system.
            for (int i = 0; i < ratesVector.size(); i++) {
                FastRate rate = (FastRate) ratesVector.elementAt(i);
                fastSystem.addFastRate(rate);
            }
        }
    }
    // Reset all variables in mathDesc.
    mathDesc.setAllVariables(varHash.getAlphabeticallyOrderedVariables());
    // REMOVE PRINTS AFTER CHECKING
    System.out.println(" \n\n------------  New Math Description -----------------");
    System.out.println(mathDesc.getVCML_database());
    return mathDesc;
}